


[Contents]  [Index] 
Collaborator: H. Gajewski , H. Stephan
Cooperation with: G. Wachutka, W. Kaindl (Technische Universität München)
Supported by: DFG: ``Physikalische Modellierung und numerische Simulation von Strom und Wärmetransport bei hoher Trägerinjektion und hohen Temperaturen'' (Physical modeling and numerical simulation of current and heat transport at high carrier injection and high temperatures) [2]
Description:
In 2002 our model [1], describing heat and carrier transport for semiconductor devices, has been advanced to silicon carbide (SiC). SiC is used in different crystal configurations (6HSiC, 4HSiC, 3CSiC). Each of these materials possesses promising properties as basic materials for highpower, hightemperature and highfrequency electronics. The reason for this are special physical characteristics, which distinguish SiC from conventional semiconductor materials such as silicon. Those are first of all:
Deriving the system of nonlinear partial differential equations for the heat and carrier transport in semiconductor devices, we abided by the following physical principles:
The postulated system of equations
describes electron, hole and energy transfer, which is nonlinearly coupled by the electrostatic potential via Poisson's equation. Here, n, p and u are electron, hole and power density, J_{n}, J_{p} and J_{u} the appropriate currents, D the dopants and G the generationrecombination rate. (The ODEs describing the dynamics of electron/hole traps were described in detail in the WIAS Annual Research Report 1998.)The determination of the equilibrium as state of maximal entropy by Lagrange's method suggests the Lagrange multipliers , and to be thermodynamic potentials. Their gradients are the driving forces for the currents. That leads to the following current, under consideration of Onsager's principle:
In the case of the anisotropic SiC, , and , and a_{nu}, a_{np} and a_{u} are matrices. From the second law of thermodynamics (entropy S increasing in time) (here d denotes the dissipation rate) it follows for the currents with and the energy carrier interaction terms ( is the heat conductivity) For this model, thermodynamically consistent algorithms were developed and implemented into our program system WIASTeSCA .
As an example we show a 6HSiC DIMOS transistora
typical highpower device ([4]). The
crystal is oriented in such a way that the electron
mobility in horizontal direction is five times higher than in the
vertical direction. Figure 2 shows the electron flow for a gate
voltage of 12 V and a drain voltage of 30 V. In comparison, Figure 3
shows the simulation result for isotropic mobility (e.g., in Si).
References:



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