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
                                Y = admittance
                                         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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