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 3) CNTFET VD Bachtold, et al., Science, Nov. 2001 VG 2) SBFET VG VD VS VG 4) Molecular Transistors? VD VS 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 • 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 • • 1938 Technology engine: Vacuum tube Proposed improvement: Solid state switch Fundamental research: Materials purity 1998 Technology engine: CMOS FET Proposed improvement: Quantum state switch Fundamental research: Materials size/shape Promise Microns to Nanometers -- Biological/Chemical/Atomic Quantum Dots dots (AFM) Quantum ~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 Control gate Floating gate n+ n+ Floating gate is replaced by QDs Flash memory with poly floating gate n+ n+ •Quantum floating gate replacing Flash memory with nanocrystal floating gates poly floating gate 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 CD CS Floating gate n+ CB n+ Leff Conventional flash Memory Vs. QD flash Memory Device •For nano-crystal floating gates charge Floating gate i sreplaced by QDs 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 Quantum dot flash memory Gate Control oxide SiO2 10 nm Ge Nanocrystals Tunnel oxide Si Drain Source Flash memory 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 s Static self-assembly – Components at global or local equilibrium s 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 s 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: s Uniform size s Controlled placement s Directed processes s Physical mechanisms, s Chemical Mechanisms s 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. sThe 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 s s s 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 ∑j V2 (Ri , R j ) 2 i, •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: 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 •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 distribute atom positions among initiators. d. After each time step calculation collects nodes. c.Send data (positions, etc.) to target.a atom information. •Communication overhead is reduced as there is no communication among the target nodes. Kinetic Monte Carlo Random hopping from site A→ B s hopping rate D0exp(-E/T), s – E = Eb = energy barrier between sites – not δE = energy difference between sites B A Eb δE Kinetic Monte Carlo s s 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 s Deposition of new particles – random position – arrival frequency from deposition rate s 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 0.7 Thickness 0.6 0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 773K 823K 873K 923K Time Simulation Results Non_Uniformity 1.6 1.5 Std. Dev. 1.4 1.3 1.2 1.1 1 0.9 20 30 Flow rate 40 60 Simulation Results Average Thickness 3.5 3 Thickness 2.5 2 1.5 1 0.5 0 20 30 Flow Rate 40 60 773K 873K Simulation Results Simulation Results sFilm is continuous and no dot formation on large scale after deposition Experimental Results sFilm is continuous and no dot formation on large scale after deposition sAfter annealing dot are formed sSubstrate 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 TIME hours Engineering 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 physical understanding quantitative prediction Structural Properties Fundamental processes, Atomic structures, Energetics, …. Shape, Size distribution, Spatial distribution, Interface structures, …. Time (sec): 10-12 10-9 10-8 Molecular Dynamics 10-6 10-7 Statistical Mechanics 10-3 100 10-6 Continuum Mechanics Length (m): 10-9 Quantum 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: To beMonte Carlo with replaced s Probabilistic approach Quantum Mechanical Molecular Dynamics s Algorithm: Calculations s Deterministic approach o Initialization s 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” . Finite Element Analysis s Substrate is partitioned into different regions. s Outer region is taken as continuum and decomposed in the form of mesh. Interatomic potentials: Lennard-Jones potential. (pair wise) 10 days Tersoff family of potential. (many body type) while (time ≤ tmx ) a The simulation on 100nX100n substrate takes about 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 sFilm is continuous and no dot formation on large scale after deposition sAfter annealing dot are formed sSubstrate type and quality affects the dot formation Multiscale simulations •Kinetic Monte Carlo (KMC) • Molecular Dynamics (MD) • Finite Element Method (FEM) sStress during annealing process is necessary to form dots. Simulation Result sFilm 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 s s 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 is a single parameter, therefore allowing easy comparison between different objects can also be incorporated into roughness related analysis It It Modeling a Rough Surface The rough surface is therefore modeled using the Mandelbrot-Weierstrass function. Mandelbrot-Weierstrass function is a summation of sinusoids of geometrically increasing frequency and decreasing amplitude, with a random phase. The 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 sQuantum dot based flash memory is likely to become a reality in near future sThis tool is being developed for Quantum Dot Deposition System sStress during annealing process is necessary to form dots. sIncorporation 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! Goodbye and Thanks for Listening about me