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

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

SIMULATION OF SELF ASSEMBLY PROCESSES

A CASE STUDY OF QUANTUM DOT GROWTH

Beyond the Si MOSFET.....

VGVD

VS

VG

VD

VS

Bachtold, et al.,Science, Nov.2001

3) CNTFET

4) Molecular Transistors?

1) MOSFET

2) SBFET VG

VS VD

Simulation Results

• Technology : 50 nm

5 Stage Ring Oscillator VDAT-04

• Technology : 180 nm

• 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 valuessimultaneously 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

• Carbon nanotube transistor by IBM and Delft University

• Molecular electronics: Fabrication of logic gatesfrom molecular switches using rotaxanemolecules

• Defect tolerant architecture, TERAMAC computerby HP architectural solution to theproblem of defects in future molecular electronics

1938 1998

Technology engine:Vacuum tube

Proposed improvement:Solid state switch

Fundamental research:Materials purity

Technology engine:CMOS FET

Proposed improvement:Quantum state switch

Fundamental research:Materials size/shape

Nanoelectronics and Computing

Promise

Microns to Nanometers -- Biological/Chemical/Atomic

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

Quantum dots

Quantum dots (AFM)

~20-30 nm

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

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 Dots

•Quantum floating gate replacing poly floating gate

n+ n+

Control gate

Floating gateTunnel oxide

Inter poly oxide

Flash memory with poly floating gate

n+ n+

Flash memory with nanocrystal floating gates

Floating gate is replaced by QDs

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

n+ n+

Floating gate

Control gateCFC

CB

CS CD

Leff

•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

n+ n+

Flash memory with nanocrystal floating gates

Floating gate i sreplaced by QDs

Conventional flash Memory Vs.

QD flash Memory Device

Flash memory

Source

Drain

Nano-

crystals

Tunnel oxide

Control oxide

Gate 10 nm

Si

Ge

SiO2


Formal definitions

• Self-assembly is the autonomous organization of componentsinto patterns or structures without human intervention

– Pre-existing components (separate or distinct parts of adisordered structure)– Reversible– Can be controlled by proper design of the components

• A self-assembling structure is one that can reform after theconstituent parts have been disassembled, isolated and thenmixed appropriately– Aided self-assembly – requiring helper machinery, not part of finalstructure.– Directed self-assembly – organization of new structures at thetime of their assembly is determined or directed by an existingstructure (also called templated self-assembly)

Self Assembly: Principles

Dynamic self-assembly– Interactions responsible for formation of structures onlyoccurs 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 bestochastically started without an initial structure



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

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,bio-

molecular, etc.Colloidal self assembly

Bio self assembly Peptide, Protein and Virus engineering

User defined surface dip pen


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


•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.

Self Assembly Process

•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 next-generation 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.

Simulations

• Hetero-epitaxy

• Crystalline material

• Smooth surface

Process Modeling (Literature)

•Molecular Dynamics (MD)

•Kinetic Monte Carlo (KMC)

CVD Process Modeling

Multiscale approach: strategy

Mesoscale simulation• Kinetic Monte Carlo• Continuum model [long time (>1 sec)]

• density functional theory• tight binding MD• classical MD [short time (< nsec)]

Atomic-scale calculation

fundamental data

• 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

Molecular Dynamics

•Pair Potentials:

•

•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,

•The functions gn provide more in depth description of the local environment than g2.

•E.g. Tersoff potetnials

Energy Calculations

)R,(RV+E=E jiji,

20 2

1

),i

)kj,

kR,

jRi,Rg),

jRi,

(RjgU(+)

jRi,

(Rji,V=E ....(

3222

1

•Initiator-Target Mechanism:

•Algorithm:

•Initialization

•Partitioning Mechanism:

Parallel Simulations (contd.)

•Tasks for Target nodes:a.Before the calculation start for MD step, receive positions of all atoms from initiator node.

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.

•Tasks for Target nodes:a.Initialize the position and type of atoms.

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

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.

