Con Focal

New Technique Called Micro displacement Printing Improves Nanoscale Fabrication Scientists will announce next month a new technique called microdisplacement printing, which makes possible the highly precise placement of molecules during the fabrication of nanoscale components for electronic and sensing devices. The new technique, which also extends the library of molecules that can be used for patterning, will be described in the 14 September issue of the journal Nano Letters by a team led by Paul S. Weiss, professor of chemistry and physics at Penn State. The new microdisplacement technique is based on a widely used patterning method known as microcontact printing--a simple way of fabricating chemical patterns that does not require clean rooms and other kinds of special and expensive environments. Both methods involve "inking" a patterned rubber-like stamp with a solution of molecules, then applying the inked stamp to a surface. "Microdisplacement gives us more control over the precision with which the patterns are placed and retained, and also allows us to use a wider range of molecules," Weiss says. One of the limitations of microcontact printing is that its precision is limited at the edges of a stamped pattern by the tendency of the applied molecules to skitter across the stamped surface, blurring or obliterating the applied pattern and destroying its usefulness. Weiss's improved microdisplacement technique solves this problem by applying a self-assembled-monolayer film--a single ordered layer of spherical adamantanethiolate molecules--to keep the stamped molecules in place on the surface. "We specifically engineered the adamantanethiol molecule to have a very weak chemical bond with the surface so that it would detach easily when bumped by a stronger-bonding molecule," Weiss explains. The molecules inked on the stamp replace the adamantanethiolate molecules wherever they touch the monolayer film, but the surrounding molecules in the film remain attached to the surface to prevent the applied molecules from wandering. "Microdisplacement printing uses many of the same procedures as microcontact printing except one first prepares the substrate by coating it with a self-assembled monolayer of adamantanethiolate, which is inexpensive and easy to apply," Weiss explains. "You dip the substrate in a solution of these molecules, pull it out, and they assemble themselves into an ordered film one molecule thick." In addition to providing more control over the precision of stamped patterns, the new microdisplacement technique also relaxes the requirements in precisely positioning a series of stamps used to apply consecutive patterns with different molecular inks. "You don't have to be extremely precise about the exact placement of the stamps as long as you apply the molecular inks in order of their bonding strengths," Weiss explains. Each successive layer of molecules either will displace or will not displace the already-applied molecules, depending on their relative bonding strengths with the underlying surface. The research was aided by the Weiss lab's unusual collection of microscopes, which enable the scientists to get a clear picture of the results of their experiments, both at the broad scale of a stamped pattern and at the narrow scale of just a single molecule. One scanning tunneling microscope that Weiss and his group designed and built themselves, for example, has 1,000 times more resolution than is needed to image an individual atom. Adamantanethiol is related to the family of alkanethiol molecules, which have been studied extensively as a model systems for their ability to form well-ordered monolayer films on gold. Weiss and his team were studying the adamantanethiolate-on-gold system when graduate student Arrelaine Dameron discovered that strongerbonding molecules easily displaced the adamantanethiolate molecules. Her discovery has led to further studies of this system by the Weiss team, including how the displacement can be applied in a broad range of applications using a variety of materials. "We have mapped out strategies in this model system and are now investigating how we can apply these strategies more broadly as the chemistry is developed for self-assembled monolayers on other substrates, especially semiconductors," Weiss says. "Our goals are to see how far we can take these kinds of simple techniques, along with our knowledge of intermolecular interactions, to bridge the 1-to-100-nanometer length

scale in nanofabrication, which even at the high end currently requires very difficult, slow, and expensive techniques." In addition to Weiss and Dameron, the Penn State research team includes postdoctoral fellows Jennifer Hampton and Susan Gillmor and graduate students Rachel Smith and T. J. Mullen. The research was supported by the Air Force Office of Scientific Research, the Army Research Office, the Defense Advanced Research Projects Agency, the National Science Foundation, the Office of Naval Research, and the Semiconductor Research Corporation. The work was performed as a part of both the Center for Nanoscale Science and the National Nanofabrication Infrastructure Network.

Theory of Confocal Microscopy Introduction to Confocal Microscopy Confocal microscopy offers several advantages over conventional widefield optical microscopy, including the ability to control depth of field, elimination or reduction of background information away from the focal plane (that leads to image degradation), and the capability to collect serial optical sections from thick specimens. The basic key to the confocal approach is the use of spatial filtering techniques to eliminate out-of-focus light or glare in specimens whose thickness exceeds the immediate plane of focus. There has been a tremendous explosion in the popularity of confocal microscopy in recent years, due in part to the relative ease with which extremely high-quality images can be obtained from specimens prepared for conventional fluorescence microscopy, and the growing number of applications in cell biology that rely on imaging both fixed and living cells and tissues. In fact, confocal technology is proving to be one of the most important advances ever achieved in optical microscopy. In a conventional widefield optical epi-fluorescence microscope, secondary fluorescence emitted by the specimen often occurs through the excited volume and obscures resolution of features that lie in the objective focal plane. The problem is compounded by thicker specimens (greater than 2 micrometers), which usually exhibit such a high degree of fluorescence emission that most of the fine detail is lost. Confocal microscopy provides only a marginal improvement in both axial (z; along the optical axis) and lateral (x and y; in the specimen plane) optical resolution, but is able to exclude secondary fluorescence in areas removed from the focal plane from resulting images. Even though resolution is somewhat enhanced with confocal microscopy over conventional widefield techniques, it is still considerably less than that of the transmission electron microscope. In this regard, confocal microscopy can be considered a bridge between these two classical methodologies. Presented in Figure 1 are a series of images that compare selected viewfields in traditional widefield and laser scanning confocal fluorescence microscopy. A thick section of fluorescently stained human medulla in widefield fluorescence exhibits a large amount of glare from fluorescent structures above and below the focal plane (Figure 1(a)). When imaged with a laser scanning confocal microscope (Figure 1(d)), the medulla thick section reveals a significant degree of structural detail. Likewise, widefield fluorescence imaging of whole rabbit muscle fibers stained with fluorescein produce blurred images (Figure 1(b)) lacking in detail, while the same specimen field (Figure 1(e)) reveals a highly striated topography in confocal microscopy. Autofluorescence in a sunflower pollen grain produces an indistinct outline of the basic external morphology (Figure 1(c)), but yields no indication of the internal structure. In contrast, a thin optical section of the same grain (Figure 1(f)) acquired with confocal techniques displays a dramatic difference between the particle core and the surrounding envelope. Historical Perspective The basic concept of confocal microscopy was originally developed by Marvin Minsky in the mid-1950s (patented in 1957) when he was a postdoctoral student at Harvard University. Minsky wanted to image neural networks in unstained preparations of brain tissue and was driven by the desire to image biological events at they occur in living systems. Minsky's invention remained largely unnoticed, due most probably to the lack of intense light sources necessary for imaging and the computer horsepower required to handle large amounts of data. Following Minsky's work, M. David Egger and Mojmir Petran fabricated a multiple-beam confocal microscope in the late 1960s that utilized a spinning (Nipkow) disk for examining unstained brain sections and ganglion cells. Continuing in this arena, Egger went on to develop the first mechanically scanned confocal laser microscope, and published the first recognizable images of cells in 1973. During the late 1970s and the 1980s, advances in computer and laser technology, coupled to new algorithms for digital manipulation of images, led to a growing interest in confocal microscopy. Fortuitously, shortly after Minsky's patent had expired, practical laser scanning confocal microscope designs were translated into working instruments by several investigators. Dutch physicist G. Fred Brakenhoff developed a scanning confocal microscope in 1979, while almost simultaneously, Colin Sheppard contributed to the technique with a theory of image formation. Tony Wilson, Brad Amos, and John White nurtured the concept and later (during the late 1980s) demonstrated the utility of confocal imaging in the examination of fluorescent biological specimens. The first commercial instruments appeared in 1987. During the 1990s, advances in optics and electronics afforded more stable and powerful lasers, high-efficiency scanning mirror units, high-throughput fiber optics, better thin film dielectric coatings, and detectors having reduced noise characteristics. In addition, fluorochromes that were more carefully matched to laser excitation lines were beginning to be synthesized. Coupled to the rapidly advancing computer processing speeds, enhanced displays, and

large-volume storage technology emerging in the late 1990s, the stage was set for a virtual explosion in the number of applications that could be targeted with laser scanning confocal microscopy. Modern confocal microscopes can be considered as completely integrated electronic systems where the optical microscope plays a central role in a configuration that consists of one or more electronic detectors, a computer (for image display, processing, output, and storage), and several laser systems combined with wavelength selection devices and a beam scanning assembly. In most cases, integration between the various components is so thorough that the entire confocal microscope is often collectively referred to as a digital or video imaging system capable of producing electronic images. These microscopes are now being employed for routine investigations on molecules, cells, and living tissues that were not possible just a few years ago. Principles of Confocal Microscopy The confocal principle in epi-fluorescence laser scanning microscopy is diagrammatically presented in Figure 2. Coherent light emitted by the laser system (excitation source) passes through a pinhole aperture that is situated in a conjugate plane (confocal) with a scanning point on the specimen and a second pinhole aperture positioned in front of the detector (a photomultiplier tube). As the laser is reflected by a dichromatic mirror and scanned across the specimen in a defined focal plane, secondary fluorescence emitted from points on the specimen (in the same focal plane) pass back through the dichromatic mirror and are focused as a confocal point at the detector pinhole aperture. The significant amount of fluorescence emission that occurs at points above and below the objective focal plane is not confocal with the pinhole (termed Out-of-Focus Light Rays in Figure 2) and forms extended Airy disks in the aperture plane. Because only a small fraction of the out-of-focus fluorescence emission is delivered through the pinhole aperture, most of this extraneous light is not detected by the photomultiplier and does not contribute to the resulting image. The dichromatic mirror, barrier filter, and excitation filter perform similar functions to identical components in a widefield epifluorescence microscope. Refocusing the objective in a confocal microscope shifts the excitation and emission points on a specimen to a new plane that becomes confocal with the pinhole apertures of the light source and detector. In traditional widefield epi-fluorescence microscopy, the entire specimen is subjected to intense illumination from an incoherent mercury or xenon arc-discharge lamp, and the resulting image of secondary fluorescence emission can be viewed directly in the eyepieces or projected onto the surface of an electronic array detector or traditional film plane. In contrast to this simple concept, the mechanism of image formation in a confocal microscope is fundamentally different. As discussed above, the confocal fluorescence microscope consists of multiple laser excitation sources, a scan head with optical and electronic components, electronic detectors (usually photomultipliers), and a computer for acquisition, processing, analysis, and display of images. The scan head is at the heart of the confocal system and is responsible for rasterizing the excitation scans, as well as collecting the photon signals from the specimen that are required to assemble the final image. A typical scan head contains inputs from the external laser sources, fluorescence filter sets and dichromatic mirrors, a galvanometer-based raster scanning mirror system, variable pinhole apertures for generating the confocal image, and photomultiplier tube detectors tuned for different fluorescence wavelengths. The general arrangement of scan head components is presented in Figure 3 for a typical commercial unit. In epi-illumination scanning confocal microscopy, the laser light source and photomultiplier detectors are both separated from the specimen by the objective, which functions as a well-corrected condenser and objective combination. Internal fluorescence filter components (such as the excitation and barrier filters and the dichromatic mirrors) and neutral density filters are contained within the scanning unit (see Figure 3). Interference and neutral density filters are housed in rotating turrets or sliders that can be inserted into the light path by the operator. The excitation laser beam is connected to the scan unit with a fiber optic coupler followed by a beam expander that enables the thin laser beam wrist to completely fill the objective rear aperture (a critical requirement in confocal microscopy). Expanded laser light that passes through the microscope objective forms an intense diffraction-limited spot that is scanned by the coupled galvanometer mirrors in a raster pattern across the specimen plane (point scanning). One of the most important components of the scanning unit is the pinhole aperture, which acts as a spatial filter at the conjugate image plane positioned directly in front of the photomultiplier. Several apertures of varying diameter are usually contained on a rotating turret that enables the operator to adjust pinhole size (and optical section thickness). Secondary fluorescence collected by the objective is descanned by the same galvanometer mirrors that form the raster pattern, and then passes through a barrier filter before reaching the pinhole aperture. The aperture serves to exclude fluorescence signals from out-of-focus features positioned above and below the focal plane, which are instead projected onto the aperture as Airy disks having a diameter much larger than those forming the image. These oversized disks are spread over a comparatively large area so that only a small fraction of light originating in planes away from the focal point passes through the aperture. The pinhole aperture also serves to eliminate much of the stray light passing through the optical system. Coupling of aperture-limited point scanning to a pinhole spatial filter at the conjugate image plane is an essential feature of the confocal microscope. When contrasting the similarities and differences between widefield and confocal microscopes, it is often useful to compare the character and geometry of specimen illumination utilized for each of the techniques. Traditional widefield epifluorescence microscope objectives focus a wide cone of illumination over a large volume of the specimen, which is

uniformly and simultaneously illuminated (as illustrated in Figure 4(a)). A majority of the fluorescence emission directed back towards the microscope is gathered by the objective (depending upon the numerical aperture) and projected into the eyepieces or detector. The result is a significant amount of signal due to emitted background light and autofluorescence originating from areas above and below the focal plane, which seriously reduces resolution and image contrast. The laser illumination source in confocal microscopy is first expanded to fill the objective rear aperture, and then focused by the lens system to a very small spot at the focal plane (Figure 4(b)). The size of the illumination point ranges from approximately 0.25 to 0.8 micrometers in diameter (depending upon the objective numerical aperture) and 0.5 to 1.5 micrometers deep at the brightest intensity. Confocal spot size is determined by the microscope design, wavelength of incident laser light, objective characteristics, scanning unit settings, and the specimen. Presented in Figure 4 is a comparison between the typical illumination cones of a widefield (Figure 4(a)) and point scanning confocal (Figure 4(b)) microscope at the same numerical aperture. The entire depth of the specimen over a wide area is illuminated by the widefield microscope, while the sample is scanned with a finely focused spot of illumination that is centered in the focal plane in the confocal microscope. In laser scanning confocal microscopy, the image of an extended specimen is generated by scanning the focused beam across a defined area in a raster pattern controlled by two high-speed oscillating mirrors driven by galvanometer motors. One of the mirrors moves the beam from left to right along the x lateral axis, while the other translates the beam in the y direction. After each single scan along the x axis, the beam is rapidly transported back to the starting point and shifted along the y axis to begin a new scan in a process termed flyback. During the flyback operation, image information is not collected. In this manner, the area of interest on the specimen in a single focal plane is excited by laser illumination from the scanning unit. As each scan line passes along the specimen in the lateral focal plane, fluorescence emission is collected by the objective and passed back through the confocal optical system. The speed of the scanning mirrors is very slow relative to the speed of light, so the secondary emission follows a light path along the optical axis that is identical to the original excitation beam. Return of fluorescence emission through the galvanometer mirror system is referred to as descanning. After leaving the scanning mirrors, the fluorescence emission passes directly through the dichromatic mirror and is focused at the detector pinhole aperture. Unlike the raster scanning pattern of excitation light passing over the specimen, fluorescence emission remains in a steady position at the pinhole aperture, but fluctuates with respect to intensity over time as the illumination spot traverses the specimen producing variations in excitation. Fluorescence emission that is passed through the pinhole aperture is converted into an analog electrical signal having a continuously varying voltage (corresponding to intensity) by the photomultiplier. The analog signal is periodically sampled and converted into pixels by an analog-to-digital (A/D) converter housed in the scanning unit or the accompanying electronics cabinet. The image information is temporarily stored in an image frame buffer card in the computer and displayed on the monitor. It is important to note that the confocal image of a specimen is reconstructed, point by point, from emission photon signals by the photomultiplier and accompanying electronics, yet never exists as a real image that can be observed through the microscope eyepieces. Laser Scanning Confocal Microscope Configuration Basic microscope optical system characteristics have remained fundamentally unchanged for many decades due to engineering restrictions on objective design, the static properties of most specimens, and the fact that resolution is governed by the wavelength of light. However, fluorescent probes that are employed to add contrast to biological specimens and, and other technologies associated with optical microscopy techniques, have improved significantly. The explosive growth and development of the confocal approach is a direct result of a renaissance in optical microscopy that has been largely fueled by advances in modern optical and electronics technology. Among these are stable multiwavelength laser systems that provide better coverage of the ultraviolet, visible, and near-infrared spectral regions, improved interference filters (including dichromatic mirrors, barrier, and excitation filters), sensitive low-noise wide band detectors, and far more powerful computers. The latter are now available with relatively low-cost memory arrays, image analysis software packages, high-resolution video displays, and high quality digital image printers. The flow of information through a modern confocal microscope is presented diagrammatically in Figure 5. Although many of these technologies have been developed independently for a variety of specifically-targeted applications, they have been gradually been incorporated into mainstream commercial confocal microscopy systems. In current microscope systems, classification of designs is based on the technology utilized to scan specimens. Scanning can be accomplished either by translating the stage in the x, y, and z directions while the laser illumination spot is held in a fixed position, or the beam itself can be raster-scanned across the specimen. Because three-dimensional translation of the stage is cumbersome and prone to vibration, most modern instruments employ some type of beam-scanning mechanism. In modern confocal microscopes, two fundamentally different techniques for beam scanning have been developed. Singlebeam scanning, one of the more popular methods employed in a majority of the commercial laser scanning microscopes, uses a pair of computer-controlled galvanometer mirrors to scan the specimen in a raster pattern at a rate of approximately one frame per second. Faster scanning rates (to near video speed) can be achieved using acousto-optic devices or oscillating mirrors. In contrast, multiple-beam scanning confocal microscopes are equipped with a spinning Nipkow disk containing an array of pinholes and microlenses. These instruments often use arc-discharge lamps for illumination instead

