Modeling the temperature-dependent Early voltage of a silicongermanium heterojunction bipolar transistor

This paper compares the temperature-dependent Early voltage of a silicon germanium heterojunction bipolar transistor (HBT) to that of a silicon bipolar junction transistor (BJT) fabricated with identical geometry. Derived is an isothermal expression for the forward Early voltage specifically suited to the base composition of a SiGe HBT. The expression includes two fit factors, one for the Si_1-xGe_x alloy and the other for the nonuniform doping density. The fit factors are functions of the device temperature and are determined through pulsed bias measurements     

Si和SiGe三极管Early效应模型及在电路仿真器中的应用综述

Early效应作为表征双极器件关键性能的因素之一,影响输出跨导、传输电流、基区渡越时间、电流增益、扩散电容等器件特性。本文从Early效应的基本定义出发,综述了Early电压的起源,模型的发展及其在Si和SiGe电路仿真器中的应用。具体为：（1）综述了Si三极管中的基本模型及在SPICE中处理过程,然后针对SPICE的缺陷,描述了VBIC模型中针对Early效应的改进。（2）由于SPICE和VBIC不能有效描述SiGe HBT中基区Ge组分引入。本文基于SiGe HBT标准化模型Mextram、HICUM对SiGe HBT的建模思想,综述了将其用于建立Early电压模型的方法。（3）总结了现有主流模型对Early效应的建模方法及优缺点。     

A new formulation of the early effect in epitaxial bipolar transistors

This paper shows that the Early effect in epitaxial bipolar transistors can be analytically modelled by a simple formulation, obtained from the base charge model, for the normal and inverse modes of operation. Based on the one-sided approximation of the two transistor junctions, three base punch-through voltages are obtained to adequately model the base charge modulation effect. With this new model it is possible to calculate the bias dependence of the Early voltages, as commonly defined. This analysis shows that the best physical parameters to describe the current dependence on the voltages are the base punch-through voltages, the only non-bias dependent parameters.     

Optimization of polysilicon emitters for BiCMOS transistor design

Practical aspects of designing polysilicon emitters for large-scale integrated circuit manufacture are presented. It is shown that by choosing the emitter dose such that the minimum base saturation current density is observed, the highest product of common emitter gain and Early voltage is obtained. In practice, this allows high values of both parameters to be chosen, giving an increased bipolar output impedance. This reduces the need for elaborate Early voltage compensation during BiCMOS circuit design. In addition, the increase in the integrated base charge gives a reduction in the punched base resistance and hence the bipolar noise figure. The increase in the total base charge permits the use of a deeper, wider base region. Therefore, maximizing the product of common emitter gain and Early voltage gives transistors with optimized performance and improved reproducibility     

Early voltage in double heterojunction bipolar transistors

The Early voltage for abrupt double heterojunction bipolar transistors (DHBTs) has been calculated by using an effective junction velocity (S_c) at the base-collector heterojunction. S_c is obtained by self-consistently partitioning thermionic and quantum mechanical tunneling currents. Unlike single heterojunction bipolar transistors (SHBTs), the Early voltage varies very rapidly at low reverse bias and approaches the SHBT-limit at sufficiently high reverse bias. This is attributed to the presence of an energy barrier at the b-c heterojunction     

Early effect of high-current-gain heterojunction bipolar transistor

The current gain ? of a high-? heterojunction bipolar transistor is usually limited, at normal operating range, by the ratio of the injected electron current to the recombination current in the space-charge region. The Early effect in these transistors is very important because the base layer is very thin in order to obtain high ?. In this case, the classical transistor models are not very suitable, and an Early voltage smaller than for a homojunction bipolar transistor is commonly observed. In the letter an analysis has been carried out taking into account the emitter current crowding effect and heterojunction characteristics. A simple analytic equation of the Early voltage is derived, and experimental results are presented.     

Early voltage in heterojunction bipolar transistors: Quantum tunneling and base recombination effects

An extension of the thermionic emission expression for Early voltage V_A for heterojunction bipolar transistors including quantum mechanical tunneling and base recombination effects is provided. The theoretical model is based on a single flux treatment of the carrier transport invoking the concise notation of scattering matrices. V_A is numerically evaluated under the WKB quantum mechanical approximation for triangular and parabolic barriers. The temperature dependence of the Early voltage is simulated numerically and compared to earlier theoretical V_A predictions and actual experimental results of V_A in heterojunction 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     

Neutral base recombination and its influence on the temperaturedependence of Early voltage and current gain-Early voltage product inUHV/CVD SiGe heterojunction bipolar transistors

