# Chapter 7 Small-Signal Admittance by VbX5MT

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```									            Chapter 7. Small-signal admittance

We will study the small signal response of the pn junction diode.
A small ac signal (va) is superimposed on the DC bias. This
results in ac current (i). Then, admittance Y is given by:

Y = i / va = G + jC

Specifically, the following parameters will be studied:

• Reverse bias junction or depletion layer capacitance
• Forward bias diffusion or charge storage capacitance
• Forward and reverse bias conductance.

1
Capacitance measurements

I = DC
i = ac
i
           G  j C
vac

i and va depend on the applied
DC bias

Model for a diode under ac                                    2
Reverse bias junction capacitance

A pn junction under reverse bias behaves like a capacitor.
Such capacitors are used in ICs as voltage-controlled capacitors.

Depletion layer width under small ac
superimposed on DC bias voltage.

Looks similar to a parallel plate capacitor.

Si A            where W is the depletion-layer width
Cj 
W               under DC bias.
3
Reverse bias junction capacitance

1/ 2
 2Si    NA  ND         
W           N N  Vbi  VA 
                               For pn junction
 q       A D             
1/ 2
 2            
  Si Vbi  VA                For p+n or pn+ junction where NB is
 qN B                         the doping on the lightly doped side

1/ 2
Si A       q NB 
CJ               2 V  V  
 A  Si               For asymmetrically doped junction
W             bi  A 

CJ increases with NB1/2
CJ decreases with applied reverse bias
4
Parameter extraction/profiling
C-V data from a pn junction is routinely used to determine the
doping profile on the lightly doped side of the junction.
1/ 2                               2
Si A       Si q N B                           Slope 
CJ           A 2V  V                                   qNBSi A2
W             bi    A  300
2
1

2
Vbi  VA  200
CJ2       2
A qNBSi                                                    1/Cj2
1
100                              [F–2 ]
If the doping on the lightly
doped side is uniform, a plot
0
–10
-20  –5 -10   0   0
0
of 1/CJ2 versus VA should be a             VA [Volts]
straight line with a slope
Intercept = Vbi
inversely proportional to NB
and an extrapolated 1/CJ2 = 0
intercept equal to Vbi.                                                       5
Forward bias diffusion capacitance, CD
CD is also called the charge storage capacitance. The variation of the
injected minority-carrier charge, which is a function of the applied
bias, results in the diffusion capacitance. Both CJ and CD are always
present, but for the forward-bias case, CD becomes dominant.

p-type                        n-type          Origin of diffusion
pn0    capacitance
np0
x

For a p+n junction, I = Qp/p where Qp is total excess charge in n-side
qVA
Dp p         qVA  
Qp  Ip  qA               pn0 exp     1  qALp pn0   e kT
Lp           kT  
dQp
q               qVA     q
CD         qALp pn0 exp           I p
dV   kT               kT     kT                             6
Forward bias conductance

qADp pn0 d  qVA        
dI                                q
GD                    e kT         kT I
dV     Lp     dV 
                             Assumes
            
p  1
q                       q
GD     I               CD     I p               Complicated at
kT                      kT                    higher frequencies.
VApplied = VA
CJ

Rs             CD
Equivalent circuit for a diode
GD

VJ                                                       7
Example
Problem: Consider a p+n junction forward biased such that the
forward current is 1 mA. Assume the lifetime of holes is 10–7 s.
Calculate the diffusion capacitance and the diffusion resistance.

Solution: CD = 3.86 nF                rd = 1/GD = 25.9 

The current through the depletion layer will mostly be carried by
(holes, electrons: choose one)?

Plot the current carried by the holes and electrons through the n-
type region, assuming that the diffusion length of holes is 1m.

8

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