of lasers to reduce specimen damage and enhance the detection of low fluorescence levels during real time image collection. Another important feature of the multiple-beam microscopes is their ability to readily capture images with an array detector, such as a charge-coupled device (CCD) camera system. All laser scanning confocal microscope designs are centered around a conventional upright or inverted research-level optical microscope. However, instead of the standard tungsten-halogen or mercury arc-discharge lamp, one or more laser systems are used as a light source to excite fluorophores in the specimen. Image information is gathered point by point with a specialized detector such as a photomultiplier tube or avalanche photodiode, and then digitized for processing by the host computer, which also controls the scanning mirrors and/or other devices to facilitate the collection and display of images. After a series of images (usually serial optical sections) has been acquired and stored on digital media, analysis can be conducted utilizing numerous image processing software packages available on the host or a secondary computer. Advantages and Disadvantages of Confocal Microscopy The primary advantage of laser scanning confocal microscopy is the ability to serially produce thin (0.5 to 1.5 micrometer) optical sections through fluorescent specimens that have a thickness ranging up to 50 micrometers or more. The image series is collected by coordinating incremental changes in the microscope fine focus mechanism (using a stepper motor) with sequential image acquisition at each step. Image information is restricted to a well-defined plane, rather than being complicated by signals arising from remote locations in the specimen. Contrast and definition are dramatically improved over widefield techniques due to the reduction in background fluorescence and improved signal-to-noise. Furthermore, optical sectioning eliminates artifacts that occur during physical sectioning and fluorescent staining of tissue specimens for traditional forms of microscopy. The non-invasive confocal optical sectioning technique enables the examination of both living and fixed specimens under a variety of conditions with enhanced clarity. With most confocal microscopy software packages, optical sections are not restricted to the perpendicular lateral (x-y) plane, but can also be collected and displayed in transverse planes. Vertical sections in the x-z and y-z planes (parallel to the microscope optical axis) can be readily generated by most confocal software programs. Thus, the specimen appears as if it had been sectioned in a plane that is perpendicular to the lateral axis. In practice, vertical sections are obtained by combining a series of x-y scans taken along the z axis with the software, and then projecting a view of fluorescence intensity as it would appear should the microscope hardware have been capable of physiclly performing a vertical section. A typical stack of optical sections (often termed a z-series) through a sunflower pollen grain revealing internal variations in autofluorescence emission wavelengths is illustrated in Figure 6. Optical sections were gathered in 0.5-micrometer steps perpendicular to the z-axis (microscope optical axis) using a dual argon-ion (488 nanometer; green fluorescence) and green helium/neon (543 nanometer; red fluorescence) laser system. Pollen grains of from this species range between 20 and 40 micrometers in diameter and yield blurred images in widefield fluorescence microscopy (see Figure 1 (c)), which lack information about internal structural details. Although only 12 of the over 48 images collected through this series are presented in the figure, they represent individual focal planes separated by a distance of approximately 3 micrometers and provide a good indication of the internal grain structure. In specimens more complex than a pollen grain, complex interconnected structural elements can be difficult to discern from a large series of optical sections sequentially acquired through the volume of a specimen with a laser scanning confocal microscope. However, once an adequate series of optical sections has been gathered, it can be further processed into a three-dimensional representation of the specimen using volume-rendering computational techniques. This approach is now in common use to help elucidate the numerous interrelationships between structure and function of cells and tissues in biological investigations. In order to ensure that adequate data is collected to produce a representative volume image, the optical sections should be recorded at the appropriate axial (z-step) intervals so that the actual depth of the specimen is reflected in the image. Most of the software packages accompanying commercial confocal instruments are capable of generating composite and multi-dimensional views of optical section data acquired from z-series image stacks. The three-dimensional software packages can be employed to create either a single three-dimensional representation of the specimen (Figure 7) or a video (movie) sequence compiled from different views of the specimen volume. These sequences often mimic the effect of rotation or similar spatial transformation that enhances the appreciation of the specimen's three-dimensional character. In addition, many software packages enable investigators to conduct measurements of length, volume, and depth, and specific parameters of the images, such as opacity, can be interactively altered to reveal internal structures of interest at differing levels within the specimen. Typical three-dimensional representations of several specimens examined by serial optical sectioning are presented in Figure 7. The pollen grain optical sections illustrated in Figures 1 and 6 were combined to produce a realistic view of the exterior surface (Figure 7(a)) as it might appear if being examined by a scanning electron microscope. The algorithm utilized to construct the three-dimensional model enables the user to rotate the pollen grain through 360 degrees for examination. The tissue culture cells in Figure 7(b) are derived from the Chinese hamster ovary (CHO) line and were transfected with a chimeric plasmid vector containing the green fluorescent protein and a human immunodeficiency virus (HIV) protein that is expressed in the nucleus (thus, labeling the nuclear region). Thick tissue sections are also easily viewed in three-dimensions constructed from optical sections. The mouse intestine section illustrated in Figure 7(c) was labeled with several fluorophores and created from a stack of 45 optical sections.

In many cases, a composite or projection view produced from a series of optical sections provides important information about a three-dimensional specimen than a multi-dimensional view. For example, a fluorescently labeled neuron having numerous thin, extended processes in a tissue section is difficult (if not impossible) to image using widefield techniques due to out-of-focus blur. Confocal thin sections of the same neuron each reveal portions of several extensions, but these usually appear as fragmented streaks and dots and lack continuity. Composite views created by flattening a series of optical sections from the neuron will reveal all of the extended processes in sharp focus with well-defined continuity. Structural and functional analysis of other cell and tissue sections also benefits from composite views as opposed to, or coupled with, three-dimensional volume rendering techniques. Advances in confocal microscopy have made possible multi-dimensional views of living cells and tissues that include image information in the x, y, and z dimensions as a function of time and presented in multiple colors (using two or more fluorophores). After volume processing of individual image stacks, the resulting data can be displayed as three-dimensional multicolor video sequences in real time. Note that unlike conventional widefield microscopy, all fluorochromes in multiply labeled specimens appear in register using the confocal microscope. Temporal data can be collected either from time-lapse experiments conducted over extended periods or through real time image acquisition in smaller frames for short periods of time. The potential for using multi-dimensional confocal microscopy as a powerful tool in cellular biology is continuing to grow as new laser systems are developed to limit cell damage and computer processing speeds and storage capacity improves. Additional advantages of scanning confocal microscopy include the ability to adjust magnification electronically by varying the area scanned by the laser without having to change objectives. This feature is termed the zoom factor, and is usually employed to adjust the image spatial resolution by altering the scanning laser sampling period. Increasing the zoom factor reduces the specimen area scanned and simultaneously reduces the scanning rate. The result is an increased number of samples along a comparable length, which increases both the image spatial resolution and display magnification on the host computer monitor. Confocal zoom is typically employed to match digital image resolution with the optical resolution of the microscope when low numerical aperture and magnification objectives are being used to collect data. Digitization of the sequential analog image data collected by the confocal microscope photomultiplier (or similar detector) facilitates computer image processing algorithms by transforming the continuous voltage stream into discrete digital increments that correspond to variations in light intensity. In addition to the benefits and speed that accrue from processing digital data, images can be readily prepared for print output or publication. In carefully controlled experiments, quantitative measurements of spatial fluorescence intensity (either statically or as a function of time) can also be obtained from the digital data. Disadvantages of confocal microscopy are limited primarily to the limited number of excitation wavelengths available with common lasers (referred to as laser lines), which occur over very narrow bands and are expensive to produce in the ultraviolet region. In contrast, conventional widefield microscopes use mercury or xenon based arc-discharge lamps to provide a full range of excitation wavelengths in the ultraviolet, visible, and near-infrared spectral regions. Another downside is the harmful nature of high-intensity laser irradiation to living cells and tissues (an issue that has recently been addressed by multiphoton and Nipkow disk confocal imaging). Finally, the high cost of purchasing and operating multi-user confocal microscope systems, which can range up to an order of magnitude higher than comparable widefield microscopes, often limits their implementation in smaller laboratories. This problem can be easily overcome by cost-shared microscope systems that service one or more departments in a core facility. The recent introduction of personal confocal systems has competitively driven down the price of low-end confocal microscopes and increased the number of individual users. Fluorescence Microscopy Fluorescence illumination and observation is the most rapidly expanding microscopy technique employed today, both in the medical and biological sciences, a fact which has spurred the development of more sophisticated microscopes and numerous fluorescence accessories. Epi-fluorescence, or incident light fluorescence, has now become the method of choice in many applications and comprises a large part of this tutorial. We have divided the fluorescence section of the primer into several categories to make it easier to organize and download. Please follow the links below to navigate to points of interest. Introductory Concepts - Fluorescence is a member of the ubiquitous luminescence family of processes in which susceptible molecules emit light from electronically excited states created by either a physical (for example, absorption of light), mechanical (friction), or chemical mechanism. Generation of luminescence through excitation of a molecule by ultraviolet or visible light photons is a phenomenon termed photoluminescence, which is formally divided into two categories, fluorescence and phosphorescence, depending upon the electronic configuration of the excited state and the emission pathway. Fluorescence is the property of some atoms and molecules to absorb light at a particular wavelength and to subsequently emit light of longer wavelength after a brief interval, termed the fluorescence lifetime. The process of phosphorescence occurs in a manner similar to fluorescence, but with a much longer excited state lifetime. Fundamental Aspects of Fluorescence Microscopy - The modern fluorescence microscope combines the power of high performance optical components with computerized control of the instrument and digital image acquisition to achieve a level of sophistication that far exceeds that of simple observation by the human eye. Microscopy now depends heavily on

electronic imaging to rapidly acquire information at low light levels or at visually undetectable wavelengths, as discussed in this Nikon MicroscopyU review article. These technical improvements are not mere window dressing, but are essential components of the light microscope as a system. Anatomy of the Fluorescence Microscope - In contrast to other modes of optical microscopy that are based on macroscopic specimen features, such as phase gradients, light absorption, and birefringence, fluorescence microscopy is capable of imaging the distribution of a single molecular species based solely on the properties of fluorescence emission. Thus, using fluorescence microscopy, the precise location of intracellular components labeled with specific fluorophores can be monitored, as well as their associated diffusion coefficients, transport characteristics, and interactions with other biomolecules. In addition, the dramatic response in fluorescence to localized environmental variables enables the investigation of pH, viscosity, refractive index, ionic concentrations, membrane potential, and solvent polarity in living cells and tissues. Practical Aspects of Fluorescence Filter Combinations - Microscope manufacturers provide proprietary filter combinations (often referred to as cubes or blocks) that contain a combination of dichroic mirrors and filters capable of exciting fluorescent chromophores and diverting the resulting secondary fluorescence to the eyepieces or camera tube. A wide spectrum of filter cubes is available from most major manufacturers, which now produce filter sets capable of imaging most of the common fluorophores in use today. Overview of Light Sources for Fluorescence Microscopy - In order to generate enough excitation light intensity to furnish secondary fluorescence emission capable of detection, powerful light sources are needed. These are usually either mercury or xenon arc (burner) lamps, which produce high-intensity illumination powerful enough to image faintly visible fluorescence specimens. Light Sources for Optical Microscopy - The performance of the various illumination sources available for optical microscopy depends on the emission characteristics and geometry of the source, as well as the focal length, magnification and numerical aperture of the collector lens system. In gauging the suitability of a particular light source, the important parameters are structure (the spatial distribution of light, source geometry, coherence, and alignment), the wavelength distribution, spatial and temporal stability, brightness, and to what degree these various parameters can be controlled. Focusing and Alignment of Arc Lamps - Mercury and xenon arc lamps are now widely utilized as illumination sources for a large number of investigations in widefield fluorescence microscopy. Visitors can gain practice aligning and focusing the arc lamp in a Mercury or Xenon Burner with this Nikon MicroscopyU interactive tutorial, which simulates how the lamp is adjusted in a fluorescence microscope. Optimization and Troubleshooting - A key feature of fluorescence microscopy is its ability to detect fluorescent objects that are sometimes faintly visible or even very bright relative to the dark (often black) background. In order to optimize this feature, image brightness and resolution must be maximized using the principles discussed in this section. We also review common problems with microscope configuration in fluorescence microscopy. Electronic Imaging Detectors - The range of light detection methods and the wide variety of imaging devices currently available to the microscopist make the selection process difficult and often confusing. This discussion is intended to aid in understanding the basics of light detection and to provide a guide for selecting a suitable detector for specific applications in fluorescence microscopy. Introduction to Fluorophores - Widefield fluorescence and laser scanning confocal microscopy rely heavily on secondary fluorescence emission as an imaging mode, primarily due to the high degree of sensitivity afforded by the techniques coupled with the ability to specifically target structural components and dynamic processes in chemically fixed as well as living cells and tissues. Many fluorescent probes are constructed around synthetic aromatic organic chemicals designed to bind with a biological macromolecule. Fluorescent dyes are also useful in monitoring cellular integrity (live versus dead and apoptosis), endocytosis, exocytosis, membrane fluidity, protein trafficking, signal transduction, and enzymatic activity. In addition, fluorescent probes have been widely applied to genetic mapping and chromosome analysis in the field of molecular genetics. Introduction to Fluorescent Proteins - The discovery of green fluorescent protein in the early 1960s ultimately heralded a new era in cell biology by enabling investigators to apply molecular cloning methods, fusing the fluorophore moiety to a wide variety of protein and enzyme targets, in order to monitor cellular processes in living systems using optical microscopy and related methodology. When coupled to recent technical advances in widefield fluorescence and confocal microscopy, including ultrafast low light level digital cameras and multitracking laser control systems, the green fluorescent protein and its color-shifted genetic derivatives have demonstrated invaluable service in many thousands of live-cell imaging experiments. Choosing Fluorophore Combinations for Confocal Microscopy - In planning multiple label fluorescence staining protocols for widefield and laser scanning confocal fluorescence microscopy experiments, the judicious choice of probes is paramount in obtaining the best target signal while simultaneously minimizing bleed-through artifacts. This interactive tutorial is designed to explore the matching of dual fluorophores with efficient laser excitation lines, calculation of emission spectral overlap values, and determination of the approximate bleed-through level that can be expected as a function of the detection window wavelength profiles. Specimen Preparation Using Synthetic Fluorophores and Indirect Immunofluorescence - Confocal microscopy was becoming more than just a novelty in the early 1980s due to the upswing in applications of widefield fluorescence to investigate cellular architecture and function. As immunofluorescence techniques, as well as the staining of subcellular

