Bipolar Transistor Model Research Articles

SIMSCAPE Electrical Modelling of the IGBT with Parameter Optimization Using Genetic Algorithm

The concept introduced by MathWorks in the Simscape product is the link representation between the SIMSCAPE library components that correspond to physical connections transmitting power. In this paper, a power insulated-gate bipolar transistor (IGBT) model using MATLAB graphical software is reproduced. An electrical IGBT behavior model using the Simscape Electronics library components is developed and analyzed. This model is parameterized using the constructor datasheet to ensure a good representation of the dynamic and static IGBT behaviors. An extraction and optimization studies of the IGBT model parameters using a stochastic algorithm implemented in Matlab are presented. The proposed method is based on the Genetic Algorithm (GA) to perfectly extract and optimize the model parameters using the mathematical model circuit equations and the provided datasheet characteristics. A simulation in the Matlab/Simulink environment and a comparison with the experimental results for an IGBT device example are carried out to demonstrate the proposed model accuracy.

An improved small signal model of InP HBT for millimeter‐wave applications

AbstractIn this letter, an improved small‐signal equivalent circuit model of InP heterojunction bipolar transistors (HBTs) for millimeter‐wave applications is presented. The proposed small‐signal model takes into account the parasitic effect in the collector part which can effectively improve the accuracy of S parameter. In the frequency range of 2–110 GHz, good agreements between the measured and model‐calculated data can be achieved to demonstrate good modeling accuracy.

Towards Monolithic Indium Phosphide (InP)-Based Electronic Photonic Technologies for beyond 5G Communication Systems

This review paper reports the prerequisites of a monolithic integrated terahertz (THz) technology capable of meeting the network capacity requirements of beyond-5G wireless communications system (WCS). Keeping in mind that the terahertz signal generation for the beyond-5G networks relies on the technology power loss management, we propose a single computationally efficient software design tool featuring cutting-edge optical devices and high speed III–V electronics for the design of optoelectronic integrated circuits (OEICs) monolithically integrated on a single Indium-Phosphide (InP) die. Through the implementation of accurate and SPICE (Simulation Program with Integrated Circuit Emphasis)-compatible compact models of uni-traveling carrier photodiodes (UTC-PDs) and InP double heterojunction bipolar transistors (DHBTs), we demonstrated that the next generation of THz technologies for beyond-5G networks requires (i) a multi-physical understanding of their operation described through electrical, photonic and thermal equations, (ii) dedicated test structures for characterization in the frequency range higher than 110 GHz, (iii) a dedicated parameter extraction procedure, along with (iv) a circuit reliability assessment methodology. Developed on the research and development activities achieved in the past two decades, we detailed each part of the multiphysics design optimization approach while ensuring technology power loss management through a holistic procedure compatible with existing software tools and design flow for the timely and cost-effective achievement of THz OEICs.

A New Circuit Model of Bipolar Junction Transistor

Bipolar junction transistor or BJT is supposed to cost much more power and areas than MOSFET, but its frequency domain response seems better than MOSFETs. In this paper, a new circuit model for BJT is proposed, and the three-terminal circuit includes two MOSFETs and one Schottky diode, which can then be denoted by one MOSFET and a reversely-biased diode. If the new circuits are applied in technology processes for manufacturing, then MOS technology may be illuminated by early BJT to fabricate new devices.

On the Mechanisms of Linearity Peak Modeling in Common-Emitter SiGe HBTs Using Mextram 505

