Two-dimensional carrier flow in a transistor structure under nonisothermal conditions

A two-dimensional mathematical model is developed to predict the internal behavior of power transistors operating under steady-state conditions. This model includes the internal self-heating effects in power transistors and is applicable to predict the transistor behavior under high-current and high-voltage operating conditions. The complete set of partial differential equations governing the bipolar semiconductor device behavior under nonisothermal conditions is solved by numerical techniques without assuming internal junctions and other conventional approximations. Input parameters for this model are the dimension of the device, doping profile, mobility expressions, generation-recombination model, and the boundary conditions for external contacts. Computer results of the analysis of a typical power transistor design are presented for specified operating conditions. The current density, electrostatic potential, carrier charge density, and temperature distribution plots within the transistor structure illustrate the combined effect of the electrothermal interaction, base conductivity modulation, current crowding, base pushout, space charge layer widening, and current spreading phenomena in power transistors.

[1]  S. Gaur,et al.  Transistor design and thermal stability , 1973 .

[2]  H. Gummel,et al.  Large-signal analysis of a silicon Read diode oscillator , 1969 .

[3]  R. Stratton,et al.  Semiconductor current-flow equations (diffusion and degeneracy) , 1972 .

[4]  D. C. Agouridis,et al.  The cutoff frequency falloff in UHF transistors at high currents , 1966 .

[5]  A. De Mari,et al.  An accurate numerical steady-state one-dimensional solution of the P-N junction , 1968 .

[6]  M. Sánchez.  Carrier heating or cooling in semiconductor devices , 1973 .

[7]  W. L. Engl,et al.  High injection in a two-dimensional transistor , 1974 .

[8]  D. Tremere,et al.  Current gain and cutoff frequency falloff at high currents , 1969 .

[9]  Martin Reiser,et al.  Computing methods in semiconductor problem , 1973, Computing Methods in Applied Sciences and Engineering.

[10]  J. Slotboom,et al.  Computer-aided two-dimensional analysis of bipolar transistors , 1973 .

[11]  G. A. Slack,et al.  Thermal Conductivity of Silicon and Germanium from 3°K to the Melting Point , 1964 .

[12]  R. Hall.  Electron-Hole Recombination in Germanium , 1952 .

[13]  R. E. Thomas,et al.  Carrier mobilities in silicon empirically related to doping and field , 1967 .

[14]  C. T. Kirk,et al.  A theory of transistor cutoff frequency (fT) falloff at high current densities , 1962, IRE Transactions on Electron Devices.

[15]  H. Gummel.  A self-consistent iterative scheme for one-dimensional steady state transistor calculations , 1964 .

[16]  A Two-Dimensional Numerical Analysis of a , 1973 .

[17]  J. Early.  Effects of Space-Charge Layer Widening in Junction Transistors , 1952, Proceedings of the IRE.

[18]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[19]  Thomas I. Seidman,et al.  Iterative scheme for computer simulation of semiconductor devices , 1972 .

[20]  N. H. Fletcher,et al.  Some Aspects of the Design of Power Transistors , 1955, Proceedings of the IRE.

[21]  C A Hogarth,et al.  Introduction to Semiconductor Physics , 1965 .

[22]  David P. Kennedy,et al.  Analysis of the Impurity Atom Distribution Near the Diffusion Mask for a Planar p-n Junction , 1965, IBM J. Res. Dev..

[23]  W. Read,et al.  Statistics of the Recombinations of Holes and Electrons , 1952 .

[24]  M. S. Mock,et al.  Transport equations in heavily doped silicon, and the current gain of a bipolar transistor , 1973 .

[25]  Raya Mertens,et al.  Transport equations in heavy doped silicon , 1973 .

[26]  R. J. Lomax,et al.  Semiconductor Device Simulation , 1974 .

[27]  P. D. Maycock,et al.  Thermal conductivity of silicon, germanium, III–V compounds and III–V alloys , 1967 .

[28]  J. L. Wirth,et al.  The Analysis of Radiation Effects in Semiconductor Junction Devices , 1967 .

[29]  D. H. Navon,et al.  Effect of non-uniform emitter current distribution on power transistor stability☆ , 1970 .