Unformatted text preview: 10) z
Ⱥ
Ⱥ 1
−VTH
1
= ⋅ log[ A z ]S + Ⱥlog I 0 +
− ⋅ log[ A z ]G Ⱥ z
ln10 ⋅ kT q z
Ⱥ Ⱥ ( € ) a. Assuming the membrane is permeable only to K+ and and the trapped K+ concentration between the membrane and the gate of the ISFET is 1 mmol/L, derive the drain current as a function of K+ concentration. Sketch this relationship with logarithmic scale on both axes. Clearly indicate the scales on each axis and the slope of the graph. For K+, z = +1: Ⱥ
Ⱥ 1
−VTH
1
log( I DS ) = ⋅ log[ A z ]S + Ⱥlog I0 +
− ⋅ log[ A z ]G Ⱥ z
ln10 ⋅ kT q z
Ⱥ Ⱥ Ⱥ
Ⱥ −VTH
= log[K + ]S + Ⱥlog I0 +
− log[K + ]G Ⱥ ln10 ⋅ kT q
Ⱥ Ⱥ Ⱥ
−0.5 Ⱥ = log[K + ]S + Ⱥ−6 +
+ 3Ⱥ Ⱥ 60 m Ⱥ = log[K + ]S − 11.3 € b. Now assume the membrane is permeable only to Cl
and the trapped Cl
concentration between the membrane and the gate of the ISFET is 1 mmol/L. As before derive and sketch, on logarithmic axes, the drain current as a function of Cl
concentration. For Cl
, z =
1: Ⱥ
Ⱥ 1
−VTH
1
log( I DS ) = ⋅ log[ A z ]S + Ⱥlog I0 +
− ⋅ log[ A z ]G Ⱥ z
ln10 ⋅ kT q z
Ⱥ Ⱥ Ⱥ
Ⱥ −VTH
= − log[C...
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 Winter '08
 PeterChen
 Natural logarithm, Vout, the00

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