Measurements

Chapter A: Algebraic Description of the Multiple Trapping Model
written as
E d (t) = E V + kT ln(νt),
(A.2)
where kT is the temperature in energy units and ν an attempt-to-escape frequency.
It has been shown by Tiedje, Rose, Orenstein, and Kastner that at any time prior
to the transit time and in the absence of recombination the carrier distribution is
determined by the demarcation energy as
∫+∞
g 0 · exp ( − E
N = F(t)
1 + exp ( ) dE. (A.3)
E−E d
kT
−∞
∆E V
)
where F(t) is an occupation factor which acts to conserve the excitation density
N. For the occupancy factor F(t) one derives
F(t) =
N
kT 0 g 0
sin(απ)
απ (νt)α , (A.4)
where α = kT/∆E V , while the time dependent drift mobility can be written as
n(t)
µ(t) ≡ µ 0
N = µ N V
0 · sin(απ)
kT 0 g 0 απ (νt)−1+α , (A.5)
where N V is the effective density of states at the mobility edge, n(t) is the density
of mobile charge carriers, and µ 0 is their mobility. Since µ(t) is defined as
µ(t) = ¯v(t)
F ,
(A.6)
where v(t) is the mean drift-velocity and F is the electric field, one can find the
displacement L(t) by integration:
L(t)
F
= N V
· sin(απ)
kTg 0 απ
( µ0
)
(νt) α
ν
Using Eq. A.1, the effective DOS in the valence band can be written as
N V =
∫ 0
−∞
( E
)
g(E) · exp
kT
(A.7)
(A.8)
For kT < ∆E V and assuming that the integral is dominated by an exponential region
of g(E) below E V one obtains for N V
N V = kTg 0
1 −
∆E kT .
V
(A.9)
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