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EE 5342 Lecture

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									EE5342 – Semiconductor
Device Modeling and
Characterization
Lecture 14 - Spring 2005

              Professor Ronald L. Carter
                    ronc@uta.edu
              http://www.uta.edu/ronc/
L14 March 3                                1
           Y-parameter data
                 Re{Y} vs. frequency
1.E+00
             1000 mV
1.E-01
              900 mV
1.E-02
1.E-03        800 mV
1.E-04        700 mV
1.E-05
1.E-06        500 mV
1.E-07
1.E-08        300 mV
1.E-09
     1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10
  L14 March 3                                     2
                 Y-parameter data
                    Im{Y} vs. frequency
1.E+00

1.E-01

1.E-02           1000 mV
1.E-03              900 mV
                  800 mV
1.E-04
                  700 mV
1.E-05
                  500 mV
1.E-06

1.E-07            300 mV

1.E-08
    1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10
   L14 March 3                                  3
Bipolar junction
transistor (BJT)
• The BJT is a “Si           E      B     C
  sandwich”              P          n       p
  Pnp (P=p+,p=p-) or
  Npn (N=n+, n=n-)     VEB                 VCB
• BJT action: npn
  Forward Active                 Depletion Region
  when VBE > 0 and
  VBC < 0                        Charge neutral Region

L14 March 3                                      4
BJT coordinate
systems
                                     Charge neutral Region
               Depletion Region


              Emitter     Base       Collector
        x’E       0       0   xB x       0    x”c
x’                                                   x”
                                                      z
      -WE             0           WB         WB+WC
L14 March 3                                               5
BJT boundary and
injection cond (npn)
                                            2
                           VBE           ni
pnE                       V  , pnE0  NE
               pnE0 exp f     
     x' 0               t 
pnE           0
         x' xE 
                            VBC          ni2
                            V  , pnC 0  NC
pnC x" 0   pnC 0 exp f     
                            t 
pnC x" x   0
           C
L14 March 3                                     6
BJT boundary and
injection cond (npn)
Note that the Base BC are inter -
dependent
                           VBE         ni2
npB                       V  , npB0  NB
               npB0 exp f     
     x  0               t 
                           VBC 
npB                       V .
               npB0 exp f     
     x  xB              t 
L14 March 3                                7
IC npn BJT
(*Fig 9.2a)




L14 March 3   8
npn BJT bands
in FA region

q(VbiE-VBE )
                               q(VbiC-VBC )
        qVBE
                                       qVBC
              injection   high field



L14 March 3                                   9
Coordinate system -
prototype npn BJT (Fig 9.8*)




L14 March 3                    10
Notation for
npn & pnp BJTs
•   NE, NB, NC E, B, and C doping (maj)
•   xE, xB, xC E, B, and C CNR widths
•   DE, DB, DC Dminority for E, B, and C
•   LE, LB, LC Lminority for E, B, and C
               (L2min = Dmin tmin)
tE0, tB0, tC0 minority carrier life-
 times for E, B, and C regions
L14 March 3                                11
Notation for
npn BJTs only
• pEO, nBO, pCO: E, B, and C thermal
    equilibrium minority carrier conc
• pE(x’), nB(x), pC(x’’): positional mathe-
    matical function for the E, B, and C
    total minority carrier concentrations
pE(x’), nB(x), pC(x’’): positional
    ma- thematical function for the
    excess minority carriers in the E, B,
    and
L14 March 3 C                             12
Notation for
pnp BJTs only
• nEO, pBO, nCO: E, B, and C thermal
  equilibrium minority carrier conc
• nE(x’), pB(x), nC (x’’): positional mathe-
  matical function for the E, B, and C
  total minority carrier concentrations
nE(x’), pB(x), nC(x’’): positional ma-
  thematical function for the excess
  minority carriers in the E, B, and C
L14 March 3                                13
npn BJT boundary
conditions
                                               VBE  
E : pE x'  xE   0, pE 0   pE 0  exp
                                                      1
                                                Vt    
                                   VBE  
     B : nB x  0   nB0  exp
                                           1 ,
                                    Vt      
                         VBC                 ni2 
   nB xB   nB0  exp
                                1 , nB0   , etc.
                          Vt     
                                                N 
                                                 B
                               VBC  
C : pC x"  0   pC 0  exp
                                       1 , pC xC   0
                                Vt      
L14 March 3                                               14
Emitter solution
in npn BJT
        pE x ' pE x'
              2
    DE       2
                              0 , pE  pE  pE0
          x'         tE 0
                          VBE              xE  x '
                  pE0  exp
                          V       1  sinh
                                                       
                                                          
                           t                  LE     
    pE x' 
                                       xE
                                  sinh
                                       LE
                   VBE       xE  x '
pE x'  pE0  exp
                   V         1 
                               x        , xE  LE
                                          
                    t            E   
L14 March 3                                                   15
Base solution
in npn BJT
     2 nB x  nB x 
            2
                            0 , nB  nB  nB0
         x         DB tB0
              nB0           VBE      xB  x 
 nB x  
                 xB          V  sinh  L
                      exp f                 
                                                
            sinh            t           B   
                 LB
         VBC     x 
         V sinh  L  and when xB  LB
   exp f         
         t       B 
               VBE    x          VBC  x 
                V  1  x   exp f V  x 
    nB0 exp f                          
               t       B         t  B 
L14 March 3                                        16
Collector solution
in npn BJT
   2 pC x"     pC x"
                              0 , pC  pC  pC0
        x"2         DC tC 0
                    VBC            xC  x" 
           pC0  exp
                           1  sinh
                                                
                                                  
                     Vt               LC     
pC x" 
                                 xC
                          sinh
                                 LC
                      x"
 pC x"  pC0          , VBC  Vt , xC  LC
                      LC
L14 March 3                                          17
Hyperbolic sine
function
        x  e  x / L   e  x / L 
                                        y           y2
 sinh                                , e 1 y         ...
       L  e  x / L   e  x / L                 2!
                                  1  x     1  x  
                          x  L              
                                               L
                                                             
 so if x  L, sinh   
                        
                                                             
                         L   1  x     1  x  
                                                          
                                  L           L           
           giving,    x  0 sinh x   x
                          lim it
                                           
                      L                  L L
L14 March 3                                                  18
npn BJT regions
of operation
                        VBC

              Reverse
                         Saturation
              Active

                                      VBE
              Cutoff      Forward
                          Active


L14 March 3                                 19
npn FA BJT minority
carrier distribution (Fig 9.4*)




L14 March 3                       20
npn RA BJT minority
carrier distribution (Fig 9.11a*)




L14 March 3                         21
npn cutoff BJT min
carrier distribution (Fig 9.10a*)




L14 March 3                         22
npn sat BJT minority
carrier distribution (Fig 9.10b*)




L14 March 3                         23
Defining currents in
FA mode npn BJT (Fig 9.13*)




L14 March 3                   24
References
1   OrCAD PSpice A/D Manual, Version 9.1,
    November, 1999, OrCAD, Inc.
2   Semiconductor Device Modeling with
    SPICE, 2nd ed., by Massobrio and
  Antognetti, McGraw Hill, NY, 1993.
* Semiconductor Physics & Devices, by
  Donald A. Neamen, Irwin, Chicago, 1997.


L14 March 3                                 25

								
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