ECE 663

AC Diode Characteristics

Resistor network supplies DC bias set pointCapacitor provides AC signal input

Vout=IdiodeR3

R3

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AC small signal resistance

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Small signal AC conductance

)()(

11 /

dcdc

kTqVs

VIkTq

VIkTq

g

eAJdVd

dVdI

Rg

Small Signal AC resistance

)(11VIq

kTg

Rdc

Resistance depends on DC set point – voltage controlled resistor

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Cdrd

Y1

Zgd i Cd 1

rdi Cd rd, Cd vary with VDC !!!

Reactance:

An equivalent circuit

Let us work out Y for reverse bias first

Reverse Bias Conductance

I

V

I constant with reverse bias voltage gd ≈ 0

I = I0(e-qVBR/kT -1) ≈ -I0

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Reverse Bias (‘Depletion’) Capacitance

• AC voltage modifies depletion width• Depletion width changes small• Looks like adding charges to parallel

plates• AC capacitance

WAK

C sJ

0

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RB capacitance C-V measurements

• Plot of 1/C2 vs V is a straight line (constant doping) and the slope gives doping profile.

• Y-intercept gives built-in voltage

02

2/1

0

2/1

0

0

21

2

2

sB

Abi

J

Abi

sBJ

AbiB

s

sJ

KqNVV

C

VVKqN

C

VVqNK

W

WAK

C

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So reverse bias equivalent circuit

WAK

C sJ

0

Rs

Notice that for reverse bias, circuit parameters are frequencyindependent, as if we’re in DC characteristics.

Why?

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Reverse bias p-n junction is a majority carrier device

Very few minority carriers have made it to the opposite side

Depletion width change requires flow of majority carriers(n from n-side and p from p-side flow in and out)

Since majority carriers move very fast by drift, they can follow the AC field instantly, so the response is ‘quasi-static’

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Just how fast are majority carriers?

Drifting charges, with fields in turn determined by charge

∂n/∂t = -(1/q)∂Jn/∂x + (gN - rN)

Jn = qnnE + qDN∂n/∂x ≈ qnnE ≈ nE

Ks0 ∂E/∂x = q(p - n + ND+ - NA

-) ≈ -qn

∂n/∂t = -n/

= Ks/n(Dielectric Relaxation Time)

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How fast is it?

= Ksn

Ks = 11.90 = 8.854 x 10-12 F/mn (@ doping 1015/cm3) ~ 4 -cm

≈ 5 ps !

As long as fields are not too fast ( < 10 GHz), chargesfollow field quasi-statically

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Let’s now go to forward bias

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Capacitance in Forward Bias

np x( )

pn x'( )

Stored charge = excess minority carriers

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AC field varies minority carrier pile-up (recall law of the

junction)

p(xn) = (ni2/ND)[eq(V + vac)/kT – 1]

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Also, minority carriers are slow and may not follow AC field quasi-

statically

Thus we expect circuit parametersto be frequency-dependent !

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How fast are minority carriers?

≈ 1/NTTvt (Minority carrier lifetime)

NT ~ 1012/cm3 (for NA ~ 1014/cm3)T ~ (10-10m)3

vt = 3kT/m ~ 105m/s

≈ 300 s

So for fast fields ( >> 1/), expect carriers to go out of phase, leading tofreq-dependent circuit parameters

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But how do we include such phase lag effects?

Back to MCDE

∂n/∂t = DN∂2n/∂x2 – n/n

Can’t drop this at AC fields !!

jn

Back to MCDE

0 = DN∂2n/∂x2 – n(1+jn)/n

n n/(1+jn)

So in Shockley equation

I = qA(ni2/ND)DN (1+jn)

/n

x [eq(V + vac)/kT – 1] idiff = G0(1+jn)vac

idiff = (Gd + jCd)vac

Square root of (1+jn)

1 + j = Aej

A = (1 + 22) = tan-1()

Real(1+j) = A1/2cos(/2)

Im(1+j) = A1/2sin(/2)

cos = 1/(1+22) = 2cos2(/2) - 1 = 1 – 2sin2(/2)

Re(1+j) = Gd

Im(1+j) = jCd

1

Gd()/G0 ~

Cd()/C0 ~ 1/

For high frequency (>> 1), minority carriers can’t follow fields, so capacitance goes down and the p-n junction becomes ‘leaky’ so its conductance goes up

In summary

• Reverse bias is a depletion capacitance, zero conductance

• It looks like a DC capacitance, except its width depends on voltage

• Forward bias looks like a frequency dependent diffusion capacitance and a diffusion conductance to give an overall admittance