For the gate contact in the HEMT two models are commonly used to model
the Schottky contact. The first model for the contact interface
condition for the potential is:

where:

(3.112) |

Thus, the potential at the boundary in the semiconductor is set to the difference of the quasi-Fermi level potential in the metal , which is equal to the potential specified at the contact, and the potential . The latter represents the potential corresponding to the work function difference energy of metal and semiconductor. The applied current equations are:

The currents are proportional to the so-called
recombination velocities and the difference of the
carrier concentration and . The carrier concentrations at the
boundary read:

while the equilibrium concentrations and can be expressed as:

For the Schottky barrier height typical values range between 0.61 eV and 0.8 eV. For the hydrodynamic case the carrier temperatures are fixed, thus thermal equilibrium is assumed similarly to the Ohmic contact. The thermal boundary conditions applied similar to the Ohmic contact, i.e. either by an thermal resistance or a isothermal boundary condition. The model presented so far can also be called a thermionic emission model: The recombination velocity in (3.113) is then to be called a thermionic emission velocity. Inserting (3.115) and (3.117) into (3.113) we obtain:

As stated by Schroeder in [249], (3.119) can thus be written as:

using = - which is already named the Schottky barrier height.
Furthermore we use:

(3.121) |

which says that the work function difference is equal to the difference of the Fermi levels of the semiconductor and the metal. The velocity is rewritten as (see (3.92)):

(3.122) |

where A is the

2001-12-21