structures using synthetic fluorophores, became widely practiced in the late 1970s, microscopists grew increasingly frustrated with their inability to distinguish or record fine detail in widefield instruments due to interference by fluorescence emission occurring above and below the focal plane. Today, confocal microscopy, when coupled to the application of new advanced synthetic fluorophores, fluorescent proteins, and immunofluorescence reagents, is one of the most sophisticated methods available to probe sub-cellular structure. The protocols described in this section address the specimen preparation techniques using synthetic fluorophores coupled to immunofluorescence that are necessary to investigate fixed adherent cells and tissue cryosections using widefield and confocal fluorescence microscopy. Fluorescence Photomicrography - Photomicrography under fluorescence illumination conditions presents a unique set of circumstances posing special problems for the microscopist. Exposure times are often exceedingly long, the specimen's fluorescence may fade during exposure, and totally black backgrounds often inadvertently signal light meters to suggest overexposure. Glossary of Terms in Fluorescence and Confocal Microscopy - The complex nomenclature of fluorescence microscopy is often confusing to both beginning students and seasoned research microscopists alike. This resource is provided as a guide and reference tool for visitors who are exploring the large spectrum of specialized topics in fluorescence and laser scanning confocal microscopy. Advanced Techniques in Fluorescence Microscopy NEW! - Laser Scanning Confocal Microscope Simulator - Perhaps the most significant advance in optical microscopy during the past decade has been the refinement of mainstream laser scanning confocal microscope (LSCM) techniques using improved synthetic fluorescent probes and genetically engineered proteins, a wider spectrum of laser light sources coupled to highly accurate acousto-optic tunable filter control, and the combination of more advanced software packages with modern high-performance computers. This interactive tutorial explores multi-laser fluorescence and differential interference contrast (DIC) confocal imaging using the Olympus FluoView FV1000 confocal microscope software interface as a model. Introduction to Confocal Microscopy - Confocal microscopy offers several advantages over conventional optical microscopy, including controllable depth of field, the elimination of image degrading out-of-focus information, and the ability to collect serial optical sections from thick specimens. The key to the confocal approach is the use of spatial filtering to eliminate out-of-focus light or flare in specimens that are thicker than the plane of focus. There has been a tremendous explosion in the popularity of confocal microscopy in recent years, due in part to the relative ease with which extremely high-quality images can be obtained from specimens prepared for conventional optical microscopy, and in its great number of applications in many areas of current research interest. Live-Cell Imaging - An increasing number of investigations are using live-cell imaging techniques to provide critical insight into the fundamental nature of cellular and tissue function, especially due to the rapid advances that are currently being witnessed in fluorescent protein and synthetic fluorophore technology. As such, live-cell imaging has become a requisite analytical tool in most cell biology laboratories, as well as a routine methodology that is practiced in the wide ranging fields of neurobiology, developmental biology, pharmacology, and many of the other related biomedical research disciplines. Among the most significant technical challenges for performing successful live-cell imaging experiments is to maintain the cells in a healthy state and functioning normally on the microscope stage while being illuminated in the presence of synthetic fluorophores and/or fluorescent proteins. Olympus FluoView Confocal Microscopy Resource Center - The new Olympus FluoViewTM FV1000 is the latest in point-scanning, point-detection, confocal laser scanning microscopes designed for today's intensive and demanding biological research investigations. Excellent resolution, bright and crisp optics, and high efficiency of excitation, coupled to an intuitive user interface and affordability are key characteristics of this state-of-the-art optical microscopy system. Multiphoton Excitation Microscopy - Multiphoton fluorescence microscopy is a powerful research tool that combines the advanced optical techniques of laser scanning microscopy with long wavelength multiphoton fluorescence excitation to capture high-resolution, three-dimensional images of specimens tagged with highly specific fluorophores. Fluorescence Resonance Energy Transfer (FRET) - The precise location and nature of the interactions between specific molecular species in living cells is of major interest in many areas of biological research, but investigations are often hampered by the limited resolution of the instruments employed to examine these phenomena. Conventional widefield fluorescence microscopy enables localization of fluorescently labeled molecules within the optical spatial resolution limits defined by the Rayleigh criterion, approximately 200 nanometers (0.2 micrometer). However, in order to understand the physical interactions between protein partners involved in a typical biomolecular process, the relative proximity of the molecules must be determined more precisely than diffraction-limited traditional optical imaging methods permit. The technique of fluorescence resonance energy transfer (more commonly referred to by the acronym FRET), when applied to optical microscopy, permits determination of the approach between two molecules within several nanometers, a distance sufficiently close for molecular interactions to occur. Total Internal Reflection Fluorescence Microscopy - Total internal reflection fluorescence microscopy (TIRFM) is an elegant optical technique utilized to observe single molecule fluorescence at surfaces and interfaces. The technique is commonly employed to investigate the interaction of molecules with surfaces, an area which is of fundamental importance to a wide spectrum of disciplines in cell and molecular biology. Spectral Imaging and Linear Unmixing - Spectral imaging and linear unmixing is becoming an important staple in the microscopist's toolbox, particularly when applied to the elimination of autofluorescence and for FRET investigations.

Instruments equipped for spectral imaging are becoming increasingly popular and many confocal microscopes now offer this capability. Widefield fluorescence and brightfield microscopy are also being used more frequently for resolving complex fluorophore and absorbing dye mixtures, a trend that should continue into the future. Fluorescence in situ Hybridization: Hardware and Software Implications in the Research Laboratory - The power of in situ hybridization can be greatly extended by the simultaneous use of multiple fluorescent colors. Multicolor fluorescence in situ hybridization (FISH), in its simplest form, can be used to identify as many labeled features as there are different fluorophores used in the hybridization. By using not only single colors, but also combinations of colors, many more labeled features can be simultaneously detected in individual cells using digital imaging microscopy. Epi-Fluorescence Illumination for Stereomicroscopy - The application of stereomicroscopes for GFP observation is now so prevalent that stereo fluorescence illuminators are more frequently referred to as GFP illuminators, even though they can be utilized for many other applications in both the life sciences and the electronics manufacturing industry. Large specimens, such as larvae, nematodes, Zebrafish, oocytes, and mature insects can be easily selected and manipulated when they are labeled with GFP and illuminated by fluorescence techniques. Laser Systems for Optical Microscopy - The lasers commonly employed in optical microscopy are high-intensity monochromatic light sources, which are useful as tools for a variety of techniques including optical trapping, lifetime imaging studies, photobleaching recovery, and total internal reflection fluorescence. In addition, lasers are also the most common light source for scanning confocal fluorescence microscopy, and have been utilized, although less frequently, in conventional widefield fluorescence investigations. Fluorescence and Phase Contrast Combination Microscopy - To minimize the effects of photobleaching, fluorescence microscopy can be combined with phase contrast illumination. The idea is to locate the specific area of interest in a specimen using the non-destructive contrast enhancing technique (phase) then, without relocating the specimen, switch the microscope to fluorescence mode. Fluorescence and Differential Interference Contrast Combination Microscopy - Fluorescence microscopy can also be combined with contrast enhancing techniques such as differential interference contrast (DIC) illumination to minimize the effects of photobleaching by locating a specific area of interest in a specimen using DIC then, without relocating the specimen, switching the microscope to fluorescence mode. Fluorescence Microscopy Digital Image Galleries Fluorescence Microscopy Digital Image Gallery - Featuring specimens collected from a wide spectrum of disciplines, the fluorescence gallery contains a variety of examples using both specific fluorochrome stains and autofluorescence. Images were captured utilizing either a Nikon DXM 1200 digital camera, an Optronics MagnaFire Peltier-cooled camera, or classical photomicrography on film with Fujichrome Provia 35 millimeter transparency film. Fluorescence Microscopy of Cells in Culture - Serious attempts at the culture of whole tissues and isolated cells were first undertaken in the early 1900s as a technique for investigating the behavior of animal cells in an isolated and highly controlled environment. The term tissue culture arose because most of the early cells were derived from primary tissue explants, a technique that dominated the field for over 50 years. As established cell lines emerged, the application of welldefined normal and transformed cells in biomedical investigations has become an important staple in the development of cellular and molecular biology. This fluorescence image gallery explores over 30 of the most common cell lines, labeled with a variety of fluorophores using both traditional staining methods as well as immunofluorescence techniques. Nikon Fluorescence Microscopy Digital Image Gallery - The widefield reflected light fluorescence microscope has been a fundamental tool for the examination of fluorescently labeled cells and tissues since the introduction of the dichromatic mirror in the late 1940s. Furthermore, advances in synthetic fluorophore design coupled to the vast array of commercially available primary and secondary antibodies have provided the biologist with a powerful arsenal in which to probe the minute structural details of living organisms with this technique. In the late twentieth century, the discovery and directed mutagenesis of fluorescent proteins added to the cadre of tools and created an avenue for scientists to probe the dynamics of living cells in culture. This gallery examines the fluorescence microscopy of both cells and tissues with a wide spectrum of fluorescent probes. Anatomy of the Fluorescence Microscope Olympus BX51 Upright Microscope - The modern upright epi-fluorescence microscope is equipped with a vertical illuminator that contains a turret of filter cubes and a mercury or xenon arc lamp housing. Light passes from the lamphouse thorough field and aperture diaphragms and into a cube that contains both excitation and emission filters and a dichroic mirror. After passing through the objective and being focused onto the specimen, reflected excitation and secondary fluorescence are filtered upon return through the cube. Next, the light (primarily secondary fluorescence) is routed to the eyepieces or detector. Olympus IX70 Inverted Microscope - Microscopes with an inverted-style frame are designed primarily for tissue culture applications and are capable of producing fluorescence illumination through an episcopic and optical pathway. Epiilluminators usually consist of a mercury or xenon lamphouse (or laser system) stationed in a port at the rear of the microscope frame. Fluorescence illumination from the arc lamp passes through a collector lens and into a cube that contains a set of interference filters, including a dichroic mirror, barrier filter, and excitation filter. After excitation of the specimen, secondary fluorescence is collected by the objective and directed through the microscope optical train. Interactive Java Tutorials

Fluorescence Microscope Light Pathways - This interactive tutorial explores illumination pathways in the Olympus BX51 research-level upright microscope. The microscope drawing presented in the tutorial illustrates a cut-away diagram of the Olympus BX51 microscope equipped with a vertical illuminator and lamphouses for both diascopic (tungsten-halogen) and epi-fluorescence (mercury arc) light sources. Sliders control illumination intensity and enable the visitor to select from a library of five fluorescence interference filter combinations that have excitation values ranging from the near ultraviolet to long-wavelength visible light. Inverted Microscope Light Pathways - Explore light pathways through an inverted tissue culture microscope equipped with for both diascopic (tungsten-halogen) and epi-fluorescence (mercury arc) illumination. Light intensity through the pathways the in microscope are controllable with sliders, as is a library of five fluorescence interference filter combinations that have excitation values ranging from the near ultraviolet to long-wavelength visible light. The "virtual" inverted microscope is also equipped with traditional (35 millimeter) and CCD camera systems to enable the visitor to observe how light rays are directed into these peripheral devices. References and Literature Sources General Fluorescence Microscopy Literature Sources - The field of fluorescence microscopy is experiencing a renaissance with the introduction of new techniques such as confocal, multiphoton, deconvolution, and total internal reflection, especially when coupled to advances in chromophore and fluorophore technology. Green Fluorescence Protein is rapidly becoming a labeling method of choice for molecular and cellular biologists who can now explore biochemical events in living cells with natural fluorophores. Taken together, these and other important advances have propelled the visualization of living cells tagged with specific fluorescent probes into the mainstream of research in a wide spectrum of disciplines. The reference materials listed below were utilized in the construction of the fluorescence section of the Molecular Expressions Microscopy Primer. ZEISS Campus Fluorescence Microscopy Reference Library - The introduction of genetically-encoded fluorescent protein fusions as a localization marker in living cells has revolutionized the field of cell biology, and the application of photostable quantum dots looms on the horizon. Live-cell imaging techniques now involved a wide spectrum of imaging modalities, including widefield fluorescence, confocal, multiphoton, total internal reflection, FRET, lifetime imaging, superresolution, and transmitted light microscopy. The references listed in this section point to review articles that should provide the starting point for a thorough understanding of live-cell imaging. Fluorescent Protein Literature Sources - The disciplines of cellular and molecular biology are being rapidly and dramatically transformed by the application of fluorescent proteins developed from marine organisms as fusion tags to track protein behavior in living cells. The most widely used of these probes, green fluorescent protein, can be attached to virtually any target of interest and still fold into a viable fluorescent species. The resulting chimera can be employed to localize previously uncharacterized proteins or to visualize and track known proteins to further understand critical events at the cellular and molecular levels. This section features a bibliography of literature sources for review articles and original research reports on the discovery, applications, and continued development of fluorescent proteins. Laser Scanning Confocal Microscopy Confocal microscopy offers several advantages over conventional optical microscopy, including controllable depth of field, the elimination of image degrading out-of-focus information, and the ability to collect serial optical sections from thick specimens. The key to the confocal approach is the use of spatial filtering to eliminate out-of-focus light or flare in specimens that are thicker than the plane of focus. There has been a tremendous explosion in the popularity of confocal microscopy in recent years, due in part to the relative ease with which extremely high-quality images can be obtained from specimens prepared for conventional optical microscopy, and in its great number of applications in many areas of current research interest. Visit the Molecular Expressions and Nikon MicroscopyU articles, galleries, interactive tutorials, and Web references using the links provided below. Laser Scanning Confocal Microscope Simulator - Perhaps the most significant advance in optical microscopy during the past decade has been the refinement of mainstream laser scanning confocal microscope (LSCM) techniques using improved synthetic fluorescent probes and genetically engineered proteins, a wider spectrum of laser light sources coupled to highly accurate acousto-optic tunable filter control, and the combination of more advanced software packages with modern high-performance computers. This interactive tutorial explores multi-laser fluorescence and differential interference contrast (DIC) confocal imaging using the Olympus FluoView FV1000 confocal microscope software interface as a model. Introduction to Confocal Microscopy - Confocal microscopy offers several advantages over conventional widefield optical microscopy, including the ability to control depth of field, elimination or reduction of background information away from the focal plane (that leads to image degradation), and the capability to collect serial optical sections from thick specimens. The basic key to the confocal approach is the use of spatial filtering techniques to eliminate out-of-focus light or glare in specimens whose thickness exceeds the immediate plane of focus. There has been a tremendous explosion in the popularity of confocal microscopy in recent years, due in part to the relative ease with which extremely high-quality images can be obtained from specimens prepared for conventional fluorescence microscopy, and the growing number of applications in cell biology that rely on imaging both fixed and living cells and tissues. In fact, confocal technology is proving to be one of the most important advances ever achieved in optical microscopy. Basic Concepts - Current instruments are highly evolved from the earliest versions, but the principle of confocal imaging advanced by Marvin Minsky, and patented in 1957, is employed in all modern confocal microscopes. In a conventional widefield microscope, the entire specimen is bathed in light from a mercury or xenon source, and the image can be viewed

