Fundamental Semiconductor Physics
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Fundamental semiconductor physics Material Classification: Conductors, Insulators, and Semi-Conductors This material can be classified as either a conductor, an insulator, or a semi-conductor. These three distinct classes of material arise from a difference in the structure of the allowed electron energy levels. In particular, every material possesses both a valence and a conduction band for electrons, and the energy difference between these two bands will determine how easily an electric current will pass through the material. Catalogue voltage detectors SOT-25
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As the name implies, the valence band contains the valence electrons of a substance. At absolute zero, all of the electrons in a substance would be contained in the valence band. However, if the substance is at a higher temperature, thermal energy can excite electrons out of the valence level and into an excited energy level. The conduction band is composed of the excited energy states of a substance, and it contains electrons that have been thermally or otherwise excited from the valence band. The electrons in the conduction band are able to freely move about the substance and conduct electricity if an external electric field is applied. Due to the lattice spacing of the atoms and other relevant factors, there is an energy gap between the highest- energy electron valence level and the lowest-energy conduction level. The width of Catalogue voltage detectors SOT-25
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this gap is dependent on the temperature and the pressure of the material and determines whether a material will be a conductor, insulator or semi- conductor. For reference, an energy level diagram for each type of material is shown in figure.
In conductors, the valence band and the conduction band overlap. Consequently, there is no energy gap to cross in order to reach the conduction band, and any energy that is added to the electron is sufficient to propel it into the conduction band. There are many electrons that are free Catalogue voltage detectors SOT-25
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to move about a conductor, so it very easy for current to flow if an external electric field is applied. In insulators, there is a distinct separation of the two bands and there is a large energy difference between them. This energy difference is so large that the thermal energy of an individual electron is not large enough to propel it from the valence band to the conduction band. Consequently, there are not many electrons in the conduction band, and it is difficult for current to flow when an external electric field is applied.
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As in insulators, there are two distinct bands in semi- conductors. However, the energy gap between these two bands is neither as large nor as significant (typically around one electron-volt) as is the band gap in insulators. At normal temperatures, the thermal energy of the material is sufficient to propel some electrons from the valence band into the conduction band, allowing some electrons to be free to conduct current. The number of free charge carriers increases with supplied energy, so the conductivity of a semi-conductor can be manipulated by outside potentials
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Fundamental semiconductor physics Band structure of a semiconductor In the parlance of solid-state physics, semiconductors (and insulators) are defined as solids in which at absolute zero (0 K), the uppermost band of occupied electron energy states, known as the valence band, is completely full. Or, to put it another way, the Fermi energy of the electrons lies within the forbidden bandgap. The Fermi energy, or Fermi level can be thought of as the energy up to which available electron states are occupied at absolute zero. Catalogue voltage detectors SOT-25
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At room temperature, there is some smearing of the energy distribution of the electrons, such that a small, but not insignificant number have enough energy to cross the energy band gap into the conduction band. These electrons which have enough energy to be in the conduction band have broken free of the covalent bonds between neighbouring atoms in the solid, and are free to move around, and hence conduct charge. The covalent bonds from which these excited electrons have come now have missing electrons, or holes which are free to move around as well. (The holes themselves don't actually move, but a neighbouring electron can move to fill the hole, leaving a hole at the place it has just come from, and in this way the holes appear to move.)
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It is an important distinction between conductors and semiconductors that, in semiconductors, movement of charge (current) is facilitated by both electrons and holes. Contrast this to a conductor where the Fermi level lies within the conduction band, such that the band is only half filled with electrons. In this case, only a small amount of energy is needed for the electrons to find other unoccupied states to move into, and hence for current to flow. The ease with which electrons in a semiconductor can be excited from the valence band to the conduction band depends on the band gap between the bands, and it is the size of this energy bandgap that serves as an arbitrary dividing line between semiconductors and insulators. Catalogue voltage detectors SOT-25
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Materials with a bandgap energy of less than about 3 electron volts are generally considered semiconductors, while those with a greater bandgap energy are considered insulators.. The current-carrying electrons in the conduction band are known as "free electrons," although they are often simply called "electrons" if context allows this usage to be clear. The holes in the valence band behave very much like positively-charged counterparts of electrons, and they are usually treated as if they are real charged particles.