An important aspect of compact modeling for RF application is to accurately model the biasing current at which transistor linearity is maximized, i.e. where the third order intercept point, IP3, peaks. We have shown recently that for common-emitter SiGe HBTs, Mextram 504.12 has problem modeling the IP3 peak behavior at high injection [1]. We have further developed a couple of new modeling options in Mextram 505 [2] for CB junction depletion capacitance intended to improve IP3 peak modeling [1]. However, the detailed mechanisms of how these improved CB junction depletion capacitance models translate into IP3 peak modeling improvement remains unclear and require further investigation.For instance, the collector current, which is the output current, consists of the transistor main current In that flows from the collector to the emitter, and the CB junction capacitance discharging current that flows from the collector to the base. With the change of CB junction depletion capacitance model, which distortion current is dominant, In or the CB discharging current, in determining IP3 peak? Through detailed analysis of the harmonic components of the individual branch currents at the collector node of the Mextram large signal equivalent circuit, we find that the In distortion current dominates in determining IP3 peak behavior.The next logic question is if the In distortion current improvement with the Mextram 505 CB depletion capacitance models is directly due to the normalized base hole charge term, q1I in Mextram terminology, that goes directly into the In expression, or indirectly due to propagation of the CB discharging current induced distortion to IN, through circuit interactions. We will show that it is the later rather than the former with carefully designed custom Verilog-A codes of Mextram, by using separate CB depletion capacitance models in the main current equation formulation and the CB depletion charge equations. Changing the CB depletion capacitance model used in the main current equation leads to no visible changes in IP3, while changing the CB depletion capacitance model used in the CB depletion charge equation leads to obvious changes in third order output current and hence IP3. This proves that the observed third order distortion current improvement in In responsible for the improved IP3 peak modeling in Mextram 505 fundamentally results from the CB depletion charge term, despite the small values of third order distortion in the CB depletion charge current itself.We will then further examine how reducing the CB junction depletion capacitance might affect IP3 and how the partition between extrinsic and intrinsic CB junction capacitance affects IP3 peak behavior. Interestingly, simply making all CB depletion capacitance extrinsic gets rid of the IP3 peak modeling problem in Mextram 504, implying that the high injection related increase of the intrinsic CB junction depletion charge control voltage Vjunc and its related smooth limiting parameter Vch are the root problems. A reduction of CB depletion capacitance, intrinsic or extrinsic, is found to be beneficial for IP3 peak improvement.[1] G. Niu, H. Zhang, Y. Li, X. Ding, M. Willemsen, and A. Scholten, “Physics and Compact Modeling of SiGe HBT Linearity Using Mextram,” ECS Transactions, 86 (7), pp. 145-154, 2018.[2] G. Niu, R. van der Toorn, J. C. J. Paasschens, W. J. Kloosterman, The Mextram Bipolar Transistor Model, 505.10, Model Definition Document, Auburn University, 2019.

Counting statistics and microreversibility in stochastic models of transistors

Multivariate fluctuation relations are established in several stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. For all these models, the transport properties are shown to satisfy Onsager’s reciprocal relations in the linear regime close to equilibrium as well as their generalizations holding in the nonlinear regimes farther away from equilibrium, as a consequence of microreversibility. In the first model, which is related to the Ebers–Moll transport model for bipolar junction transistors, there is no internal state variable and particle exchanges between the ports are described as a Markov jump process with constant rates. In the second model, the rates linearly depend on an internal random variable, representing the occupancy of the transistor by charge carriers. The third model has rates nonlinearly depending on the internal occupancy, as in single-electron transistors. For the first and second models, finite-time multivariate fluctuation relations are also established, giving insight into the convergence towards the asymptotic form of multivariate fluctuation relations in the long-time limit.