directly by eye or projected onto an image capture device or photographic film. In contrast, the method of image formation in a confocal microscope is fundamentally different. Illumination is achieved by scanning one or more focused beams of light, usually from a laser or arc-discharge source, across the specimen. This point of illumination is brought to focus in the specimen by the objective lens, and laterally scanned using some form of scanning device under computer control. The sequences of points of light from the specimen are detected by a photomultiplier tube (PMT) through a pinhole (or in some cases, a slit), and the output from the PMT is built into an image and displayed by the computer. Although unstained specimens can be viewed using light reflected back from the specimen, they usually are labeled with one or more fluorescent probes. Imaging Modes - A number of different imaging modes are used in the application of confocal microscopy to a vast variety of specimen types. They all rely on the ability of the technique to produce high-resolution images, termed optical sections, in sequence through relatively thick sections or whole-mount specimens. Based on the optical section as the basic image unit, data can be collected from fixed and stained specimens in single, double, triple, or multiple-wavelength illumination modes, and the images collected with the various illumination and labeling strategies will be in register with each other. Live cell imaging and time-lapse sequences are possible, and digital image processing methods applied to sequences of images allow z-series and three-dimensional representation of specimens, as well as the time-sequence presentation of 3D data as four-dimensional imaging. Reflected light imaging was the mode used in early confocal instruments, but any of the transmitted light imaging modes commonly employed in microscopy can be utilized in the laser scanning confocal microscope. Specimen Preparation and Imaging - The procedures for preparing and imaging specimens in the confocal microscope are largely derived from those that have been developed over many years for use with the conventional wide field microscope. In the biomedical sciences, a major application of confocal microscopy involves imaging either fixed or living cells and tissues that have usually been labeled with one or more fluorescent probes. A large number of fluorescent probes are available that, when incorporated in relatively simple protocols, specifically stain certain cellular organelles and structures. Among the plethora of available probes are dyes that label nuclei, the Golgi apparatus, the endoplasmic reticulum, and mitochondria, and also dyes such as fluorescently labeled phalloidins that target polymerized actin in cells. Regardless of the specimen preparation protocol employed, a primary benefit of the manner in which confocal microscopy is carried out is the flexibility in image display and analysis that results from the simultaneous collection of multiple images, in digital form, into a computer. Fluorophores for Confocal Microscopy - Biological laser scanning confocal microscopy relies heavily on fluorescence as an imaging mode, primarily due to the high degree of sensitivity afforded by the technique coupled with the ability to specifically target structural components and dynamic processes in chemically fixed as well as living cells and tissues. Many fluorescent probes are constructed around synthetic aromatic organic chemicals designed to bind with a biological macromolecule (for example, a protein or nucleic acid) or to localize within a specific structural region, such as the cytoskeleton, mitochondria, Golgi apparatus, endoplasmic reticulum, and nucleus. Other probes are employed to monitor dynamic processes and localized environmental variables, including concentrations of inorganic metallic ions, pH, reactive oxygen species, and membrane potential. Fluorescent dyes are also useful in monitoring cellular integrity (live versus dead and apoptosis), endocytosis, exocytosis, membrane fluidity, protein trafficking, signal transduction, and enzymatic activity. In addition, fluorescent probes have been widely applied to genetic mapping and chromosome analysis in the field of molecular genetics. Spectral Bleed-Through Artifacts in Confocal Microscopy - The spectral bleed-through of fluorescence emission (often termed crossover or crosstalk), which occurs due to the very broad bandwidths and asymmetrical spectral profiles exhibited by many of the common fluorophores, is a fundamental problem that must be addressed in both widefield and laser scanning confocal fluorescence microscopy. The phenomenon is usually manifested by the emission of one fluorophore being detected in the photomultiplier channel or through the filter combination reserved for a second fluorophore. Bleed-through artifacts often complicate the interpretation of experimental results, particularly if subcellular colocalization of fluorophores is under investigation or quantitative measurements are necessary, such as in resonance energy transfer (FRET) and photobleaching (FRAP) studies. Choosing Fluorophore Combinations for Confocal Microscopy - In planning multiple label fluorescence staining protocols for widefield and laser scanning confocal fluorescence microscopy experiments, the judicious choice of probes is paramount in obtaining the best target signal while simultaneously minimizing bleed-through artifacts. This interactive tutorial is designed to explore the matching of dual fluorophores with efficient laser excitation lines, calculation of emission spectral overlap values, and determination of the approximate bleed-through level that can be expected as a function of the detection window wavelength profiles. Laser Systems for Optical Microscopy - The lasers commonly employed in optical microscopy are high-intensity monochromatic light sources, which are useful as tools for a variety of techniques including optical trapping, lifetime imaging studies, photobleaching recovery, and total internal reflection fluorescence. In addition, lasers are also the most common light source for scanning confocal fluorescence microscopy, and have been utilized, although less frequently, in conventional widefield fluorescence investigations. Laser Safety - The two major concerns in safe laser operation are exposure to the beam and the electrical hazards associated with high voltages within the laser and its power supply. While there are no known cases of a laser beam contributing to a person's death, there have been several instances of deaths attributable to contact with high voltage laserrelated components. Beams of sufficiently high power can burn the skin, or in some cases create a hazard by burning or

damaging other materials, but the primary concern with regard to the laser beam is potential damage to the eyes, which are the part of the body most sensitive to light. Acousto-Optic Tunable Filters (AOTFs) - Several benefits of the AOTF combine to greatly enhance the versatility of the latest generation of confocal instruments, and these devices are becoming increasing popular for control of excitation wavelength ranges and intensity. The primary characteristic that facilitates nearly every advantage of the AOTF is its capability to allow the microscopist control of the intensity and/or illumination wavelength on a pixel-by-pixel basis while maintaining a high scan rate. This single feature translates into a wide variety of useful analytical microscopy tools, which are even further enhanced in flexibility when laser illumination is employed. Resolution and Contrast in Confocal Microscopy - All optical microscopes, including conventional widefield, confocal, and two-photon instruments are limited by fundamental physical factors in the resolution that they can achieve. In a perfect optical system, resolution is limited by numerical aperture of the optical components and by the wavelength of the light, both incident and detected. The concept of resolution is inseparable from contrast, and is defined as the minimum separation between two points that results in a certain contrast between them. In a real fluorescence microscope, contrast is determined by the number of photons collected from the specimen, the dynamic range of the signal, optical aberrations of the imaging system, and the number of picture elements (pixels) per unit area. Non-Coherent Light Sources for Confocal Microscopy - The traditional illumination system in the modern widefield microscope utilizes a tungsten-halogen source for transmitted light and a short-arc lamp for fluorescence excitation. Various lasers have been utilized as a light source for widefield observation by a few investigators, but the advent of the confocal microscope vastly increased laser use in microscopy. This discussion reviews the merits and limitations of noncoherent (or non-laser) light sources in confocal microscopy, both as light sources for confocal illumination and as secondary sources for widefield microscopy in confocal microscopes. Two initial issues frequently arise when illumination systems for confocal microscopes are considered, and these have a direct bearing on the choice of light sources for a particular instrument. Confocal Microscope Objectives - For any conventional optical microscope configuration, the objective is the most critical component of the system in determining the information content of the image. The contrast and resolution of fine specimen detail, the depth within the specimen from which information can be obtained, and the lateral extent of the image field are all determined by the design of the objective and its performance under the specific conditions employed for the observation. Additional demands are imposed on the objective in scanning confocal techniques, in which this crucial imaging component also serves as the illumination condenser and is often required to perform with high precision at a wide range of wavelengths and at very low light levels without introducing unacceptable image-degrading noise. Confocal Microscope Scanning Systems - Confocal imaging relies upon the sequential collection of light from spatially filtered individual specimen points, followed by electronic signal processing and ultimately, the visual display as corresponding image points. The point-by-point signal collection process requires a mechanism for scanning the focused illuminating beam through the specimen volume under observation. Three principal scanning variations are commonly employed to produce confocal microscope images. Fundamentally equivalent confocal operation can be achieved by employing a laterally translating specimen stage coupled to a stationary illuminating light beam (stage scanning), a scanned light beam with a stationary stage (beam scanning), or by maintaining both the stage and light source stationary while scanning the specimen with an array of light points transmitted through apertures in a spinning Nipkow disk. Each technique has performance features that make it advantageous for specific confocal applications, but that limit the usefulness in others. Signal-to-Noise Considerations - In any quantitative assessment of imaging capabilities utilizing digital microscopy techniques, including confocal methods, the effect of signal sampling on contrast and resolution must be considered. The measured signal level values do not directly represent the number of photons emitted or scattered by the specimen, but are proportional to that number. Furthermore, each individual sample of signal intensity is only an approximation of the number of collected photons, and will vary with repeated measurement. The variation, referred to as noise, imparts an uncertainty in the quantification of intensity, and therefore in the contrast and resolution of the image data. Electronic Light Detectors: Photomultipliers - In modern widefield fluorescence and laser scanning confocal optical microscopy, the collection and measurement of secondary emission gathered by the objective can be accomplished by several classes of photosensitive detectors, including photomultipliers, photodiodes, and solid-state charge-coupled devices (CCDs). In confocal microscopy, fluorescence emission is directed through a pinhole aperture positioned near the image plane to exclude light from fluorescent structures located away from the objective focal plane, thus reducing the amount of light available for image formation. As a result, the exceedingly low light levels most often encountered in confocal microscopy necessitate the use of highly sensitive photon detectors that do not require spatial discrimination, but instead respond very quickly with a high level of sensitivity to a continuous flux of varying light intensity. Critical Aspects of Confocal Microscopy - Quantitative three-dimensional imaging in fluorescence microscopy is often complicated by artifacts due to specimen preparation, controllable and uncontrollable experimental variables, or configuration problems with the microscope. This article, written by Dr. James B. Pawley, catalogs the most common extraneous factors that often serve to obscure results collected in fluorescence widefield and confocal microscopy. Among the topics discussed are the laser system, optical component alignment, objective magnification, bleaching artifacts, aberrations, immersion oil, coverslip thickness, quantum efficiency, and the specimen embedding medium. Aberrations in Multicolor Confocal Microscopy - Refinements in design have simplified confocal microscopy to the extent that it has become a standard research tool in cell biology. However, as confocal microscopes have become more

powerful, they have also become more demanding of their optical components. In fact, optical aberrations that cause subtle defects in image quality in widefield microscopy can have devastating effects in confocal microscopy. Unfortunately, the exacting optical requirements of confocal microscopy are often hidden by the optical system that guarantees a sharp image, even when the microscope is performing poorly. Optics manufacturers provide a wide range of microscope objectives, each designed for specific applications. This report demonstrates how the trade-offs involved in objective design can affect confocal microscopy. Three-Color Imaging for Confocal Microscopy - The laser scanning confocal microscope (LSCM) is routinely used to produce digital images of single-, double-, and triple-labeled fluorescent samples. The use of red, green and blue (RGB) color is most informative for displaying the distribution of up to three fluorescent probes labeling a cell, where any colocalization is observed as a different additive color when the images are colorized and merged into a single three-color image. In this section we present a simplified version of a previously published method for producing three-color confocal images using the popular image manipulation program, Adobe Photoshop. In addition, several applications of the threecolor merging protocol for displaying confocal images are discussed. Note that these digital methods are not confined to images produced using the LSCM and can be applied to digital images imported into Photoshop from many different sources. Basics of Confocal Reflection Microscopy - Confocal reflection microscopy can be utilized to gather additional information from a specimen with relatively little extra effort, since the technique requires minimum specimen preparation and instrument re-configuration. In addition, information from unstained tissues is readily available with confocal reflection microscopy, as is data from tissues labeled with probes that reflect light. The method can also be utilized in combination with more common classical fluorescence techniques. Examples of the latter application are detection of unlabeled cells in a population of fluorescently labeled cells and for imaging the interactions between fluorescently labeled cells growing on opaque, patterned substrata. Applications in Confocal Microscopy - The broad range of applications available to laser scanning confocal microscopy includes a wide variety of studies in neuroanatomy and neurophysiology, as well as morphological studies of a wide spectrum of cells and tissues. In addition, the growing use of new fluorescent proteins is rapidly expanding the number of original research reports coupling these useful tools to modern microscopic investigations. Other applications include resonance energy transfer, stem cell research, photobleaching studies, lifetime imaging, multiphoton microscopy, total internal reflection, DNA hybridization, membrane and ion probes, bioluminescent proteins, and epitope tagging. Many of these powerful techniques are described in these reviews. Confocal Microscopy Image Gallery - The Nikon MicroscopyU Confocal Image Gallery features digital image sequences captured using a Nikon PCM-2000 confocal microscope scanning system coupled to an Eclipse E-600 upright microscope. Successive serial optical sections were recorded along the optical axis of the microscope over a range of specimen planes. These sequences are presented as interactive Java tutorials that allow the visitor to either "play" the series of sections automatically, or to utilize a slider to scroll back and forth through the images. Olympus FluoView Laser Scanning Confocal Microscopy - The new Olympus FluoViewTM FV1000 is the latest in pointscanning, point-detection, confocal laser scanning microscopes designed for today's intensive and demanding biological research investigations. Excellent resolution, bright and crisp optics, and high efficiency of excitation, coupled to an intuitive user interface and affordability are key characteristics of this state-of-the-art optical microscopy system. Marvin Lee Minsky (1927-Present) - While at Harvard University, Marvin Minsky made his primary contribution to the field of optics by inventing the confocal scanning microscope. Despite the theoretical benefits of the confocal approach for biological purposes, Minsky's microscope originally generated little interest. In hindsight it has become apparent that the technology of the period limited Minsky's demonstration of the potential of the confocal approach. Yet, years later, with the advent of such applicable devices as lasers, sensitive low-noise photodetectors, and fast microcomputers with image processing capabilities, Minsky's microscopy technique has become widespread in biological research. Interactive Java Tutorials Laser Scanning Confocal Microscopy - (approximately a 30 second download on 28.8K modems) Several methods have been developed to overcome the poor contrast inherent with imaging thick specimens in a conventional microscope. Specimens having a moderate degree of thickness (5 to 15 microns) will produce dramatically improved images with either with confocal or deconvolution techniques. The thickest specimens (20 microns and above) will suffer from a tremendous amount of extraneous light in out-of-focus regions, and are probably best-imaged using confocal techniques. This tutorial explores imaging specimens through serial z-axis optical sections utilizing a virtual confocal microscope. Comparing Confocal and Widefield Fluorescence Microscopy - Confocal microscopy offers several distinct advantages over traditional widefield fluorescence microscopy, including the ability to control depth of field, elimination or reduction of background information away from the focal plane (that leads to image degradation), and the capability to collect serial optical sections from thick specimens. The basic key to the confocal approach is the use of spatial filtering techniques to eliminate out-of-focus light or glare in specimens whose thickness exceeds the dimensions of the focal plane. This interactive tutorial explores and compares the differences between specimens when viewed in a confocal versus a widefield fluorescence microscope. Colocalization of Fluorophores in Confocal Microscopy - Two or more fluorescence emission signals can often overlap in digital images recorded by confocal microscopy due to their close proximity within the specimen. This effect is known as colocalization and usually occurs when fluorescently labeled molecules bind to targets that lie in very close or identical

spatial positions. This interactive tutorial explores the quantitative analysis of colocalization in a wide spectrum of specimens that were specifically designed either to demonstrate the phenomenon, or to alternatively provide examples of fluorophore targets that lack any significant degree of colocalization. Reflected Confocal Microscopy: Integrated Circuit Inspection - Examine individual layers on the surface of integrated circuits with this interactive tutorial. Digital images for the tutorial were collected with a Nikon Optiphot C200 reflected light confocal microscope. For each sequence, a series of z-axis optical sections was recorded as the microscope was successively focused (at 1-micrometer steps) deeper within the patchwork of circuitry on the surface of the silicon chips. Excitation Photobleaching Patterns - Multiphoton fluorescence microscopy utilizes diffraction-limited focusing by a high numerical aperture objective to localize the spatial concentration of excitation light to narrow region near the focal point. In contrast, the excitation region of a laser scanning confocal microscope is similar to that of a widefield microscope. This tutorial compares excitation-induced photobleaching patterns that occur near the focal region in both multiphoton and confocal microscopy systems. Olympus FluoView Resource Center Interactive Java Tutorials - Explanations for many of the exceedingly complex concepts in laser scanning confocal microscopy can significantly benefit from the assistance of interactive tutorials that enable the student to obtain instanteous (real-time) response to changes in variables. The tutorials in section address the basic aspects of confocal microscopy instrumentation, laser systems, detectors, image processing, resolution, contrast, and many other aspects of the technique. All interactive Java tutorials require the Java Virtual Machine, which is available without cost as a browser plug-in from Sun Microsystems. References and Resources Recommended Books on Confocal Microscopy - A surprisingly limited number of books dealing with various aspects of laser scanning and spinning disk confocal microscopy and related techniques are currently available from the booksellers. This section lists the FluoView Resource Center website development team's top 12 recommended books. Although the volumes listed in this section deal pricipally with confocal microscopy and related methodology, there exist a number of additional books that contain focused treatments of the materials described below, and these should also be consulted for specific techniques and timely review articles. ZEISS Campus Confocal Microscopy Reference Library - A majority of the literature pertaining to review articles on laser scanning confocal microscopy has been published in textbooks, edited article collections, and symposia, with only an intermittent sprinkling of papers in the scientific journals. The reviews listed in this section should be available to students and investigators who have access to subscriptions through their host institutions. Confocal Microscopy Web Resources - Laser scanning confocal microscopy (LSCM), a tool that has been extensively utilized for inspection of semiconductors, is now becoming a mainstream application in cell biology. The links provided in this section from the Molecular Expressions web site offer tutorials, instrumentation, application notes, technical support, glossaries, and reference materials on confocal microscopy and related techniques. Basic Concepts in Laser Scanning Confocal Microscopy (PDF; 2.8 Mb) - Laser scanning confocal microscopy has become an invaluable tool for a wide range of investigations in the biological and medical sciences for imaging thin optical sections in living and fixed specimens ranging in thickness up to 100 micrometers. Modern instruments are equipped with 3-5 laser systems controlled by high-speed acousto-optic tunable filters (AOTFs), which allow very precise regulation of wavelength and excitation intensity. Coupled with photomultipliers that have high quantum efficiency in the near-ultraviolet, visible and near-infrared spectral regions, these microscopes are capable of examining fluorescence emission ranging from 400 to 750 nanometers. Download this review article to learn more.

