Performance limitations of silicon bipolar transistors

The author considers some performance limitations of silicon bipolar transistors, assuming our ability to fabricate small geometric devices, by device analysis using an accurate two-dimensional numerical solution of classic semiconductor transport equations. The applicability of mathematical equations used to represent carrier transport in small geometric bipolar transistors and silicon-material parameters, such as bandgap narrowing with doping, ionization coefficients, and lifetime, used in the model has also been considered. The terminal characteristics, the internal behaviour, and performance limitations due to voltage and current operating levels of bipolar transistors with emitter depths and basewidths ranging from 0.4 /spl mu/m to 30 nm have been analyzed.     

Numerical modeling of hot carriers in submicrometer Silicon BJT's

Conventional semiconductor equations do not accurately describe carrier transport phenomena particularly in submicrometer semiconductor devices because of the use of the local field-dependent mobility. In this work, a hot-carrier transport model is used in the numerical simulation of submicrometer silicon bipolar junction transistors (BJT's). The hot-carrier effect, velocity overshoot, is predicted in this model and the results compare favorably with those obtained by the Monte Carlo method, which consumes much more computer time. A heuristic iterative procedure has been developed that proves to be very efficient in solving the five coupled nonlinear semiconductor equations including the energy balance equations.     

BILOW-simulation of low-temperature bipolar device behavior

The BILOW simulation program for investigating bipolar transistor behavior in the temperature range 77-300 K is discussed. Differences between the numerical approaches required for simulation of low-temperature behavior compared to room-temperature simulation are presented. Efficient numerical models for the physical parameters in the carrier transport equations and Poisson's equation for the temperature range of 77-300 K, including a new highly accurate numerical model for the temperature and doping concentration dependence of carrier mobility, are discussed. A temperature- and doping-concentration-dependent model for apparent bandgap narrowing is also discussed. The internal characteristics of a typical bipolar transistor are simulated over the 300-77 K range. The behavior of current gain β and the unity gain frequency f_T versus collector current density for different temperatures are calculated and discussed     

Physical limitations of the diffusive approximation in semiconductor device modeling

Criteria for occurrence of the quasineutral diffusion mode have been investigated in terms of a generalized approach that takes into account the dependences of the electron and hole velocities on the electric field. These criteria should be used to describe the carrier transport in bases of forward biased bipolar semiconductor devices (diodes, thyristors, and power bipolar transistors in the saturation mode). The criteria appreciably differ from the previously obtained commonly accepted criteria. It is demonstrated that equations describing the carrier transport in the quasineutral approximation in n- and p-type semiconductors are different. These equations are used to obtain analytical conditions in which the diffusion mode is operative. The applicability limits of the diffusion approximation in simulation of semiconductor structures are found. The analytical results are confirmed by a numerical experiment.     

Ring oscillator circuit simulation with physical model for GaAs/GaAlAs heterojunction bipolar transistors

Switching performance is simulated for GaAs/GaAlAs heterojunction bipolar transistors (HBT's) by combining a realistic physical device model that involves numerical solutions for carrier transport equations and Poisson's equation with our own circuit simulator that enables direct access to the device model embedded in arbitrary circuits. Based on simulated results for five-stage ring oscillators, discussion is given as to how the switching performance depends on the circuit configuration such as current mode logic (CML) without and with emitter follower, and direct-coupled transistor logic (DCTL), inclusion or exclusion of external base areas, and choice for single-or double-heterojunction transistors.     

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.     

Numerical analysis and interpretation of the small-signalminority-carrier transport in bipolar devices

A simple and efficient one-dimensional numerical technique is presented that determines the small-signal minority-carrier transport in the quasineutral regions of bipolar devices, such as diodes and transistors, under sinusoidal excitation. The technique is applied to study small-signal properties of p-n junction diodes and bipolar transistors. Examples treated include the frequency dependence of transistor current gain, the diffusion capacitance of a quasineutral base or emitter, and base-layer carrier propagation delay     

Industrial application of heterostructure device simulation

We give an overview of the state-of-the-art of heterostructure RF-device simulation for industrial application based on III-V compound semiconductors. The work includes a detailed comparison of device simulators and current transport models to be used, and addresses critical modeling issues. Results from two-dimensional hydrodynamic simulations of heterojunction bipolar transistors (HBTs) and high electron mobility transistors (HEMTs) with MINIMOS-NT are presented in good agreement with measured data. The simulation examples are chosen to demonstrate technologically important issues which can be addressed and solved by device simulation.     

Rigorous modeling of high-speed semiconductor devices

We present a review of industrial heterostructure devices based on SiGe/Si and III–V compound semiconductors analyzed by means of numerical simulation. A comparison of device simulators and current transport models is given and critical modeling issues are addressed. Results from two-dimensional hydrodynamic analyses of heterojunction bipolar transistors (HBTs) are presented in good agreement with measured data. The examples are chosen to demonstrate technologically relevant issues which can be addressed by device simulation.     

Transport equations for highly doped devices and heterostructures

An overview of the transport equations describing electron and hole motion and density in solids with nonuniform band structure is presented. This includes materials with graded composition, like heterojunctions, and devices with highly doped regions, like the emitter region of modern bipolar transistors and solar cells. Effects due to carrier degeneracy, changes in the energy band edges, and changes in the density of states produce terms in the carrier- and current-density equations in addition to those found in the conventional Shockley model. These new terms are derived and discussed.The general energy-band diagram relating the electrostatic potential, electron affinity and bandgap is given. The current densities are written in terms of gradients of quasi-Fermi level and the carrier densities in terms of normalization integrals. The concepts of generalized drift and diffusion are discussed. Connections to the work by Van Overstraeten et al. and to Lundstrom et al. are given. The transport equations in the nondegenerate limit are presented. The special case of minority-carrier flow in quasi-neutral material is given. Key approximations used in device analysis are discussed.     

