Abstract
The numerical modelling of devices involves the solution of sets of coupled partial differential equations, which in turn involve the solution of simultaneous nonlinear equations after discretisation has taken place. It is not possible in a single paper to fully describe all the numerical techniques involved in this process, and in this paper we will concentrate on the finite difference approach. Descriptions of the Finite Element method (Selberherr 1984, Mobbs 1989), the Boundary Element method and the Multigrid method (Ingham 1989) can be found elsewhere. Motivation for considering certain techniques will be given by examining the equations involved in the modelling of a two-dimensional MESFET. Finite differences are introduced in section 2, the solution of simultaneous equations discussed in section 3, and the discretisation of the current continuity equations and energy equation discussed in section 4. In section 5 we give details of the implementation for the case of the MESFET , and for a one-dimensional p-n junction. Finally in section 6 we discuss parameter determination.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barton T (1989) Computer simulations. Semiconductor device modelling (Snowden CM ed, Springer-Verlag, London, Berlin): 227–247
Broyden CG (1972) in Numerical methods for unconstrained optimisation (Murray W ed., Academic Press, New York )
Clarke ME (1989) Equivalent circuit models for silicon devices. Semiconductor device modelling (Snowden CM ed.,Springer-Verlag, London, Berlin ):128–142
Curtis A and Reid JK (1974) The choice of step-length when using differences to approximate Jacobian matrices. J Inst Math Appl 13:121–126
de Graaff HC and Klaassen FM (1990) Compact transistor modelling for circuit design. Springer-Verlag, Wien, New York
De Mari A (1968) An accurate numerical steady-state one-dimensional solution of the p-n junction. Solid State Electronics 11:33–58
Doganis K and Scharfetter DL (1983) General optimisation and extraction of IC device model parameters. IEEE Trans ED-30: 1219–1228
Feng YK and Hintz A (1988) Simulation of submicrometer GaAs MESFETs using a full dynamic transport model. IEEE Trans ED-35: 1419–1431
Hildebrand FB (1956) Introduction to numerical analysis. McGraw-Hill, New York, Toronto, London
Ingham DB (1989) Numerical techniques - finite difference and boundary element method. Semiconductor device modelling (Snowden CM ed., Springer-Verlag, London, Berlin):34–48
Jesshope CR (1979) Comp Phys Comm 17:383–391
Kurata M (1982) Numerical analysis for semiconductor devices. Lexington Books, Lexington, Toronto
McAndrew CC, Singhal K and Heasell EL (1985) A consistent nonisothermal extension of the Scharfetter-Gummel stable difference approximation. IEEE ED Lett EDL6:446–447
Mobbs SD (1989) Numerical techniques - the finite element method. Semiconductor device modelling (Snowden CM ed., Springer-Verlag, London, Berlin):49–59
Press WH, Flannery BP, Teukolsky SA and Vetterling WT (1986) Numerical Recipes. Cambridge University Press, Cambridge, London, New York
Reiser M (1972a) Large-scale numerical simulation in semiconductor device modelling. Computer Methods in App Mech and Eng 1:17–38
Reiser M (1972b) A two-dimensional numerical FET model for dc- ac- and large signal analysis. IBM Research J, April, RZ499
Scharfetter DL and Gummel HK (1969) Large signal analysis of a silicon Read diode oscillator. IEEE Trans ED-16: 64–77
Scraton RE (1987) Further numerical methods. Edward Arnold, London, Baltimore
Selberherr S (1984) Analysis and simulation of semiconductor devices. Springer-Verlag, Vienna, New York
Smith GD (1985) Numerical solution of partial differential equations: finite difference methods. Clarendon Press, Oxford
Snowden CM(ed) (1988) Semiconductor device modelling. Peter Peregrinus,London
Snowden CM and Loret D (1987) Two-dimensional hot electron models for short-gate-length GaAs MESFETs. IEEE Trans ED-34: 212–223
Stern F (1970) Iteration methods for calculating self-consistent fields in semiconductor inversion layers. J Comp Phys 6:56–67
Stern F and Das Sarma S (1984) Electron energy levels in GaAs-Ga1−x AlxAs heterojunctions. Phys Rev B30:840–848
Stoer J and Bulirsch R (1980) Introduction to numerical analysis. Springer-Verlag, New York
Stone HL (1968) Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J Num Anal 5:530–558
Tang T-W (1984) Extension of the Scharfetter-Gummel algorithm to the energy balance equation. IEEE Trans ED-31:1912–1914
Varga RS (1962) Matrix iterative algebra. Prentice Hall Inc, New Jersey
Wang S-J, Lee J-Y and Chang C-Y (1986) An efficient and reliable approach for semiconductor device parameter extraction. IEEE Trans CAD-5:170–179
Ward DE and Doganis K (1982) Optimised extraction of MOS model parameters. IEEE Trans CAD-1:163–168
Wilkinson JH and Reinsch C (1971) Handbook for automatic computation, vol 2. Springer-Verlag, Berlin
Xue H, Howes MJ and Snowden CM (1991) The modified semiconductor equations and associated algorithms for physical simulation. Int J Num Modelling: Electronic Networks, Devices and Fields 4:107–122
Young DM (1971) Iterative solution of large linear systems. Academic Press, New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag London Limited
About this chapter
Cite this chapter
Cole, E.A.B. (1993). Numerical Methods and their Application to Device Modelling. In: Snowden, C.M., Miles, R.E. (eds) Compound Semiconductor Device Modelling. Springer, London. https://doi.org/10.1007/978-1-4471-2048-3_1
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2048-3_1
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2050-6
Online ISBN: 978-1-4471-2048-3
eBook Packages: Springer Book Archive