X-Parameters Based Characterization and Compact Modeling of SiGe HBT Linearity

Linearity is an important SiGe HBT RF characteristics that has received a great deal of research for decades. For relatively small signal RF circuits such as LNAs, linearity is often characterized by measuring 3rd order intercept points, IP3, using a spectrum analyzer, or better, a Nonlinear Vector Network Analyzer (NVNA). For highly linear common-base SiGe HBTs, however, we find that the distortions generated within the RF source, which itself is also a transistor circuit, can be amplified by the HBT under test, which then interfere with the HBT’s distortions, making experimental validation of distortion in compact modeling difficult, or even impossible, for biases of high IP3. The devices used are the high voltage SiGe HBTs from NXP’s QUBIC4Xi technology. We overcome this problem with X-parameter (an invention of Keysight) measurements that are uniquely capable of removing the unwanted RF source harmonics as well as correcting for source mismatch [1], leading to more accurate transistor IP3 measurement. Fig. 1 shows the fundamental and 3rd order Pout versus Pin measured on an on-wafer through structure, with and without using X-parameters. Using X-parameters, the 3rd order harmonic output power is significantly reduced, increasing measurement system’s OIP3 to about 50 dBm.X-parameters approximate the generally nonlinear relationship between reflected waves and incident waves at the fundamental and harmonic frequencies, by a linear expansion around the system response excited by a relatively large fundamental stimulus at port 1, a situation of practical interest for amplifiers and mixers, as shown in Fig. 2. Nonlinear effects are relatively weak so that harmonic components can be superposed. The reflected wave at port p and harmonic index k, Bpk , relates to the large incident wave A11 , and all the small signal incident waves aql (port k, harmonic index l) by Eqs. (1) and (2) embedded in Fig. 2. The term P is the phase of the large signal fundamental incident wave. The superscript “*” means taking complex conjugate. N is number of ports, and K is number of harmonics. In our measurements, N=2, K=3.Fig. 3 shows output IP3 (OIP3) versus VCB for IE=1, 10, 20 and 30 mA, calculated from two FB type X-parameters, XFB23 and XFB21. Fundamental frequency is 2GHz. The Mextram 505.1 model does an excellent job in modeling IP3. While IP3 is an important linearity figures-of-merit, just like fT and fmax are for current and power gains, IP3 is not a complete representation of transistor linearity, just like fT and fmax represent only current and power gain for specific circuit terminations. At a given bias and fundamental frequency, there are for instance 78 X-parameters, for up to order 3 harmonics, including FB, S and T types, while only two FB type X-parameters are used for IP3. A logic question is if our compact model, in this case, Mextram, is capable of accurately modeling the complete X-parameter set, which represent distortion behavior much more completely. A systematic comparison of measured and modeled X-parameters is thus called for. Unfortunately, X-parameters are not supported yet by ICCAP, an industry standard device modeling tool also from Keysight, due to the complexity of X-parameter simulation. Out of necessity, here we use ADS to simulate X-parameters and then manually overlay simulation results with measurement by post-processing, a tedious process, particularly when model parameters are tuned. To a large extent, Mextram 505.1 [2], the latest version, is found to accurately model nearly all the X-parameters for a quite large range of emitter current and collector voltage biasing conditions.As an example, we show in Fig. 4 the FB and S type X-parameters as a function of VCB, for an IE of 30mA. A11 corresponds to an input power of -5dBm. The T type X-parameters for this current are small and below noise floor of measurement, and thus not shown. In the full paper we will also discuss the importance of modeling avalanche, particularly its biasing current dependence as it relates to Kirk’s effect, in modeling X-parameters, as well as how to use behavior of specific X-parameters to identify the dominant distortion mechanism, e.g. CB capacitance nonlinearity, avalanche nonlinearity, or transport current nonlinearity.[1] D. Root, J. Verspecht, J. Horn, and M. Marcu, X-Parameters, Characterization, Modeling and Design of Nonlinear RF and Microwave Components, Cambridge Press, 2013.[2] G. Niu et al., The Mextram Bipolar Transistor Model, version 505.1.0, Auburn University, 2019. Figure 1

Real-Time Simulation of Power Electronic Systems Based on Predictive Behavior

The field-programmable gate array (FPGA) based hardware-in-the-loop (HiL) test, which minimizes the time-step of the real-time simulation below 500 ns, is an enabling technology for the development of the control unit of high-power electronic systems (HPE). In order to improve the time performance of FPGA-based HiL, this article proposes a novel parallel structure using the predictive behavior of the power electronic system. With this structure, we design an improved system-level solver applied to HPE. A piecewise insulated-gate bipolar transistor (IGBT) model is used to determine the state of the switch, offering a quasi-realistic model of the power converter. A parallel integration method is also implemented to solve the status of the circuit elements. Moreover, the proposed parallel structural can execute both the IGBT model and circuit element model at the same time, thus, reducing the simulation time-step significantly. The numerical accuracy of the solution, the architecture design, and the issue of the parallel computation are discussed in detail. An ac-dc-ac topology is presented as a case study. At last, a 25 ns time step in the National Instruments FlexRIO platform is achieved. Results comparison with the reference model is also identified and discussed.