Fundamental semiconductor physics Catalogue voltage detectors SOT-25
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Material Classification: Conductors, Insulators, and Semi-Conductors This material can be classified as either a conductor, an insulator, or a semi-conductor. These three distinct classes of material arise from a difference in the structure of the allowed electron energy levels. In particular, every material possesses both a valence and a conduction band for electrons, and the energy difference between these two bands will determine how easily an electric current will pass through the material. As the name implies, the valence band contains the valence electrons of a substance. At absolute zero, all of the electrons in a substance would be contained in the valence band. However, if the Catalogue voltage detectors SOT-25
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substance is at a higher temperature, thermal energy can excite electrons out of the valence level and into an excited energy level. The conduction band is composed of the excited energy states of a substance, and it contains electrons that have been thermally or otherwise excited from the valence band. The electrons in the conduction band are able to freely move about the substance and conduct electricity if an external electric field is applied. Due to the lattice spacing of the atoms and other relevant factors, there is an energy gap between the highest- energy electron valence level and the lowest-energy conduction level. The width of this gap is dependent on the temperature and the pressure of the material and determines whether Catalogue voltage detectors SOT-25
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a material will be a conductor, insulator or semi- conductor. For reference, an energy level diagram for each type of material is shown in figure.
In conductors, the valence band and the conduction band overlap. Consequently, there is no energy gap to cross in order to reach the conduction band, and any energy that is added to the electron is sufficient to propel it into the conduction band. There are many electrons that are free to move about a conductor, so it very easy for current to flow if an external electric field is applied. Catalogue voltage detectors SOT-25
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In insulators, there is a distinct separation of the two bands and there is a large energy difference between them. This energy difference is so large that the thermal energy of an individual electron is not large enough to propel it from the valence band to the conduction band. Consequently, there are not many electrons in the conduction band, and it is difficult for current to flow when an external electric field is applied. As in insulators, there are two distinct bands in semi- conductors. However, the energy gap between these two bands is neither as large nor as significant (typically around one electron-volt) as is the band gap in insulators. At normal temperatures, the thermal energy of the material is sufficient to propel some electrons from the valence band into the conduction band, allowing Catalogue voltage detectors SOT-25
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some electrons to be free to conduct current. The number of free charge carriers increases with supplied energy, so the conductivity of a semi-conductor can be manipulated by outside potentials
Fundamental semiconductor physics Energy Bands Sometimes valence electrons are shared, becoming a bond between two atoms - covalent bonding. This is the bonding type in diamond-crystal lattice semiconductors such as silicon Catalogue voltage detectors SOT-25
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semiconductors. However, it is more interesting to analyze energy-related aspects rather than spatial aspects such as bonds. Therefore the concept of energy bands is coming in handy. An almost continuous band of allowed energies of electrons comes about when atoms are brought in close proximity to each other, this is because of the interatomic forces and is foreseen in the Pauli exclusion principle. “Almost”, well, one energy level is split into N levels when N atoms are brought together, and these N levels can accommodate at most 2N electrons due to spin degeneracy.
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Remember, N is huge! Now, since the separation between the energy levels within the band is much smaller than the thermal energy possessed by an electron at room temperature the band can be viewed as continuous. Ec is the lowest possible conduction band energy, while Ev is the highest possible valence band energy. The band gap energy, Eg, is furthermore defined as (Ec Ev). Eg is the energy it takes to break a bond in the spatial view of the crystal. The band gap energies for some semiconductors at T = 300 K are: Eg = 1.42 eV in GaAs and 1.12 eV in Si. You do remember that 1 eV = 1.602?10-19 J, don’t you?
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Current Flow and the Concept of Holes Using the concept of energy bands, the pure semiconductor (ideally, i.e. T 0 K) contains a completely filled (with electrons) valence band and a completely empty conduction band. Completely filled bands do contain plenty of electrons but do not contribute to the conductivity of the material. This is due to the fact that the electrons can not gain energy since all energy levels are already filled. As semiconductors are of primary interest in this text, we now introduce a simplified energy band diagram for semiconductors and define some key parameters. The diagram is shown in the figure below:
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A simplified energy band diagram used to describe semiconductors. Shown are the valence and conduction band as indicated by the valence band edge Ev and the conduction band edge Ec. The vacuum level, EVACUUM and the electron affinity, c are also indicated on the figure. The diagram identifies the almost-empty conduction band simply by a line which indicates the bottom of the conduction band and is labeled Ec. Similarly the top of the valence band is indicated with a line labeled Ev. Note: The actual bandstructures of semiconductors is more complex than the reader is lead to believe by the discussion above. So, semiconductors distinguish themselves from metals and insulators by the fact that they contain an "almostCatalogue voltage detectors SOT-25
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empty" conduction band and an "almost-full" valence band. This also means that we will have to deal with the transport of carriers in both bands. To facilitate the discussion of the transport in the "almost-full" valence band we will introduce the concept of holes in a semiconductor. It is important for the reader to understand that one could deal with only electrons (since these are the only real particles available in a semiconductor) if one is willing to keep track of all the electrons in the "almost-full" valence band.
