Transcript EE 5340 Semiconductor Device Theory Lecture 18 – Spring 2011 Professor Ronald L.

EE 5340
Semiconductor Device Theory
Lecture 18 – Spring 2011
Professor Ronald L. Carter
[email protected]
http://www.uta.edu/ronc
Test 2 – Tuesday 05Apr11
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11 AM Room 129 ERB
Covering Lectures 11 to19
Open book - 1 legal text or ref., only.
You may write notes in your book.
Calculator allowed
A cover sheet will be included with
full instructions. For examples see
http://www.uta.edu/ronc/5340/tests/.
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Ideal diode equation
for EgN = EgN
Js = Js,p + Js,n = hole curr + ele curr
Js,p = qni2Dp coth(Wn/Lp)/(NdLp), [cath.]
= qni2Dp/(NdWn), Wn << Lp, “short”
= qni2Dp/(NdLp), Wn >> Lp, “long”
Js,n = qni2Dn coth(Wp/Ln)/(NaLn), [anode]
= qni2Dn/(NaWp), Wp << Ln, “short”
= qni2Dn/(NaLn), Wp >> Ln, “long”
Js,n<<Js,p when Na>>Nd , Wn & Wp cnr wdth
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Ideal diode equation
for heterojunction
• Js = Js,p + Js,n = hole curr + ele curr
Js,p = qniN2Dp/[NdLptanh(WN/Lp)], [cath.]
= qniN2Dp/[NdWN], WN << Lp, “short”
= qniN2Dp/(NdLp), WN >> Lp, “long”
Js,n = qniP2Dn/[NaLntanh(WP/Ln)], [anode]
= qniP2Dn/(NaWp), Wp << Ln, “short”
= qniP2Dn/(NaLn), Wp >> Ln, “long”
Js,p/Js,n ~ niN2/niP2 ~ exp[[EgP-EgN]/kT]
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Bipolar junction
transistor (BJT)
• The BJT is a “Si
sandwich”
Pnp (P=p+,p=p-) or
Npn (N=n+, n=n-)
• BJT action: npn
Forward Active
when VBE > 0 and
VBC < 0
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E
B
P
n
VEB
C
p
VCB
Depletion Region
Charge neutral Region
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npn BJT topology
IE
x’
IC
IB
x’E
0
0
xB
0
-WE
N-Emitter p-Base
Depletion
Region
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x
0
WB
x”c
x”
z
WB+WC
n-Collector
Charge Neutral
Region
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BJT boundary and
injection cond (npn)
2
ni
 VBE 
 , pnE 0 
 pnE 0 exp f
pnE
x' 0 
NE
 Vt 
0
pnE
x' xE 
2
n
 VBC 
 , pnC 0  i
pnC x" 0   pnC 0 exp f
NC
V
 t 
pnC x" x   0
C
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BJT boundary and
injection cond (npn)
Note that the Base BC are inter dependent
2
n
 VBE 
 , npB0  i
npB
 npB0 exp f
NB
x  0 
V
 t 
 VBC 
 .
npB
 npB0 exp f
x  xB
 Vt 
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IC npn BJT
(*Fig 9.2a)
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npn BJT bands in FA region
q(VbiE-VBE )
qVBE
q(VbiC-VBC )
qVBC
injection
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high field
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Coordinate system - prototype npn
BJT (Fig 9.8*)
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Notation for npn & pnp BJTs
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NE, NB, NC
xE, xB, xC
DE, DB, DC
LE, LB, LC
E, B, and C doping (maj)
E, B, and C CNR widths
Dminority for E, B, and C
Lminority for E, B, and C
(L2min = Dmin tmin)
tE0, tB0, tC0 minority carrier lifetimes for E, B, and C regions
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Notation for npn BJTs only
• pEO, nBO, pCO: E, B, and C thermal
equilibrium minority carrier conc
• pE(x’), nB(x), pC(x’’): positional mathematical function for the E, B, and C
total minority carrier concentrations
pE(x’), nB(x), pC(x’’): positional mathematical function for the excess
minority carriers in the E, B, and C
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Notation for pnp BJTs only
• nEO, pBO, nCO: E, B, and C thermal
equilibrium minority carrier conc
• nE(x’), pB(x), nC (x’’): positional mathematical function for the E, B, and C
total minority carrier concentrations
nE(x’), pB(x), nC(x’’): positional mathematical function for the excess
minority carriers in the E, B, and C
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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  

 ni2 

 VBC  
nB xB   nB0  exp
  1 , nB0   , etc.
 Vt  

 NB 

 VBC  
C : pC x"  0   pC 0  exp
  1 , pC xC   0
 Vt  

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Emitter solution in npn BJT
 2 pE x' pE x'
DE

 0 , pE  pE  pE0
2
tE 0
x'

xE  x"

 VBE  

pE0  exp
  1  sinh
LE
 Vt  


pE x' 
xE
sinh
LE

 VBE   xE  x'
 , xE  LE
pE x'  pE0  exp
  1 
 Vt   xE 

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Base solution in npn BJT
 2 nB x  nB x 


0
,

n

n

n
B
B
B0
2
DB tB 0
x

VBE
nB x' 
expf 

xB 
 Vt
sinh
nB0
LB
VBC
expf 
 Vt
x

sinh 

 LB

VBE
 nB0 expf 
 Vt

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 xB  x

 sinh 

 LB

 


 and when x B  LB


x
 1 
 x B

VBC
  expf 
 Vt

 x

 x B



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Collector solution in npn BJT
 2 pC x"
2
x"
pC x"

 0 , pC  pC  pC0
DC tC 0


xC  x" 
 VBC  

pC0  exp
  1  sinh
Vt  
LC



pC x" 
xC
sinh
LC
 x"
pC x"  pC0
, VBC  Vt , xC  LC
LC
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Hyperbolic tangent function
2
y
e x / L   e  x / L 
y
,
e
1y
 ...
x / L 
 x / L 
2!
e
e
 1  x     1  x  




x 
L
L

 

so if x  L, tanh   
 L   1  x     1  x  

 

L
L

 

x

tanh   
L


 lim 
x x

giving, 
tanh   

x
L L

0


L

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npn BJT regions of operation
VBC
Reverse
Active
Cutoff
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Saturation
Forward
Active
VBE
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npn FA BJT minority carrier
distribution (Fig 9.4*)
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npn RA BJT minority carrier
distribution (Fig 9.11a*)
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npn cutoff BJT min carrier
distribution (Fig 9.10a*)
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npn sat BJT minority carrier
distribution (Fig 9.10b*)
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npn BJT currents in the
forward active region ©RLC
JnE
JnC
JRB=JnE-JnC
IE =
-JEAE
IC =
JCAC
JGC
JpE
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JRE
IB=-(IE+IC ) JpC
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References
* Semiconductor Physics and Devices,
2nd ed., by Neamen, Irwin, Boston,
1997.
**Device Electronics for Integrated
Circuits, 2nd ed., by Muller and
Kamins, John Wiley, New York, 1986.
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