电子科技大学：《材料设计与计算 Materials Design and Computation》课程教学资源（课件讲稿）MDC 15 Examples of MCMC：Reaction-Diffusion（R-D）model

Examples of MCMC:Reaction-Diffusion (R-D)model >Defect-induced threshold voltage shift/instability (VT)has been a reliability issue in metal-oxide-semiconductor (MOS)transistors > Interface defects are generally assumed to arise from the dissociation of interfacial Si-H bonds at the silicon/dielectric interface The dissociation of Si-H bond during the defect creation The repassivation of broken Si-bonds during the defect annealing H diffusion H2 diffusion and H-H2 inter-conversion

Examples of MCMC: Reaction-Diffusion (R-D) model  Defect-induced threshold voltage shift/instability (VT) has been a reliability issue in metal-oxide-semiconductor (MOS) transistors  Interface defects are generally assumed to arise from the dissociation of interfacial Si-H bonds at the silicon/dielectric interface  The dissociation of Si-H bond during the defect creation  The repassivation of broken Si-bonds during the defect annealing  H diffusion  H2 diffusion and H-H2 inter-conversion

Examples of MCMC:Reaction-Diffusion(R-D)model dN=kp(No-Nr)-kgNnNn dt dNB=Du dx H dt =D, dt

Examples of MCMC: Reaction-Diffusion (R-D) model

Examples of MCMC:Reaction-Diffusion(R-D)model 1-Pr 1-PDH-PR 1-PDH PDH No-NIT NH2 。。。有。金象金有象非e参东e表。象 PR PDH PDH Nr Markov model for probabilistic motion in an R-D system having H diffusion

Examples of MCMC: Reaction-Diffusion (R-D) model

Examples of MCMC:Reaction-Diffusion(R-D)model =DH dt dN dz NL-kn[N9]'+冰N2, /入(0) H dt DH2 g[了-g d dNDH dt dNn-kn Ni+knaNnz dN2=DH2 dz? dt divaoWe

Examples of MCMC: Reaction-Diffusion (R-D) model

Examples of MCMC:Reaction-Diffusion(R-D)model 1-PDH-1-2pDH 1-2PpH 1-Pr PR-PH -PH -PH Pe PDH PDH No-NIT NH2 Nr 0.5PH PH2 0.5PH PH2 0.5PH PH2 N2° N:2 .( 1-PoH2-1-2Po2 1-2PDH2 0.5pz -0.5PH2 -0.5p2 Markov model for probabilistic motion in an R-D system having H-H2 diffusion

Examples of MCMC: Reaction-Diffusion (R-D) model

Quantum Monte Carlo >Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. > One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation)of the quantum many-body problem. >The diverse flavor of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi- dimensional integrals that arise in the different formulations of the many-body problem. >The quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function,going beyond mean field theory and offering an exact solution of the many-body problem in some circumstances

Quantum Monte Carlo Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. The diverse flavor of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi￾dimensional integrals that arise in the different formulations of the many-body problem. The quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean field theory and offering an exact solution of the many-body problem in some circumstances

A few problems using QMC 。Surface Chemistry ·Simple Chemical ·Metal-Insulator Reactions Transitions ·Melting of Silicon ·Point Defects in Determining Smallest Semi-Conductors Stable Fullerene ·Excited States

• Surface Chemistry • Metal-Insulator Transitions • Point Defects in Semi-Conductors • Excited States • Simple Chemical Reactions • Melting of Silicon • Determining Smallest Stable Fullerene A few problems using QMC

Why use QMC turbines, materials synthetic drug bridges... design chemistry design mechanical properties of materials chemical reactions properties of defects forces on atoms ◆ quantum mechanics atomic numbers

Why use QMC

The Root of QMC:The Schrodinger equation Believed to be capable of describing almost all interactions in life Handles many electrons in the equation r:-ril 亚(1,2，，rN)=EΨ(1，r2,,rN)· (i)

• Believed to be capable of describing almost all interactions in life • Handles many electrons in the equation The Root of QMC: The Schrodinger equation

Variational Monte Carlo >Variational Monte Carlo (VMC)is a quantum Monte Carlo method that applies the variational method to approximate the ground state of a quantum system. >The basic building block is a generic wave function |(a))depending on some parameters a.The optimal values of the parameters a is then found upon minimizing the total energy of the system. >Generate sets of Random positions as Result of Comparing Electron Positions to the many-electron wavefunction

Variational Monte Carlo Variational Monte Carlo (VMC) is a quantum Monte Carlo method that applies the variational method to approximate the ground state of a quantum system. The basic building block is a generic wave function |Ψ(a)⟩ depending on some parameters a. The optimal values of the parameters a is then found upon minimizing the total energy of the system. Generate sets of Random positions as Result of Comparing Electron Positions to the many-electron wavefunction