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Unformatted text preview: ISFET. Below the threshold, the drain current is approximately: I DS ≈ I0 ⋅ e VGS −VTH
kT q where: I0 =1 µΑ, VTH = 0.5 V, T = 300K, and q = 1.6 × 10
19 C. Nernst Potential for an ion Az where z is valence of the ion Az
€ VGS = VG − VS = RT ln [ z ]S zF € [A ] G kT RT
=
For your reference: q
F
Plug in VGS into IDS: I DS −VTH ȹ
VGS
−VTH ȹ
VGS
ȹ ȹ kT q
kT q
kT q
RT F
ȹ ⋅ e
ȹ ⋅ e
≈ I0 ⋅ e
= ȹ I0 ⋅ e
= ȹ I 0 ⋅ e
ȹ ȹ
ȹ ȹ
€
ȹ Ⱥ
ȹ Ⱥ
z
RT [ A ] S
ȹ z ȹ
z
ln z
1 ȹ [ A ] S ȹ
1 [ A ]S
zF [ A ]
−VTH ȹ
−VTH ȹ
−VTH ȹ
ln
ln z
G
ȹ ȹ ȹ z ȹ [ A z ] ȹ
z [A ]
G
= ȹ I0 ⋅ e kT q ȹ ⋅ e RT F = ȹ I0 ⋅ e kT q ȹ ⋅ e
= ȹ I0 ⋅ e kT q ȹ ⋅ e ȹ G Ⱥ
ȹ ȹ
ȹ ȹ
ȹ ȹ
ȹ Ⱥ
ȹ Ⱥ
ȹ Ⱥ
VGS −VTH
kT q −VTH ȹ
ȹ = ȹ I0 ⋅ e kT q ȹ ⋅ e
ȹ ȹ
ȹ Ⱥ ȹ A z
ln ȹ z
ȹ A
ȹ 1/ z [ ]S ȹ
ȹ
[ ]G ȹ
Ⱥ 1z
−VTH ȹ ȹ ȹ [A z ]S ȹ
= ȹ I0 ⋅ e kT q ȹ ⋅ ȹ z ȹ
ȹ ȹ ȹ A ȹ
ȹ Ⱥ ȹ [ ]G Ⱥ € 1z
Ⱥȹ −VTH ȹ ȹ Ⱥ Ⱥ [A z ]S ȹ Ⱥ log( I DS ) ≈ logȺȹ I0 ⋅ e kT q ȹ ⋅ ȹ z ȹ Ⱥ ȹ ȹ ȹ A ȹ
Ⱥ
ȹ Ⱥ ȹ [ ]G Ⱥ Ⱥ Ⱥ Ⱥ −VTH
kT q 1
= log I0 +
+ ⋅ log[ A z ]S − log[ A z ]G
ln(...
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 Winter '08
 PeterChen

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