Kinetic Monte Carlo Simulation of Two-dimensional Semiconductor Quantum Dots Growth

Transcription

1 Kinetic Monte Carlo Simulation of Two-dimensional Semiconductor Quantum Dots Growth by Ernie Pan Richard Zhu Melissa Sun Peter Chung Computer Modeling and Simulation Group The University of Akron

2 Outline Crystal (QDs) Growth Back Ground Simulation Method Application of QDs Growth QDs Epitaxial Growth Kinetic Monte Carlo (KMC) Two-dimensional (2D) QDs Growth KMC 2D Growth Model Growth Parameters Dependence of QDs Shape and Distribution Temperature T Surface coverage c Flux rate F Interruption time t i Substrate Orientation Dependence of QDs Ordering Strain Energy Distribution QDs Patterns with Different Substrate Directions QDs Patterns with Different Growth Parameters 2

3 Simulation Methods Kinetic Monte Carlo (KMC) o Stochastic techniques o Random numbers and probability statistics Molecular Dynamics (MD) o Newton s second law o Interactions between molecules Different laws of physics used to describe materials at different scales 3

4 Crystal (QDs( QDs) ) Growth - Examples Very Large Diamonds Produced Very Fast May 6, 25 Carnegie Institution Washington, D.C. -- Researchers at the Carnegie Institution s Geophysical Laboratory have produced - carat, half-inch thick single-crystal diamonds at rapid growth rates ( micrometers per hour) using a chemical vapor deposition (CVD) process. AMD, IBM announce breakthrough in strained silicon transistor December 3, 24 AMD and IBM today announced that they have developed a new and unique strained silicon transistor technology aimed at improving processor performance and power efficiency. The breakthrough process results in up to a 24 percent transistor speed increase, at the same power levels, compared to similar transistors produced without the technology. 4

5 QDs for Light Emitting Diodes First white LED using quantum dots created July 5, 23 Sandia National Laboratories Highly efficient, low-cost quantum dot-based lighting would represent a revolution in lighting technology through nanoscience. Economy Energy Environment Comparing with traditional light devices: Energy saving Longer life time Comparing with traditional LEDs: Color adjustable Nontoxic Cheaper 5

6 QDs Epitaxial Growth Physical Vapor Deposition Chemical Vapor Deposition Ga(CH 3 ) 3 + AsH 3 GaAs+3CH 4 Ga(CH 3 ) 3 AsH 3 Epitaxial Growth Modes: a) b) Volmer-Weber (VW) c) Frank-Van der Merwe (FM) Stranski-Krastanov (SK) Substrate Substrate SK Mode QDs Pictures 6

7 Outline Crystal (QDs) Growth Back Ground Simulation Method Application of QDs Growth QDs Epitaxial Growth Kinetic Monte Carlo (KMC) Two-dimensional (2D) QDs Growth KMC 2D Growth Model Growth Parameters Dependence of QDs Shape and Distribution Temperature T Surface coverage c Flux rate F Interruption time t i Substrate Orientation Dependence of QDs Ordering Strain Energy Distribution QDs Patterns with Different Substrate Directions QDs Patterns with Different Growth Parameters 7

8 KMC 2D Growth Model Hopping probability y E p = ν exp s + E n E k T B str ( x, y) ν Attempt frequency E E s, n Bonding energies to the surface and to the neighboring atoms E str (x,y) Strain energy field T Temperature k B Boltzmann s constant x First box, including nearest and next nearest neighbors E n = ( n gn' ) Eb + ( m gm' ) αeb Second box E b Bonding energies of a single nearest neighbor α, g Reduction factor for next nearest neighbors n, m # of nearest and next nearest atoms in original positions (n 4, m 4) n', m' # of nearest and next nearest atoms in new positions (n' 4, m' 4) 8

9 Flow Chart of 2D KMC QDs Growth Model KMC algorithm --- three main parts ) Calculate the probability P (µ ν) for the transition from the current state µ to a new state ν; 2) Calculate the time increment t by using the value P; Simulation time t = & Hopping steps n= Randomly grow seeds (Flux rate) Form a probability list of each atom r p [i] i = Atom Form cumulative function R i = r j (I=,2.N) I j= Find i by R < ur R, u (,] i i Carry out event i 3) Increase the simulation time t by t to mimic the elapsed step. End Update simulation time t=t+ t ( t= /R ) Yes t>t Total No Update hopping steps n=n+ Calculate strain energy Yes n>25 No Current coverage >Final coverage Yes No 9

10 Outline Crystal (QDs) Growth Back Ground Simulation Method Application of QDs Growth QDs Epitaxial Growth Kinetic Monte Carlo (KMC) Two-dimensional (2D) QDs Growth KMC 2D Growth Model Growth Parameters Dependence of QDs Shape and Distribution Temperature T Surface coverage c Flux rate F Interruption time t i Substrate Orientation Dependence of QDs Ordering Strain Energy Distribution QDs Patterns with Different Substrate Directions QDs Patterns with Different Growth Parameters

11 Growth Parameters Temperature T Four Growth Parameters: Temperature T Surface coverage c Flux rate F Interruption time t i p = ν exp E s + E n E k B T str ( x, y)

