Computation of Strained Epitaxial Growth in Three Dimensions by Kinetic Monte Carlo

A numerical method for computation of heteroepitaxial growth in the presence of strain is presented. The model used is based on a solid-on-solid model with a cubic lattice. Elastic effects are incorporated using a ball and spring type model. The growing film is evolved using Kinetic Monte Carlo (KMC) and it is assumed that the film is in mechanical equilibrium. The strain field in the substrate is computed by an exact solution which is efficiently evaluated using the fast Fourier transform. The strain field in the growing film is computed directly. The resulting coupled system is solved iteratively using the conjugate gradient method. Finally we introduce various approximations in the implementation of KMC to improve the computation speed. Numerical results show that layer-by-layer growth is unstable if the misfit is large enough resulting in the formation of three dimensional islands

Kinetic Monte Carlo Simulation of Strained Heteroepitaxial Growth with Intermixing

An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are incorporated using a ball and spring model. While idealized, this model nevertheless captures many aspects of heteroepitaxial growth, including nucleation, surface diffusion, and long range effects due elastic interaction. The algorithm combines a fast evaluation of the elastic displacement field with an efficient implementation of a rejection-reduced kinetic Monte Carlo based on using upper bounds for the rates. The former is achieved by using a multigrid method for global updates of the displacement field and an expanding box method for local updates. The simulations show the importance of intermixing on the growth of a strained film. Further the method is used to simulate the growth of self-assembled stacked quantum dots

Fast kinetic Monte Carlo simulation of strained heteroepitaxy in three dimensions

Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Green's function formalisms for boundary values in the associated lattice elasticity problems. The computational efficiency is further enhanced by using a superparticle surface coarsening approximation. Atomic hoppings simulating surface diffusion are sampled using a multi-step acceptance-rejection algorithm. It utilizes quick estimates of the atomic elastic energies from extensively tabulated values modulated by the local strain. A parameter controls the compromise between accuracy and efficiency of the acceptance-rejection algorithm.Comment: 10 pages, 4 figures, submitted to Proceedings of Barrett Lectures 2007, Journal of Scientific Computin

Multiscale Kinetic Monte Carlo Simulation of Self-Organized Growth of GaN/AlN Quantum Dots

A three-dimensional kinetic Monte Carlo methodology is developed to study the strained epitaxial growth of wurtzite GaN/AlN quantum dots. It describes the kinetics of effective GaN adatoms on an hexagonal lattice. The elastic strain energy is evaluated by a purposely devised procedure: first, we take advantage of the fact that the deformation in a lattice-mismatched heterostructure is equivalent to that obtained by assuming that one of the regions of the system is subjected to a properly chosen uniform stress (Eshelby inclusion concept), and then the strain is obtained by applying the Green’s function method. The standard Monte Carlo method has been modified to implement a multiscale algorithm that allows the isolated adatoms to perform long diffusion jumps. With these state-of-the art modifications, it is possible to perform efficiently simulations over large areas and long elapsed times. We have taylored the model to the conditions of molecular beam epitaxy under N-rich conditions. The corresponding simulations reproduce the different stages of the Stranski–Krastanov transition, showing quantitative agreement with the experimental findings concerning the critical deposition, and island size and density. The influence of growth parameters, such as the relative fluxes of Ga and N and the substrate temperature, is also studied and found to be consistent with the experimental observations. In addition, the growth of stacked layers of quantum dots is also simulated and the conditions for their vertical alignment and homogenization are illustrated. In summary, the developed methodology allows one to reproduce the main features of the self-organized quantum dot growth and to understand the microscopic mechanisms at play

An Examination of Kinetic Monte Carlo Methods with Application to a Model of Epitaxial Growth

