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Homework 3 Solutions

# For ca2 z 2 1 vth 1 log i ds log a z s

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Unformatted text preview: 10) z Ⱥ Ⱥ 1 −VTH 1 = ⋅ log[ A z ]S + Ⱥlog 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 + Ⱥlog I0 + − ⋅ log[ A z ]G Ⱥ z ln10 ⋅ kT q z Ⱥ Ⱥ Ⱥ Ⱥ −VTH = log[K + ]S + Ⱥlog 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 + Ⱥlog I0 + − ⋅ log[ A z ]G Ⱥ z ln10 ⋅ kT q z Ⱥ Ⱥ Ⱥ Ⱥ −VTH = − log[C...
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