© 2012 Eric Pop, UIUC ECE 340: Semiconductor Electronics 1

ECE 340 Lecture 37Narrow-base P-N diode

•One last touch-up before we get to bipolar transistors

•Let’s recall some math:

•What is a typical minority carrier diffusion length in Si?

•How does it compare to modern device lengths?

xx eex 21)sinh( xx eex

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Note: download the “Narrow-Base/BJT”

handout online!

© 2012 Eric Pop, UIUC ECE 340: Semiconductor Electronics 2

• Let’s revisit p-n carrierdistributions:

• 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 3

• 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:

• We have the “narrow” or “short” ℓ < Lp linear approximation:

• 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:

/,0( ) px Lnp x p e

,0( ) 1nxp x pL

( ) 0p x

© 2012 Eric Pop, UIUC ECE 340: Semiconductor Electronics 4

• Total injected (stored) minority charge at forward bias is the area under the “triangle”:

• Easy to write the hole diffusion current for “narrow” diode:

• Compare with “long” diode hole diffusion current from L23:

• Total diode current if: It’s a p+/n (NA >> ND) diode

It’s a p/n (NA ~ ND) diode

121

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