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

– E = Eb = energy barrier between sites

– not δE = energy difference between sites

A

B

δEEb

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

Kinetic Monte Carlo

Software Architecture

Simulation Results

Simulation Results

Simulation Results

Average Thickness at 30SCCM

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 2 3 4

Time

Thic

kness 773K

823K

873K

923K

Simulation Results

Non_Uniformity

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

20 30 40 60

Flow rate

Std

. Dev

.

Simulation Results

Average Thickness

0

0.5

1

1.5

2

2.5

3

3.5

20 30 40 60

Flow Rate

Th

ickn

ess

773K

873K

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

Simulation Results

• 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 simulation

DISTANCE

TIME

Angstrom meters

femtosec

hours

QM

MD

MESO

Continuum

Atoms Engineering

Multiscale Modeling and SimulationMultiscale Modeling and SimulationChallenges and OpportunitiesChallenges and Opportunities

The emerging fields of nanotechnology and biotechnology impose new challenges and opportunities.

The ability to predict and control phenomena and nano-devices 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 NanoengineeringMultiscale Modeling of Nanoengineering

Time (sec): 10-12 10-9 10-6 10-3 100

Length (m): 10-9 10-8 10-7 10-6

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

Quantum Mechanics

Molecular Dynamics

Statistical Mechanics

ContinuumMechanics

StructuralProperties

Atomistic behaviors

physical understanding

quantitative prediction

Fundamental processes,Atomic structures, Energetics, ….

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

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.


• Kinetic Monte Carlo (KMC)

• Molecular Dynamics (MD)

• Finite Element Method (FEM)


Simulation of self-assembly processesSimulation of self-assembly processes

for nano devicesfor nano devices OBJECTIVES- Development of methods to explain growth of thin films and quantum dots.

- Electrical modelling of nano devices.

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.

Interatomic potentials:

Lennard-Jones potential. (pair wise)

Tersoff family of potential. (many body type)

Phase-I

Simulation Schemes:

Molecular Dynamics Deterministic approach Algorithm:

o Initializationo Decide the time duration

((tmax)o Loop

do {generate new

configurations }while (time ≤ tmax)

Monte Carlo Probabilistic approach Algorithm:

o Initializationo Generating the

random trialso Evaluate acceptance

criteriono Reject or accept the

move on the basis of “acceptance criterion” .

Finite Element Analysis Substrate is

partitioned into different regions.

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

To be replaced with Quantum Mechanical

Calculations

The simulation on 100nX100n substrate takes about 10 days on 1 Teraflop machine (without FEM!)


FEM Coding :

Mesh generation and Visualisation


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


Multiscale simulations

•Kinetic Monte Carlo (KMC)

• Molecular Dynamics (MD)

• Finite Element Method (FEM)

Summary

Simulation Result

Film is continuous and no dot formation on

large scale after deposition

Experimental ResultsFilm is continuous and no dot formation on large scale after depositionAfter annealing dot are formed Substrate type and quality affects the dot formation

Stress during

annealing process is

necessary to form dots.

Future Work

Fabrication In Quantum dots

1) Deposition of modern compound semiconductors or organic compound

2) Spontaneous structure formation in these systems, the so-called self-assembly of nanoscale islands

Control and stabilisation of molecular assemblies at the nanometer scale are crucial steps in the fabrication of nano-scale devices.

However, the intrinsic surface properties such as roughness and defects largely decide the formation of these devices

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.

RoughnessFuture Work

•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 non-graphics processing.

•NVIDIA's CUDA (Compute Unified Device Architecture): High performance computing platform uses massive multithreading on multicore architecture.

•(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.

Acceleration using GPUs

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

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

RMS roughness=0.7

RMS roughness=0.2



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.

ConclusionsConclusions

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

Thank You!Thank You!

AcknowledgmentsAcknowledgments:: Institute of High Performance Institute of High Performance Computing , Singapore Computing , Singapore NUS, SingaporeNUS, Singapore

B.Tech Students at VNITB.Tech Students at VNIT

Goodbye and Thanks for Listening about me

Dr Rajendra Patrikar

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