Asymptotic electron energy flux equations for hot-carrier transport simulation

In isothermal device simulations, the Bernoulli function has to be computed carefully to avoid potential numerical difficulties. Problems may arise when the difference in discretized potential values between two nodes is sufficiently small. In nonisothermal hot-carrier transport, additional asymptotic cases can arise depending on the difference in the electron temperature values. In this letter, all possible limiting expressions for the electron energy flux are presented. A parallel treatment will lead to the corresponding equations for current densities.     

Modeling facet heating in ridge lasers

A numerical self-consistent model to study facet heating in semiconductor lasers is presented. The model consists of the solutions of the 3D heat equation and the 1D longitudinal carrier and photon rate equations. The model is used to investigate facet heating in a ridge laser structure and the results are compared with the predictions of similar models using lower dimensional thermal equations. The results show that a large scale 3D thermal approach must be taken to study facet heating if overestimations in facet temperature are to be avoided. The importance in the overall facet heating process of a non-linear thermal conductivity and Joule heating generated outside the active region is looked at. Although the different thermal behavior at the facets of InGaAsP/InP and AlGaAs/GaAs lasers has previously been explained in terms of their different surface recombination velocity, interesting results are obtained when the laser structures are compared with emphasis placed on their basic thermal properties. The results show that a combination of dimensionality of the heat flow and the temperature dependence of the thermal conductivity are important factors in the determination of the facet temperature.     

A multidimensional laser simulator for edge-emitters includingquantum carrier capture

A multidimensional semiconductor laser simulator is presented which follows a rate equation approach for the coupling between optics and electronics. Capture and emission rates for the bound and free carriers are used for the quantum well. The electronic equations and the optical equations are solved in a self-consistent manner for one, two, and three dimensions. As an example, an InGaAs quantum-well ridge laser is analyzed, and the multidimensional simulation approach for Fabry-Perot device structures is discussed. A three-dimensional (3-D) simulation of a device with a truncated contact shows the applicability of the simulator to complex laser cavity designs     

Recrystallization of Electrodeposited Copper Thin Films During Annealing

The microstructure evolution of electrodeposited copper thin films was studied at room and elevated temperatures. The effects of isothermal and nonisothermal treatments were investigated. The heating rate in nonisothermal treatment was found to significantly control the recrystallization temperature and time. The Johnson–Mehl–Avrami–Kolmogorov model was applied to describe the fraction recrystallized under isothermal conditions. It was proven that the recrystallization of copper films during nonisothermal annealing can be modeled using the additivity rule. Based on the isothermal results, a model was applied to predict the recrystallization kinetics during nonisothermal heat treatments.     

Self-consistent modeling of heating and MOSFET performance in 3-D integrated circuits

We present a new method for finding the temperature profile of vertically stacked three-dimensional (3-D) digital integrated circuits (ICs). Using our model, we achieve spatial thermal resolution at the desired circuit level, which can be as small as a single MOSFET. To resolve heating of 3-D ICs, we solve nonisothermal device equations self-consistently with lumped heat flow equations for the entire 3-D IC. Our methodology accounts for operational variations due to technology nodes (hardware: device), chip floor plans (hardware: layout), operating speed (hardware: clock frequency), and running applications (software). To model hardware, we first decide on an appropriate device configuration. We then calculate elements of the lumped thermal network using the 3-D IC layout. To include software, chip floor plan, and duty cycle-related performance variations, we employ a statistical Monte Carlo type algorithm. In this paper, we investigate performance of vertically stacked 3-D ICs, with each layer modeled after a Pentium III. Our calculated results show that layers within the stacked 3-D ICs, especially the ones in the middle, may greatly suffer from thermal heating.     

Two-dimensional model of heat flow in broad-area laser diode: Discussion of the upper boundary condition

This paper presents a discussion of the upper boundary condition, which should be assumed in calculations of temperature distribution in a laser diode. Using the isothermal condition instead of convection or thermal insulation is proposed. Theoretical results are compared with temperature map obtained by thermoreflectance method. The model is based on the solution of two-dimensional, stationary heat conduction equation obtained by separation-of-variables approach. Full analytical expressions are provided. All considerations deal with p-side down mounted devices.     