12 Growth Parameters Temperature T 55K 65K 75K 8K 85K 95K Growth of InAs/GaAs. Flux rate F=.Ml/s, coverage c=2% and interruption time t i =2s on a 2 2 grid. Optimal T centered at 75-8K 2 (Pan, Zhu, and Chung, JNN, 24)

13 Growth Parameters Surface Coverage c % 2% Four Growth Parameters: Temperature T Surface coverage c Flux rate F Interruption time t i 3% 4% 5% Growth of InAs/GaAs. Temperature T=7K, flux rate F=.Ml/s, interruption time t i =2s on a 2 2 grid. Optimal c centered at 2% 3 (Pan, Zhu, and Chung, JNN, 24)

14 Growth Parameters Flux Rate F Ml/s.Ml/s.Ml/s Increasing island size Growth of InAs/GaAs. Temperature T=7K, coverage c=2% and interruption time t i =2s on a 2 2 grid. Deposition stops after.2s on the left, 2s in the middle, and 2s on the right. Strain energy field is not included for simplicity. Four Growth Parameters: Temperature T Surface coverage c Flux rate F Interruption time t i 4 (Pan, Zhu, and Chung, JNN, 24)

15 Growth Parameters Interruption Time t i s s Four Growth Parameters: Temperature T Surface coverage c Flux rate F Interruption time t i 5s s 5s 2s Growth of InAs/GaAs. Temperature T=75K, flux rate F=.Ml/s, coverage c=2% on a 2 2 grid Equilibrium 5 (Pan, Zhu, and Chung, JNN, 24)

16 Outline Crystal (QDs) Growth Back Ground Simulation Method Application of QDs Growth QDs Epitaxial Growth Kinetic Monte Carlo (KMC) Two-dimensional (2D) QDs Growth KMC 2D Growth Model Growth Parameters Dependence of QDs Shape and Distribution Temperature T Surface coverage c Flux rate F Interruption time ti Substrate Orientation Dependence of QDs Ordering Strain Energy Distribution QDs Patterns with Different Substrate Directions QDs Patterns with Different Growth Parameters 6

17 AMD, IBM announce breakthrough in strained silicon transistor December 3, 24 Strained Semiconductors AMD and IBM today announced that they have developed a new and unique strained silicon transistor technology aimed at improving processor performance and power efficiency. The breakthrough process results in up to a 24 percent transistor speed increase, at the same power levels, compared to similar transistors produced without the technology Å Å InAs GaAs InAs GaAs InAs growth on GaAs substrate 7 Maximum mistfit strain: 7%

18 Strain Energy Distribution x E p = ν exp E str 8 ( y) = C ijkl elastic moduli z 2 C ijkl Unit crystal of GaAs A s + En E k T γ ( y; x) γ ( y; x) da( x) ij B kl str y Isotropic condition (C -C 2 )/2=C 44 C 2 =53.8GPa C 44 =59.4GPa x z (3) () () C =72.6GPa y Elastic moduli of GaAs () C = C = C = C = Elastic moduli of GaAs () Elastic moduli of GaAs (3) Elastic moduli of Iso () GPa GPa GPa GPa

19 Strain Energy Distribution x() Grid Iso x() Grid GaAs () y() Grid y() Grid x(-2) Grid GaAs () y(-) Grid x(33-2) Grid (Pan, Zhu, and Chung, JAP, 26) GaAs (3) y(-) Grid

20 QDs Patterns with Different Substrate Directions x() Grid Iso x() Grid GaAs () Iso GaAs () y() Grid y() Grid x(-2) Grid GaAs () x(33-2) Grid GaAs (3) GaAs () GaAs (3) y(-) Grid y(-) Grid QDs patterns T=75K, F=.Ml/s, c=2%, and t i =2s, on a 2 2 grid. 2 (Pan, Zhu, and Chung, JAP, 26)

21 Compare of Experimental and Simulated QDs Patterns (Zhong and Bauer, APL 24) (Brune et al., Phys. Rev. B 995) (Seyedmohammadi website) GaAs () GaAs () GaAs (3) (Pan, Zhu, and Chung, JAP, 26) (Pan, Zhu, and Chung, JAP, 26) (Pan, Zhu, and Chung, JAP, 26) 2

22 QDs Patterns vs. Temperatures GaAs (Iso) GaAs () GaAs () GaAs (3) T=55K T=65K T=75K Flux rate F=.Ml/s, coverage c=2% and interruption time t i =2s on a 2 2 grid 22 (Pan, Zhu, and Chung, JAP, 26)

23 QDs Patterns vs. Coverage c c=% c=2% c=3% c=5% GaAs (Iso) GaAs () GaAs () GaAs (3) Temperature T=75K, flux rate F=.Ml/s, interruption time t i =2s on a 2 2 grid 23 (Pan, Zhu, and Chung, JAP, 26)

24 QDs Patterns vs. Interruption Time t i GaAs (Iso) GaAs () GaAs () GaAs (3) t i =s t i =s t i =2s Temperature T=75K, flux rate F=.Ml/s, coverage c=2% on a 2 2 grid 24 (Pan, Zhu, and Chung, JAP, 26)

25 25 The End