Self assembled monolayer (SAM) A self assembled monolayer (SAM) is an organized layer of amphiphilic molecules in which one end of the molecule, the “head group” shows a special affinity for a substrate. SAMs also consist of a tail with a functional group at the terminal end as seen in Figure 1.

Fig: 1 SAMs are created by the chemisorption of hydrophilic “head groups” onto a substrate from either the vapor or liquid phase[1] followed by a slow two-dimensional organization of hydrophobic “tail groups”[2]. Initially, adsorbate molecules form either a disordered mass of molecules or form a “lying down phase” [1], and over a period of hours, begin to form crystalline or semicrystalline structures on the substrate surface[3][4]. The hydrophilic “head groups” assemble together on the substrate, while the hydrophobic tail groups assemble far from the substrate. Areas of close-packed molecules nucleate and grow until the surface of the substrate is covered in a single monolayer. Adsorbate molecules adsorb readily because they lower the surface energy of the substrate[3] and are stable due to the strong chemisorption of the “head groups.” These bonds create monolayers that are more stable than the physisorbed bonds of LangmuirBlodgett films[5][6]. Thiol-metal bonds, for example, are on the order of 100 kJ/mol, making the bond stable in a wide variety of temperature, solvents, and potentials[4]. The monolayer packs tightly due to van der Waals interactions[3][6], thereby reducing its own free energy[3]. The adsorption can be described by the Langmuir adsorption isotherm if lateral interactions are neglected. If they cannot be neglected, the adsorption is better described by the Frumkin isotherm[4].

Contents •

1 Types of SAMs

•

2 Preparation of SAMs

•

3 Characterization of SAMs

•

4 Applications of SAMs

•

5 References

•

6 Further reading

Types of SAMs Selecting the type of head group depends on the application of the SAM[3]. Typically, head groups are connected to an alkyl chain in which the terminal end can be functionalized (i.e. adding –OH, -NH3, or –COOH groups) to vary the wetting and interfacial properties[5][7]. An

appropriate substrate is chosen to react with the head group. Substrates can be planar surfaces, such as silicon and metals, or curved surfaces, such as nanoparticles. Thiols and disulfides are the most commonly used on noble metal substrates. Currently, gold is the standard for these head groups. Gold is an inert and biocompatible material that is easy to acquire. It is also easy to pattern via lithography, a useful feature for applications in nanoelectromechanical systems (NEMS)[3]. Additionally, it can withstand harsh chemical cleaning treatments[4]. Silanes are generally used on nonmetallic oxide surfaces[3].

Preparation of SAMs Metal substrates for use in SAMs can be produced through physical vapor deposition techniques, electrodeposition or electroless deposition[3]. Alkanethiol SAMs produced by adsorption from solution are made by immersing a substrate into a dilute solution of alkane thiol in ethanol for 12 to 72 hours at room temperature and dried with nitrogen [3][4][8]. SAMs can also be adsorbed from the vapor phase. For example, chlorosilane SAMs (which can also be adsorbed from the liquid phase), are often created in a reaction chamber by silanization in which silane vapor flows over the substrate to form the monolayer[9].

Characterization of SAMs The structures of SAMs are most commonly determined using scanning probe microscopy techniques such as atomic force microscopy (AFM) and scanning tunneling microscopy (STM). More recently, however, diffractive methods have also been used[3]. The structure can be used to characterize the kinetics and defects found on the monolayer surface. These techniques have also shown physical differences between SAMs with planar substrates and nanoparticle substrates. Kinetics There is evidence that SAM formation occurs in two steps, an initial fast step of adsorption and a second slower step of monolayer organization. Many of the SAM properties, such as thickness, are determined in the first few minutes. However, it may take hours for defects to be eliminated via annealing and for final SAM properties to be determined[1][4]. The exact kinetics of SAM formation depends on the adsorbate, solvent and substrate properties. In general, however, the kinetics are dependent on both preparations conditions and material properties of the solvent, adsorbate and substrate[1]. Specifically, kinetics for adsorption from a liquid solution are dependent on[3]: •

Temperature – room temperature preparation improves kinetics and reduces defects.

•

Concentration of adsorbate in the solution – low concentrations require longer immersion times[3][4] and often create highly crystalline domains[4].

•

Purity of the adsorbate – impurities can affect the final physical properties of the SAM

•

Dirt or contamination on the substrate – imperfections can cause defects in the SAM

The final structure of the SAM is also dependent on the chain length and the structure of both the adsorbate and the substrate. Steric hindrance and metal substrate properties, for example, can affect the packing density of the film[3][4], while chain length affects SAM thickness[6]. Defects Though the slow step in SAM formation often removes defects from the film defects are included in the final SAM structure. Defects can be caused by both external and intrinsic factors. External factors include the cleanliness of the substrate, method of preparation, and

purity of the adorbates[3][4]. SAMs intrinsically form defects due to the thermodynamics of formation. “The high coverage of the adsorbate present in the SAM is, in fact, thermodynamically unstable”[10].

Nanoparticle Properties The structure of SAMs is also dependent on the curvature of the substrate. SAMs on nanoparticles including colloids and nanocrystals, “stabilize the reactive surface of the particle and present organic functional groups at the particle-solvent interface”[11]. These organic functional groups are useful for applications, such as immunoassays, that are dependent on chemical composition of the surface[3].

Applications of SAMs Areas of application for SAMs include biology, electrochemistry and electronics, nanoelectromechanical systems (NEMS) and microelectromechanical systems (MEMS), and everyday household goods. SAMs can serve as models for studying membrane properties of cells and organelles and cell attachment on surfaces [3]. SAMs can also be used to modify the surface properties of electrodes for electrochemistry, general electronics, and various NEMS and MEMS[3]. For example, the properties of SAMs can be used to control electron transfer in electrochemistry. They can serve to protect metals from harsh chemicals and etchants. SAMs can also reduce sticking of NEMS and MEMS components in humid environments. In the same way, SAMs can alter the properties of glass. A common household product, Rain-X, utilizes SAMs to create a hydrophobic monolayer on car windshields to keep them clear of rain.

SAMS Introduction

Self-assembled monolayers (SAMs) can be prepared using different types of molecules and different substrates. Widespread examples are alkylsiloxane monolayers, fatty acids on oxidic materials and alkanethiolate monolayers. All these systems have been reviewed in great detail, and the interested reader is directed to, e.g., the book Ultrathin Organic Films by A. Ulman. Here, we will concentrate exclusively on SAMs of functionalized alkanethiols on gold surfaces. This type of SAMs holds great promise for applications in several different areas. Some examples of suggested and implemented applications are molecular recognition, SAMs as model substrates and biomembrane mimetics in studies of biomolecules at surfaces, selective binding of enzymes to surfaces, chemical force microscopy, metallization of organic materials, corrosion protection, molecular crystal growth, alignment of liquid crystals, pH-sensing devices, patterned surfaces on the µm scale, electrically conducting molecular wires and photoresists.

Figure 1. Number of published articles dealing with self-assembled monolayers per year, according to searches in the Chemical Abstracts and Science Citation Index databases. Research in this area began in 1983 and has seen an increasing number of published papers every year since then (see Figure1). The principle is simple: A molecule which is essentially an alkane chain, typically with 10-20 methylene units, is given a head group with a strong preferential adsorption to the substrate used. Thiol (S-H) head groups and Au(111) substrates have been shown to work excellently. The thiol molecules adsorb readily from solution onto the gold, creating a dense monolayer with the tail group pointing outwards from the surface. By using thiol molecules with different tail groups, the resulting chemical surface functionality can be varied within wide limits. Alternatively, it is also possible to chemically functionalize the tail groups by performing reactions after assembly of the SAM. Preparation

The preferred crystal face for alkanethiolate SAM preparation on gold substrates is the (111) direction, which can be obtained either by using single crystal substrates or by evaporation of thin Au films on flat supports, typically glass or silicon. A schematic outline of the SAM preparation procedure on such gold substrates is given in Figure 2, together with a schematic of a mixed SAM (see below). Several different solvents are usable at the low thiol concentrations (typically 1-2 mM) that are used in preparation of SAMs, but care must be taken when using mixed thiol solutions, since the final composition of the monolayer depends upon the relative solubilities of the different thiols. The most commonly used solvent is ethanol. It is advisable to minimize the water content in the solvent if the SAMs are to be used in UHV; this will limit incorporation of water into the SAM structure which reduces outgassing and increases repeatability in the UHV experiments. Even though a selfassembled monolayer forms very rapidly on the substrate, it is necessary to use adsorption times of 15 h or more to obtain well-ordered, defect-free SAMs. Multilayers do not form, and adsorption times of two to three days are optimal in forming highest-quality monolayers. In preparing SAMs for UHV use, meticulous rinsing and drying are of course highly important.

Figure 2. Preparation of SAMs. The substrate, Au on Si, is immersed into an ethanol solution of the desired thiol(s). Initial adsorption is fast (seconds); then an organization phase follows which should be allowed to continue for >15 h for best results. A schematic of a fully assembled SAM is shown to the right. As mentioned above, the tail group that provides the functionality of the SAM can be widely varied. CH3-terminated SAMs are commercially available; other functional groups can be synthesized by any well-equipped chemical laboratory, providing almost infinite possibilities of variation. In addition, chemical modification of the tail group is entirely possible after formation of the SAM, expanding the available range of functionalities even further. Examples of functionalities used at our laboratory are: •

-CH3

•

-OH

•

-(C=O)OCH3

•

-O(C=O)CH3

•

-O(C=O)CF3

•

-O(C=O)C6H5

•

-COOH

•

-OSO3H

Mixed SAMs By mixing two differently terminated thiols in the preparation solution, we can prepare mixed SAMs. The relative proportion of the two functionalities in the assembled SAM will then depend upon several parameters, like the mixing ratio in solution, the alkane chain lengths, the solubilities of the thiols in the solvent used, and the properties of the chain-terminating groups. In general, the composition will not be the same in the SAM as in the preparation solution. Measurements with a surface- sensitive probe like, e.g., X-ray photoelectron spectroscopy are necessary to calibrate the mixing ratio. In cases where the two thiol molecules are of equal alkyl chain length and no special circumstances (like bulky tail

groups) are at hand, the SAM composition will be almost identical to the composition of the solution, though. This is the case for mixtures of HS(CH2)15CH3 and HS(CH2)16OH. Molecular Gradients Another useful SAM preparation method is the formation of two-component molecular gradients, as first described by Liedberg and Tengvall (Langmuir 11 (1995), 3821). By crossdiffusion of two differently terminated thiols through an ethanol-soaked polysaccharide gel (Sephadex LH-20, a chromatography material) that is covering the gold substrate, a continuous gradient of 10-20 mm length may be formed. The principle of preparation is outlined in Figure 3. Ethanol solutions of each of the two thiols are simultaneously injected into two glass filters at opposite ends of the gold substrate. The presence of the polysaccharide gel makes the diffusion and the thiol attachment to the surface slow enough for a gradient of macroscopic dimension (several mm) to form.

Figure 3. Schematic illustration of the preparation of two-component alkanethiolate gradients. (a) The two different thiols, represented by X and O, are injected into glass filters. (b) They diffuse slowly through the polysaccharide gel and attach to the gold substrate. (c) Top view showing the placement of the gold substrate between the filters. (d) Schematic illustration of a fully assembled gradient. Characteristics SAMs have been thoroughly characterized using a large number of surface analytical tools. Among the most frequently used techniques are infrared spectroscopy, ellipsometry, studies of wetting by different liquids, x-ray photoelectron spectroscopy, electrochemistry, and scanning probe measurements. It has been clearly shown that SAMs with an alkane chain length of 12 or more methylene units form well-ordered and dense monolayers on Au(111) surfaces. The thiols are believed to attach primarily to the threefold hollow sites of the gold surface, losing the proton in the process and forming a (sqrt(3)×sqrt(3))R30° overlayer structure (shown in Figure 4). The distance between pinning sites in this geometry is 5.0 Å, resulting in an available area for each molecule of 21.4 Å2. Since the van der Waals diameter of the alkane chain is somewhat too small (4.6 Å) for the chain to completely occupy that area, the chains will tilt, forming an angle of approximately 30° with the surface normal. Depending on chain length and chain-terminating group, various superlattice

structures are superimposed on the (sqrt(3)×sqrt(3))R30° overlayer structure. The most commonly seen superlattice is the c(4×2) reconstruction, where the four alkanethiolate molecules of a unit cell display slightly different orientations when compared with each other.

Figure 4. A schematic model of the (sqrt(3)×sqrt(3))R30° overlayer structure formed by alkanethiolate SAMs on Au(111). The Au-thiolate bond is strong - homolytic bond strength 44 kcal/mol - and contributes to the stability of the SAMs together with the van der Waals forces between adjacent methylene groups, which amount to 1.4-1.8 kcal/mol. The latter forces add up to significant strength for alkyl chains of 10-20 methylenes and play an important role in aligning the alkyl chains parallel to each other in a nearly all-trans configuration. At low temperatures, typically 100 K, the order is nearly perfect, but even at room temperature there are only few gauche defects, concentrated to the outermost alkyl units. One convenient method of checking a SAM for well-ordered and dense structure is infrared reflection-absorption spectroscopy (IRAS). The CH stretching vibrations of the alkyl chain are very sensitive to packing density and to the presence of gauche defects, which makes them ideally suited as probes to determine SAM quality. In particular, the antisymmetric CH2 stretching vibration (d-) at ~2918 cm-1 is a useful indicator; its position varies from 2916 or 2917 cm-1 for SAMs of exceptional quality or cooled below room temperature, via 2918 cm-1 which is the normal value for a high-quality SAM, to ~2926 cm-1 which is indicative of a heavily disordered, "spaghetti-like" SAM. A typical IRAS spectrum of the CH stretching region of a hexadecanethiolate (HS(CH2)15CH3 ) SAM is shown in Figure 5.