A consistent nonisothermal extension of the Scharfetter—Gummel stable difference approximation

Computer simulation is becoming an increasingly important aspect of device analysis and design, and it is well known that stability of the associated numerical solution procedures is enhanced by use of the Scharfetter-Gummel (SG) approximation. Accurate transport models utilizing carrier temperature as a crucial parameter are emerging, however the SG expression is valid only for isothermal analyses. In this letter, a consistent nonisothermal extension of the SG stable difference approximation is presented. Simplifications of the new expression are shown to agree with previous results.     

Rate equation model for nonequilibrium operating conditions in aself-organized quantum-dot laser

A nonequilibrium rate equation model is presented and analyzed for the self-organized quantum dot (QD) laser. The model assumes the QD zero dimensional levels are coupled to a thermal electron distribution in the wetting layer through reservoir rate equations. By including the energy dependence of the wetting layer reservoir versus temperature, the model accounts for the spectral narrowing of the gain with increasing temperature, the negative temperature coefficient of the lasing threshold, and a reduction of the spectral hole burning with increasing temperature, all found experimentally in QD lasers     

强激光大气传输非线性热畸变效应的解析分析

高功率激光在大气中传输时产生的非线性热畸变效应对激光的传输形成严重的限制，使光束质量严重下降，到达靶面的光强远低于初始光强。文中分析了非线性热畸变形成的物理机制，从光波大气中传输的标量波动方程以及流体动力学方程组出发，对稳态和瞬态的各种非线性热畸变现象进行了分析，给出了非线性热畸变效应与激光参数的相关性，获得了较为满意的结果。     

Analysis of a wavelength selectable cascaded DFB laser based on the transfer matrix method

A novel cascaded DFB laser,which consists of two serial gratings to provide selectable wavelengths,is presented and analyzed by the transfer matrix method.In this method,efficient facet reflectivity is derived from the transfer matrix built for each serial section and is then used to simulate the performance of the novel cascaded DFB laser through self-consistently solving the gain equation,the coupled wave equation and the current continuity equations.The simulations prove the feasibility of this kind of wavelength selectable laser and a corresponding designed device with two selectable wavelengths of 1.51μm and 1.53μm is realized by experiments on InP-based multiple quantum well structure.     

激光大气传输非线性效应数值模拟与分析

对激光通过大气传输的主要非线性过程进行数值模拟，列出大气的流体动力学方程组和与大气互作用的波方程．推导出受激热瑞利散射引起的小扰动不稳定性的波与大气的耦合方程，还对湍流作了处理，依据这些理论基础，编制了一套四维程序，用来模拟热晕及补偿、小扰动不稳定性、热晕与湍流的互作用过程．理论结果和实验十分符合．     

Two-dimensional carrier flow in a transistor structure under nonisothermal conditions

A two-dimensional mathematical model is developed to predict the internal behavior of power transistors operating under steady-state conditions. This model includes the internal self-heating effects in power transistors and is applicable to predict the transistor behavior under high-current and high-voltage operating conditions. The complete set of partial differential equations governing the bipolar semiconductor device behavior under nonisothermal conditions is solved by numerical techniques without assuming internal junctions and other conventional approximations. Input parameters for this model are the dimension of the device, doping profile, mobility expressions, generation-recombination model, and the boundary conditions for external contacts. Computer results of the analysis of a typical power transistor design are presented for specified operating conditions. The current density, electrostatic potential, carrier charge density, and temperature distribution plots within the transistor structure illustrate the combined effect of the electrothermal interaction, base conductivity modulation, current crowding, base pushout, space charge layer widening, and current spreading phenomena in power transistors.     

VDMOS全热程的温度分布

本文提出一种VDMOS全热程的电模型,给出用电网络法计算包含有源区、衬底、支座和热沉在内的全热程温度分布。同时在稳态非等温条件下求解一组包括热导方程、泊松方程和连续性方程的偏微分方程组。两种方法所获得的有源区温度分布符合很好。     

Finite element method applied to stress simulation of high power 980nm pump lasers

A three dimensional analysis on stress and strain in the central and in the mirror area of a InGaAs---GaAs ridge laser diode structure is presented. The analysis is based on a finite element method model, which couples thermal behaviour of laser to its mechanical structure. The impact of process parameters on reliability of device is discussed, and results are given for process and operation induced stress.     

