where
–
circular frequency. Surface-specific (ohm/cm
2
) active resistance in the
general case has the form [10]
1
[
(
,,)
(
,,)],
S
ns
s
s
ps
s
s
R
q
ny
q
py
−
=+
(2)
where
q
is the charge of the electron,
,
ns
ps
−
the mobility of the electrons and
holes,
,
ss
np−
the over-shock of electrons and holes in the near-surface layer of the
semiconductor,
s
y−
the surface of the three-dimensional electrostatic potential,
−
the dimensionless coefficient characterizing the volumetric properties of the gas sensor
semiconductor,
−
the dimensionless coefficient characterizing the degree of
violation of the thermodynamic equilibrium in the semiconductor. The concentration
of excess electrons and holes is described by expression [10]
0
1
0
1
(
1)
(
,,)
(
)
,
2
(,,)
S
y
S
S
D
y
e
ny
n
L
dy
fy
−
−
=+
(3)
0
0
1
(
1)
(
,,)
(
)
,
2
(,,)
s
y
S
S
D
y
e
py
p
L
dy
fy
−
−
=+
(4)
where
00
,
np−
the equilibrium concentration of electrons and holes in the volume
of the semiconductor,
y− the dimensionless electrostatic potential, the function
(,,)
fy
has the form [10]
1
1
1
2
(,,)
(
)(
1)
(
)(
1)
(
)
,
y
y
fy
e
e
y
−
−
−
=
+
−+
+
−+
−
(5)
1
2
0
2
,
2
D
i
kT
L
qn
=
(6)
where
0
,
−
the dielectric constants of semiconductor and vacuum,
k−
Boltzmann's constant,
i
n
– are the concentration of electrons in their own
semiconductor,
D
L−
the distance of electric field penetration into their own
semiconductor, T− the absolute temperature. It should be noted that in formula (5) the
negative sign in front of the square bracket corresponds to the positive sign, and the
positive sign - to the negative value of the dimensionless electrostatic potential.
Substitution of expressions (3) and (4) in equation (2) describes the specific resistance
of the semiconductor gas sensor
1
1
0
1
(
)(
1)
(
)(
1)
(
,,)
,
2
(,,)
s
y
y
s
S
S
i
ps
D
y
e
b
e
Ry
qn
L
dy
fy
−
−−
+
−+
+
−
=
(7)
where
/
s
ns
ps
b
=−
the ratio of electron mobility to hole mobility. Integral in
expression (7) does not have a decoupling in analytical form and should be calculated
numerically, but at a significant value of the surface potential for the electron
- 487 -