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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+
Quantum dot flash memory
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
Quantum dot flash memory
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
Self Assembly: Principles
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
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
Self Assembly: Principles
Key Issues: Uniform size Controlled placement Directed processes Physical mechanisms, Chemical Mechanisms Biochemical Processes
Self Assembly: Principles
•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 simulation
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.
Multiscale simulation
• Kinetic Monte Carlo (KMC)
• Molecular Dynamics (MD)
• Finite Element Method (FEM)
Multiscale simulation
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!)
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
Multiscale simulation
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.
Modeling a Rough Surface
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
Modeling a Rough Surface
Modeling a Rough Surface
Finding
Capacitance:
Finding
Potential:
Modeling a Rough Surface
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