Query: mathematical modelling of semiconductor device

Candidate papers:

abstract: Mathematical modelling of non linearity due to charge injection phenomenon with variation in desired characteristics of complementary metal oxide semiconductor (CMOS) image sensor (CIS) and correlated double sampling (CDS) circuits is presented. Existing suppression strategies of charge injection effect for CIS and CDS circuits lack in accuracy because of the absence of knowledge of its effect with variation in major device parameters related to switching transistors viz. width (W) length (L) sense node capacitance (Cpd and photon current (I ph) Therefore, variations in these parameters under the effect of charge injection have been experimentally studied. Based on the outcomes, it can be concluded that four parameter logistic regression symmetrical sigmoid function is the best fit for the non linearity introduced. Also, the devised mathematical model could be utilised as an activation function to train the biological neurons in CIS centred biomedical applications. A brief illustration of the same has been included for electrical stimulation of retinal cells. Further, the higher values of I ph, Cpd and scaling of switching transistors as W min and L L min can prove effective in reducing the non linearity. Contrary to previous studies, the higher value of Cpd utilising the normal photodiode found suitable for charge injection suppression in CIS.
author_names: Ashish Tiwari

R H Talwekar
title: Analysis and mathematical modelling of charge injection effect for efficient performance of CMOS imagers and CDS circuit
venue: IET Circuits Devices Syst.
year: 2020

abstract: Since the introduction of SPICE non linear controlled voltage and current sources, they have become a central feature in the interactive development of behavioural device models and circuit macromodels. The current generation of SPICE based open source general public license circuit simulators, including Qucs, Ngspice and Xyce(c) implements a range of mathematical operators and functions for modelling physical phenomena and system performance. The Qucs equation defined device is an extension of the SPICE style non linear B type controlled source which adds dynamic charge properties to behavioural sources, allowing for example, voltage and current dependent capacitance to be easily modelled. Following, the standardization of Verilog A, it has become a preferred hardware description language where analogue models are written in a netlist format combined with more general computer programming features for sequencing and controlling model operation. In traditional circuit simulation, the generation of a Verilog A model from a schematic, with embedded non linear behavioural sources, is not automatic but is normally undertaken manually. This paper introduces a new approach to the generation of Verilog A compact device models from Qucs circuit schematics using a purpose built analogue module synthesizer. To illustrate the properties and use of the Qucs Verilog A module synthesiser, the text includes a number of semiconductor device modelling examples and in some cases compares their simulation performance with conventional behavioural device models. Copyright (c) 2016 John Wiley Sons, Ltd.
author_names: Mike Brinson

Vadim Kuznetsov
title: A new approach to compact semiconductor device modelling with Qucs Verilog A analogue module synthesis
year: 2016

abstract: In this paper, concepts of mathematics and computer science were applied to electronics engineering field, specifically very large scale integration (VLSI) design and semiconductor industry. Presently one of the major challenges faced by the semiconductor industry is continuously growing leakage current with technology scaling. Transistor is the smallest structural unit of any chip or semiconductor device. Subthreshold leakage current is known as one of the most dominant leakage current components of transistor. In this paper, mathematical relationship between transistor structure and subthreshold leakage current was found. An algorithm was designed for automatic tracking of the transistor structure. Simulation setup was formed by applying some mathematical formula on the outputs of the algorithm. Results of TCAD software simulation were found to be very close to a well known mathematical formula. As complementary metal oxide semiconductor (CMOS) is the most popular technology for semiconductor device fabrication in present days, the same was used for simulation purpose.
author_names: D Mukherjee

B V Ramana Reddy
title: Algorithm design, software simulation and mathematical modelling of subthreshold leakage current in CMOS circuits
year: 2018

abstract: the output voltage from the sustainable energy like photovoltaic (PV) arrays and fuel cells will be at less amount of level. This must be boost considerably for practical utilization or grid connection. A conventional boost converter will provides low voltage gain while Quadratic boost converter (QBC) provides high voltage gain. QBC is able to regulate the output voltage and the choice of second inductor can give its current as positive and whereas for boost increases in the voltage will not able to regulate the output voltage. It has low semiconductor device voltage stress and switch usage factor is high. Analysis and design modelingof Quadratic boost converter is proposed in this paper. A power with 200 W is developed with 12 V input voltage and yield 60 V output voltage and the outcomes are approved through recreation utilizing MATLAB/SIMULINK MODEL. Keywords Quadratic Boost converter (QBC) Photovoltaic (PV) DC DC converter.
author_names: Surya Prabha
title: Mathematical modelling and Performance analysis of Quadratic Boost Converter
year: 2018

abstract: The aim of the proposed paper is discussing problematics related to the thermal modelling of power electronic components. More in detail, the electro thermal relationship is investigated for the selected power diode, while analysis shall serve for system optimization considering thermal performance with the use of highly accurate 3D simulation model. The presented approach describes the procedure of the simulation model development, whereby the main part is discussing necessities relevant for material property identification through the indirect procedure, i.e, material properties are not known from the manufacturer. Electro thermal dependencies are defined within the proposed model, while this model enables parametric changes of the geometrical properties of the device. Added value of this procedure is the possibility of its use in exact determination of the lifetime of a semiconductor component using mathematical models taking into account operational variables (current, voltage, temperature, etc. The proposed model is verified and validated through thermovision experimental measurements within defined operational conditions.
author_names: Miroslav Pavelek