We present the first comprehensive investigation of neutral base recombination (NBR) in ultra-high vacuum/chemical vapor deposited (UHV/CVD) SiGe heterojunction bipolar transistors (HBT's), and its influence on the temperature characteristics of Early voltage (V_A ) and current gain-Early voltage product (βV_A). We show that a direct consequence of NBR in SiGe HBT's is the degradation of V_A when transistors are operated with constant-current input (forced-I_B) as opposed to a constant-voltage input (forced-V_BE). In addition, experimental and theoretical evidence indicates that with cooling, V_A in SiGe HBT's degrades faster than in Si bipolar junction transistors (BJT's) for forced-I_B mode of operation. Under the forced-V_BE mode of operation, however, SiGe HBT's exhibit a thermally-activated behavior for both V_A and βV_A, in agreement with the first-order theory. The differences in V_A as a function of the input bias and temperature for SiGe HBT's are accurately modeled using a modified version of SPICE. The performance of various practical SiGe HBT circuits as a function of temperature, in the presence of NBR, is analyzed using this calibrated SPICE model     

A new approach for direct observation of base width modulation invertical bipolar transistors

A new DC measurement technique that allows direct observation of the forward and reverse Early effects is described. The technique employs a special test structure and is used to accurately determine the Early voltage parameters in the Gummel-Poon model. The improvements provided by this method over existing parameter extraction techniques are realized by using a direct measurement of the normalized base charge as a function of the emitter and collector junction biases. The new technique described here allows the Early voltage parameters to be extracted as a function of applied bias in a straightforward manner and is suitable for high volume measurements for statistical characterization and for process monitoring in an industrial setting     

Calculation of the breakdown characteristics of bipolar transistors using a two-dimensional model

The location of avalanche-breakdown in the common emitter output characteristics of bipolar transistors has been calculated for a circular emitter geometry. A two-dimensional model takes account of the very important voltage drop across the base spreading resistance. The dependence of the breakdown points on the bias voltage and the series resistance at the base terminal can be described by simple formulas, which agree quite well with experimental results.     

"Bipolar-mode" transistors on a voltage-controlled scheme

A buried-gate vertical JFET (BVFET) operated under forward gate bias shows saturating or nonsaturating drain current characteristics simply by Changing the channel cross section area. BVFET with a proper channel cross section has similar characteristics to a "bipolar-mode" SIT (BSIT) or a depleted base transistor (DBT). A generalized picture is derived relating these forward-biased JFET's to the conventional bipolar transistor (BPT). Analysis of BVFET has proved that the operation of BSIT is completely the same as that of BPT with its base voltage controlled. The current saturation mechanism is discussed in detail in this paper.     

Bias, frequency, and area dependencies of high frequency noise inAlGaAs/GaAs HBT's

The noise figure of the heterojunction bipolar transistor (HBT) in the microwave frequency range is studied, and an improved physical noise model is developed. Unlike the conventional high frequency noise model, which considers only the bias current dependence, the present model includes both the effects of voltage and current on the noise behavior. In addition, the frequency- and area-dependent natures of the HBT noise at very high frequencies are incorporated in the model. It is found that the voltage dependence of the high frequency noise in the HBT results from the self-heating effect, which gives rise to a higher HBT lattice temperature than the ambient temperature. Also, the free-carrier transport delay time must be considered to properly model the frequency dependence of noise since the inverse of this time is comparable with the frequency. Furthermore, the area dependence of noise is dominated by changes in the base resistance and emitter-base junction capacitance. Results for the minimum noise factor calculated from the model compare favorably with those obtained from measurements     

Mechanism of Dynamic Bias Temperature Instability in p- and nMOSFETs: The Effect of Pulse Waveform

The waveform effect on dynamic bias temperature instability (BTI) is systematically studied for both p- and nMOSFETs with ultrathin SiON gate dielectrics by using a modified direct-current current–voltage method to monitor the stress-induced interface trap density. Interface traps are generated at the inversion gate bias (negative for pMOSFETs and positive for nMOSFETs) and are partially recovered at the zero or accumulation gate bias. Devices under high-frequency bipolar stress exhibit a significant frequency-dependent degradation enhancement. Approximate analytical expressions of the interface trap generation for devices under the static, unipolar, or bipolar stress are derived in the framework of conventional reaction–diffusion (R–D) model and with an assumption that additional interface traps$(N_ it^ast)$are generated in each cycle of the dynamic stress. The additional interface trap generation is proposed to originate from the transient trapped carriers in the states at and/or near the$hboxSiO_2/hboxSi$interface upon the gate voltage reversal from the accumulation bias to the inversion bias quickly, which may accelerate dissociation of Si–H bonds at the beginning of the stressing phase in each cycle. Hence,$N_ it^ast$depends on the interface-state density, the voltage at the relaxation (i.e., accumulation) bias, and the transition time of the stress waveform (the fall time for pMOSFETs and the rise time for nMOSFETs). The observed dynamic BTI behaviors can be perfectly explained by this modified R–D model.     

