Page 188 - Electrical Properties of Materials

170 Principles of semiconductor devices

a piece of metal, all that happens is that the electrons, which are already there,
acquire some ordered motion. When a forward bias is applied to a p–n junction
minority carriers get injected into both regions. These minority carriers were
not there originally in such a high density; they came as a consequence of the
applied voltage.
The distinction between ordinary conduction and minority carrier injection
is important. It is the latter which makes transistor action possible.

9.5 Junction capacity

I would like to say a few more words about the reverse biased junction. Its
most interesting property (besides the high resistance) is that the presence of
two layers of space charge in the depletion region makes it look like a capacitor.
We may calculate its capacitance in the following way. We first derive the
relationship between the width of the depletion layer in the n-region and the
U 0 is the ‘built-in’ voltage.
voltage in the junction, which may be obtained from eqns (9.2) and (9.8). We
get
U 1 is the applied voltage in the
1/2
2 U 0 N A
reverse direction. x n = . (9.18)
eN D (N D + N A )
For reverse bias the only difference is that the barrier becomes larger, that
is U 0 should be replaced by U 0 + U 1 , yielding

1/2
2 (U 0 + U 1 )N A
x n = . (9.19)
eN D (N D + N A )
The total charge of the donor atoms is
1/2

N A N D
Q = eN D x n = 2 e(U 0 + U 1 ) . (9.20)
N A + N D
Now a small increase in voltage will add charges at the boundary—as hap-
pens in a real capacitance. We may, therefore, define the capacitance of the
junction (per unit area) as
R
1
∂Q e N A N D
1/2
C = = . (9.21)
∂U 1 2(U 0 + U 1 ) N A + N D

R (U 1 ) C (U 1 )
We can now assign an equivalent circuit to the junction and attribute a
physical function to the three elements (Fig. 9.8). R 1 is simply the ohmic
resistance of the ‘normal’, that is not depleted, semiconductor. R(U 1 )isthe
junction resistance. It is very small in the forward direction (0.1–10 typ-
8
6
ically) and large in the reverse direction (10 –10 typically). C(U 1 )isthe
capacitance that varies with applied voltage, given by eqn (9.21). Clearly, this
Fig. 9.8 equation loses validity for strong forward bias because the depletion layer is
The equivalent circuit of a p–n then flooded by carriers. This is actually borne out by our equivalent circuit,
junction.
which shows that the capacity is shorted-out when R(U 1 ) becomes small. With