Dr Rajendra Patrikar

Nanoelectronics

SIMULATION OF SELF ASSEMBLY PROCESSES A CASE STUDY OF QUANTUM DOT GROWTH Rajendra M. Patrikar Department of Electronics and Computer Science and Engineering VNIT, Nagpur

SIMULATION OF SELF ASSEMBLY PROCESSES A CASE STUDY OF QUANTUM DOT GROWTH       

Introduction Quantum Dots and it’s application Simulation and Implementation Results Multiscale Modelling and Results Future work Conclusion

Beyond the Si MOSFET..... 1) MOSFET VS

VG

3) CNTFET VD Bachtold, et al., Science, Nov. 2001

2) SBFET

VG

VG VD

VS

VS

4) Molecular Transistors? VD

Simulation Results • Technology : 50 nm

• Technology : 180 nm

5 Stage Ring Oscillator

VDAT-04

Nanoelectronics and Computing • Quantum Computing - Takes advantage of quantum mechanics instead of being limited by it - Digital bit stores info. in the form of ‘0’ and ‘1’; qubit may be in a superposition state of ‘0’ and ‘1’ representing both values simultaneously until a measurement is made - A sequence of N digital bits can represent one number between 0 and 2N-1; N qubits can represent all 2N numbers simultaneously

1938

1998

Technology engine: Vacuum tube

Technology engine: CMOS FET

Proposed improvement: Solid state switch

Proposed improvement: Quantum state switch

Fundamental research: Materials purity

Fundamental research: Materials size/shape

•

Carbon nanotube transistor by IBM and Delft University

•

Molecular electronics: Fabrication of logic gates from molecular switches using rotaxane molecules

•

Defect tolerant architecture, TERAMAC computer by HP architectural solution to the problem of defects in future molecular electronics

Promise

Microns to Nanometers -- Biological/Chemical/Atomic

Quantum Dots Quantum dots (AFM)

~20-30 nm

Quantum dots

Unique physical and chemical properties are determined by their structural properties.

Quantum Dots

 Eletronic components: diodes, lasers, and photo

detectors with novel properties such as higher efficiency, lower threshold, or useful frequencies of operation  self-assembly is a good alternative to conventional

methods of producing microelectronic structures

Applications

•

Quantum-dot LED

•

Quantum-dot Microwave Photon counter

•

Quantum-dot information storage and computing

•

Quantum-dot in Biological “Tagging”

Quantum Dots

• • •

Quantum dots are coming in commercial world very fast Many new companies are started in developed countries to commercialize this technology It is expected that quantum dots will have sizable contribution in nanotechnology market

Quantum dot flash memory Inter poly oxide Tunnel oxide

n+

Control gate Floating gate

n+

Flash memory with poly floating gate

•Quantum floating gate replacing

poly floating gate

Floating gate is replaced by QDs

n+

n+

Flash memory with nanocrystal floating gates

Quantum dot flash memory

Tunnel oxide

n+

n+

Conventional flash Memory Vs. QD flash Memory Device •Scaling limitations arising from,

-High oxide thickness to avoid charge loss from FG -High programming / erasing voltages due to Channel Hot Electron injection, F-N tunneling, … -Limits the Leff shrinkage Control gate

CFC

CS

n+

Floating gate

CB

Leff

CD

n+

Conventional flash Memory Vs. QD flash Memory Device •For nano-crystal floating gates charge

loss to the contact regions is minimized -Nano-crystals are isolated from each other -Thin oxide is permissible -Lower programming voltage is possible -Charging the QD by Coulomb blockade

Floating gate i sreplaced by QDs

n+

n+

Flash memory with nanocrystal floating gates

Quantum dot flash memory

Gate

SiO2

10 nm

Control oxide

Flash memory

Drain

Nanocrystals

Source

Tunnel oxide

Ge Si

Self Assembly: Principles Formal definitions • Self-assembly is the

autonomous organization of components into patterns or structures without human intervention – Pre-existing components (separate or distinct parts of a disordered structure) – Reversible – Can be controlled by proper design of the components • A self-assembling structure is one that can reform after the constituent parts have been disassembled, isolated and then mixed appropriately – Aided self-assembly – requiring helper machinery, not part of final structure. – Directed self-assembly – organization of new structures at the time of their assembly is determined or directed by an existing structure (also called templated self-assembly)

Self Assembly: Principles Dynamic self-assembly – Interactions responsible for formation of structures only occurs if the system is dissipating energy ■

