Biomedical Engineering Reference
In-Depth Information
b
I
I
R
G
a
C
V
G
+
d
V
ad
I
ba
R
(
ab
|
dc
) =
R
(
ab
|
dc
)
R
(
bc
|
ad
)
π
t
2
I
n
2
{
R
(
ab
|
dc
) +
R
(
bc
|
ad
)
r
=
f
∆
V
ad
I
bc
where
R
(
bc
|
ad
) =
δ
R
(
bd
|
ca
)
ρ
t
B
µ =
FIGURE 6.9
Van der Pauw measurement of resistivity and carrier mobility.
2
e
n m
[
]
n x
( )
−
n
=
N
−
N x
( )
(6.13)
1
2
D
1
*
2
2
ε
ω
2 0
We then know both
N
D
(
d
) and
u
(
d
), from which we can derive
N
D
versus
u
.
An attractive experiment for measurement of the drift mobility of the
carriers in implanted layers is the “time of flight” measurement. In this
technique [10], “a relatively compact group of excess carriers, released or
injected by some form of impulsive excitation, is caused by an externally
applied electric field to traverse a known distance in more or less coherent
fashion, and the time of its arrival is measured. In the absence of all diffu-
sion, recombination, relaxation, and deep trapping effects, the drift mobil-
ity is given by μ =
d/E
τ, where
d
is the known distance,
E
is the applied
field, and τ is the observed transit time.” Techniques are currently under
investigation to transform the experiment from the time domain to the
frequency domain. It is believed that the “Fourier transform” method of
drift mobility measurement will have practical advantages over the time-
of-flight method.
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