1 Prof. Ming-Jer Chen Department of Electronics Engineering National Chiao-Tung University October 9, 2014 DEE4521 Semiconductor Device Physics Lecture 3b: Transport: Generation and Recombination (g-r) Transport: Generation and Recombination (g-r)

2 This lecture accompanies pp. 131–153 of textbook. Textbook pages involved

Energy band diagram of the semiconductor of Figure 3.18, under electrical bias and optical illumination. The combination rate R, thermal generation rate G th, and the optical generation rate G op are illustrated. Figure 3.19 Bulk Generation or Recombination rate: per unit volume per unit time Microscopic Picture

4 Optical injection: A powerful means to address g-r process.

5 Quasi-Fermi Levels

(a) Illustration of minority carrier diffusion in a surface-illuminated p-type semiconductor. The absorption is assumed to occur at the surface (how to make it real?). (b) Plots of the excess minority carrier concentration as a function of distance into the bar with increasing time. As the excess carriers are generated at the surface, they diffuse to regions of lower concentration, where they recombine. Figure 3.22 Transient Example 1

Illustration of quasi Fermi levels for electrons and holes for the steady-state nonequilibrium case of Figure 3.22, with external field = 0. Figure 3.24 Level Split due to Carrier (Optical) Injection Equilibrium n o = N C exp(-(E C -E F )/k B T) = n i exp((E F -E i )/k B T) p o = N V exp(-(E F -E V )/k B T) = n i exp((E i -E F )/k B T) Quasi-Equilibrium (or non-equilibrium with a small field applied) n = N C exp(-(E C -E Fn )/k B T) = n i exp((E Fn -E i )/k B T) p = N V exp(-(E Fp -E V )/k B T) = n i exp((E i -E Fp )/k B T)

8 R – G = Equilibrium Quasi-equilibrium Net recombination rate Principle of detailed balance Hole lifetime Electron lifetime n-type bulk p-type bulk For optical injection (photon absorption) case Thermal generation rate Assume trap level E t at midgap Thermal recombination rate

The geometry for determining the continuity equation. The rate at which carriers accumulate in the incremental volume depends on the incoming and outgoing currents as well as the recombination and generation within the region dx. Figure 3.17 Then we can write the Continuity Equation according to the Conservation of Flux in two channels (one of conduction band and one of valence band): For p-type semiconductor: dn/dt =  dF n /dx + (G n –R n ) = (1/q)(dJ n /dx) + (G – R) = d  n/dt = (1/q)(dJ n /dx) + (G op –(  n/  n )) dp/dt =  dF p /dx + (G p –R p ) =  (1/q)(dJ p /dx) + (G – R) = d  p/dt =  (1/q)(dJ p /dx) + (G op –(  n/  n ))

The geometry for determining the continuity equation. The rate at which carriers accumulate in the incremental volume depends on the incoming and outgoing currents as well as the recombination and generation within the region dx. Figure 3.17 Then we can write the Continuity Equation according to Conservation of Flux in two channels (one of conduction band and one of valance band): For n-type semiconductor: dn/dt =  dF n /dx + (G n –R n ) = (1/q)(dJ n /dx) + (G – R) = d  n/dt = (1/q)(dJ n /dx) + (G op –(  p/  p )) dp/dt =  dF p /dx + (G p –R p ) =  (1/q)(dJ p /dx) + (G – R) = d  p/dt =  (1/q)(dJ p /dx) + (G op –(  p/  p ))

11 These expressions may be misleading from the aspect of the the conservation of flux.

Schematic of a circuit used to measure minority carrier lifetime in semiconductors. Figure 3.18 Steady State Example 2

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14 Valid only for a sample thickness of no more than the reciprocal of the absorption coefficient .

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17 Variation of excess carriers in a semiconductor under pulsed illumination. (a) When the light is turned on, the excess carrier concentration increases exponentially. For the complete pulse, (b) the rise and fall time constants are equal to the minority carrier lifetimes. Figure 3.20

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19 Plot of minority carrier lifetime in uncompensated high quality Si as a function of doping concentration N A or N D. Figure 3.21

20 Example 3 (average time for a carrier to stay in a band)

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22 This thought experiment is quite interesting.