Static self-assembly – Components at global or local equilibrium ■

Stigmergic building – Current state of structure acts as stimulus to further action – Term originally comes from termite nest building – Related to multi-step directed self-assembly, but can be stochastically started without an initial structure ■

Self Assembly: Principles Physical self assembly Mechanical Field -templating, strain, etc.  Use of structured strain  Electrical and magnetic (including photon) fields  Surface energy – catalyst seeding Chemical and Bio-chemical self assembly  Chemical bonding Conjugating - e.g., triple conjugation of QDs will beachieved at the Y-Junction, whileQDs are trapped at the junction

Self Assembly: Principles Methods for Self-assembly Physical self assembly MBE, CVD, etc. Templates: Electrochemical, mechanical, Sol gel, etc. Chemical self assembly Molecular self assembly, polymer self assembly, protein, DNA,biomolecular, etc. Colloidal self assembly Bio self assembly Peptide, Protein and Virus engineering User defined surface dip pen

Self Assembly: Principles Key Issues: ■ Uniform size ■ Controlled placement ■ Directed processes ■ Physical mechanisms, ■ Chemical Mechanisms ■ Biochemical Processes

Self Assembly Process •Self Assembly Process : objects interact with each other

autonomously to generate higher order complex structures. •Self Assembled Quantum Dots (SAQDs) can be grown via

vapour phase deposition. (MOCVD, MBE systems) •Layer-by-layer deposition of semiconductor material develops

the strained semiconductor films. Release of the accumulated strain energy causes array of nanostructures. •For circuit fabrication and memory applications stable and

uniform arrays of quantum dots are essential. •General experiments are unable to explain size distribution and

growth dynamics are function of kinetics or thermodynamic conditions.

Simulations •Computer experiments play a very important role in technology

today. •In the past, technology was characterized by interplay between

experiment and theory. • In experiment, a system is subjected to measurements, and

results, expressed in numeric form, are obtained. •In theory, a model of the system is constructed, usually in the

form of a set of mathematical equations.

Simulations

•The model is then validated by its ability to describe the system •In many cases, this implies a considerable amount of

simplification. ■The advent of high speed computers| which started to be

used in the 50s altered the picture by inserting a new element right in between experiment and theory: THE COMPUTER EXPERIMENT

Simulations ■

■

■

Quantum dots have the potential to revolutionize semiconductor devices. Considerable international research now focuses on developing methods for growing arrays of quantum dots because of their potential application in nextgeneration devices. In order to interpret measurements, design experiments, and eventually develop and characterize actual devices, it is necessary to have a mathematical model for calculation and simulation of properties. The model must be multiscale in order to bridge the length scales from nano- to macroscopic scales and must account for nonlinear effects inside and close to the quantum dots.

Process Modeling (Literature)

• Hetero-epitaxy • Crystalline material • Smooth surface

CVD Process Modeling

•Molecular Dynamics (MD) •Kinetic Monte Carlo (KMC)

Multiscale approach: strategy Mesoscale simulation • Kinetic Monte Carlo • Continuum model

[long time (>1 sec)]

fundamental data

Atomic-scale calculation • density functional theory • tight binding MD • classical MD

[short time (< nsec)]

Molecular Dynamics • Molecular Dynamics I sused to determine the movement of the particles as they approach the substrate based on the kinematics of the particles rnext = r + deltat*vel + 0.5*(deltat*deltat) * acc

• Kinetic Monte Carlo class contains the determine the position of the particle after deposition on the substrate

Energy Calculations •Pair Potentials: E = E0 +

•

1 V2 (Ri , R j ) ∑ 2 i, j

•E0 is structure dependent reference energy, V2 is effective pair potential

as a function of position of atomic nuclei. (e.g. Lennard Jones potential) •Simple to implement, ideal for mono-atomic systems. •Unable

to explain complex systems. (e.g. Strongly covalent semiconductors, as it neglects the effect of local environment). •Cluster Fnctionals: The generalized form, E=

1 ∑ V (R R ) + ∑ U( ∑ g 2 (Ri,R j ), ∑ g3 ( Ri,R j , Rk ),....) 2 i, j 2 i, j i j j,k

•The functions gn provide more in depth description of the local

environment than g2. •E.g. Tersoff potetnials

Parallel Simulations (contd.) •Initiator-Target Mechanism: •Algorithm: •Initialization •Partitioning Mechanism: •Tasks for Target nodes:

•Tasks for Target nodes:

a.Initialize the position and type of atoms.

a.Before the calculation start for MD step,

b.Map N atoms evenly on (P-1) processors.

receive positions of all atoms from initiator node.

c. Before the start of time step i.e. MD step

distribute atom positions among initiators. d. After each time step calculation collects

atom information.

b. Perform MD calculations on the allocated

nodes. c.Send data (positions, etc.) to target.a

•Communication overhead is reduced as there is no communication among the

target nodes.

