Page 244 - Organic Electronics in Sensors and Biotechnology

An Intr oduction to Or ganic Photodetectors 221

The rise time and cutoff frequency are closely related as can be
seen from the following analysis. The current i generated by the pho-
todiode is divided into two parts i and i that flow through the inter-
c RL
nal capacitance and the external load resistor, respectively (inset to
Fig. 6.15):
i = i + i (6.26)
C RL

(Here, we are assuming R << R and so we can ignore the negligible
L SH
current that flows through the shunt resistance.) The photodiode and
load resistor are connected in parallel and are consequently subjected
to the same potential difference, allowing us to write
iZ = i R (6.27)
C C RL L
where Z = 1/(2πjfc) is the complex impedance of the capacitance.
C
Hence, we can write
i
c =
2π jfC iR L (6.28)
RL
from which it follows that

i = i 2π jfCR (6.29)
C R L
Substituting into Eq. (6.26), we obtain

i = 1 → i | | = 1 (6.30)
+
RL 12π jfCR RL 1 ( fCR) 2
+ 2π
The 3 dB cutoff frequency f occurs when the signal falls by a factor 2,
C
i.e., when 2πfCR = 1 Æ f = 1/(2πCR). Hence, in the RC-limited regime,
L
the rise time and the cutoff frequency are related by
ln9 . 035
Δt = RCln9 = = (6.31)
r 2π f f
C C

6.4.3 Intrinsic Photodiode Noise Characteristics

Thermal Noise
Above we discussed how photodiodes can be modeled as a current
generator in parallel with a diode, a shunt resistor, and a capacitor. In
the immediate vicinity of V = 0, the slope of the current-voltage curve
is linear, meaning it is possible to drop the diode from the equivalent
circuit representation and use the shunt resistance alone to account