A travelling-wave rate equation analysis for semiconductor lasers

A travelling-wave rate equation model for the investigation of the transient effects in a semiconductor laser is presented. The model includes the spatial dependence of the photon and excess carrier densities and may be applied to lasers with non-uniform current injection and inhomogeneous material properties. Details of the numerical algorithm which enables the equations to be solved are given. Numerical results show that unpumped regions and defects inside a laser can shorten the optical pulses obtained by gain-switching.     

Nd-glass burst laser with kW average power output

Demonstrations of operation of a compact neodymium glass laser with average output powers greater than 1 kW for several seconds are reported. The laser is based on the thermal inertia laser (TIL) concept wherein a neodymium-doped glass rod is pumped uniformly without cooling during a burst mode of laser operation. Design principles for TIL devices and scaling to 100 kW class lasers are discussed. Experimental results for a low repetition-rate proof-of-concept pulsed device (30 J, 0.2 Hz) and a high repetition-rate pulsed prototype (40 J, 36 Hz) are presented and compared to numerical solutions for the laser rate equations with temperature dependent cross-sections     

A physics-based, analytical heterojunction bipolar transistormodel, including thermal and high-current effects

A detailed, analytical model for predicting the DC and high-frequency performance of AlGaAs/GaAs graded heterojunction bipolar transistors (HBTs) is presented. The model is developed based on the relevant device physics, such as current-induced base pushout and thermal effects. The current gain, cutoff frequency, and maximum frequency versus the collector current density, which is a function of the applied voltage as well as the corresponding temperature in the HBT, are calculated. The results suggest that the conventional HBT model, which assumes the HBT temperature is the same as that of the ambient, can overestimate the three figures of merit considerably when the collector current density is high. Furthermore, it is shown that the present model correctly explains such experimentally observed HBT high-current behavior as the rapid falloff of the current gain and cutoff frequency. The model predictions compare favorably with the results obtained from a model which solves numerically the Poisson and continuity equations coupled with the lattice heat equation     

Effect of HF discharge structure on etch nonuniformity in plasma-chemical reactor

Numeric simulation is used to study the effect of the high-frequency (HF) discharge structure on the process of plasma-chemical etching of silicon in a mixture of CF₄/O₂. The calculations are carried out using a mathematical model of a nonisothermal reactor, in which the gas mixture motion was described with the help of equations of multicomponent hydrodynamics, taking into account the convection-diffusion transport of individual mixture components. In order to determine the characteristics of low-temperature plasma the hydrodynamic model of axial-symmetric HF discharge was used, including the continuity equations for electrons and positive ions, the energy balance equation for electrons, and the Poisson equation for electric potential. The effect of the HF discharge structure on the generation and mass exchange of active particles in a plasma-chemical etching reactor is studied.     

混合频率激光对CCD探测器损伤机理

为了进行对CCD探测器的损伤机理的探索研究,提出了采用双光束合成器件产生混合频率激光的原理与方法．利用Zemax软件模拟了双光束合成器件,同时对远场光斑进行了采集．基于热传导和热弹性力学的基本关系式建立了混合频率激光辐CCD探测器遮光铝膜层的热力耦合数学物理模型,对热传导方程和应力平衡方程进行了半解析求解,计算得到混合频率激光辐照CCD探测器的遮光铝膜层的瞬态温度场和环向热应力场,并通过数值仿真比较了不同工作模式激光光源对CCD的损伤效果．     

A simple rate-equation-based thermal VCSEL model

Motivated by the potentially large number of devices and simulations involved in optoelectronic system design, and the associated need for compact optoelectronic device models, we present a simple thermal model of vertical-cavity surface-emitting laser (VCSEL) light-current (LI) characteristics based on the laser rate equations and a thermal offset current. The model was implemented in conventional SPICE-like circuit simulators, including HSPICE, and used to simulate key features of VCSEL LI curves, namely, thermally dependent threshold current and output-power roll-over for a range of ambient temperatures. The use of the rate equations also allows simulation in other non-dc operating regimes. Our results compare favorably to experimental data from three devices reported in the literature