Kinetic Monte Carlo Random hopping from site A→ B ■ hopping rate D0exp(-E/T), ■

– E = Eb = energy barrier between sites – not δE = energy difference between sites

B A

Eb

δE

Kinetic Monte Carlo ■

Interacting particle system – Stack of particles above each lattice point

■

Particles hop to neighboring points – random hopping times – hopping rate D= D0exp(-E/T), – E = energy barrier, depends on nearest neighbors

■

Deposition of new particles – random position – arrival frequency from deposition rate

■

Simulation using kinetic Monte Carlo method – Gilmer & Weeks (1979), Smilauer & Vvedensky, …

Kinetic Monte Carlo

Software Architecture

Simulation Results

Simulation Results

Simulation Results

Simulation Results Average Thickness at 30SCCM 0.9 0.8

Thickness

0.7 0.6

773K

0.5

823K

0.4

873K

0.3

923K

0.2 0.1 0 1

2

3

Time

4

Simulation Results

Non_Uniformity 1.6

Std. Dev.

1.5 1.4 1.3 1.2 1.1 1 0.9 20

30

40 Flow rate

60

Simulation Results

Average Thickness 3.5

Thickness

3 2.5 2

773K

1.5

873K

1 0.5 0 20

30

40 Flow Rate

60

Simulation Results Simulation Results ■Film is continuous and no dot formation on large scale

after deposition Experimental Results ■Film is continuous and no dot formation on large scale

after deposition ■After annealing dot are formed ■Substrate type and quality affects the dot formation

Multiscale simulation •

Multiscale simulation is emerging as a new scientific field.

•

The idea of multiscale modeling is straightforward: one computes information at a smaller (finer) scale and passes it to a model at a larger (coarser) scale by leaving out degrees of freedom as one moves from finer to coarser scales.

•

The obvious goal of multiscale modeling is to predict macroscopic behavior of an engineering process from first principles (bottom-up approach).

Multiscale Modeling and Simulation Challenges and Opportunities

Atoms

Engineering

TIME hours

Continuum MESO MD

femtosec

QM Angstrom

DISTANCE meters

Multiscale simulation The emerging fields of nanotechnology and biotechnology impose new challenges and opportunities. The ability to predict and control phenomena and nanodevices with resolution approaching molecular scale while manipulating macroscopic (engineering) scale variables can only be realized via multiscale simulation (top-down approach). Multiscale modeling is heavily used to simulate materials’ self-organization for pattern formation leading to quantum dots.

Multiscale Modeling of Nanoengineering Its success will offer tremendous opportunities for guiding the rational design and fabrication of a variety of nanosystems!

Atomistic behaviors

quantitative prediction

physical understanding

Shape, Size distribution, Spatial distribution, Interface structures, ….

Fundamental processes, Atomic structures, Energetics, ….

Time (sec):

10-12

Length (m): 10-9 Quantum Mechanics

Structural Properties

10-9 10-8 Molecular Dynamics

10-6 10-7 Statistical Mechanics

10-3

100 10-6 Continuum Mechanics

Multiscale simulation

Molecular simulations at either a classical or quantum level are generally required to arch at a time step smaller than the smallest time scales of a system, which is typically often of the order of 10-15 seconds. As the system grows larger, the computational time taken in solving the calculations for the simulation can increase enormously But time scales corresponding to changes in a large systems overall morphology, milliseconds, seconds, or even years for very glassy materials. Thus, there is a huge spatial and time gap between what can be solved through molecular simulation, and the time scales that are often important.

Multiscale simulation

• Kinetic Monte Carlo (KMC) • Molecular Dynamics (MD) • Finite Element Method (FEM)

Simulation of self-assembly processes for nano devices OBJECTIVES - Development of methods to explain growth of thin films and quantum dots. - Electrical modelling of nano devices. Phase-I Process Model: Assembly of atoms on the substrate is divided into three phases:  Phase-I the flight of particle in the test space.  Phase-II movement of particle along the surface.  Phase-III interaction with substrate. Simulation Schemes: Carlo with To beMonte replaced ■ Probabilistic approach Quantum Mechanical Molecular Dynamics ■ Algorithm: Calculations ■ Deterministic approach o Initialization ■ Algorithm: o Generating the random o Initialization trials o Decide the time duration o Evaluate acceptance ((tmax ) criterion o Loop o Reject or accept the do { generate new move on the basis of configurations } “acceptance criterion” . while (time ≤ tmax )

Finite Element Analysis ■ Substrate is partitioned into different regions. ■

Outer region is taken as continuum and decomposed in the form of mesh.

