22.3 Photodiodes
607
and therefore (with (22.36))
V RT =
e N D
2 s
L
2
− L
2 e N D
s
(V D2 − V 2 )
− V D ,
(22.42)
with V D = (V D1 − V D2 ), vanishing for a symmetric MSM structure. At and after reach-through the
electric field varies linearly from 0 to L within the semiconductor. The point of zero electric field shifts
towards contact 2. At the flat-band voltage this point has reached the contact 2 and the width of the
depletion layer at contact 2 is zero. This condition leads (as long as no breakdown occurred) to
V FB =
e N D
2 s
L
2
− V D .
(22.43)
The maximum electric field is at contact 1 and is given (for V > V FB ) by
E m1 =
V + V FB + 2 V D
L
.
(22.44)
If in a part of the structure the critical field E B for impact ionization is reached (this will be at contact
1, since the field is highest there), the diode breaks down. Therefore the breakdown voltage is given by
V B ≈ E B L − V FB − 2 V D .
(22.45)
The current-voltage characteristic for a Si-MSM structure is shown in Fig. 22.23. At small voltages
only small currents flow since one contact is in reverse bias. The hole current is much smaller than the
electron current. Only those holes that diffuse through the neutral region contribute to the hole current.
After reach-through the barrier φ p2 + V D2 − V 2 for hole injection is strongly reduced that leads to strong
hole injection. Beyond the flat-band voltage the hole current increases only weakly since a lowering of
the barrier occurs only via the Schottky effect. For high fields (V > V FB , before breakdown) the hole
current is
j p1 = A
∗
p T
2 exp
−βφ p2
exp
ββφ p2
= j p,s exp
ββφ p2
,
(22.46)
and the total current is
j = j n,s exp (ββφ n1 ) + j p,s exp
ββφ p2
,
(22.47)
with j n,s = A
∗
n T
2 exp(−βφ n1 ) and j p,s = A
∗
p T
2 exp(−βφ p2 ).
In a MSM photodetector the metal contacts are typically formed in an interdigitated structure on
the semiconductor surface (Fig. 22.24). These contacts shield some of the active area from photons.
An increase in quantum efficiency can be achieved with transparent contacts (e.g. ZnO or ITO) and an
antireflection (AR) coating.
The dark current is given by (22.47) and is minimal when electron and hole saturation currents are
identical. This conditions leads to the optimal barrier height
φ n = E g − φ ph =
1
2
β
−1 ln
m e
m hh
+
1
2
E g
(22.48)
close to middle of the band gap. For InP and optimal barrier φ n = 0.645 eV a dark current of 0.36 pA/cm
2
is expected for a field of 10 V/ µ m. For deviating barrier height the current increases exponentially.
The current-voltage characteristic of an InGaAs:Fe MSM photodetector is shown in Fig. 22.25 for a
dark environment and various illumination levels.
607
and therefore (with (22.36))
V RT =
e N D
2 s
L
2
− L
2 e N D
s
(V D2 − V 2 )
− V D ,
(22.42)
with V D = (V D1 − V D2 ), vanishing for a symmetric MSM structure. At and after reach-through the
electric field varies linearly from 0 to L within the semiconductor. The point of zero electric field shifts
towards contact 2. At the flat-band voltage this point has reached the contact 2 and the width of the
depletion layer at contact 2 is zero. This condition leads (as long as no breakdown occurred) to
V FB =
e N D
2 s
L
2
− V D .
(22.43)
The maximum electric field is at contact 1 and is given (for V > V FB ) by
E m1 =
V + V FB + 2 V D
L
.
(22.44)
If in a part of the structure the critical field E B for impact ionization is reached (this will be at contact
1, since the field is highest there), the diode breaks down. Therefore the breakdown voltage is given by
V B ≈ E B L − V FB − 2 V D .
(22.45)
The current-voltage characteristic for a Si-MSM structure is shown in Fig. 22.23. At small voltages
only small currents flow since one contact is in reverse bias. The hole current is much smaller than the
electron current. Only those holes that diffuse through the neutral region contribute to the hole current.
After reach-through the barrier φ p2 + V D2 − V 2 for hole injection is strongly reduced that leads to strong
hole injection. Beyond the flat-band voltage the hole current increases only weakly since a lowering of
the barrier occurs only via the Schottky effect. For high fields (V > V FB , before breakdown) the hole
current is
j p1 = A
∗
p T
2 exp
−βφ p2
exp
ββφ p2
= j p,s exp
ββφ p2
,
(22.46)
and the total current is
j = j n,s exp (ββφ n1 ) + j p,s exp
ββφ p2
,
(22.47)
with j n,s = A
∗
n T
2 exp(−βφ n1 ) and j p,s = A
∗
p T
2 exp(−βφ p2 ).
In a MSM photodetector the metal contacts are typically formed in an interdigitated structure on
the semiconductor surface (Fig. 22.24). These contacts shield some of the active area from photons.
An increase in quantum efficiency can be achieved with transparent contacts (e.g. ZnO or ITO) and an
antireflection (AR) coating.
The dark current is given by (22.47) and is minimal when electron and hole saturation currents are
identical. This conditions leads to the optimal barrier height
φ n = E g − φ ph =
1
2
β
−1 ln
m e
m hh
+
1
2
E g
(22.48)
close to middle of the band gap. For InP and optimal barrier φ n = 0.645 eV a dark current of 0.36 pA/cm
2
is expected for a field of 10 V/ µ m. For deviating barrier height the current increases exponentially.
The current-voltage characteristic of an InGaAs:Fe MSM photodetector is shown in Fig. 22.25 for a
dark environment and various illumination levels.