Figure 5. IRAS spectrum of a hexadecanethiolate SAM in the CH stretching region. The most prominent vibrations are indicated. d+ and d- are the symmetric and antisymmetric CH2 stretches; r+ and r- are the symmetric and

antisymmetric CH3 stretches, respectively. At the measurement temperature used (82 K), the ra- and rb-components of the r- peak are resolved. Thickness measurements using ellipsometry yield SAM thicknesses that are in good agreement with the 30° chain tilt mentioned above. For example, reported ellipsometric thicknesses of hexadecanethiolate SAMs lie in the 21±1 Å range, to compare with the 21.2 Å that result if a fully extended hexadecanethiol molecule of 24.5 Å length is tilted 30°. Contact angle measurements further confirm that alkanethiolate SAMs are very dense and that the contacting liquid only interacts with the topmost chemical groups. Reported advancing contact angles with water range from 111° to 115° for hexadecanethiolate SAMs. At the other end of the wettability scale, there are hydrophilic monolayers, e.g., SAMs of 16-mercaptohexadecanol (HS(CH2)16OH), that display water contact angles of <10°. These two extremes are only possible to achieve if the SAM surfaces are uniform and expose only the chain-terminating group at the interface. Mixed SAMs of CH3- and OH-terminated thiols can be tailor-made with any wettability (in terms of contact angle) between these limiting values. The characteristics of mixed two-component SAMs depend strongly upon the precise chemical identity of the components and upon their proportion in the preparation solution, as already stated above. Apart from the composition of the SAMs, the issue of island formation is very important for mixed monolayers. In mixed CH3/CO2CH3 SAMs, scanning tunnelling microscopy (P. Weiss et.al.) has revealed island formation on the 20-50 Å scale. For mixed SAMs of hexadecanethiol and 16mercaptohexadecanol, which is a commonly used model system at our lab, IRAS, wetting, laser desorption spectroscopy and TOF-SIMS data (both by us and other investigators) support a picture of randomly pinned, well-mixed monolayers, although mixing at a true molecular level has neither been contradicted nor confirmed at the present stage. Undoubtedly though, macroscopic phase segregation into single component domains does not occur. Electron Beam Lithography (EBL) refers to a lithographic process that uses a focused beam of electrons to form the circuit patterns needed for material deposition on (or removal from) the wafer, in contrast with optical lithography which uses light for the same purpose. Electron lithography offers higher patterning resolution than optical lithography because of the shorter wavelength possessed by the 10-50 keV electrons that it employs. Given the availability of technology that allows a small-diameter focused beam of electrons to be scanned over a surface, an EBL system doesn't need masks anymore to perform its task (unlike optical lithography, which uses photomasks to project the patterns). An EBL system simply 'draws' the pattern over the resist wafer using the electron beam as its drawing pen. Thus, EBL systems produce the resist pattern in a 'serial' manner, making it slow compared to optical systems. A typical EBL system consists of the following parts: 1) an electron gun or electron source that supplies the electrons; 2) an electron column that 'shapes' and focuses the electron beam; 3) a mechanical stage that positions the wafer under the electron beam; 4) a wafer handling system that automatically feeds wafers to the system and unloads them after processing; and 5) a computer system that controls the equipment.

Figure 1. Example of an electron beam lithography equipment from Jeol The resolution of optical lithography is limited by diffraction, but this is not a problem for electron lithography. The reason for this is the short wavelengths (0.2-0.5 angstroms) exhibited by the

electrons in the energy range that they are being used by EBL systems. However, the resolution of an electron lithography system may be constrained by other factors, such as electron scattering in the resist and by various aberrations in its electron optics. Just like optical lithography, electron lithography also uses positive and negative resists, which in this case are referred to as electron beam resists (or e-beam resists). E-beam resists are e-beamsensitive materials that are used to cover the wafer according to the defined pattern. Electron beam lithography is a rapidly maturing technology that has opened the realm of submicron design to the semiconductor device and circuit designer. This improved pattern resolution has already yielded devices and circuits exhibiting higher density, higher operating frequency, and lower operating power than has been possible with other lithography methods.

Extreme ultraviolet lithography (also known as EUV or EUVL) Contents •

1 EUVL optics

•

2 EUV exposure of photoresist

•

3 EUVL Defects

•

4 Unexpected Resolution Limits ○

4.1 Shot noise

○

4.2 Proximity effect (secondary electrons)

○

4.3 Photoelectron trajectories

○

4.4 Efficient photoresist heating

○

4.5 Point spread function of resist

•

5 EUVL Demonstrations

•

6 Commercial viability

Extreme ultraviolet lithography (also known as EUV or EUVL) is a next-generation lithography technology using the 13.5 nm EUV wavelength. EUVL optics EUVL is a significant departure from the deep ultraviolet lithography used today. All matter absorbs EUV radiation. Hence, EUV lithography needs to take place in a vacuum. All the optical elements, including the photomask, must make use of defect-free Mo/Si multilayers which act to reflect light by means of interlayer interference; any one of these mirrors will absorb around 30% of the incident light. This limitation can be avoided in maskless interference lithography systems. However, the latter tools are restricted to producing periodic patterns only. The pre-production EUVL systems built to date contain at least two condenser multilayer mirrors, six projection multilayer mirrors, and a multilayer object (mask)[1]. Since the optics already absorbs 96% of the available EUV light, the ideal EUV source will need to be sufficiently bright. EUV source development has focused on plasmas generated by laser or discharge pulses. The mirror responsible for collecting the light is directly exposed to the plasma and is therefore vulnerable to damage from the high-energy ions[2][3] and other

debris[4]. This damage associated with the high-energy process of generating EUV radiation has precluded the successful implementation of practical EUV light sources for lithography. The wafer throughput of an EUVL exposure tool is a critical metric for manufacturing capacity. Given that EUV is a technology requiring high vacuum, the throughput is limited (aside from the source power) by the transfer of wafers into and out of the tool chamber, to a few wafers per hour.[5] Another aspect of the pre-production EUVL tools is the off-axis illumination (at an angle of 6 degrees)[6] on a multilayer mask. The resulting asymmetry in the diffraction pattern causes shadowing effects which degrade the pattern fidelity.[7] EUVL's shorter wavelength also increases flare, resulting in increased line width roughness[8]. Heating per feature volume (e.g., 20 nm cube) is higher per EUV photon compared to a DUV photon, due to the larger photon energy. In addition, EUV lithography results in more heating due to the vacuum environment, in contrast to the water cooling environment of immersion lithography. Heating is also a particularly serious issue for multilayer mirrors used, because EUV is absorbed within a thin distance from the surface. The heating density is higher. As a result, water cooling is expected to be used for the high heating load; however, the resulting vibration is a concern.[9]

EUV exposure of photoresist When an EUV photon is absorbed, photoelectrons and secondary electrons are generated by ionization, much like what happens when X-rays or electron beams are absorbed by matter[10]. It has been estimated that about 4 secondary electrons on average are generated for every EUV photon, although the generation volume is not definite. [11] These secondary electrons have energies of a few to tens of eV and travel tens of nanometers inside photoresist (see below) before initiating the desired chemical reaction. This is very similar to the photoelectron migration for the latent image formation in silver halide photographic films. A contributing factor for this rather large distance is the fact that polymers have significant amounts of free volume[12]. In a recent actual EUV print test,[13] it was found 30 nm spaces could not be resolved, even though the optical resolution and the photoresist composition were not the limiting factor. In particular, for photoresists utilizing chemical amplification for higher throughput:[14][15] e- + acid generator -> anion -> dissociated anion products

This reaction occurs after the electron has essentially slowed to a halt, since it is easiest to capture at that point. EUV photoresist images often require resist thicknesses roughly equal to the pitch[16]. This is not only due to EUV absorption causing less light to reach the bottom of the resist but also to forward scattering from the secondary electrons (similar to low-energy electron beam lithography). Since the photon absorption depth exceeds the electron escape depth, as the released electrons eventually slow down,they dissipate their energy ultimately as heat. An EUV dose of 1 mJ/cm2 generates an equivalent photoelectron dose of 10.9 μC/cm2. Current demonstration doses exceed 10 mJ/cm2, or equivalently, 109 μC/cm2 photoelectron dose.

The use of higher doses and/or reduced resist thicknesses to produce smaller features only results in increased irradiation of the layer underneath the photoresist. This adds another significant source of photoelectrons and secondary electrons which effectively reduce the image contrast. In addition, there is increased possibility of ionizing radiation damage to the layers below.

EUVL Defects EUVL faces specific defect issues analogous to those being encountered by immersion lithography. Whereas the immersion-specific defects are due to unoptimized contact between the water and the photoresist, EUV-related defects are attributed to the inherently ionizing energy of EUV radiation. The first issue is positive charging, due to ejection of photoelectrons[17] freed from the top resist surface by the EUV radiation. This could lead to electrostatic discharge or particle contamination as well as the device damage mentioned above. A second issue is contamination deposition on the resist from ambient or outgassed hydrocarbons, which results from EUV- or electron-driven reactions[18]. A third issue is etching of the resist by oxygen[19], argon or other ambient gases, which have been dissociated by the EUV radiation or the electrons generated by EUV. Ambient gases in the lithography chamber may be used for purging and contamination reduction. These gases are ionized by EUV radiation, leading to plasma generation in the vicinity of exposed surfaces, resulting in damage to the multilayer optics and inadvertent exposure of the sample[20]. Of course mask defects are also a known source of defects for EUVL. The mask defects comprise multilayer defects and defects buried under the multilayer as well as pattern defects. The buried defects are particularly insidious, and even 10 nm defects may be considered risky.[21] The phase shift caused by an undetected 3 nm mask substrate flatness variation is sufficient to produce a printable defect. The principle behind this is a quarterwavelength deviation from the flat surface produces a half-wavelength optical path difference after reflection. The light that is reflected from the flat surface is 180 degrees out of phase with the light reflected from the quarter-wavelength deviation.[22] It has been shown that even a 1 nm deviation from flatness would lead to a substantial reduction (~20%) of the image intensity.[23] In fact, defects of atomic scale height (0.3-0.5 nm) with 100 nm FWHM can still be printable by exhibiting 10% CD impact.[24] Like a lens, any defect which effectively produces a phase shift scatters light outside the defect region. The amount of light that is scattered can be calculated. Furthermore, the edge of a phase defect will further reduce reflectivity by more than 10% if its deviation from flatness exceeds 3 degrees, due to the deviation from the target angle of incidence of 84 degrees with respect to the surface. Even if the defect height is shallow, the edge still deforms the overlying multilayer, producing an extended region where the multilayer is sloped. The more abrupt the deformation, the narrower the defect edge extension, the greater the loss in reflectivity.

Unexpected Resolution Limits Given that EUV is a significant reduction in wavelength compared to current lithography wavelengths, one would expect significantly better resolution. However, the resolution is ultimately determined by the interaction volume in the image recording medium, i.e., the photoresist. As noted above, the low energy electrons released by EUV could blur the original EUV image. In addition, there are statistical effects, especially for feature areas less than 1500 square nanometers.

Shot noise

The required dose sensitivity of 5 mJ/cm2 implies only several thousand EUV photons or so accumulate in such a small area. With the natural Poisson distribution due to the random arrival times of the photons, there is an expected natural dose variation of at least a few percent 3 sigma, making the exposure process fundamentally uncontrollable for features less than about 40 nm. Increasing the dose will reduce the shot noise, but will also increase the flare dose and generate more free electrons. The free electrons will spread out before slowing to a stop. Since the free electron density is lower than the initial photon density, the shot noise is always effectively larger than expected from just considering the EUV dose. Proximity effect (secondary electrons)

In a classic experiment by Feder et al. at IBM,[25] an erbium layer on a PMMA resist layer was exposed to X-rays. The erbium layer absorbed the X-rays strongly, producing low energy secondary electrons. The X-rays which were not absorbed continued to penetrate into the PMMA, where they were only lightly absorbed. Upon removal of the erbium layer and subsequent PMMA development in solvent, the resist removal rate was found to be accelerated for the top 40 nm of the PMMA film, while it was much more gradual for the rest of the film. The accelerated rate was due to the secondary electron exposure, while the gradual rate was due to the X-ray absorption. This proved the secondary electron exposure range of 40 nm. A more recent experiment was performed by Carter et al. at MIT and University of Wisconsin-Madison,[26] where the X-ray absorber generating the electrons was beneath the PMMA resist rather than on top of it. In this case, the accelerated dissolution of PMMA started approximately 50 nm above the substrate. The significance of this secondary electron range is the appearance of a "proximity effect" for distances on the order of 50 nm or less. This causes the exposure tolerance to be reduced dramatically as feature sizes decrease below this range. Even though features can still print below this range, the resolution is not repeatable. The difference in experimentally determined ranges above (40 nm vs. 50 nm) is already an indication of the lack of repeatability. The secondary electron exposure can also be thought of as a blur effect. The blur is generally not included in optical-only image simulations. Photoelectron trajectories

Kotera et al. performed EUV photoelectron trajectory simulations, showing their range to be 30 nm.[27][28] The spread of the energy deposition by these electrons can account for the observed line edge roughness. The top layer exposure is effectively less because electrons emitted from the surface never come back. Efficient photoresist heating

Ritucci et al., reported on the improved thermal ablation efficiency for EUV wavelengths compared to DUV wavelengths.[29] Since EUV exceeds the bandgap of all materials, it is more easily absorbed than longer wavelengths, and the same dose of incident energy results in more heating; even ~100 mJ/cm2 would be hot enough to result in ablation. The resolution of chemically amplified photoresists is determined by thermally driven acid diffusion (spreading). It is worth noting that even at the ablation dose of 100 mJ/cm 2, the shot noise for a 1 nm pixel is still significant (3σ/avg = 36%), which could severaly impact a critical dimension (CD) for which the pixel is at least 5%, i.e., 20 nm or less.

Point spread function of resist

Kozawa et al. determined the point spread function of EUV chemically amplified resists using a basic acid generation calculation and simulation fit. The range of acid generation extended ~20 nm from the absorption point, entailing a ~40 nm resolution limit.[30] Given that photoresists easily diffuse acid molecules, it would be no surprise that the smaller and lighter electrons produced by EUV or other ionizing radiation would diffuse faster and further, rendering the expected optical resolution meaningless.

EUVL Demonstrations In 1996, a collaboration between Sandia National Laboratories, University of California at Berkeley, and Lucent Technologies, produced NMOS transistors with gate lengths from 75 nm to 180 nm. The gate lengths were defined by EUV lithography[31]. The device saturation current at 130 nm gate length was ~0.2 mA/um. A 100 nm gate device showed subthreshold swing of 90 mV/decade and saturated transconductance of 250 mS/mm. A commercial NMOS at the same design rule patterned by then-state-of-the-art DUV lithography[32] showed 0.94 mA/um saturation current and 860 mS/mm saturated transconductance. The subthreshold swing in this case was less than 90 mV/decade. In February 2008, a collaboration including IBM and AMD, based at the College of Nanoscale Science and Engineering (CNSE) in Albany, New York, used EUV lithography to pattern 90 nm trenches in the first metal layer of a 45 nm node test chip.[33] No specific details on device performance were given.[34] However, the lithographic performance details given still indicated much to be desired:[35] •

CD uniformity: 6.6%

•

Overlay: 17.9 nm x, 15.6 nm y, possibly correctable to 6.7 nm x, 5.9 nm y

•

Power: 1 W at wafer (>200 W required for high volume), with a dose of 3.75 mJ/cm2

•

Defects: 1/sq. cm.

The high defect level may not be unexpected as AMD's 45 nm node Metal 1 design rule was 90 nm while the same EUV exposure theoretically could result in printed defects below 30 nm originating from mask defects larger than 100 nm. Optical lithography pushed beyond its natural resolution limit has a significant advantage in this regard. Apparently, the CNSE EUV tool suffered from a well-known 16% flare problem. [36] Flare effects may be difficult to separate from the secondary electron effects discussed earlier. Also in July 2008, IMEC printed ~60 nm contacts using their installed EUV tool.[37] Doses of 12-18 mJ/cm2 were used. In August 2008, SEMATECH demonstrated a 22 nm half-pitch using chemically-amplified photoresist. However, even at 15 mJ/cm2, the linewidth roughness was very significant, 56 nm, so that even the image pitch regularity was challenged.[38] In April 2009, IMEC fabricated 22 nm SRAM cells where the contact and Metal 1 layers (~45 nm design rule) were printed with EUV lithography.[39] However, it was acknowledged that EUV would not be ready when companies start using 22 nm. In addition, it was commented that the feature edge profiles indicated slope asymmetry related to the characteristic EUV illumination asymmetry.