The simulation on 100nX100n substrate takes about

Interatomic potentials: Lennard-Jones potential. (pair wise) 10 days Tersoff family of potential. (many body type)

on 1 Teraflop machine (without FEM!)

Multiscale simulation

Multiscale simulation  FEM Coding :

Mesh generation and Visualisation

Multiscale simulation FEM Coding : Initialising of the nodes Define Interpolation functions Calculate the Jacobian matrix Strain-displacement matrix computation The element stiffness matrix is calculated. Strain calculations by solving stiffness matrix.

These calculations show that atomic clusters are displaced and separated because of strain

Summary Experimental Results ■Film is continuous and no dot formation on large

scale after deposition ■After annealing dot are formed ■Substrate type and quality affects the dot formation

Multiscale simulations •Kinetic Monte Carlo (KMC) • Molecular Dynamics (MD) • Finite Element Method (FEM)

■Stress during

annealing process is necessary to form dots.

Simulation Result ■Film is continuous and no dot formation on large

scale after deposition

Future Work Fabrication In Quantum dots 1) Deposition of modern compound semiconductors or organic compound 2) Spontaneous structure formation in these systems, the socalled self-assembly of nanoscale islands Control and stabilisation of molecular assemblies at the nanometer scale are crucial steps in the fabrication of nanoscale devices. However, the intrinsic surface properties such as roughness and defects largely decide the formation of these devices

Roughness Future Work Most of the processes used for electronic device fabrication results in rough surfaces because of self-affine characteristics Due to ideal approximation in simulations, the effect of nano

roughness is not taken into account when performing calculations The incorporation of nano roughness in calculations will

improve the accuracy of simulations.

Acceleration using GPUs •Graphics Processing Unit (GPU) can be employed as a data

parallel computing device. It consists of multiple cores, high bandwidth memory and efficient for both graphic and nongraphics processing. •NVIDIA's CUDA (Compute Unified Device Architecture):

High performance computing platform multithreading on multicore architecture.

uses

massive

•(e.g. Configuration of device: NVIDIA Tesla C870 GPU

computing board: Memory buffer of 1536 MB GDDR3 memory, 128 processor cores ) •Offers Host runtime library & Device runtime library for ease

of programming.

Modeling a Rough Surface

■

■

The concept of self similar fractals is used to model the rough surface. Reasons: – Other roughness parameters e.g. autocovariance, power spectrum, r.m.s roughness etc are scale dependent, or exist as a spectrum. – Comparisons are thus difficult and the parameters cannot be used in analytic relationships. – R.m.s roughness provides the vertical magnitude of roughness but does not give spatial information. – Previous studies show that the fractal dimension (DF) can quantitatively describe surface microscopic roughness.

Advantages of self similar fractals  The

Fractal Dimension is independent of the probing scale

 It

is a single parameter, therefore allowing easy comparison between different objects

 It

can also be incorporated into roughness related analysis

Modeling a Rough Surface

 The

rough surface is therefore modeled using the Mandelbrot-Weierstrass function.

 The

Mandelbrot-Weierstrass function is a summation of sinusoids of geometrically increasing frequency and decreasing amplitude, with a random phase.

The Mandelbrot-Weierstrass function





 

The summation is carried out for n = -M to n = M where M is a large number specified by the user. b is the frequency multiplier value: it varies typically between 1.1 to 3.0. D is the fractal dimension ¢ is a randomly generated phase

Modeling a Rough Surface

RMS roughness=0.2

RMS roughness=0.7

Modeling a Rough Surface

Modeling a Rough Surface Finding Capacitance:

Finding Potential:

The Mandelbrot-Weierstrass function

Mandelbrot's fractal theory, fractal dimension could be obtained in images by the concept of Brownian motion.  Einstein in year 1905 succeeded in stating the

mathematical laws governing the Brownian motion.

Conclusions ■Quantum dot based flash memory is likely to become a

reality in near future ■This tool is being developed for Quantum Dot

Deposition System ■Stress during annealing process is necessary to form

dots. ■Incorporation of surface roughness and other defects in

the simulation is likely to improve predictability

Acknowledgments:

Institute of High Performance Computing , Singapore NUS, Singapore B.Tech Students at VNIT

Thank You!

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