Michal Frivaldsky

Peter Sojka

Jan Morgos
title: Electro Thermal Modelling and Experimental Verification of Power Semiconductor Diode
year: 2020

abstract: Overview and physical equations. Overview of device modelling. Quantum mechanics. Equilibrium thermodynamics and statistical mechanics. Density of states and applications 1. Density of states and applications 2. The transport equations and the device equations. Mathematical and numerical methods. Basic approximation and numerical methods. Fermi and associated integrals. The upwinding method. Solution of equations: the Newton and reduced method. Solution of equations: the phaseplane method. Solution of equations: the multigrid method. Approximate and numerical solutions of the Schrodinger equation. Genetic algorithms and simulated annealing. Grid generation.
author_names: Eric A B Cole
title: Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming
year: 2009

abstract: A mathematical model describing the coupling of electrical, optical and thermal effects in semiconductor lasers is introduced. Through a systematic asymptotic expansion, the governing system of differential equations is reduced to a single second order boundary value problem. This highly nonlinear equation describes the time independent maximum temperature in the boundary layer adjacent to the mirror facet. The solution of the problem is a multi valued function of current. The graph of the maximum steady state temperature as a function of current gives a fold shaped response curve, which indicates that no bounded steady state exists beyond a critical value of current. For certain device parameters and initial conditions, thermal runaway occurs. A mechanism for the sudden mode of semiconductor laser failure is described in terms of thermal runaway.
author_names: W R Smith
title: Mathematical modelling of thermal runaway in semiconductor laser operation
year: 2000

abstract: Fermi integrals arise in the mathematical and numerical modelling of microwave semiconductor devices. In particular, associated Fermi integrals involving two arguments arise in the modelling of HEMTs, in which quantum wells form at the material interfaces. The numerical evaluation of these associated integrals is time consuming. In this paper, these associated integrals are replaced by simpler functions which depend on a small number of optimal parameters. These parameters are found by optimizing a suitable cost function using a genetic algorithm with simulated annealing. A new method is introduced whereby the transition probabilities of the simulated annealing process are based on the Bose Einstein distribution function, rather than on the more usual Maxwell Boltzmann statistics or Tsallis statistics. Results are presented for the simulation of a four layer HEMT, and show the effect of the approximation for the associated Fermi integrals. A comparison is made of the convergence properties of the three different statistics used in the simulated annealing process. Copyright (c) 2007 John Wiley Sons, Ltd.
author_names: Eric A B Cole
title: Integral evaluation in semiconductor device modelling using simulated annealing with Bose Einstein statistics
year: 2007

abstract: Fermi integrals arise in the mathematical and numerical modelling of microwave semiconductor devices. In particular, associated Fermi integrals involving two arguments arise in the modelling of HEMTs, in which quantum wells form at the material interfaces. The numerical evaluation of these associated integrals is time consuming. In this paper, these associated integrals are replaced by simpler functions which depend on a small number of optimal parameters. These parameters are found by optimizing a suitable cost function using a genetic algorithm with simulated annealing. A new method is introduced whereby the transition probabilities of the simulated annealing process are based on the Bose Einstein distribution function, rather than on the more usual Maxwell Boltzmann statistics or Tsallis statistics. Results are presented for the simulation of a four layer HEMT, and show the effect of the approximation for the associated Fermi integrals. A comparison is made of the convergence properties of the three different statistics used in the simulated annealing process. Copyright (c) 2007 John Wiley Sons, Ltd.
author_names: Eric A B Cole
title: Integral evaluation in semiconductor device modelling using simulated annealing with Bose Einstein statistics: Research Articles
year: 2007

abstract: In this paper mathematical and computational aspects of device modelling are treated. Four main subjects are discussed; the analytical model, the discretizations, the non linear and the linear systems of equations. On the one hand the most commonly used numerical techniques are described; on the other hand several new techniques are presented. Noteworthy new techniques are the generalized upwind box scheme and the mixed variable approach. Aspects such as the choice of variables and the singularly perturbed nature of the problem are treated. Properties of the matrices involved are presented in a systematic way. Throughout the paper a standard one dimensional diode is used to illustrate the concepts involved. Finally several realistic two dimensional examples are given.
author_names: S J Polak

Cornelis den Heijer

Wha Wil Schilders

Peter A Markowich
title: Semiconductor device modelling from the numerical point of view
year: 1987