In this paper, the homotopy deformation method to solve the nonlinear stationary semiconductor equations with Fermi-Dirac statistic is used. This method introduces an arti cial transient problem. The time discretization is based on the nonlinear implicit scheme with local time steps. In order to have an automatic adaptation of local time step parameters, we introduce arclength predictor-corrector continuation methods. The fondamental goal of these methods is to overcome the unstabilities or the failure of the classical Newton-Raphson's schemes which appear when the nonlinearity is Strong or near Limit or Bifurcation points. The approximate procedure of our system using a Galerkin method that makes use of a mixed nite element approach is used. A peculiar feature of this mixed formulation is that the electric displacement D and the current densities j n and j p for electrons and holes, are taken as unknowns, together with the potential and quasi Fermi levels n and p. This allows D, j n and j p to be determined directly and accurately. The above algorithms appear to be e cient, robust and to give satisfactory results. Numerical results are presented, in one and two dimension, for some realistic devices : an Heterojunction Diode (quasi-1D problem) and an Heterojunction Bipolar Transistor (HBT) working in ampli er mode.
Purpose The purpose of this paper is to develop and apply accurate and original models to understand and analyze the effects of the fabrication temperatures on thermal-induced stress and speed performance of nano positively doped metal oxide semiconductor (pMOS) transistors. Design/methodology/approach The speed performances of nano pMOS transistors depend strongly on the mobility of holes, which itself depends on the thermal-induced extrinsic stress σ. The author uses a finite volume method to solve the proposed system of partial differential equations needed to calculate the thermal-induced stress σ accurately. Findings The thermal extrinsic stress σ depends strongly on the thermal intrinsic stress σ0, thermal intrinsic strain ε0, elastic constants C11 and C12 and the fabrication temperatures. In literature, the effects of fabrication temperatures on C11 and C12 needed to calculate thermal-induced stress σ0 have been ignored. The new finding is that if the effects of fabrication temperatures on C11 and C12 are ignored, then, the values of stress σ0 and σ will be overestimated and, then, not accurate. Another important finding is that the speed performance of nano pMOS transistors will increase if the fabrication temperature of silicon-germanium films used as stressors is increased. Practical implications To predict correctly the thermal-induced stress and speed performance of nano pMOS transistors, the effects of fabrication temperatures on the elastic constants required to calculate the thermal-induced intrinsic stress σ0 should be taken into account. Originality/value There are three levels of originalities. The author considers the effects of the fabrication temperatures on extrinsic stress σ, intrinsic stress σ0 and elastic constants C11 and C12.
In this work we use the PROCOM sofware to model Mg doped GaN film growth by MOCVD. The 2/3D conservation equations of mass, energy, momentum and species are solved by the nonsymmetric conjugate gradient method with block preconditioning (H. C. Elman, Preconditioned conjugate gradient methods for nonsymmetric systems of linear equations (Yale University Research Report, 1981) [5]). A kinetics model with gas/surface adduct formation has been incorporated with detailed Mg dopant reaction mechanism. We reproduced broad doping profiles caused by memory effects and verified that the formation of (NH 3 ) 2 -MgCp 2 and NH 3 -MgCp 2 adducts play an important role in p-doping of GaN and related Group III nitrides.1 Introduction The group III nitrides, including GaN and its alloys with AlN and InN, have a number of properties, including a direct, wide band gap, high thermal conductivity, and high thermal stability, that makes them important for green-to-UV optoelectronics and high-power electronic devices. For the p-type doping of GaN and its alloys, the dominant species employed is magnesium, which is typically delivered during metal organic chemical vapour deposition (MOCVD) via the organo-metallic precursor magnesocene (MgCp 2 ) (Cp = cyclopentadienyl group). However, the performance of many of these devices is presently limited by the various difficulties associated with Mg doping, such as its deep acceptor nature, the formation of Mg-H complexes, and the memory effect commonly present in metalorganic chemical vapour deposition (MOCVD). Tight control of doping profiles is required for optimal device performance. Therefore, understanding Mg incorporation and its redistribution behaviour in MOCVD is very important. In this work we use PROCOM [4] to model Mg doped GaN film growth by MOCVD. The process involves complex gas-phase and surface reactions combined with flow, heat transfer, and mass transfer processes. The results of these physical and chemical rate processes determine the quality of the deposited layers in terms of film thickness, composition uniformity as well as impurity incorporation.
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