Biomedical Engineering Reference
In-Depth Information
Fig. 5.8
Simplified model of the total gate capacitance (C
g
) of a DMFET, corresponding to
receptor immobilization and analyte binding. Gate oxide, airgap, analyte, and receptor can be
modeled as the capacitances C
ox
, C
air
, C
anlt
,andC
rcpt
, respectively
To determine the dielectric effect of biomolecules, we initially assume that the
analyte is weakly charged or neutral. The V
T
value of the DMFET can then be
adapted from a modification of the V
T
value of a conventional FET and is defined
by the following equation:
Q
DEP
C
g
:
V
T
D
V
FB
˙
2 B
˙
(5.3)
Here, V
FB
is the flat band voltage, 2
B
is the surface potential, C
g
is the total gate
capacitance, and Q
dep
is the depletion-layer charge. Equation
5.3
is considered to
have a positive sign for n-channel FETs and a negative sign for p-channel FETs.
As shown in Fig.
5.8
, the gate oxide, airgap, analyte, and receptor can be modeled
as the capacitances C
ox
, C
air
, C
anlt
,andC
rcpt
, respectively. They are connected in
series, resulting in the total gate capacitance (C
g
/ given by the following equation:
1
C
g
D
1
C
rcpt
C
1
C
anlt
C
1
C
air
C
1
C
ox
D
t
rcpt
k
rcpt
"
0
C
t
anlt
k
anlt
"
0
C
t
air
"
0
C
t
ox
k
ox
"
0
: (5.4)
In this equation, "
0
is the permittivity of air, k
rcpt
is the dielectric constant of the
receptors, k
anlt
is the dielectric constant of the analytes, k
ox
is the dielectric constant
of gate oxide, t
rcpt
is the thickness of the receptors, t
anlt
is the thickness of the analyte,
t
air
is the thickness of air, and t
ox
is the thickness of the gate oxide.
Filling this nanogap (k
1) with analytes (k
anlt
>1) bound to receptors
increases the total gate capacitance and results in a signal change, that is, V
T
.
According to Eqs.
5.3
and
5.4
, V
T
can be given as
D
1
C
g;
anlt
D˙
ˇ
Q
dep
ˇ
1
C
g;
anlt
V
T
D
V
T;
anlt
V
T;
anlt
t
anlt
k
anlt
"
0
K
1
1
ˇ
Q
dep
ˇ
t
anlt
"
0
D˙
D
k
anlt
(5.5)
where K
t
anlt
="
0
denotes the response coefficient. Again, the equation
has a positive sign for n-channel FETs and a negative sign for p-channel FETs.
D˙j
Q
dep
j