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The concepts of holes is introduced based on the notion that it is a whole lot easier to keep track of the missing particles in an "almost-full" band, rather than keeping track of the actual electrons in that band. We will now first explain the concept of a hole and then point out how the hole concept simplifies the analysis. Holes are missing electrons. They behave as particles with the same properties as the electrons would have occupying the same states except that they carry a positive charge. This definition is illustrated further with the figure below which presents the simplified energy band diagram in the presence of an electric field. Catalogue voltage detectors SOT-25
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Fundamental semiconductor physics Purity and perfection of semiconductor materials Semiconductors with predictable, reliable electronic properties are difficult to mass-produce because of the required chemical purity, and the perfection of the crystal structure, which are needed to make devices. Because the presence of impurities in very small proportions can have such big effects on the properties of the material, the level of chemical purity needed is extremely high. Techniques for achieving such high purity include zone Catalogue voltage detectors SOT-25
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refining, in which part of a solid crystal is melted. Impurities tend to concentrate in the melted region, leaving the solid material more pure. A high degree of crystalline perfection is also required, since faults in crystal structure such as dislocations, twins, and stacking faults, create energy levels in the band gap, interfering with the electronic properties of the material. Faults like these are a major cause of defective devices in production processes. The larger the crystal, the harder it is to achieve the necessary purity and perfection; current mass production processes use sixinch diameter crystals which are grown as cylinders and sliced into wafers. Catalogue voltage detectors SOT-25
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Fundamental semiconductor physics The chip A transistor is essentially a replacement for a vacuum tube. When tiny transistors replaced bulky vacuum tubes, the first applications resulted in electronic devices that accomplished the same as tube-based devices, but were much smaller. This encouraged engineers to build more functions into the same devices since there was now more room. By the end of the 1950s, electronics manufacturers were faced with circuits of increasing complexity. Computers, for example, Catalogue voltage detectors SOT-25
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contained tens of thousands of transistors. Assembly often required hundreds of thousands of interconnections, all of which had to be soldered by hand. Electronic devices, such as computers and radios, use several different types of components. Some are very fast switches. Others act as electronic gates, allowing certain messages to get through while rejecting others, or restricting flow of current to a single direction. In a computer such gates become logic circuits that, for example, combine two statements into one using the electronic equivalents to the logical connectives and, or, or if-then. Another component amplifies a signal. After the invention of the transistor, various configurations of transistors were created to perform these functions, components still referred to by such traditional names as resistor, Catalogue voltage detectors SOT-25
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capacitor, diode, and so forth. In each case the method was to add specific impurities to different regions of a semiconductor chip, a process called doping. The idea of placing several components on a single chip came separately to two people who worked independently. Jack Kilby, an electronics engineer, in 1958 joined a team at Texas Instruments that studied ways to reduce the size of computer circuits. Kilby created a semiconductor chip that carried an oscillator made of several components, such as switches, resistors, capacitors, and diodes, all made from doped semiconductors. Although these components were on a single chip, Kilby had Catalogue voltage detectors SOT-25
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not developed a suitable way to connect them, and had to create interconnections in the traditional way. He demonstrated his oscillator-on-a-chip to executives from Texas Instruments on September 12, 1958, and filed for a patent a few months later. Robert Noyce, a physicist, was the head of research at the recently founded Fairchild Semiconductor. That company had developed the "planar" technology for the manufacture of transistors. In that method, large numbers of transistors were created on a single wafer, which subsequently was cut up to yield the single transistors. Noyce realized that this technology would be suitable for creating an entire circuit on such a wafer. But he also found a way to make Catalogue voltage detectors SOT-25
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connections between the components on the wafer by laying down conducting tracks. The result is termed an integrated circuit, but most people simply call it a chip. Noyce filed a patent for his integrated circuit one year after Kilby did, and was granted it in April 1961. Kilby's patent application was rejected because he had not solved the problem of interconnecting the components on the chip. A legal battle between Kilby and Noyce ensued, which ultimately was won by Noyce by decision of the Court of Customs and Patents Appeals in November 1969. Fairchild Semiconductor and Texas Instruments, however, had already agreed to share the licensing of integrated circuits in Catalogue voltage detectors SOT-25
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1966. Noyce and Kilby, regarded by the technical community as coinventors, a view both have accepted, jointly received the National Medal of Science for their invention.
