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3.3.4.2 The Ohmic Contact: Thermal Treatment

In an electro-thermal simulations two thermal boundary conditions can be applied. The first is the condition of a thermal resistance where the energy flux $ \mathbf{S_n}$ through the Ohmic contact is determined using:

    $\displaystyle \mathbf{n} \cdot \mathbf{S_n} = \frac{{\it T}_\mathrm{L}-{\it T}_\mathrm{C}}{R_{TH}}$ (3.108)

i.e., the fluxes are proportional to the temperature gradient. $ R_{TH}$ represents a global thermal resistance of materials surrounding the device, and $ {\it T}_\mathrm{C}$ the contact temperature, i.e. the temperature of the heat reservoir assumed. If the thermal resistance $ R_{TH}$ is set to zero, an isothermal boundary condition is applied:
    $\displaystyle {\it T}_\mathrm{C}={\it T}_\mathrm{L}$ (3.109)

For a macroscopic definition of $ R_{TH}$, see Chapter 6. For the drift-diffusion transport model, similar to the semiconductor-semiconductor interface, the following entries are supplied:
    $\displaystyle \frac{\mathbf{J_n}}{q} \cdot \big( \Delta E_C + \varphi_m \big) + \frac{\mathbf{J_p}}{q}\cdot \big( \Delta E_V+ \varphi_m \big) = $div$\displaystyle _{A} \mathbf{S_L}$ (3.110)

For the hydrodynamic case the thermal heat flow is accounted for self-consistently.


next up previous
Next: 3.3.4.3 Schottky Contact Up: 3.3.4 Semiconductor-Metal Interfaces: The Previous: 3.3.4.1 The Ohmic Contact:
Quay
2001-12-21