Through the assembly of procedural information about physical processes, the kinetic Monte Carlo method offers a simple and efficient stochastic approach to model the temporal evolution of a system. While suitable for a variety of systems, the approach has found widespread use in the simulation of epitaxial growth. Motivated by chem- ically reacting systems, we discuss the developments and elaborations of the kinetic Monte Carlo method, highlighting the computational cost associated with realizing a given algorithm. We then formulate a solid-on-solid bond counting model of epitax- ial growth which permits surface atoms to advance the state of the system through three events: hopping, evaporation, and condensation. Finally, we institute the ki- netic Monte Carlo method to describe the evolution of a crystalline structure and to examine how temperature influences the mobility of surface atoms

Rejection Enhanced Off-Lattice Kinetic Monte Carlo

We introduce a new kinetic Monte Carlo (KMC) algorithm for off-lattice simulation. In off-lattice KMC one needs to calculate the rates for all possible moves from the current state by searching the energy landscape for index-1 saddle points surrounding the current basin of attraction. We introduce a rejection scheme where the true rates are replaced by rate estimates. This is done by first associating each saddle point with a key atom defined to be the atom that moves the most or that corresponds to the largest energy change if the transition were to take a place, then constructing an estimate for the total rate associated with each atom by using a nearest-neighbor bond count. These estimates allow one to select a set of possible transitions, one of which is accepted or rejected based on a localized saddle point search focused on a particular atom. In principle, this allows a performance boost that scales with the number of particles in the system. We test the method on a growing two-species nanocluster with an emerging core-shell structure bound by Lennard-Jones potential. In addition to that, we give a detailed review for the dimer method used in this study to locate index-1 saddle points on the potential energy surface

Monte Carlo simulation of silicon-germanium transistors

Self-consistent Monte Carlo simulation studies of n-channel Si/SiGe modulation doped field effect transistors (MODFETs) and silicon-on-insulator lateral bipolar junction transistors (SOI- LBJTs) are reported in this thesis. As a preliminary to the device studies Monte Carlo simulations of electron transport in bulk Si strained as if grown on Si(_0.77)Ge(_0.23) and Si(_0.55)Ge(_0.45) substrates have been carried out at 300 K, for field strengths varied from 10(^4) to 2 x 10(^7) Vm(^-1). The calculations indicate an enhancement of the average electron drift velocity when Si is tensilely strained in the growth plane. The enhancement of electron velocity is more marked at low and intermediate electric fields, while at very high fields the velocity saturates at about the same value as unstrained Si. In addition the ensemble Monte Carlo method has been used to study the transient response to a stepped electric field of electrons in strained and unstrained Si. The calculations suggest that significant velocity overshoots occurs in strained material. Simulations of n-channel Si/Si(_1=z)Ge(_z) MODFETs with Ge fractions of 0.23, 0.25, and 0.45 have been performed. Five depletion mode devices with x = 0.23 and 0.25 were studied. The simulations provide information on the microscopic details of carrier behaviour, including carrier velocity, kinetic energy and carrier density, as a function of position in the device. Detailed time-dependent voltage signal analysis has been carried out to test device response and derive the frequency bandwidth. The simulations predict a current gain cut-off frequency of 60 ± 10 GHz for a device with a gate length of 0.07 /nm and a channel length of 0.25 um. Similar studies of depletion and enhancement mode n-channel Si/Sio.55Geo.45 MODFETs with a gate length of 0.18 /im have been carried out. Cut-off frequencies of 60 ±10 GHz and 90± 10 GHz are predicted for the depletion and enhancement mode devices respectively. A Monte Carlo model has also been devised and used to simulate steady state and transient electron and hole transport in SOI-LBJTs. Four devices have been studied and the effects of junction depth and silicon layer thickness have been investigated. The advantage of the silicon-on-insulator technology SOI device is apparent in terms of higher collector current, current gain, and cut-off frequency obtained in comparison with an all-silicon structure. The simulations suggest that the common-emitter current gain of the most promising SOI-LBJT structure considered could have a cut-off frequency approaching 35 ± 5 GHz