Fundamental semiconductor physics Doping of semiconductors One of the main reasons that semiconductors are useful in electronics is that their electronic properties can be greatly altered in a controllable way by adding small amounts of impurities. These impurities are called dopants. Catalogue voltage detectors SOT-25
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Heavily doping a semiconductor can increase its conductivity by a factor greater than a billion. In modern integrated circuits, for instance, heavily-doped polycrystalline silicon is often used as a replacement for metals. Intrinsic and extrinsic semiconductors An intrinsic semiconductor is one which is pure enough that impurities do not appreciably affect its electrical behavior. In this case, all carriers are created by thermally or optically excited electrons from the full valence band into the empty conduction band. Thus equal numbers of electrons and holes are present in an intrinsic semiconductor. Electrons and holes flow in Catalogue voltage detectors SOT-25
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opposite directions in an electric field, though they contribute to current in the same direction since they are oppositely charged. Hole current and electron current are not necessarily equal in an intrinsic semiconductor, however, because electrons and holes have different effective masses (crystalline analogues to free inertial masses). The concentration of carriers is strongly dependent on the temperature. At low temperatures, the valence band is completely full, making the material an insulator (see electrical conduction for more information). Increasing the temperature leads to an increase in the number of carriers and a corresponding increase in conductivity. This principle is used in thermistors. This behavior Catalogue voltage detectors SOT-25
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contrasts sharply with that of most metals, which tend to become less conductive at higher temperatures due to increased phonon scattering. An extrinsic semiconductor is one that has been doped with impurities to modify the number and type of free charge carriers. N-type doping The purpose of n-type doping is to produce an abundance of mobile or "carrier" electrons in the material. To help understand how n-type doping is accomplished, consider the case of silicon Catalogue voltage detectors SOT-25
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(Si). Si atoms have four valence electrons, each of which is covalently bonded with one of four adjacent Si atoms. If an atom with five valence electrons, such as those from group VA of the periodic table (eg. phosphorus (P), arsenic (As), or antimony (Sb)), is incorporated into the crystal lattice in place of a Si atom, then that atom will have four covalent bonds and one unbonded electron. This extra electron is only weakly bound to the atom and can easily be excited into the conduction band. At normal temperatures, virtually all such electrons are excited into the conduction band. Since excitation of these electrons does not result in the formation of a hole, the number of electrons in such a material far exceeds the number of holes. In this case the electrons are the majority carriers and the holes are the minority carriers. Because the fiveelectron atoms have an extra electron to "donate", they are called donor atoms. Note that each Catalogue voltage detectors SOT-25
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movable electron within the semiconductor is never far from an immobile positive dopant ion, and the n-doped material normally has a net electric charge of zero.
Fundamental semiconductor physics Doping of semiconductors (page 2) P-type doping
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The purpose of p-type doping is to create an abundance of holes. In the case of silicon, a trivalent atom (such as boron) is substituted into the crystal lattice. The result is that one electron is missing from one of the four covalent bonds normal for the silicon lattice. Thus the dopant atom can accept an electron from a neighboring atoms' covalent bond to complete the fourth bond. Such dopants are called acceptors. The dopant atom accepts an electron, causing the loss of one bond from the neighboring atom and resulting in the formation of a "hole." Each hole is associated with a nearby negative-charged dopant ion, and the semiconductor remains electrically neutral as a whole. However, once each hole has wandered away into the lattice, one proton in the atom at the hole's location will be "exposed" and no longer cancelled by an electron. For this reason a hole behaves as a quantity of positive charge. When a sufficiently Catalogue voltage detectors SOT-25
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large number of acceptor atoms are added, the holes greatly outnumber the thermally-excited electrons. Thus, the holes are the majority carriers, while electrons are the minority carriers in ptype materials. Blue diamonds (Type IIb), which contain boron (B) impurities, are an example of a naturally occurring p-type semiconductor. P-n junctions A p-n junction may be created by doping adjacent regions of a semiconductor with p-type and ntype dopants. If a positive bias voltage is placed on the p-type side, the dominant positive carriers (holes) are pushed toward the junction. At the same time, the dominant negative carriers Catalogue voltage detectors SOT-25
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(electrons) in the n-type material are attracted toward the junction. Since there is an abundance of carriers at the junction, the junction behaves as a conductor, and the voltage placed across the junction produces a current. As the clouds of holes and electrons are forced to overlap, electrons fall into holes and become part of the population of immobile covalent bonds. However, if the bias polarity is reversed, the holes and electrons are pulled away from the junction. Since only very few new electron/hole pairs are created at the junction, the existing mobile carriers are swept away to leave a Depletion Zone; a region of relatively non-conducting silicon. The reversed bias voltage will produce only a very low current across the junction. The p-n junction is the basis of an electronic device called a diode, which allows electric charges to flow in only one direction. Similarly, a third semiconductor region can be doped n-type or p-type to form a Catalogue voltage detectors SOT-25
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three-terminal device, such as the bipolar junction transistor (which can be either p-n-p or n-p-n).