低温硅双极晶体管基区优化设计

常规双极晶体管在７７Ｋ下电流增益和频率性能都严重退化。本文首先分析了低温双极晶体管基区Ｇｕｍｍｅｌ数，基区方块电阻，渡越时间和穿通电压等参数与温度及基区掺杂的关系，然后讨论了低温双极器件基区的优化设计问题。     

Electric measurement of impurity concentration in p-type epitaxially grown and ion-implanted base regions

A new destruction free method of evaluation of the impurity densities in the base region of a p-epitaxial transistor based on the Gummel-Poon model of the bipolar transistor is presented. An Early voltage measurement method is used to determine the impurity densities at the edges of the base region and the Gummel number of the base from the change of the Gummel charge Q_b. The feasibility of our method is demonstrated by experimental results which are also used to determine the error ranges of the method which are within ±20%. The method is very easy to apply because it only used d.c. current and voltage measurements.     

Analysis of the early voltage in bipolar transistors

The Early voltage of the bipolar transistor is calculated considering the current gain of the device due to the emitter injection efficiency as well as the volumetric recombination in the base. The impurity profile in the base is assumed to be exponential. The calculated values and the measured values of the Early voltage VAare seen to be in good agreement. Seven high-voltage transistors having a wide range of physical and device parameters were taken for the experimental verification. The Early voltage is seen to increase with the increase in the diffusion length of minority carriers in the base where as it decreases when the emitter Gummel number rises. Curves are also plotted showing the effect of other parameters on VA. The values of VAare also calculated when the minority-carrier lifetime in the base is infinite and these values are compared with the corresponding measured values. As a check on the analysis, comparison is made between the calculated and the measured values of the Early voltage of the devices in the inverse mode of operation. The agreement is good.     

Theory of electrothermal behavior of bipolar transistors: Part I -single-finger devices

A detailed theoretical and numerical analysis of the electrothermal behavior of single-finger bipolar transistors is proposed. Two models of different complexities are introduced to investigate self-heating effects in bipolar junction transistors (BJTs) and heterojunction bipolar transistors (HBTs) biased with a constant base-emitter voltage source or with a constant base current source. In the constant base-emitter voltage case, simple relations are derived for determining the onset of the flyback behavior in the output characteristics which defines the boundary of the safe operating region. The model indicates that the flyback behavior disappears at high V/sub BE/ values, and predicts a thermal hysteresis phenomenon at high currents. It is also shown that at high current levels the electrothermal behavior is dominated by ohmic base pushout. If a constant base current is applied, the model shows that both BJTs and HBTs are unconditionally thermally stable. The transient behavior is also considered, and the temperature evolution is investigated for different bias conditions. The model shows that, if the device is biased in the thermally unstable region, thermal breakdown occurs within a finite time instant in the limit case of a zero ballast resistance. Finally, the reduction in the safe operating area due to avalanche effects and to the temperature dependence of thermal conductivity is discussed, and a simplified model is proposed.     

Si-SiO_2界面陷阱引起的双极晶体管h_(FE)漂移的模型与模拟

本文表明,Si-SiO_2界面过渡层中的载流子陷阱对硅体内电子存在慢俘获作用,这将导致npn型双极晶体管电流放大系数h_(FE)随时间的正向漂移。从这种物理机制出发,建立了相应的数学模型。经计算机模拟分析,求得了h_(FE)随时间的漂移曲线以及温度、发射结偏压、基区表面势对这种漂移的影响。结果表明,基区表面势对漂移量的大小有重要影响,高温老化是漂移失效筛选的有效手段。     

THE EFFECT OF DOPANT OUTDIFFUSION ON THE NEUTRAL BASE RECOMBINATION CURRENT IN Si/SiGe/Si HETEROJUNCTION BIPOLAR TRANSISTORS

A new analytical model for the base current of Si/SiGe/Si heterojunction bipolar transistors(HBTs) has been developed. This model includes the hole injection current from the base to the emitter, and the recombination components in the space charge region(SCR) and the neutral base. Distinctly different from other models, this model includes the following effects on each base current component by using the boundary condition of the excess minority carrier concentration at SCR boundaries: the first is the effect of the parasitic potential barrier which is formed at the Si/SiGe collector-base heterojunction due to the dopant outdlffusion from the SiGe base to the adjacent Si collector, and the second is the Ge composition grading effect. The effectiveness of this model is confirmed by comparing the calculated result with the measured plot of the base current vs. the collector-base bias voltage for the ungraded HBT. The decreasing base current with the increasing the collector-base reverse bias voltage is successfully explained by this model without assuming the short-lifetime region close to the SiGe/Si collector-base junction, where a complete absence of dislocations is confirmed by transmission electron microscopy (TEM)[1]. The recombination component in the neutral base region is shown to dominate other components even for HBTs with a thin base, due to the increased carrier storage in the vicinity of the parasitic potential barrier at collector-base heterojunction.