Lecture

							                    Lecture #19

                         OUTLINE
              • pn junctions (cont’d)
                 – Charge control model

              Reading: Finish Chapter 6.3




Spring 2007         EE130 Lecture 19, Slide 1
       Minority-Carrier Charge Storage
• When VA>0, excess minority carriers are stored
  in the quasi-neutral regions of a pn junction:
                                                             
   QN  qA           n p ( x)dx                QP  qA pn ( x)dx
                 xp                                          xn

           qAn p ( x p ) LN                          qApn ( xn ) LP




Spring 2007                 EE130 Lecture 19, Slide 2
   Derivation of Charge Control Model
• Consider a forward-biased pn junction. The total
  excess hole charge in the n quasi-neutral region is:
                          
                       QP  qA  pn ( x, t )dx
                                xn
• The minority carrier diffusion equation is (without GL):
                     pn       2pn pn
                           DP       
                      t        x 2   p

• Since the electric field is very small,
                                     p n
                     J P  qDP       x


• Therefore:     ( qp n )   J   qp n
                             P 
                     t        x   p

Spring 2007         EE130 Lecture 19, Slide 3
                           (Long Base Diode)
• Integrating over the n quasi-neutral region:
                                         1        
                               J P ()          

             qA  pn dx   A  dJ P  qA  pn dx
          t  x n
                        
                               J p ( xn )
                                            p  xn
                                                     
                                                      



• Furthermore, in a p+n junction:
              J P ()

         A       dJ
              J p ( xn )
                           P     AJ P ()  AJ P ( xn )  AJ P ( xn )  iDIFF


                    dQP          Q
• So:                    iDIFF  P
                     dt          p

Spring 2007                        EE130 Lecture 19, Slide 4
              Charge Control Model
We can calculate pn-junction current in 2 ways:
    1. From slopes of np(-xp) and pn(xn)
    2. From steady-state charges QN, QP stored in each
       excess-minority-charge distribution:
                  dQP                 QP
                       AJ P ( xn )     0
                   dt                 τp
                                           QP
               AJ P ( xn )  I P ( xn ) 
                                           τp
                                             QN
                Similarly, I N ( x p ) 
                                              τn

Spring 2007           EE130 Lecture 19, Slide 5
Charge Control Model for Narrow Base
•    For a narrow-base diode, replace p and/or
     n by the minority-carrier transit time tr
    –    time required for minority carrier to travel across the
         quasi-neutral region
    – For holes on narrow n-side:
                  WN             1
        QP  qA pn ( x)dx  qA pn ( xn )WN
                  xn              2
                           dpn        p ( x )
        I P  AJ P  qADP       qADP n n
                            dx            WN
                     QP WN          2
         τ tr , p     
                     IP    2 DP
                                                           WP 2
    – Similarly, for electrons on narrow p-side: τ tr ,n 
                                                            2 DN
Spring 2007            EE130 Lecture 19, Slide 6
                       Summary
• Under forward bias, minority-carrier charge is stored
  in the quasi-neutral regions of a pn diode.

    – Long base: QN  qA
                           ni2 qVA / kT
                          NA
                                e        
                                         1 LN       
                 QP  qA
                         ni2 qVA / kT
                         ND
                              e       1 LP     

    – Short base: QN  qA
                           1 ni2 qVA / kT
                           2 NA
                                 e            
                                           1 WP         
                   QP  qA
                            1 ni2 qVA / kT
                            2 ND
                                  e            
                                            1 WN        
Spring 2007         EE130 Lecture 19, Slide 7
• The steady-state diode current can be viewed as the
  charge supply required to compensate for charge
  loss via recombination (long base) or collection at the
  contacts (short base)
                     QN QP                                  LN D N      L   D
    – Long base: I                              Note that        and P  P
                     τn τ p                                 τn   LN     τ p LP



                      QN       QP
    – Short base: I         
                      τ tr ,n τ tr , p

                         
                           WP 2                    
                                                        WN 2
                                                          
         where τ tr ,n                      τtr , p
                            2 DN                        2DP
Spring 2007              EE130 Lecture 19, Slide 8