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As the name implies, the valence band contains the valence electrons of a substance. At absolute zero, all of the electrons in a substance would be contained in the valence band. However, if the substance is at a higher temperature, thermal energy can excite electrons out of the valence level and into an excited energy level. The conduction band is composed of the excited energy states of a substance, and it contains electrons that have been thermally or otherwise excited from the valence band. The electrons in the conduction band are able to freely move about the substance and conduct electricity if an external electric field is applied. Due to the lattice spacing of the atoms and other relevant factors, there is an energy gap between the highest- energy electron valence level and the lowest-energy conduction level. The width of Catalogue voltage detectors SOT-25
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this gap is dependent on the temperature and the pressure of the material and determines whether a material will be a conductor, insulator or semi- conductor. For reference, an energy level diagram for each type of material is shown in figure.
In conductors, the valence band and the conduction band overlap. Consequently, there is no energy gap to cross in order to reach the conduction band, and any energy that is added to the electron is sufficient to propel it into the conduction band. There are many electrons that are free Catalogue voltage detectors SOT-25
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to move about a conductor, so it very easy for current to flow if an external electric field is applied. In insulators, there is a distinct separation of the two bands and there is a large energy difference between them. This energy difference is so large that the thermal energy of an individual electron is not large enough to propel it from the valence band to the conduction band. Consequently, there are not many electrons in the conduction band, and it is difficult for current to flow when an external electric field is applied.
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As in insulators, there are two distinct bands in semi- conductors. However, the energy gap between these two bands is neither as large nor as significant (typically around one electron-volt) as is the band gap in insulators. At normal temperatures, the thermal energy of the material is sufficient to propel some electrons from the valence band into the conduction band, allowing some electrons to be free to conduct current. The number of free charge carriers increases with supplied energy, so the conductivity of a semi-conductor can be manipulated by outside potentials
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Fundamental semiconductor physics Band structure of a semiconductor In the parlance of solid-state physics, semiconductors (and insulators) are defined as solids in which at absolute zero (0 K), the uppermost band of occupied electron energy states, known as the valence band, is completely full. Or, to put it another way, the Fermi energy of the electrons lies within the forbidden bandgap. The Fermi energy, or Fermi level can be thought of as the energy up to which available electron states are occupied at absolute zero. Catalogue voltage detectors SOT-25
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At room temperature, there is some smearing of the energy distribution of the electrons, such that a small, but not insignificant number have enough energy to cross the energy band gap into the conduction band. These electrons which have enough energy to be in the conduction band have broken free of the covalent bonds between neighbouring atoms in the solid, and are free to move around, and hence conduct charge. The covalent bonds from which these excited electrons have come now have missing electrons, or holes which are free to move around as well. (The holes themselves don't actually move, but a neighbouring electron can move to fill the hole, leaving a hole at the place it has just come from, and in this way the holes appear to move.)
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It is an important distinction between conductors and semiconductors that, in semiconductors, movement of charge (current) is facilitated by both electrons and holes. Contrast this to a conductor where the Fermi level lies within the conduction band, such that the band is only half filled with electrons. In this case, only a small amount of energy is needed for the electrons to find other unoccupied states to move into, and hence for current to flow. The ease with which electrons in a semiconductor can be excited from the valence band to the conduction band depends on the band gap between the bands, and it is the size of this energy bandgap that serves as an arbitrary dividing line between semiconductors and insulators. Catalogue voltage detectors SOT-25
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Materials with a bandgap energy of less than about 3 electron volts are generally considered semiconductors, while those with a greater bandgap energy are considered insulators.. The current-carrying electrons in the conduction band are known as "free electrons," although they are often simply called "electrons" if context allows this usage to be clear. The holes in the valence band behave very much like positively-charged counterparts of electrons, and they are usually treated as if they are real charged particles.
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Material Classification: Conductors, Insulators, and Semi-Conductors This material can be classified as either a conductor, an insulator, or a semi-conductor. These three distinct classes of material arise from a difference in the structure of the allowed electron energy levels. In particular, every material possesses both a valence and a conduction band for electrons, and the energy difference between these two bands will determine how easily an electric current will pass through the material. As the name implies, the valence band contains the valence electrons of a substance. At absolute zero, all of the electrons in a substance would be contained in the valence band. However, if the Catalogue voltage detectors SOT-25
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substance is at a higher temperature, thermal energy can excite electrons out of the valence level and into an excited energy level. The conduction band is composed of the excited energy states of a substance, and it contains electrons that have been thermally or otherwise excited from the valence band. The electrons in the conduction band are able to freely move about the substance and conduct electricity if an external electric field is applied. Due to the lattice spacing of the atoms and other relevant factors, there is an energy gap between the highest- energy electron valence level and the lowest-energy conduction level. The width of this gap is dependent on the temperature and the pressure of the material and determines whether Catalogue voltage detectors SOT-25
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a material will be a conductor, insulator or semi- conductor. For reference, an energy level diagram for each type of material is shown in figure.
