To account for self-heating effects in semiconductor devices,
the lattice heat flow equation has to be solved.
![$\displaystyle \mathrm{div}(\kappa_L\cdot\mathrm{grad}\,T_\mathrm{L}) = \rho_{\mathrm{L}}\cdot c_{\mathrm{L}}\cdot \frac{\partial T_\mathrm{L}}{\partial t} - H$](img273.png) |
(3.25) |
The coefficients
,
, and
are the mass density, specific heat, and thermal
conductivity of the respective materials.
The model for the heat generation,
, depends on the transport model
employed. In the drift-diffusion case
equals the JOULE heat,
![$\displaystyle H= \mathrm{grad}\left(\frac{\ensuremath{E_\mathrm{c}}}{{\mathrm{q...
...si\right)\cdot{\mathbf{J}}_p + R\cdot(\ensuremath{E_\mathrm{c}}- E_\mathrm{v}),$](img278.png) |
(3.26) |
whereas in the energy transport case the relaxation terms are used
![$\displaystyle H = \frac{3\cdot {\mathrm{k_B}}}{2}\cdot\left( n\cdot\frac{T_n -T...
...{\varepsilon,n}} + p\cdot\frac{T_p -T_\mathrm{L}}{\tau_{\varepsilon,p}}\right).$](img279.png) |
(3.27) |
T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation