Page 48 - Photonics Essentials an introduction with experiments

Photodiodes

42 Photonic Devices

The same procedure can be followed to calculate the current carried
by holes. The total current is obtained by adding together the two ex-
pressions. In practice, it is almost always the case that the diode is
doped much more heavily on one side than the other. Low doping on
one side of a photodiode is necessary to keep the capacitance low and
the breakdown voltage suitably large. In this case we will assume
2
that n n p p . Then it follows that n p p n . (Use n n p n = n i to confirm
this). Therefore,
D e
J TOT J n = q [n p (e qV A /kT – 1) – G L e ] (3.13)
L e
Finally, we can simplify this expression by noting the following re-
lationships:
2 2
n i n i
n p = = ; and D e e = L e 2
p p N a
2
qD e n i
J TOT = [e qV A /kT – 1] – qL e G L
L e N a

Regular I–V Current from photons (3.14)
Illuminating the photodiode with a flux of photons with energy
greater than the band gap will create an excess minority carrier flux
of G L L e . Equation 3.14 shows that the photodiode current will be lin-
early proportional to this flux. Since no approximations were neces-
sary to derive this result, we can expect the linear relationship to hold
over many orders of magnitude of photon flux. This result is key to
the performance of photodiode detectors. The linear photodetection
response can be compared to the dependence of the photodiode cur-
rent on an applied voltage. The current–voltage relationship is quite
nonlinear. A second, equally important result is that the photodiode
response to a photon flux is independent of the bias voltage on the pho-
todiode.
Equation 3.14 shows that the photodiode response to a photon flux
is superimposed on the current–voltage equation. When the diode is
forward biased, the forward current will soon exceed the photocur-
rent. While the photocurrent is independent of the bias voltage, it
may be swamped by the conventional forward diffusion current of the
diode, resulting from the applied bias. On the other hand, in reverse
bias of a few volts, the result is:

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