4.1 Volume Models
 
In all semiconductor segments Poisson's equation and the continuity equation for each simulated carrier type have to be solved. Poisson's equation, derived from the third Maxwell equation, reads:
 

,

(16)

 
where  is the total electric charge density,  denotes the displacement vector, q is the electronic charge, n and p are the electron and hole concentrations,  and  are the concentrations of ionized donors and acceptors, and  is the concentration of ionized deep traps.

The continuity equation for electrons and holes can be derived taking the zero order momentum of the Boltzmann equation [44, 45]:
 

(17)

 

.

(18)

 
Taking the first order momentum, the Boltzmann equation yields the current densities for electron and holes:
 

(19)

 

.

(20)

Here, N_C and N_V are the effective densities of states in the conduction and valence band respectively, E_C and E_V denote the conduction and the valence band edges, and µ_n and µ_p are the mobilities of electrons and holes, respectively. These parameters account for different materials. k_B is the Boltzmann constant. If the temperature T_n of electrons and T_p of holes are constant, i. e. equal to the lattice temperature, (19) and (20) reduce to the equations for drift diffusion. For a hydrodynamic model T_n and T_p have to be taken into account. In this case the energy transport equations obtained from the second order momentum of the Boltzmann equation
 

(21)

 
and
 

(22)

 
have to be added, where
 

(23)

 
and
 

(24)

 
are the energy fluxes for electrons and holes,  and  are the energy relaxation times, and and are the energy of electrons and holes, respectively [6]. At room temperature the drift kinetic energy of the carriers is relatively low compared to the random kinetic energy of the carriers and can be neglected. Therefore the approximation
 

(25)

 
for the carrier energy can be used. According to the Wiedemann­Franz law the thermal conductivities of electrons and holes are calculated by
 

.

(26)

 

• 4.2 Interface Models
• 4.2.1 Semiconductor Hetero Interfaces
• 4.2.2 Semiconductor Passivation Interface
• 4.3 Physical Parameters
• 4.3.1 Effective Mass and Band Edge Energy
• 4.3.2 Mobility

   
Next: 4.2 Interface Models Up: 4 Description of the Simulator Previous: 4 Description of the Simulator