Potential diagram of Schottky barrier (n-type material)

N. Newman, MSE494/598 Handout #8 page 1


Potential diagram of Schottky barrier (n-type material)

Metal Semiconductor

CBM

VBM

b

Fermi-level


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


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


1/CT2 = 2 (Vapplied - Vd) / (q Nd A2)

1/CT2

Vapplied

Slope o 1/Ndc

Vd


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)


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)


NPN Bipolar Junction Transistor (BJT)

Potential diagram of Schottky barrier (n-type material)

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