NDLI: The Role of Semiconductor Device Diameter and Energy-Band Bending in Convergence of Picard Iteration for Gummel's Map

Content Provider	IEEE Xplore Digital Library
Author	Jerome, J.W.
Copyright Year	1982
Abstract	Steady-state semiconductor-device simulation is studied. A mathematical analysis of the so-called Lipschitz constant of the Gummel map, in the Slotboom variables, is given in terms of the device diameter d and the band-bending. This constant is directly related to the convergence of Picard iteration, within a convex, compact solution set, determined by the steady state, Van Roosbroeck system maximum principles. Allowing for specified gradient singularities, of order cr /sup -1/2/, we obtain an asymptotic dependence of d /sup 5/2/ as d -> 0. Functions of sup-inf boundary values of the data also appear, particularly as related to doping concentrations, in the representation of the band-bending. For simplicity, constant mobilities and zero recombination are assumed, at thermodynamic equilibrium. The setting is general, but motivated by FET devices. For micron devices at room temperature, convergence and unique solutions are expected up to, perhaps, band-bending of 0.42 /sup -2/3/ log c(kT) electronvolts in width across the intrinsic energy level. The definition of the Gummel map used herein employs the potential equation as a fractional step, based upon given values of the Slotboom variables. The continuity equations are then solved for the values associated with the Gummel map. The condition given for convergence of Picard iteration also guarantees uniqueness of solutions of the device model for prescribed doping and contact conditions. Finally, the constant c is estimated on the basis of heuristic considerations.
Sponsorship	IEEE Council on Electronic Design Automation IEEE Circuits and Systems Society
Starting Page	489
Ending Page	495
Page Count	7
File Size	991291
File Format	PDF
ISSN	02780070
Volume Number	4
Issue Number	4
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1985-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Semiconductor devices Convergence Steady-state Doping Equations Mathematical analysis Radiative recombination Spontaneous emission Thermodynamics FETs
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Electrical and Electronic Engineering Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

The role of semiconductor device diameter and energy-band bending in convergence of Picard iteration for Gummel's map

Investigation into the properties of the explicit method for the resolution of the semiconductor device equations

Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling

Fast and simple method for calculating the minority-carrier current in arbitrarily doped semiconductors

A method for generating structurally aligned grids for semiconductor device simulation

A new preconditioner for CGS iteration in solving large sparse nonsymmetric linear equations in semiconductor device simulation

An explicit method of numerical integration for the complete set of semiconductor device equations

Simulation and modeling of p-n-p-n optical switches

SIERRA: a 3-D device simulator for reliability modeling

The Role of Semiconductor Device Diameter and Energy-Band Bending in Convergence of Picard Iteration for Gummel's Map

Similar Documents

The role of semiconductor device diameter and energy-band bending in convergence of Picard iteration for Gummel's map

Investigation into the properties of the explicit method for the resolution of the semiconductor device equations

Rigorous thermodynamic treatment of heat generation and conduction in semiconductor device modeling

Fast and simple method for calculating the minority-carrier current in arbitrarily doped semiconductors

A method for generating structurally aligned grids for semiconductor device simulation

A new preconditioner for CGS iteration in solving large sparse nonsymmetric linear equations in semiconductor device simulation

An explicit method of numerical integration for the complete set of semiconductor device equations

Simulation and modeling of p-n-p-n optical switches

SIERRA: a 3-D device simulator for reliability modeling

The Role of Semiconductor Device Diameter and Energy-Band Bending in Convergence of Picard Iteration for Gummel's Map