In conductors, the valence band and the conduction band overlap. Consequently, there is no energy gap to cross in order to reach the conduction band, and any energy that is added to the electron is sufficient to propel it into the conduction band. There are many electrons that are free to move about a conductor, so it very easy for current to flow if an external electric field is applied. Catalogue voltage detectors SOT-25
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In insulators, there is a distinct separation of the two bands and there is a large energy difference between them. This energy difference is so large that the thermal energy of an individual electron is not large enough to propel it from the valence band to the conduction band. Consequently, there are not many electrons in the conduction band, and it is difficult for current to flow when an external electric field is applied. As in insulators, there are two distinct bands in semi- conductors. However, the energy gap between these two bands is neither as large nor as significant (typically around one electron-volt) as is the band gap in insulators. At normal temperatures, the thermal energy of the material is sufficient to propel some electrons from the valence band into the conduction band, allowing Catalogue voltage detectors SOT-25
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some electrons to be free to conduct current. The number of free charge carriers increases with supplied energy, so the conductivity of a semi-conductor can be manipulated by outside potentials
Fundamental semiconductor physics Energy Bands Sometimes valence electrons are shared, becoming a bond between two atoms - covalent bonding. This is the bonding type in diamond-crystal lattice semiconductors such as silicon Catalogue voltage detectors SOT-25
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semiconductors. However, it is more interesting to analyze energy-related aspects rather than spatial aspects such as bonds. Therefore the concept of energy bands is coming in handy. An almost continuous band of allowed energies of electrons comes about when atoms are brought in close proximity to each other, this is because of the interatomic forces and is foreseen in the Pauli exclusion principle. “Almost”, well, one energy level is split into N levels when N atoms are brought together, and these N levels can accommodate at most 2N electrons due to spin degeneracy.
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Remember, N is huge! Now, since the separation between the energy levels within the band is much smaller than the thermal energy possessed by an electron at room temperature the band can be viewed as continuous. Ec is the lowest possible conduction band energy, while Ev is the highest possible valence band energy. The band gap energy, Eg, is furthermore defined as (Ec Ev). Eg is the energy it takes to break a bond in the spatial view of the crystal. The band gap energies for some semiconductors at T = 300 K are: Eg = 1.42 eV in GaAs and 1.12 eV in Si. You do remember that 1 eV = 1.602?10-19 J, don’t you?
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Current Flow and the Concept of Holes Using the concept of energy bands, the pure semiconductor (ideally, i.e. T 0 K) contains a completely filled (with electrons) valence band and a completely empty conduction band. Completely filled bands do contain plenty of electrons but do not contribute to the conductivity of the material. This is due to the fact that the electrons can not gain energy since all energy levels are already filled. As semiconductors are of primary interest in this text, we now introduce a simplified energy band diagram for semiconductors and define some key parameters. The diagram is shown in the figure below:
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A simplified energy band diagram used to describe semiconductors. Shown are the valence and conduction band as indicated by the valence band edge Ev and the conduction band edge Ec. The vacuum level, EVACUUM and the electron affinity, c are also indicated on the figure. The diagram identifies the almost-empty conduction band simply by a line which indicates the bottom of the conduction band and is labeled Ec. Similarly the top of the valence band is indicated with a line labeled Ev. Note: The actual bandstructures of semiconductors is more complex than the reader is lead to believe by the discussion above. So, semiconductors distinguish themselves from metals and insulators by the fact that they contain an "almostCatalogue voltage detectors SOT-25
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empty" conduction band and an "almost-full" valence band. This also means that we will have to deal with the transport of carriers in both bands. To facilitate the discussion of the transport in the "almost-full" valence band we will introduce the concept of holes in a semiconductor. It is important for the reader to understand that one could deal with only electrons (since these are the only real particles available in a semiconductor) if one is willing to keep track of all the electrons in the "almost-full" valence band.
