606
22 Light-to-Electricity Conversion
(a)
(b)
(c)
Fig. 22.22 Band diagram (upper parts) and electric field distribution (lower parts) in a MSM diode for various bias
conditions: a at reach-through voltage V RT , b at flat-band voltage V FB and c for V > V FB . Adapted from [1840]
The reverse current at contact 1 is
j n1 = A
∗
n T
2 exp (−βφ n1 ) exp (ββφ n1 )
1 − exp (−βV 1 )
,
(22.38)
where φ n1 is the barrier reduction due to the Schottky effect (Sect. 21.2.3 and (21.27)). The forward
current at contact 2 is
j n2 = −A
∗
n T
2 exp (−βφ n2 ) exp (ββφ n2 )
1 − exp (βV 2 )
.
(22.39)
For a symmetric structure, i.e. φ n1 = φ n2 and V D1 = V D2 = V D , (22.37)–(22.39) yield together
with (21.27)
e
3 N D
8π 2 3
s
1/4
(V D + V 1 )
1/4
− (V D − V 2 )
1/4
=
1
β
ln
exp (βV 2 ) − 1
1 − exp (−βV 1 )
.
(22.40)
Together with (22.36) a numerical or graphical solution can be found. Initially (for small voltages) the
injected hole current (from contact 2) is much smaller than the electron current and diffusion occurs
in the neutral region.
The reach-through voltage V RT is reached when the width of the neutral region is reduced to zero
(Fig. 22.22a). At the juncture of the two depletion regions inside the semiconductor material the electric
field is zero and changes sign. For a larger voltage V FB flat-band conditions are present at contact 2,
i.e. the electric field is zero at contact 2 (Fig. 22.22b). At even larger voltage V B breakdown occurs.
At V = V RT we have
w 1 =
2 s
e N D
(V 1 + V D1 )
1/2
(22.41a)
w 2 =
2 s
e N D
(V D2 − V 2 )
1/2
(22.41b)
L = w 1 + w 2 ,
(22.41c)
22 Light-to-Electricity Conversion
(a)
(b)
(c)
Fig. 22.22 Band diagram (upper parts) and electric field distribution (lower parts) in a MSM diode for various bias
conditions: a at reach-through voltage V RT , b at flat-band voltage V FB and c for V > V FB . Adapted from [1840]
The reverse current at contact 1 is
j n1 = A
∗
n T
2 exp (−βφ n1 ) exp (ββφ n1 )
1 − exp (−βV 1 )
,
(22.38)
where φ n1 is the barrier reduction due to the Schottky effect (Sect. 21.2.3 and (21.27)). The forward
current at contact 2 is
j n2 = −A
∗
n T
2 exp (−βφ n2 ) exp (ββφ n2 )
1 − exp (βV 2 )
.
(22.39)
For a symmetric structure, i.e. φ n1 = φ n2 and V D1 = V D2 = V D , (22.37)–(22.39) yield together
with (21.27)
e
3 N D
8π 2 3
s
1/4
(V D + V 1 )
1/4
− (V D − V 2 )
1/4
=
1
β
ln
exp (βV 2 ) − 1
1 − exp (−βV 1 )
.
(22.40)
Together with (22.36) a numerical or graphical solution can be found. Initially (for small voltages) the
injected hole current (from contact 2) is much smaller than the electron current and diffusion occurs
in the neutral region.
The reach-through voltage V RT is reached when the width of the neutral region is reduced to zero
(Fig. 22.22a). At the juncture of the two depletion regions inside the semiconductor material the electric
field is zero and changes sign. For a larger voltage V FB flat-band conditions are present at contact 2,
i.e. the electric field is zero at contact 2 (Fig. 22.22b). At even larger voltage V B breakdown occurs.
At V = V RT we have
w 1 =
2 s
e N D
(V 1 + V D1 )
1/2
(22.41a)
w 2 =
2 s
e N D
(V D2 − V 2 )
1/2
(22.41b)
L = w 1 + w 2 ,
(22.41c)