Biomedical Engineering Reference
In-Depth Information
establishes a relationship between conductivity and field strength:
s ¼
nzev
=
E
½
15
:
3
The drift velocity, v, is directly proportional to the local electric field
strength and the constant relating of the two quantities is defined as
mobility. Equation 15.4 is expressed in subscripted form to specify the
contribution of the i
th
species to electrical mobility:
m
i
¼
v
i
=
E
i
½
15
:
4
Equation 15.3 can now be expressed in terms of mobility
s
i
¼
ð
n
i
z
i
e
Þm
i
½
15
:
5
At times, it is desirable to make use of absolute mobility, B
i
, which is defined
as drift velocity per unit of applied force:
B
i
¼
v
i
=
F
i
¼
v
i
=
Z
i
eE
½
15
:
6
In terms of absolute mobility, the conductivity is expressed by:
n
i
z
i
2
e
2
B
i
s
i
¼
½
15
:
7
Equation 15.7 relates conductivity with the most important variable, n
i
, and
the absolutemobility, B
i
; whereas z
i
and e remain constant for a givenmaterial.
Generally, in solids, more than one charge carrier can contribute to the
electrical conduction. In this case, the total conductivity is the sum of partial
conductivities attributed to different charge carriers. That is, for the i
th
charge carrier, equation 15.5 is applicable and then the total conductivity,
σ
,
is expressed by:
s ¼ s
1
þ s
2
þ þs
i
þ
½
15
:
8
The fraction of total conductivity contributed by each charge carrier is
t
i
¼ s
i
=s
½
15
:
9
where t
i
is termed the transport number of the i
th
species. The sum of all the
transport numbers must be unity:
t
1
þ
t
2
þþ
t
i
þ¼
1
½
15
:
10
15.2.2 Space charge
Space charge refers to an accumulation or depletion of local, uncompen-
sated charges in solids. It may result from the absorption of charged species