Commercial viability EUVL has been the subject of ongoing research and development by many groups. The predicted optical resolution capability has been demonstrated in some special cases where the impact of the actual asymmetry of a realistic EUV scanner has been avoided. With the asymmetry considered, the optical resolution limit is not so straightforward to guarantee. However, general optical resolution is not the only limiting factor for EUV. The difficulties of EUV stem mainly from the dramatically higher energy of the EUV photon (92 eV for EUV light vs. 6.4 eV for 193 nm light), which underlies the difficulty of damagefree generation and control of EUV light and confining the energy absorption within materials. The current development tools have a throughput of 4 wafers per hour with a 120 W source.[40] For a 100 WPH requirement, therefore, a 3 kW source would be needed, which is not available in the foreseeable future. However, EUV photon count is determined by the number of electrons generated per photon which are collected by a photodiode; since this is essentially the highly variable secondary yield of the initial photoelectron, the dose measurement will be impacted by high variability. In fact, data by Gullikson et al[41] indicated ~10% natural variation of the photocurrent responsivity. Due to its lack of readiness, EUVL has also recently been supplanted by double patterning as the lithography of choice for upcoming technology generations. Samsung[42] and IM Flash Technologies[43] have already started using spacer double patterning for their 3X nm NAND Flash. At the same time, Intel had also presented double patterning, specifically double exposure, as a viable alternative path to its 11 nm node.[44] As of 2009, Intel reported being able to print down to 24 nm with EUV, while on the other hand, by using 193 immersion lithography with double patterning, 15 nm was achieved.[45][46] Some observers have noted[47] that 16 nm capability would require a larger illumination angle than the current 6°, and hence require a fundamental change to the current EUV multilayer optics infrastructure.

1. Classification of Solids Throughout the field of condensed matter physics, scientists classify different materials in a variety of different ways which we shall examine here. Fundamentally we can talk of the three broad states of matter: solid, liquid and gas.

Solids, Liquids and Gases In a solid, the atoms which make up the material are fixed in some kind of rigid structure. As you heat the solid up the atoms will jiggle about a bit, but they will still be essentially jiggling about a fixed position. This is why a solid feels rigid when you push against it. If you heat the solid up enough, however, the atoms will eventually break loose from their fixed positions and wander around randomly. If the atoms remain fairly closely packed together then the material will have become a liquid. Heat them up still more and it is possible to make the atoms fly apart to form a very loosely defined group in which the atoms can travel long distances without hitting each other. If this happens the material has become a gas. Condensed matter physics deals with the first two of these states of matter. We can also, however, further subdivide the solids in a number of different ways. I shall outline two of these types of classification: classification due to thermal/electrical properties, and classification due to structural properties.

The Structure of Solids Broadly speaking, solids can fall into one of two categories: those which possess long-range-order in the disposition of their atoms, and those which do not. The first type of material is known as a crystal, while the second is termed an amorphous material.

That is, in a crystal the sites of atoms are determined simply by repeating some sub-unit of the crystal at regular intervals to fill all space. Mathematically we describe a crystal in terms of a regularly arranged set of points whose distribution throughout space looks identical from any point in the set (the lattice), and a prescription telling us how many atoms of each type to associate with each point and where they should go in relation to that point (the basis). For example, the sodium chloride crystal structure is based upon the face centred cubic lattice in which the lattice points are arranged as if at the corners of an array of adjoining cubes, but with an additional lattice point at the centre of each face. The basis then dictates that each lattice site be given two atoms (one sodium and one chlorine) separated from each other by a distance equal to half the cube side length. Different materials have different underlying lattices and different kinds of basis. There are an infinite number of possible atomic bases, but symmetry dictates that there are only 14 possible different types of lattice (in 3D), and that these can be further categorised into just 7 different types of symmetry. The 14 different lattices are known as Bravais lattices, and the 7 different symmetry groups are known as the crystal systems. Crystals are the most widely studied solids from the theoretical point of view, because we can learn about the behaviour of an entire crystal just by studying a very small portion (remember, the structure simply repeats itself at regular intervals). Furthermore, crystals are extremely important in everyday life, in industry, in science and technology: metals are crystalline, for example. Amorphous materials are less well-studied, which is a shame since they are also very important in the real world. A good example of an amorphous material is glass. However, the lack of a repeating structure means that these materials are much more difficult to deal with from the theoretical point of view. Consequently they won't feature at all in the following material.

Electronic and Thermal Properties of Solids This section starts easy and then gets just a little bit hard....

Everybody knows that metals generally conduct electricity and heat very well. This is why they are used for electrical wiring and for saucepans. At the other end of the scale everybody knows that plastics conduct both electricity and heat relatively poorly. This is why they are used for insulating electrical wiring from the outside world. Carrying this a step further we can suggest that all solids can be classified into those which conduct electricity and heat well at room temperature (conductors-clever or what?) and those which do not (insulators-what a surprise!). You can probably guess that if one actually tries to classify materials along these lines, one is likely to find a rather awkward bunch of materials whose properties lie midway between the two extremes. With characteristic imagination these are known as semiconductors. This rather belies the true nature of these materials because not all of their properties are simply related to those of conductors and insulators: semiconductors are rather special.

To understand just why they are special, we will need to look into the thermal and electronic properties of solids in a little more detail.... The atoms which make up a solid are made up of a compact heavy core (the nucleus) surrounded by several much-lighter electrons. The nucleus has a positive electric charge, while the electrons have a negative charge. This causes the electrons to be attracted to the nucleus. A neutral atom has just enough electrons to exactly balance the charge of the nucleus. However, some of the electrons are so tightly bound to the nucleus by this attraction that we may as well think of the nucleus plus its core electrons as a single entity (the ion core whose positive charge is equal to that of the nucleus less the negative charge of the core electrons. This means that we only have to worry about the behaviour of the remaining loosely bound electrons (known as the valence electrons). When atoms combine to form a solid it is the attraction between the positive ion cores and the valence electrons which holds the material together. While the ion cores occupy fixed positions (either in an amorphous or a crystalline structure) the valence electrons whiz around between them, forming a kind of electrostatic glue. In some materials this "glue" is piled up into distinct bonds between particular ion cores (so-called covalent bonding), but in others the electrons are more evenly distributed in the space between the ion cores (known as metallic bonding). A third form of bonding occurs when some of the valence electrons from one atomic species are donated wholesale to another atomic species. Atoms of the species which donates electrons become positive ions and atoms of the species which accepts the electrons become negative ions. This leads to a direct electrostatic attraction between the ions and is known as ionic bonding.

These different forms of bonding are largely responsible for the different thermal and electrical properties of conductors and insulators. Both electrical current and heat are transmitted through these solids by the motion of electrons (to be strictly accurate, heat is also transmitted through vibrations of the atomic structure, but we'll ignore this for the moment). In a metallically bonded material the electrons can drift easily between the ion cores, but in a covalently bonded material they have to "hop" from one bond to the next in order to move. In an ionically bonded material the valence electrons are tightly bound to ioncores which are themselves "tied" to fixed ionic sites in the crystal structure. Thus ionic solids are generally poor conductors, covalent solids may be slightly better, and metals are the best of all. The difference between conductors and insulators can also be seen by using the techniques of Quantum Mechanics to calculate the energies of possible states that the electrons can occupy. In both conductors and insulators the valence electrons settle into the lowest energy states available (the so-called valence band states). The electrons in these states are whizzing around very rapidly, but in totally random directions so that there is no overall motion in any one direction. Thus there is no electrical current and no flow of heat. If we want to make electricity or heat flow through the material we must either apply an electric field or heat one part of the sample. When we do this we raise the energy of some of the electrons and they will flow in such a way to carry the electrical or thermal energy away from its source. However, there must be unoccupied quantum mechanically allowed states available for the electrons to occupy when we raise their energies (conduction band states ). In conductors there are unoccupied conduction band states with energies ranging from the highest energy of the valence band upward, so it is easy to move electrons from the valence

band (where they do not contribute to the current) into the conduction band (where they do). In insulators, however, the lowest energy unoccupied conduction band state is significantly higher in energy than the highest energy valence band state (i.e. there is a band gap between the valence and conduction bands). This means that electrons cannot enter the conduction band until they have been given extra energy at least equal to the band gap energy. Consequently it takes much more energy to make an insulator conduct electricity than it does to make a conductor do the same. In terms of its valence and conduction bands (its band structure) a semiconductor looks just like an insulator with a very small band gap. Because of the small band gap the semiconductor can be adjusted to behave in a variety of novel ways by including small numbers of impurity atoms (doping the semiconductor). For example, if the impurity atoms have more valence electrons than each of the semiconductor atoms then an occupied band with energy just below the conduction band is created. These electrons can easily be excited into the conduction band and so the conduction of the material is improved. On the other hand, if impurity atoms are included which have fewer valence electrons than the semiconductor atoms then an unoccupied band with energy just above the valence band is created. Electrons from the valence band can easily be excited up to this band. Once there they are fairly tightly bound to the impurity atoms and so cannot move any great distance, but the positively charged holes that they left behind in the valence band can move, and it is these which can carry current. Thus there are two types of doped semiconductors: n-type materials in which the current is carried by negatively charged electrons in the conduction band, and p-type materials in which the current is carried by positively charged holes in the valence band. Most common semiconductors are either elements from group IV of the periodic table (Si, Ge, Sn), or are compounds formed from elements on either side of group IV. Thus there are so-called III-V semiconductors (GaAs, GaP, InP, AlAs, GaN, etc....) and also II-VI semiconductors (ZnSe, CdTe, etc....). By combining these different materials in their undoped, n-type and p-type forms, semiconductor devices can be manufactured with very special electronic properties. It is these properties which allow modern computers and other electronic equipment to function, and this in turn provides the driving force behind much of the current effort to understand the physics of semiconductors.

2. Some Basic Ideas about Quantum Mechanics Modern physics is dominated by the concepts of Quantum Mechanics. This page aims to give a brief introduction to some of these ideas.

Until the closing decades of the last century the physical world, as studied by experiment, could be explained according to the principles of classical (or Newtonian) mechanics: the physics of everyday life. By the turn of the century, however, the cracks were beginning to show and the disciplines of Relativity and Quantum Mechanics were developed to account for them. Relativity came first, and described the physics of very massive and very fast objects, then came Quantum Mechanics in the 1920's to describe the physics of very small objects. Neither of these theories provide an easy intuitive picture of the world, since they contradict the predictions of familiar Newtonian Mechanics in the regimes for which they were

developed. Nevertheless, both schemes reproduce the Newtonian results when applied to the everyday world. In seeking to understand the physics of semiconductors at an atomic level we must start from a Quantum Mechanical viewpoint, since the entities with which we will be dealing (electrons, atoms, etc) are so very small.

Waves and Particles At the macroscopic scale we are used to two broad types of phenomena: waves and particles. Briefly, particles are localised phenomena which transport both mass and energy as they move, while waves are de-localised phenomena (that is they are spread-out in space) which carry energy but no mass as they move. Physical objects that one can touch are particle-like phenomena (e.g. cricket balls), while ripples on a lake (for example) are waves (note that there is no net transport of water: hence no net transport of mass).

In Quantum Mechanics this neat distinction is blurred. Entities which we would normally think of as particles (e.g. electrons) can behave like waves in certain situations, while entities which we would normally think of as waves (e.g. electromagnetic radiation: light) can behave like particles. Thus electrons can create wave-like diffraction patterns upon passing through narrow slits, just like water waves do as they pass through the entrance to a harbour. Conversely, the photoelectric effect (i.e. the absorption of light by electrons in solids) can only be explained if the light has a particulate nature (leading to the concept of photons). Such ideas led DeBroglie to the conclusion that all entities had both wave and particle aspects, and that different aspects were manifested by the entity according to what type of process it was undergoing. This became known as the Principle of Wave-Particle Duality. Furthermore, DeBroglie was able to relate the momentum of a "particle" to the wavelength (i.e. the peak-to-peak distance) of the corresponding "wave". The DeBroglie relation tells us that p=h/lambda, where p is the particle's momentum, lambda is its wavelength and h is Planck's constant. Thus it is possible to calculate the quantum wavelength of a particle through knowledge of its momentum. This was important because wave phenomena, such as diffraction, are generally only important when waves interact with objects of a size comparable to their wavelength. Fortunately for the theory, the wavelength of everyday objects moving at everyday speeds turns out to be incredibly small. So small in fact that no Quantum Mechanical effects should be noticeable at the macroscopic level, confirming that Newtonian Mechanics is perfectly acceptable for everyday applications (as required by the Correspondence Principle). Conversely, small objects like electrons have wavelengths comparable to the microscopic atomic structures they encounter in solids. Thus a Quantum Mechanical description, which includes their wave-like aspects, is essential to their understanding. Hopefully the foregoing discussion provides a convincing enough argument to use Quantum Mechanical ideas when dealing with electrons in solids. Next we must address the question of how exactly one describes electrons in a wave-like manner.

The Schrodinger Equation OK, OK, I know I said I would avoid equations, but I can't write about Quantum Mechanics and not mention the biggie now can I ? What I will do is try to talk about the ideas behind the equation, and its consequences, rather than dwell on the form of the equation itself. Given the current limitations of html I'm not even going to try and write it out for you, its easy enough to find in any QM textbook.

There are actually two Schrodinger equations: time-dependent and time-independent. We'll start with the time-dependent version and see what all the fuss is about....

The approach suggested by Schrodinger was to postulate a function which would vary in both time and space in a wave-like manner (the so-called wavefunction) and which would carry within it information about a particle or system. The time-dependent Schrodinger equation allows us to deterministically predict the behaviour of the wavefunction over time, once we know its environment. The information concerning environment is in the form of the potential which would be experienced by the particle according to classical mechanics (if you are unfamiliar with the classical concept of potential an explanation is available). Whenever we make a measurement on a Quantum system, the results are dictated by the wavefunction at the time at which the measurement is made. It turns out that for each possible quantity we might want to measure (an observable) there is a set of special wavefunctions (known as eigenfunctions) which will always return the same value (an eigenvalue) for the observable. e.g..... EIGENFUNCTION psi_1(x,t) psi_2(x,t) psi_3(x,t) psi_4(x,t) etc....

always returns a_1 a_2 a_3 a_4 etc....

EIGENVALUE

where (x,t) is standard notation to remind us that the eigenfunctions psi_n(x,t) are dependent upon position (x) and time (t).

Even if the wavefunction happens not to be one of these eigenfunctions, it is always possible to think of it as a unique superposition of two or more of the eigenfunctions, e.g.... psi(x,t) = c_1*psi_1(x,t) + c_2*psi_2(x,t) + c_3*psi_3(x,t) + .... where c_1, c_2,.... are coefficients which define the composition of the state.

If a measurement is made on such a state, then the following two things will happen: 1. The wavefunction will suddenly change into one or other of the eigenfunctions making it up. This is known as the collapse of the wavefunction and the probability of the wavefunction collapsing into a particular eigenfunction depends on how much that eigenfunction contributed to the original superposition. More precisely, the probability that a given eigenfunction will be chosen is proportional to the square of the coefficient of that eigenfunction in the superposition, normalised so that the overall probability of collapse is unity (i.e. the sum of the squares of all the coefficients is 1). 2. The measurement will return the eigenvalue associated with the eigenfunction into which the wavefunction has collapsed. Clearly therefore the measurement can only ever yield an eigenvalue (even though the original state was not an eigenfunction), and it will do so with a probability determined by the composition of the original superposition. There are clearly only a limited number of discrete values which the observable can take. We say that the system is quantised (which means essentially the same as discretised).