An accurate charge control approach for modeling excess phase shiftin the base region of bipolar transistors

The conventional charge control approach is extended to enable the accurate determination of excess phase shift in the ac common-emitter current gain of bipolar transistors arising from distributed stored minority carrier charge in the neutral base. Generalized expressions, valid for transistors with arbitrary impurity profiles and position-dependent transport parameters, are presented from which the excess phase shift can be determined solely from device structure and process data. The ac model parameters which result from the extended charge control approach are used in an existing high-frequency compact nonquasi-static bipolar model which is suitable for SPICE simulation     

异质结双极晶体管基区复合电流的解析模型

从求解异质结双极晶体管基区的二维电流连续性方程出发，推导出了基区少数载流子浓度的解析解，由此获得了基区各种复合电流的解析表达式。基于该模型完成了算法研究和软件编制，计算出了器件所能达到的理论电流增益。     

Numerical solution of the semiconductor transport equations with current boundary conditions

The semiconductor transport equations are solved by a hybrid finite-element method with current specified as a boundary condition at device contacts. Single carrier or bipolar devices of arbitrary shape, operating under transient or steady-state conditions, can be simulated with current sources or simple circuit elements connected to device terminals. This paper describes the numerical technique and device applications.     

Physics-based modeling of submicron GaN permeable base transistors

We present the first physics-based nonstationary modeling of a submicron GaN permeable base transistor. Three different transport models are compared: drift-diffusion, energy balance, and ensemble Monte Carlo. Transport parameters and relaxation times used by the carrier transport equations are consistently derived from particle simulation. The current-voltage (I-V) characteristics predicted with the energy balance model are in good agreement with those obtained from direct Monte Carlo device simulation. On the other hand, the drift-diffusion approach appears to be inadequate for the device under study, even if improved high-field mobility models are adopted     

Emitter efficiency,transit times and current gain of bipolar transistors

A generalized theory of emitter efficiency, transit times, and current gain of bipolar transistors have been developed by taking non-uniform doping and carrier concentrations, bandgap narrowing, mobility, diffusion coefficient, bulk and surface recombinations, and others into consideration. The final expressions exhibit forms identical to the traditional ones for non-degenerate semiconductors with position-independent device parameters. Numerical calculations carried out on a simpler model resulting from the use of approximate models for various parameters demonstrate effects of these parameters on emitter efficiency, transit times and current gain. These calculations point, in particular, to the importance of optimum doping concentrations in the emitter and base regions for obtaining maximum current gain, and of bandgap narrowing in determining the performance limitations of bipolar transistors.     

基区复合电流对双极晶体管厄利电压的影响

推导了在考虑了基区复合电流后双极晶体管厄利电压的理论表达式。用该表达式计算了 Si/Si Ge异质结双极晶体管的厄利电压 ,并且与仿真结果进行了比较。比较结果表明 ,两种情况下计算出的厄利电压值符合良好     

Simulation and design of InAlAs/InGaAs pnp heterojunction bipolartransistors

The performance capabilities of InP-based pnp heterojunction bipolar transistors (HBT's) have been investigated using a drift-diffusion transport model based on a commercial numerical simulator. The low hole mobility in the base is found to limit the current gain and the base transit time, which limits the device's cutoff frequency. The high electron majority carrier mobility in the n⁺ InGaAs base allows a reduction in the base doping and width while maintaining an adequately low base resistance. As a result, high current gain (>300) and power gain (>40 dB) are found to be possible at microwave frequencies. A cutoff frequency as high as 23 GHz and a maximum frequency of oscillation as high as 34 GHz are found to be possible without base grading. Comparison is made with the available, reported experimental results and good agreement is found. The analysis indicates that high-performance pnp InP-based HBT's are feasible, but that optimization of the transistor's multilayer structure is different than for the npn device     

Si-SiGe-Si异质结双极晶体管的数字模拟

报道了Si-SiGe-Si异质结双极晶体管的数字模拟结果。采用有限差分法解半导体器件的载流子输运方程,求出各点上的载流子浓度及其电位,由此可确定器件的直流特性。器件的发射区掺杂浓度为1.4×10~(17)cm~(-3),基区掺杂浓度为7×10~(18)cm~(-3),SiGe基区中Ge摩尔含量为0.31,模拟得到的最高电流增益为390。数字模拟得到的晶体管特性曲线与实验结果符合良好。     

Mathematical modeling of semiconductor-on-insulator (SOI) device operation

Numerical modeling of SOI devices is proposed through use of a bipolar carrier and time-dependent approach. Poisson's equation and the current continuity equations for electrons and holes are solved simultaneously. The former is solved over the whole area of the device in question, and the electrostatic potential at the silicon-insulator interface is determined so as to fulfill Gauss's theorem. To achieve accurate numerical calculations and to obtain a stable convergence in the numerical scheme, a variable transformation is employed in the current continuity equation. That is, quasi-Fermi potentials for electrons and holes rather than carrier densities are directly analyzed. An insulated layer is modeled in the current continuity equation using the zero intrinsic-carrier density and zero mobility to realize zero conductance in an insulator. Sample calculations demonstrate a quick and stable convergence in the numerical scheme, and clarify the operational mechanism of SOI devices. This modeling should become a helpful aid in SOI device design.