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The concepts of holes is introduced based on the notion that it is a whole lot easier to keep track of the missing particles in an "almost-full" band, rather than keeping track of the actual electrons in that band. We will now first explain the concept of a hole and then point out how the hole concept simplifies the analysis. Holes are missing electrons. They behave as particles with the same properties as the electrons would have occupying the same states except that they carry a positive charge. This definition is illustrated further with the figure below which presents the simplified energy band diagram in the presence of an electric field. Catalogue voltage detectors SOT-25
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Fundamental semiconductor physics Purity and perfection of semiconductor materials Semiconductors with predictable, reliable electronic properties are difficult to mass-produce because of the required chemical purity, and the perfection of the crystal structure, which are needed to make devices. Because the presence of impurities in very small proportions can have such big effects on the properties of the material, the level of chemical purity needed is extremely high. Techniques for achieving such high purity include zone Catalogue voltage detectors SOT-25
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refining, in which part of a solid crystal is melted. Impurities tend to concentrate in the melted region, leaving the solid material more pure. A high degree of crystalline perfection is also required, since faults in crystal structure such as dislocations, twins, and stacking faults, create energy levels in the band gap, interfering with the electronic properties of the material. Faults like these are a major cause of defective devices in production processes. The larger the crystal, the harder it is to achieve the necessary purity and perfection; current mass production processes use sixinch diameter crystals which are grown as cylinders and sliced into wafers. Catalogue voltage detectors SOT-25
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Fundamental semiconductor physics The chip A transistor is essentially a replacement for a vacuum tube. When tiny transistors replaced bulky vacuum tubes, the first applications resulted in electronic devices that accomplished the same as tube-based devices, but were much smaller. This encouraged engineers to build more functions into the same devices since there was now more room. By the end of the 1950s, electronics manufacturers were faced with circuits of increasing complexity. Computers, for example, Catalogue voltage detectors SOT-25
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contained tens of thousands of transistors. Assembly often required hundreds of thousands of interconnections, all of which had to be soldered by hand. Electronic devices, such as computers and radios, use several different types of components. Some are very fast switches. Others act as electronic gates, allowing certain messages to get through while rejecting others, or restricting flow of current to a single direction. In a computer such gates become logic circuits that, for example, combine two statements into one using the electronic equivalents to the logical connectives and, or, or if-then. Another component amplifies a signal. After the invention of the transistor, various configurations of transistors were created to perform these functions, components still referred to by such traditional names as resistor, Catalogue voltage detectors SOT-25
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capacitor, diode, and so forth. In each case the method was to add specific impurities to different regions of a semiconductor chip, a process called doping. The idea of placing several components on a single chip came separately to two people who worked independently. Jack Kilby, an electronics engineer, in 1958 joined a team at Texas Instruments that studied ways to reduce the size of computer circuits. Kilby created a semiconductor chip that carried an oscillator made of several components, such as switches, resistors, capacitors, and diodes, all made from doped semiconductors. Although these components were on a single chip, Kilby had Catalogue voltage detectors SOT-25
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not developed a suitable way to connect them, and had to create interconnections in the traditional way. He demonstrated his oscillator-on-a-chip to executives from Texas Instruments on September 12, 1958, and filed for a patent a few months later. Robert Noyce, a physicist, was the head of research at the recently founded Fairchild Semiconductor. That company had developed the "planar" technology for the manufacture of transistors. In that method, large numbers of transistors were created on a single wafer, which subsequently was cut up to yield the single transistors. Noyce realized that this technology would be suitable for creating an entire circuit on such a wafer. But he also found a way to make Catalogue voltage detectors SOT-25
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connections between the components on the wafer by laying down conducting tracks. The result is termed an integrated circuit, but most people simply call it a chip. Noyce filed a patent for his integrated circuit one year after Kilby did, and was granted it in April 1961. Kilby's patent application was rejected because he had not solved the problem of interconnecting the components on the chip. A legal battle between Kilby and Noyce ensued, which ultimately was won by Noyce by decision of the Court of Customs and Patents Appeals in November 1969. Fairchild Semiconductor and Texas Instruments, however, had already agreed to share the licensing of integrated circuits in Catalogue voltage detectors SOT-25
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1966. Noyce and Kilby, regarded by the technical community as coinventors, a view both have accepted, jointly received the National Medal of Science for their invention.
