Transcript ECE 340, Univ. Illinois Urbana-Champaign

Note: download the
“Narrow-Base/BJT”
handout online!
ECE 340 Lecture 37
Narrow-base P-N diode
• One last touch-up before we get to bipolar transistors
• Let’s recall some math:
sinh( x) 
tanh(x) 
e
x

1 x x
e e
2

sinh(x)
cosh(x)
x 2 x3
 1 x   
2! 3!
cosh( x) 

1 x
e  e x
2
ctnh( x) 

1
tanh(x)
xn
 (1)

n!
n
(what if 0 < x << 1?)
• What is a typical minority carrier diffusion length in Si?
• How does it compare to modern device lengths?
© 2012 Eric Pop, UIUC
ECE 340: Semiconductor Electronics
1
• Let’s revisit p-n carrier
distributions:
• Draw “usual” distributions under forward bias (see L23-L24):
• Now if the n-side is shorter than the diffusion length (ℓ < Lp):
© 2012 Eric Pop, UIUC
ECE 340: Semiconductor Electronics
2
• Remember, the (metal) contacts at the ends of the p-n
junction can be thought of as infinite source/sink of carriers
• So instead of the “long” (ℓ > Lp) exponentially decaying:
 p( x)  pn,0e
 x / Lp

• We have the “narrow” or “short” ℓ < Lp linear approximation:
 x
 p( x)  pn,0 1   
 L
• What is the physical meaning of the diffusion length Lp?
• Note the diode is now too narrow (short) for any hole
recombination in the n-region. So, all recombination
happens at the contact which sets a boundary condition for
our excess minority carrier concentration:  p( x  )  0
© 2012 Eric Pop, UIUC
ECE 340: Semiconductor Electronics
3
• Total injected (stored) minority charge at forward bias is the
area under the “triangle”:
ni2 qV / kT
1
1
Qp  qp Al   qAl
e
1
2
2
ND


• Easy to write the hole diffusion current for “narrow” diode:
dp
J p  qD p

dx
• Compare with “long” diode hole diffusion current from L23:
Dp ni2 qV kT
Jp  q
(e
 1)
Lp N D
• Total diode current if:
 It’s a p+/n (NA >> ND) diode
 It’s a p/n (NA ~ ND) diode
© 2012 Eric Pop, UIUC
ECE 340: Semiconductor Electronics
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