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Potential diagram of Schottky barrier (n-type material)
Metal Semiconductor
CBM
VBM
b
Fermi-level
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Electrostatics of p++ / n junction or n-Schottky barrier
d2V/dx2 = - /q Nd+ + + + + + +
E = dV/dx = - / dx = - q Nd x
V = - q Nd x dx = - q Nd x2 / 2
x=0
-qNdxd/
Ex=xd
-V
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Transition Capacitance of p++ / n junction
or n-Schottky barrier
Vd - Vapplied = - q Nd xd2 / 2
i.e. xd = (Vapplied-Vd) 2 / q Nd
PARALLEL PLATE CAPACITOR C = A / xd
CT = A [q Nd / 2 (Vapplied - Vd)]1/2
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1/CT2 = 2 (Vapplied - Vd) / (q Nd A2)
1/CT2
Vapplied
Slope o 1/Ndc
Vd
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Nd 1 Nd 2
Vapplied
1/CT2
Slope o 1/Nd 1c
Vd
Slope o 1/Nd 2c
Nd 2 >> Nd 1
Can tailor C(V) by the control of the doping profile, for example for a hyperabrupt junction C is proportional to V-2
facilitating = (LC)-1/2 being proportional to a control voltage
1/CT2 = 2 (Vapplied - Vd) / (q Nd A2)
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Diffusion Capacitance of p++ / n junction
In forward bias, holes are injected into the n-type region.
QD = A q pno Lp (evD/VT - 1) = (Lp
2/Dp) I = I
CD = dQ/dV = dI / dV = I / (n Vt)
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NPN Bipolar Junction Transistor (BJT)
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