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

DUET Carrier Transport Model
κ n
=
nk B T n µ n P
(2.23)
κ p
= pk B T p µ p P
(2.24)
It is apparent that the carrier mobility, µ, is the key parameter to other transport coefficients, and the
mobility can be obtained either from the theoretical calculation or more often through empirical or
semi-empirical formulation by fitting the analysis/simulation results to the experimental data. We will
discuss in a great detail the mobility modeling in CHAPTER 3. Finally, the rate of net loss of carrier
kinetic energy is modeled as follows:
3
3
u wn = -- ( u
2 SRH + u rad )k B T n – ( u n, Auger – g nimp , ) E g ( T L ) + --k
2 B T p –
3
w
--g k
2 B T n ( T n ) – w n ( T L )
n – ----------------------------------------
pimp ,
τ wn
(2.25)
3
3
u wp = --( u
2 SRH + u rad )k B T p – ( u p, Auger – g pimp , ) E g ( T L ) + --k
2 B T n –
3
w
--g k
2 B T p ( T p )–
w p ( T L )
p – -----------------------------------------
nimp ,
τ wp
(2.26)
where u SRH , u rad , and u Auger are net carrier loss rates due to SRH, Auger, and radiative
recombinations, respectively, g imp is the generation rate due to the impact ionization (II). Note that for
both Auger recombination and II, we need to distinguish if they are caused by electrons or holes. The
last term on RHS of each above expression represents the energy exchange between the carriers and
lattice.
A special case for the above general description (Eqs. (2.15)-(2.17)) is when only the lattice
temperature is of concern, i.e., the carriers can be considered to have the same temperature as the
lattice. Such a scenario is often encountered in, say, the simulation of power devices. We can then lump
Eqs. (2.15)-(2.17) by requiring all temperatures being the same (designated T) and need to solve the
following thermal diffusion equation only.
∂ 3
----- c (2.27)
∂t L + --( n+
p)k ⎝
⎛ 2
B ⎠
⎞ T = ∇ ⋅ ( κL ∇T – s – s ) + j n p n ⋅ E n + j p ⋅ E p + u SRH E g ( T )
Together with Poisson’s (Eq. (2.12)) and carrier continuity equations (Eqs. (2.13)-(2.14)), these four
equations are solved for four state variables: ψ, n, p, and T (for both lattice and carriers).
PISCES-2ET – 2D Device Simulation for Si and Heterostructures 11