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 multidimensional 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