Page 70 - Photonics Essentials an introduction with experiments

Electrical Response Time of Diodes

64 Photonic Devices

bility. For example, in a photodiode made from InGaAs (E g = 0.75 eV,
2
g = 1.6 m), the electron mobility is about 10,000 cm /V-sec, whereas
2
the hole mobility is only 500 cm /V-sec. Therefore, D e = 250 and D h = 12
at room temperature. The minority carrier diffusion length for elec-
trons and holes is similar: L e ~ L h = 4 m. If the photodiode is designed
so that most of the light is incident on and absorbed on the n-side, then
the characteristic diffusion time would be about 20 nanoseconds. If we
design the diode so that most of the light is absorbed on the p-side, then
the diffusion time is much shorter: 600 picoseconds. In a well-designed
photodiode made of direct band gap material, most of the light can be
absorbed in the depletion region so that diffusion operates only on the
uppermost part of the diode required for electrical contact. This region
can easily be reduced in thickness to 0.5 m of p-type material. In this
case, the diffusion response time is shorter still: 10 picoseconds!
Note that the diffusion time depends on the square of the diffusion
length. The diffusion length is the average distance a minority carrier
can move before it recombines with a majority carrier. In a direct band
gap material like InGaAs, this distance is a few microns. For an indi-
rect band gap material, this distance is longer, typically by a factor of
100. The diffusion length is longer because recombination also involves
the participation of phonons. Note that increasing L by 100 means that
is now 10,000 times longer, and the response time required to collect
all the diffusing photo-generated carriers is closer to the microsecond
regime than the picosecond regime.

Example 4.1
A silicon photodiode, produced on an n-type substrate, is uniformly il-
luminated. The diffusion length for minority electrons is 10 –2 cm. The
diffusion length for holes is 5 × 10 –3 cm. The mobility of electrons is
–1
–1
2
2
–1
–1
1000 cm V -sec , whereas the mobility of holes is 500 cm V -sec .
Estimate the diffusion-limited response time.
The pn-junction would be formed by diffusion of p dopants into the
n-type substrate. This depth is typically 1 m or less. Since the thick-
ness of the p region is much less than a diffusion length, we can neg-
lect the contribution of diffusing minority carrier electrons compared
to that of the holes.
kT cm 2
Diffusion constant of holes = D h = h = 0.025 × 500 = 12.5
q sec
Diffusion time = Diffusion time of holes =
–3 2
(5 × 10 ) 25 × 10 –6
= = = 2 × 10 –6 sec
12.5 12.5

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