Static Thermal Coupling Factors in Multi-Finger Bipolar Transistors: Part II-Experimental Validation

In this paper, we extend the model developed in part-I of this work to include the effects of the back-end-of-line (BEOL) metal layers and test its validity against on-wafer measurement results of SiGe heterojunction bipolar transistors (HBTs). First we modify the position dependent substrate temperature model of part-I by introducing a parameter to account for the upward heat flow through BEOL. Accordingly the coupling coefficient models for bipolar transistors with and without trench isolations are updated. The resulting modeling approach takes as inputs the dimensions of emitter fingers, shallow and deep trench isolation, their relative locations and the temperature dependent material thermal conductivity. Coupling coefficients obtained from the model are first validated against 3D TCAD simulations including the effect of BEOL followed by validation against measured data obtained from state-of-art multifinger SiGe HBTs of different emitter geometries.

SPICE Compact BJT, MOSFET, and JFET Models for ICs Simulation in the Wide Temperature Range (From −200 °C to +300 °C)

The temperature range of SPICE models of bipolar and field-effect transistors is extended from the standard commercial level ( -60 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C⋯+150 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C) to harsh conditions level ( -200 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C⋯+300 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C) for low/high-temperature ICs design. This is done by including additional equations for temperature-dependent parameters, and by connecting additional elements to the device equivalent circuit to take into account the thermal effects. The universal automated methodology of model parameters extraction from the experimental data measured at low and high temperatures is proposed. The good agreement between simulated and measured device characteristics is achieved. The RMS error is not more than 10%-20%.

Limitations and Guidelines for Damage Estimation Based on Lifetime Models for High-Power IGBTs in Realistic Application Conditions

Statistical lifetime models for high-power insulated-gate bipolar transistors (IGBTs) are developed based on results from power-cycling experiments and relate lifetime expectancy to the well-defined conditions of a laboratory experiment. In most cases, predefined cyclic-stress conditions are repeatedly applied until the power device under test reaches its end of life. However, in real applications, power modules are exposed to nonrepetitive stress patterns that can be very different from the power-cycling conditions. A well-established lifetime estimation method suggests decomposing the stress pattern into individual components, whose damage can be calculated using a lifetime model. These damage contributions are then summed up in order to estimate the consumed or the remaining lifetime of a device. When comparing the estimation results to field measurements though, they often fail to match the real behavior of a power device. This article points out the uncertainties that appear in this process of applying a lifetime model on stress patterns deriving from field applications. The main purpose is to present typical sources of errors and discuss how severely these may impact the lifetime estimation.

A New Lumped-Charge Modeling Method for Power Semiconductor Devices

This article proposes a new lumped-charge model for power semiconductor devices. The existing lumped-charge model, due to its linear modeling method, has some limitations that will impair the accuracy of the model. First, this article analyses the restriction of the traditional lumped-charge modeling method. Then, based on the limitation analysis, a new lumped-charge modeling method is presented and improves the accuracy of the traditional one while keeping its advantages. In this new model, the relationship between the ambipolar current and the LCs in the power devices is redefined. Finally, the new method is implemented to an insulated-gate bipolar transistor (IGBT) model and a PiN freewheeling diode. The accuracy of the models is verified by experiment including both the static and transient characteristics and compared with the traditional IGBT model.

