Journal of Networks - Academy Publisher

where the ambipolar diffusion coefficient Da isgivenby[20]
Da = 2DnDp
(Dn + Dp)
(66)
We use the boundary conditions of the mixed type. We assume
a finite surface recombination rate s0 on the top surface z =0
which yields [23]
∂n
∂z |z=0 = s0
n (z =0) (67)
Da
On the other hand, a kind of an ohmic contact at the interface
of the layer and the substrate[27] z = d prescribes the
condition
n (z = d) =0 (68)
We are interested in the time-dependent part of the photocarrier
concentration n1 (z, t) which is responsible for the UWB
RF signal detection. Hence we should solve equation (65) with
the boundary conditions (67) and (68). In general case of the
UWB RF signal f (t) we carry out the Fourier transform of
equation (65) with respect to time. We obtain
∂
Da
2N1 (z, ω)
∂z2 −
where
and
�
N1 (z,ω) =
F (ω) =
iω + 1
τ
�∞
−∞
�∞
−∞
�
N1 (z, ω)+g0 (z) F (ω) =0
(69)
n1 (z,t)exp(−iωt) dt (70)
f (t)exp(−iωt) dt (71)
The boundary conditions (67) and (68) can be applied to the
general solution of (69). The result has the form.
N1 (z, ω) =
×{−g0 (z)+ �
1
Laeq
F (ω) τ (1 − iωτ)
� �
1+(ωτ) 2�
� α 2 L 2 aeq − 1
1
�
s0
cosh (d/Laeq)+ sinh (d/Laeq)
Da
� � � �
∂g0 s0
(z − d)
×[ (0) − g0 (0) sinh
∂z Da
Laeq
� � �
1 z
+g0 (d) cosh +
Laeq Laeq
s0
� ��
z
sinh ]} (72)
Da Laeq
where
150 JOURNAL OF NETWORKS, VOL. 5, NO. 2, FEBRUARY 2010
L 2 aeq = Daτ (1 − iωτ)
1+(ωτ) 2
(73)
The expression (72) for N1 (z,ω) averaged over the layer
thickness d can be used as the frequency response of the illuminated
layer when f (t) =δ (t) and consequently F (ω) =
1. Using the explicit expression (58) for g0 (z) we obtain
expression (45).
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