Fundamental semiconductor physics Doping of semiconductors One of the main reasons that semiconductors are useful in electronics is that their electronic properties can be greatly altered in a controllable way by adding small amounts of impurities. These impurities are called dopants. Catalogue voltage detectors SOT-25
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Heavily doping a semiconductor can increase its conductivity by a factor greater than a billion. In modern integrated circuits, for instance, heavily-doped polycrystalline silicon is often used as a replacement for metals. Intrinsic and extrinsic semiconductors An intrinsic semiconductor is one which is pure enough that impurities do not appreciably affect its electrical behavior. In this case, all carriers are created by thermally or optically excited electrons from the full valence band into the empty conduction band. Thus equal numbers of electrons and holes are present in an intrinsic semiconductor. Electrons and holes flow in Catalogue voltage detectors SOT-25
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opposite directions in an electric field, though they contribute to current in the same direction since they are oppositely charged. Hole current and electron current are not necessarily equal in an intrinsic semiconductor, however, because electrons and holes have different effective masses (crystalline analogues to free inertial masses). The concentration of carriers is strongly dependent on the temperature. At low temperatures, the valence band is completely full, making the material an insulator (see electrical conduction for more information). Increasing the temperature leads to an increase in the number of carriers and a corresponding increase in conductivity. This principle is used in thermistors. This behavior Catalogue voltage detectors SOT-25
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contrasts sharply with that of most metals, which tend to become less conductive at higher temperatures due to increased phonon scattering. An extrinsic semiconductor is one that has been doped with impurities to modify the number and type of free charge carriers. N-type doping The purpose of n-type doping is to produce an abundance of mobile or "carrier" electrons in the material. To help understand how n-type doping is accomplished, consider the case of silicon Catalogue voltage detectors SOT-25
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(Si). Si atoms have four valence electrons, each of which is covalently bonded with one of four adjacent Si atoms. If an atom with five valence electrons, such as those from group VA of the periodic table (eg. phosphorus (P), arsenic (As), or antimony (Sb)), is incorporated into the crystal lattice in place of a Si atom, then that atom will have four covalent bonds and one unbonded electron. This extra electron is only weakly bound to the atom and can easily be excited into the conduction band. At normal temperatures, virtually all such electrons are excited into the conduction band. Since excitation of these electrons does not result in the formation of a hole, the number of electrons in such a material far exceeds the number of holes. In this case the electrons are the majority carriers and the holes are the minority carriers. Because the fiveelectron atoms have an extra electron to "donate", they are called donor atoms. Note that each Catalogue voltage detectors SOT-25
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movable electron within the semiconductor is never far from an immobile positive dopant ion, and the n-doped material normally has a net electric charge of zero.
Fundamental semiconductor physics Doping of semiconductors (page 2) P-type doping
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The purpose of p-type doping is to create an abundance of holes. In the case of silicon, a trivalent atom (such as boron) is substituted into the crystal lattice. The result is that one electron is missing from one of the four covalent bonds normal for the silicon lattice. Thus the dopant atom can accept an electron from a neighboring atoms' covalent bond to complete the fourth bond. Such dopants are called acceptors. The dopant atom accepts an electron, causing the loss of one bond from the neighboring atom and resulting in the formation of a "hole." Each hole is associated with a nearby negative-charged dopant ion, and the semiconductor remains electrically neutral as a whole. However, once each hole has wandered away into the lattice, one proton in the atom at the hole's location will be "exposed" and no longer cancelled by an electron. For this reason a hole behaves as a quantity of positive charge. When a sufficiently Catalogue voltage detectors SOT-25
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large number of acceptor atoms are added, the holes greatly outnumber the thermally-excited electrons. Thus, the holes are the majority carriers, while electrons are the minority carriers in ptype materials. Blue diamonds (Type IIb), which contain boron (B) impurities, are an example of a naturally occurring p-type semiconductor. P-n junctions A p-n junction may be created by doping adjacent regions of a semiconductor with p-type and ntype dopants. If a positive bias voltage is placed on the p-type side, the dominant positive carriers (holes) are pushed toward the junction. At the same time, the dominant negative carriers Catalogue voltage detectors SOT-25
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(electrons) in the n-type material are attracted toward the junction. Since there is an abundance of carriers at the junction, the junction behaves as a conductor, and the voltage placed across the junction produces a current. As the clouds of holes and electrons are forced to overlap, electrons fall into holes and become part of the population of immobile covalent bonds. However, if the bias polarity is reversed, the holes and electrons are pulled away from the junction. Since only very few new electron/hole pairs are created at the junction, the existing mobile carriers are swept away to leave a Depletion Zone; a region of relatively non-conducting silicon. The reversed bias voltage will produce only a very low current across the junction. The p-n junction is the basis of an electronic device called a diode, which allows electric charges to flow in only one direction. Similarly, a third semiconductor region can be doped n-type or p-type to form a Catalogue voltage detectors SOT-25
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three-terminal device, such as the bipolar junction transistor (which can be either p-n-p or n-p-n).
For dad Catalogue voltage detectors SOT-25
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Catalogue voltage detectors SOT-25
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Catalogue voltage detectors USP-4 SOT-25
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Catalogue voltage detectors SOT-25 USP-6C
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