Once the wavefunction has collapsed into one particular eigenfunction it will stay in that state until it is perturbed by the outside world. The fundamental limitation of Quantum

Mechanics lies in the Heisenberg Uncertainty Principle which tells us that certain quantum measurements disturb the system and push the wavefunction back into a superposed state once again. For example, consider a measurement of the position of a particle. Before the measurement is made the particle wavefunction is a superposition of several position eigenfunctions, each corresponding to a different possible position for the particle. When the measurement is made the wavefunction collapses into one of these eigenfunctions, with a probability determined by the composition of the original superposition. One particular position will be recorded by the measurement: the one corresponding to the eigenfunction chosen by the particle. If a further position measurement is made shortly afterwards the wavefunction will still be the same as when the first measurement was made (because nothing has happened to change it), and so the same position will be recorded. However, if a measurement of the momentum of the particle is now made, the particle wavefunction will change to one of the momentum eigenfunctions (which are not the same as the position eigenfunctions). Thus, if a still later measurement of the position is made, the particle will once again be in a superposition of possible position eigenfunctions, so the position recorded by the measurement will once again come down to probability. What all this means is that one cannot know both the position and the momentum of a particle at the same time because when you measure one quantity you randomise the value of the other. See below.... notation: x=position, p=momentum action | wavefunction after action -----------------|----------------------------------------------------start | superposition of x and/or p eigenfunctions measure x | x eigenfunction = superposition of p eigenfunctions measure x again | same x eigenfunction measure p | p eigenfunction = superposition of x eigenfunctions measure x again | x eigenfunction (not necessarily same one as before)

Precisely what constitutes a measurement and the process by which the wavefunction collapses are two issues I am not even going to touch on. Suffice to say they are still matters for vigorous debate ! At any rate, in a macroscopic system the wavefunctions of the many component particles are constantly being disturbed by measurement-like processes, so a macroscopic measurement on the system only ever yields a time- and particle- averaged value for an observable. This averaged value need not, of course, be an eigenvalue, so we do not generally observe quantisation at the macroscopic level (the correspondence principle again). If we are to investigate the microscopic behaviour of particles we would (in an ideal world) like to know the wavefunctions of any individual particles at any given instant in time.... The time-dependent Schrodinger equation allows us to calculate the wavefunctions of particles, given the potential in which they move. Importantly, all the solutions of this equation will vary over time in some kind of wave-like manner, but only certain solutions will vary in a predictable pure sinusoidal manner. These special solutions of the time-dependent Schrodinger equation turn out to be the energy eigenfunctions, and can be written as a timeindependent factor multiplied by a sinusoidal time-dependent factor related to the energy (in fact the frequency of the sine wave is given by the relation E=h*frequency). Because of the

simple time-dependence of these functions the time-dependent Schrodinger equation reduces to the time-independent Schrodinger equation for the time-independent part of the energy eigenfunctions. That is to say that we can find the energy eigenfunctions simply by solving the time-independent Schrodinger equation and multiplying the solutions by a simple sinusoidal factor related to the energy. It should therefore always be remembered that the solutions to the time-independent Schrodinger equation are simply the amplitudes of the solutions to the full time-dependent equation. The bottom line is that we can use the time-dependent Schrodinger equation (or often the simpler time-independent version) to tell us what the wavefunctions of a quantum system are, entirely deterministically. That is, we do not have to resort to the language of probability. Once we try to apply this knowledge to the real world (i.e. to predict the outcome of measurements, etc) then we have to speak in terms of probabilities. As a last point, it is important to realise that there is no real physical interpretation for the wavefunction. It simply contains information regarding the system to which it refers. However, one of the most important characteristics of a wavefunction is that the square of its magnitude is a measure of the probability of finding a particle described by the wavefunction at a given point in space. That is, in regions where the square of the magnitude of the wavefunction is large, the probability of finding the particle in that region is also large, and vice versa. This is not intended to be an exhaustive description of what is a very subtle and complex subject, indeed it cannot be so, given my intention to avoid equations wherever possible. The interested reader is urged to consult one of the large number of textbooks on the subject, some of which are listed in the reading list on the contents page. We shall, however, expand greatly upon the basic framework of Quantum Mechanics in later chapters....

3. The Many Body Problem and Density Functional Theory In this chapter we shall take a look at perhaps the most fundamental difficulty in condensed matter theory (the Many Body problem) and at a particularly successful way of avoiding it (Density Functional Theory, or DFT). We shall see in what situations DFT can give meaningful results and also in which situations it fails. The purpose of this work as a whole is to look at ways of moving beyond DFT, but a thorough understanding of the starting point is, of course, essential....

The Many-Body Problem So what is a many-body situation, and why is it such a problem? Let us start with a classical example. Consider a hard ball (ball A) moving in some kind of force field which may be spatially and temporally varying, but which is uncoupled to the motion of the ball (i.e. unaltered by the presence of the ball). If we know the force on the ball at every point in space and time then we can easily calculate the trajectory of the ball by using Newton's laws. This situation is that of a single particle moving in an external field. It doesn't matter that the field is varying; as long as the variation does not depend upon the position or velocity of the ball the problem remains easy. Now add a second hard ball (ball B) to the problem, and furthermore let us attach it to the first by means of a spring. At a ball separation equal to the natural length of the spring there will be no force between the balls, but in general the spring will either be stretched or compressed and so ball A will exert a force on ball B and vice versa. The motion of the balls is still described perfectly well by Newton's classical laws of motion, but now the motion of

ball A is intimately linked with the motion of ball B. That is, one cannot solve the trajectories of ball A and ball B separately: their equations of motion are coupled and must be solved simultaneously. Fortunately, with two balls this is not too much of a problem. However, if there are many balls then the problem rapidly becomes insoluble. It should be stressed that the balls are still subject to Newton's laws, but the difficulty of solving the equations which result from those laws increases rapidly because of the coupling. This is the essence of the Many Body Problem. However, all is not doom and gloom. Imagine that the balls are not connected by springs, what happens then? The answer is that the balls move precisely as single particles until they collide with each other. Now the problem has become easier again, because we can use single particle theory to describe the trajectories of individual balls, until such times as they instantaneously scatter off each other. Thus we don't have to solve any equations simultaneously. Instead we have to know a bit about scattering theory. Now, it would not be correct to describe these balls simply as single particles because that would be to ignore the effect of the scattering, but we can call them single-particle-like particles or, to use the accepted term, quasiparticles. Somewhere between these last two cases there is a grey area in which the balls interact with each other only when they are within a certain range of each other. That is, when the balls are well-separated, they do not significantly interact, but when they come close together they exert a force on each other. In the limit when the critical range is very small this situation reduces to the single-particle case, and in the opposite limit of a very large critical range the situation is that of a true many body problem. Thus the applicability of the quasiparticle approach to a given many body problem is largely dependent on the range of the inter-particle forces involved. The electrons in a solid interact strongly both with the ion cores making up the crystal structure and with each other. The electron-ion interaction does not constitute a many body problem, however, because the ions are essentially stationary on the time-scale of the motion of the electrons (i.e. the electronic and ionic degrees of freedom are not coupled). On the other hand, the electron equations of motion are most certainly strongly coupled to each other by the electrostatic interaction. The long range nature of the electrostatic interaction does not bode well for a quasiparticle description. Nevertheless, the most successful current method for electronic structure calculations in solids is based on the even more radical approximation of single-particle behaviour. In order to understand the problem better let us look at some of the different approaches taken by different workers over the years....

Hartree and Hartree-Fock Theory To describe completely the quantum mechanical behaviour of electrons in solids it is strictly necessary to calculate the many-electron wavefunction for the system. In principle this may be obtained from the time-independent Schrodinger equation, but in practice the potential experienced by each electron is dictated by the behaviour of all the other electrons in the solid. Of course, the influence of nearby electrons will be much stronger than that of faraway electrons since the interaction is electrostatic in nature, but the fact remains that the motion of any one electron is strongly coupled to the motion of the other electrons in the system. To solve the Schrodinger equation directly for all these electrons would thus require us to solve a system of around 10^23 simultaneous differential equations. Such a calculation is beyond the capabilities of present-day computers, and is likely to remain so for the foreseeable future.

One of the earliest attempts to solve the problem was made by Hartree. He simplified the problem by making an assumption about the form of the many-electron wavefunction, namely that it was just the product of a set of single-electron wavefunctions. In a uniform system these wavefunctions would take the form of simple plane waves. Having made this assumption it was possible to proceed using the variational principle. This principle is a very powerful concept in mathematics. In the form most commonly applied to theoretical physics it states that if a given system may be described by a set of unknown parameters then the set of parameter values which most correctly describes the ground state of the system (i.e. the state in which the system exists when not perturbed by outside influences) is just that set of values which minimises the total energy. A simple example of this principle is the case of a ball sitting in a valley in a gravitational field. The system may be described by a single parameter: the height of the ball above the bottom of the valley. The ground state of the system may be determined by finding the value of this parameter which minimises the total energy. Clearly this value of the parameter corresponds to the ball sitting at the very bottom of the valley. By using the variational method Hartree found the Hamiltonian equation of the manyelectron system (just a fancy name for the equation of motion). In fact, for an N-electron system there are N equations; one for each of the N single-electron wavefunctions which made up the many-electron product wavefunction. These equations turned out to look very much like the time-independent Schrodinger equation, except the potential (the Hartree potential) was no longer coupled to the individual motions of all the other electrons, but instead depended simply upon the time-averaged electron distribution of the system. This important fact meant that it was possible to treat each electron separately as a singleparticle. Consequently the Hartree approximation allows us to calculate approximate singleparticle wavefunctions for the electrons in crystals, and hence calculate other related properties. Unfortunately, the Hartree approximation does not provide us with particularly good results. For example, it predicts that in a neutral uniform system there will be no binding energy holding the electrons in the solid. This, of course, is in direct contradiction to the experimental evidence that electrons must be given a finite amount of energy before they can be liberated from solids. The most obvious reason for the failure of the Hartree approach lies in the initial assumption of a product wavefunction. The famous Pauli exclusion principle states that it is not possible for two fermions (the class of particles to which electrons belong) to exist at the same point in space with the same set of quantum numbers (the parameters which define a particle's quantum mechanical state). This principle is manifest as an effective repulsion between any pair of identical fermions possessing the same set of quantum numbers. Mathematically, the Pauli exclusion principle can be accounted for by ensuring that the wavefunction of a set of identical fermions is antisymmetric under exchange of any pair of particles. That is to say that the process of swapping any one of the fermions for any other of the fermions should leave the wavefunction unaltered except for a change of sign. Any wavefunction possessing that property will tend to zero (indicating zero probability) as any pair of fermions with the same quantum numbers approach each other. The Hartree product wavefunction is symmetric (i.e. stays precisely the same after interchange of two fermions) rather than antisymmetric, so the Hartree approach effectively ignores the Pauli exclusion principle! The Hartree-Fock approach is an improvement over the Hartree theory in that the manyelectron wavefunction is specially constructed out of single-electron wavefunctions in such a way as to be antisymmetric. The wavefunction has to be much more complicated than the

Hartree product wavefunction, but it can be written in a compact way as a so-called Slater determinant (for those who know what a determinant is). Starting from this assumption it is once again possible to derive the Hamiltonian equation for the system through the variational principle. Just as before, this results in a simple equation for each single-electron wavefunction. However, this time in addition to the Hartree potential (which described the direct Coulomb interaction between an electron and the average electron distribution) there is now a second type of potential influencing the electrons, namely the so-called exchange potential. The exchange potential arises as a direct consequence of including the Pauli exclusion principle through the use of an antisymmetrised wavefunction. We can get a visual impression of the effect of exchange by considering the region surrounding a given electron with a particular quantum mechanical spin. In this context spin is a quantum mechanical property (in some ways analogous to mechanical spin) which is related to magnetism. Electrons can be either in the spin-up state or the spin-down state (loosely you could think of spin-up electrons spinning clockwise, say, with spin-down electrons spinning anticlockwise) . In a non-magnetic sample half of the electrons will be spin-up while the other half will be spin-down. If we look at an electron with spin-up, then the Pauli exclusion principle means that other nearby spin-up electrons will be repelled. Spindown electrons will not be affected since they have a different spin quantum number. Thus our spin-up electron is surrounded by a region which has been depleted of other spin-up electrons. Thus this region is positively charged (remember that the average electron distribution exactly balances the positive charge of the ion cores, and that this region is relatively depleted of electrons). Similarly, if we had considered a spin-down electron from the start, then we would have found a region depleted of other spin-down electrons. The edge of the electron depleted region is not clearly defined, but nevertheless we call this region the exchange hole. Notably, the exchange potential contributes a binding energy for electrons in a neutral uniform system, so correcting one of the major failings of the Hartree theory. However, in calculating many other properties the Hartree-Fock approach is actually worse than the Hartree approach. How is it that improving the physics which went into the theory can actually give us worse answers? The reason the Hartree-Fock theory gives worse answers than the Hartree theory is simply that there is another piece of physics which we are still ignoring. To some extent it cancels out with the exchange effect and so when we use the Hartree approach (i.e. we ignore both effects) we get reasonable results. On the other hand the Hartree-Fock approach includes the exchange effect but ignores the other effect, which balances it somewhat, completely. This new effect is the electrostatic correlation of electrons.... Ignoring the Pauli exclusion principle generated exchange hole for the moment, we can also visualise a second type of hole in the electron distribution caused by simple electrostatic processes. If we consider the region immediately surrounding any electron (spin is now immaterial) then we should expect to see fewer electrons than the average, simply because of their electrostatic repulsion. Consequently each electron is surrounded by an electrondepleted region known either as the Coulomb hole (because of its origin in the electrostatic interaction) or the correlation hole (because of it origin in the correlated motion of the electrons). Just as in the case of the exchange hole the electron depleted region is slightly positively charged. The effect of the correlation hole is twofold. The first is obviously that the negatively charged electron and its positively charged hole experience a binding force due to simple electrostatics. The second effect is more subtle and arises because any entities

which interact with the electron over a length scale larger than the size of the correlation hole will not interact with the bare electron but rather with the electron+correlation hole (which of course has a smaller magnitude charge than the electron alone). Thus any other interaction effects, such as exchange, will tend to be reduced (i.e. screened) by the correlation hole. Clearly we can now see why the Hartree-Fock approach fails for solids: firstly the exchange interaction should be screened by the correlation hole rather than acting in full, and secondly the binding between the correlation hole and electron has been ignored. At this point I should mention that the Hartree-Fock approach gives quite creditable results for small molecules. This is because there are far fewer electrons involved than in a solid, and so correlation effects are minimal compared to exchange effects. Although neither of the above methods succeeded in solving the many-body problem of electrons in solids they did at least elucidate the important physical processes which we must describe: namely exchange and correlation. The breakthrough which revolutionised the field came in 1964, and we shall meet these two concepts again when we examine this watershed in the next section....

Density Functional Theory The methods of the previous section were both essentially based upon the variational principle. As already mentioned, this is an extremely powerful approach, but it depends for its success upon a good parametric description of the problem in the first instance. To go back to the "ball in the valley" example from the previous section it is clear that choosing the height of the ball as our adjustable parameter is a good idea, but that choosing the ambient temperature instead is not. We can vary the temperature all we like, but still get no nearer to finding a solution. Similarly, in quantum mechanics, the better the form of wavefunction we take (i.e. the more suited it is to describing the problem at hand) then the better results we will get from the variational approach. Thus the Hartree-Fock antisymmetric wavefunction allowed us correctly to describe the exchange interaction, whereas the Hartree product wavefunction did not. Accordingly we can view the ultimate failure of both of these models as being due to not having good enough approximate forms for the wavefunction to start with. This is hardly surprising, since we assumed that the many-electron wavefunction was expressible in terms of many single-electron wavefunctions, which is not necessarily possible at all. Hohenberg and Kohn, in 1964, suggested that the problem really was that the manyelectron wavefunction was too complicated an entity to deal with as the fundamental variable in a variational approach. Firstly, it cannot adequately be described without ~10^23 parameters, and secondly it has the complication of possessing a phase as well as a magnitude. They chose instead to use the electron density as their fundamental variable. That is, they considered the ground state of the system to be defined by that electron density distribution which minimises the total energy. Furthermore, they showed that all other ground state properties of the system (e.g. lattice constant, cohesive energy, etc) are functionals of the ground state electron density. That is, that once the ground state electron density is known all other ground state properties follow (in principle, at least). In 1965, Kohn and Sham showed that the Hamiltonian equation derived from this variational approach took a very simple form. The so-called Kohn-Sham equation is similar in form to the time-independent Schrodinger equation, except that the potential experienced by the electrons is formally expressed as a functional of the electron density. Again it is effectively a single-particle equation. In addition to the contribution from the electron-ion interaction, the

electron-electron interaction potential is split for convenience into two parts: the Hartree potential, which we have met before, and an exchange-correlation potential, whose form is, in general, unknown. Application of this theory to real-life situations involves heavy computational effort. For many years now, density functional theory has been used with great success to investigate the ground state properties of solids, both in the bulk form and at surfaces and interfaces (see, for example, my recent work on silicon surfaces and gallium arsenide surfaces). However, as a variational approach, it cannot reliably be used to provide information about excited states of the system (i.e. states other than the ground state). In particular, density functional calculations in semiconductors are well known to place the excited states of electrons (i.e. conduction band states) too close in energy to the excited states of holes (i.e. valence band states), resulting in predicted band gaps which are 50100% too small. In order to rectify this problem it is necessary to go beyond the single-particle approach epitomised by density funtional theory and instead utilise a quasiparticle approach, as described in the next chapter.