Component-Level Thermo-Electromagnetic Nonlinear Transient Finite Element Modeling of Solid-State Transformer for DC Grid Studies

Highly-detailed equipment models for electromagnetic transient simulation provide an accurate insight into the system characteristics and behavior. In this article, a coupled field-circuit cosimulation employing detailed component-level models is proposed for the solid-state transformer. To reveal comprehensive thermo-electromagnetic information of the equipment, a high-order nonlinear insulated-gate bipolar transistor (IGBT) model is utilized for the modular multilevel converter, while the finite element method (FEM) is adopted in modeling the transformer. The heavy computational challenge posed by the complexity of these models is alleviated by exploiting model parallelism and the subsequent processing by massively parallel architecture of the graphics processing unit, e.g., a pair of coupled voltage-current sources is adopted for reducing the order of the matrix equation in the circuit part, while in the FEM-based models, a matrix-free nodal domain decomposition solution is utilized to parallelize the overall system to the maximum. A multirate scheme is applied for a further computational burden reduction of the cosimulation due to a large disparity in the appropriate time-steps between power semiconductor switches and the magnetic component. Simulation of a multiterminal dc system including the SST is carried out, and the accuracy of proposed models are validated by offline tools such as SaberRD, ANSYS, and PSCAD/EMTDC.

An Electrical Transient Model of IGBT-Diode Switching Cell for Power Semiconductor Loss Estimation in Electromagnetic Transient Simulation

An electrical transient model (ETM) of insulated-gate bipolar transistor (IGBT)-diode switching cell is developed by coupling a temperature-dependent IGBT model with power loss model. The nonlinear behavior of IGBT and the reverse recovery characteristic of the diode are considered in this model to simulate the transient switching waveforms. Based on the transient waveforms of ETM under various operating conditions, the power loss estimation method (PLEM) for IGBT is developed. In addition to traditional modeling techniques that only uses ideal switch, this paper uses the model to replicate the power loss behaviors of semiconductor devices in circuit simulation by looking up tables. The proposed ETM is simulated in PSCAD/EMTDC with nanosecond time step, whereas the overall system application can be simulated with conventional time step in range of microsecond. By this way, the model can promise reasonable accuracy as well as an acceptable fast solving speed. The proposed ETM and PLEM have been implemented in PSCAD/EMTDC simulator and validated by experimental results using a double pulse test bench and boost converter test platform.

An Improved SPICE Model of SiC BJT Incorporating Surface Recombination Effect

The SiC bipolar junction transistor (BJT) offers an attractive alternative to the more popular SiC mosfet . It is important to develop an accurate SPICE model for the SiC BJT to enable its use in power electronic applications. The current gain of an SiC BJT may degrade considerably at high current levels and/or at high temperatures largely due to the surface recombination effect. In this paper, an improved SPICE behavioral model that accurately accounts for the current gain depending on the collector current and the junction temperature is proposed for the SiC BJT. In this paper, the conventional Gummel–Poon model is extended to include this important physical effect by adding a diode between the external base and emitter terminals of the BJT. A two-step model parameter extraction method is developed. First, the basic Gummel–Poon model parameters are extracted from low-current measurement data, and then, the new surface recombination model parameters are extracted by observing the difference between the measured high-level base current and the standard Gummel–Poon model prediction. The simulated static and switching characteristics of the new SiC BJT model match the measured data very well. Finally, the new SPICE model is used in the performance assessment of a proportional base driver technique embedded in a 3.6-kW boost converter, demonstrating its validity in helping with the optimum design of power electronic applications based on SiC BJTs.

The Impact of Temperature and Switching Rate on Dynamic Transients of High-Voltage Silicon and 4H-SiC NPN BJTs: A Technology Evaluation

This paper reports the application of silicon bipolar junction transistor (BJT) modeling techniques to the modeling of dynamic behavior of high-voltage 4H-SiC BJTs, and the experimental validation thereof. High-voltage silicon BJTs are impractical due to their low current gain that requires a bulky base driver. Emergence of high-voltage 4H-SiC vertical NPN BJTs with a tenfold higher gain enables the application of efficient drivers, with ratings close to those of IGBTs. This paper demonstrates the advantages offered by 4H-SiC BJTs by means of wide-scale measurements at 800 V and 10 A in a range of temperatures up to 175 °C and adjusted base driver switching rates. This paper shows that the turn- off storage delay in the SiC BJT is two orders of magnitude lower than that of the silicon device. It also shows that the turn- on switching transients of SiC device are by an order of magnitude and the turn- off transients are by two orders of magnitude faster than that of its silicon counterpart, resulting in a tenfold reduction of the switching energy. It also demonstrates the temperature dependence of switching transients of the silicon BJT, and the relative temperature-invariance of the SiC device's performance. This paper concludes with validation of the transient models for the 4H-SiC NPN BJT, showing that the model is sufficiently accurate for transient switching and loss calculations.

