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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,