602
22 Light-to-Electricity Conversion
Fig. 22.16 NEP as a
function of the resistance
R eq for a Si photodiode.
From [1838]
10
-10
10
10
10
10
10
-11
-12
-13
-14
-15
R ( )
eq
10
10
3
10
5
10
7
10
9
10
11
D
I =10µA
B
I =10µA
B
I =10nA
B
I =100nA
B
I =1nA
B
I =0
B
22.3.3 Pin Photodiodes
The depletion layer in pn-diodes is relatively thin such that the incident light is not completely absorbed.
An almost complete absorption of light can be achieved by using a thick intrinsic absorption layer. The
field in the intrinsic region is constant or slowly varying linearly (Fig. 21.72). The generation rate per
unit area decreases exponentially following the Lambert-Beer law (9.16) as shown in Fig. 22.17c:
G(x) = G 0 exp(−α x) .
(22.30)
The initial generation rate G 0 = 0 α is given by the incident photon flux per unit area 0 and the
reflectance of the surface R as 0 = P opt (1 − R)/(Ahν).
The drift current in the i-region collects all those carriers (if recombination in the depletion layer is
neglected). The electron drift current is given by
j dr = −e
w
0
G(x) dx = e 0
1 − exp(−α w)
,
(22.31)
with w being the thickness of the depletion layer that is approximately the same as the thickness of the
i-region. In the bulk (neutral) region (x > w) the minority-carrier density is determined by drift and
diffusion
7 (10.78). The diffusion current density at x = w is thus given by
j diff = e 0 exp(−α w)
α L p
1 + α L p
+ e p n 0
D p
L p
.
(22.32)
The first term is due to the diffusion current of photo-generated carriers (10.78), the second term due
to thermally generated carriers (21.133). The total current j tot = j diff + j dr is given by
7 At the edge of the depletion layer, x = w, all photo-generated carriers are transported away instantly, thus the excess
carrier density from photo-generated carriers is zero there and (10.78) applies.
22 Light-to-Electricity Conversion
Fig. 22.16 NEP as a
function of the resistance
R eq for a Si photodiode.
From [1838]
10
-10
10
10
10
10
10
-11
-12
-13
-14
-15
R ( )
eq
10
10
3
10
5
10
7
10
9
10
11
D
I =10µA
B
I =10µA
B
I =10nA
B
I =100nA
B
I =1nA
B
I =0
B
22.3.3 Pin Photodiodes
The depletion layer in pn-diodes is relatively thin such that the incident light is not completely absorbed.
An almost complete absorption of light can be achieved by using a thick intrinsic absorption layer. The
field in the intrinsic region is constant or slowly varying linearly (Fig. 21.72). The generation rate per
unit area decreases exponentially following the Lambert-Beer law (9.16) as shown in Fig. 22.17c:
G(x) = G 0 exp(−α x) .
(22.30)
The initial generation rate G 0 = 0 α is given by the incident photon flux per unit area 0 and the
reflectance of the surface R as 0 = P opt (1 − R)/(Ahν).
The drift current in the i-region collects all those carriers (if recombination in the depletion layer is
neglected). The electron drift current is given by
j dr = −e
w
0
G(x) dx = e 0
1 − exp(−α w)
,
(22.31)
with w being the thickness of the depletion layer that is approximately the same as the thickness of the
i-region. In the bulk (neutral) region (x > w) the minority-carrier density is determined by drift and
diffusion
7 (10.78). The diffusion current density at x = w is thus given by
j diff = e 0 exp(−α w)
α L p
1 + α L p
+ e p n 0
D p
L p
.
(22.32)
The first term is due to the diffusion current of photo-generated carriers (10.78), the second term due
to thermally generated carriers (21.133). The total current j tot = j diff + j dr is given by
7 At the edge of the depletion layer, x = w, all photo-generated carriers are transported away instantly, thus the excess
carrier density from photo-generated carriers is zero there and (10.78) applies.