Improvement of the mathematical model of single­phase half­bridge inverter in state­variable form

The mathematical model of the insulated-gate bipolar transistor in the IGBT module is improved due to the determination of analytical expressions for dynamic spurious capacitances of the device. The expressions are obtained by analytical differentiation of functions that approximate the dependence of the spurious capacitances of the transistor on the voltage between the collector and the emitter. The method of forming a mathematical model of the IGBT voltage inverter in the form of matrix differential equations of state in the Cauchy form and nonlinear equations is proposed. There are no restrictions on the number of transistors and the configuration of the circuit. The method is based on the matrix-topological method of electrical circuits analyzing. The application of this method is illustrated by the example of a single-phase half-bridge inverter with resistive load. The urgency of improving the mathematical model of the IGBT inverter is caused by the need to analyze the electrical safety of the state of the variable frequency circuit between the frequency converter and the motor. Existing models of frequency-controlled electric drives do not take into account a number of factors that significantly affect the accuracy of the simulation. Such factors include the dynamic nature of the IGBT spurious capacitances and the disconnection of one of the machine phases from the network during the dead time when switching adjacent power switches of the inverter. The obtained mathematical model differs from the well-known in advanced representation of separate elements by nonlinear differential equations and taking into account mutual influences. The proposed approach allows to investigate the high-frequency transient components of currents and voltages in electrical systems with semiconductor converters. This simplifies taking into account the recharging processes of the IGBT capacitances during a dead time when switching adjacent power switches in the model. The peculiarities of the IGBT inverter switching transients are revealed, in particular, the significant exceeding, more than twice, of the transistor current during opening the operating current at the end of the switching process.

Physics-Based Compact Model of Parasitic Bipolar Transistor for Single-Event Transients in FinFETs

A physics-based compact model of the parasitic bipolar current induced by an energetic particle is presented for single-event transients in FinFETs. The terminal charges are modeled to predict the body voltage of the FinFET in the transient correctly. The models are implemented using Verilog-A and are verified through 3-D technology computer-aided design (TCAD) simulations. The results of the modeling show good agreement with the TCAD data, for both structural variations and energy variations of the energetic particles.

A Coupled Circuit-Ambipolar Diffusion Equation Model and Its Solution Methodology for Insulated Gate Bipolar Transistors

To eliminate the inefficiencies of the existing physics-based planar-gate insulated gate bipolar transistor (IGBT) model without considering an arbitrary free-carrier injection condition and 2-D effects at the MOS end of the drift region in the transient performance simulations, a coupled circuit-ambipolar diffusion equation model and its numerical solution methodology is proposed. Moreover, the proposed model treads the nonlinearity in a complete transient manner. The accuracy of the proposed model is validated by comparing the computed results with both experimental ones and those of an existing model.

Modelling of the active defects influence on the electrical characteristics of an SiGe-HBT

In this paper, a new conduction model for SiGe heterojunction bipolar transistors (HBTs) is proposed. The combined effect of the granular nature of the polycrystalline emitter and the defects caused by the etching process are introduced to explain the electrical conduction properties. This model is based on solving the ambipolar transport equation while considering the quantum effects present at the grain boundaries. The simulation allowed us to obtain the two-dimensional distributions of the minority and majority carriers in the structure and showed the limiting effect of the diffusion of free carriers by grain boundaries, which is especially significant for the minority free carriers. It was observed that at low and middle injection levels, the deep level-defects caused by the etching process lead to a decrease in the current gain. However, the defects present in the grain boundaries are able to limit this reduction. At high injection levels, the electrical characteristics are very close to those obtained in the absence of defects at the interfaces.