PISCES-2ET and Its Application Subsystems - Stanford Technology ...

DUET Carrier Transport Model
are all defined and can be evaluated from the even part of the distribution function f in the momentum
space ( f 0 in Eq. (2.1) for DUET model), and are thus related to each other. For continuity of
presentation, the expressions for these coefficients are not given here, rather they can be found in
APPENDIX A. We now consider the rates for energy generation g w and loss r w , from which
u w = r w – g w
(2.11)
r w is related to both carrier recombination and energy transferring from carriers to the lattice. At
present, three recombination mechanisms are considered in the model and they are Shockley-Reed-
Hall (SRH), Auger, and radiative recombinations. For g w , only the impact ionization, which is the
inverse process of Auger recombination, is taken into account 1 . With all relevant mechanisms
identified, we are able to list the complete set of equations for the DUET model and their auxiliary
expressions as follows:
Poisson’s equation:
+ –
∇⋅ (–
ε∇ψ)
= q( p – n + N D – N A )
where dielectric constant, ε , is not to be confused with carrier kinetic energy, ε .
(2.12)
Carrier continuity equations:
∂n
-----
∂t
1
--∇ ⋅ j
q n – u
∂p 1
----- = –--∇ ⋅ j
∂t q p – u
where u is the net recombination rate of electron-hole pairs.
=
(2.13)
(2.14)
Carrier (kinetic) energy balance equations:
∂w
-------- n
= – ∇ ⋅ s
∂t
n + j n ⋅ E n – u wn
(2.15)
1. Thus, photo-generation as discussed in Section 3.3.2 applies only to the conservation of carrier
population.
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 9