Semiconductors - Carrier Recombination

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SUMMARY

The discussion revolves around the analysis of carrier recombination in a silicon sample doped with acceptors at a concentration of 3E16 cm-3. An excess electron-hole pair (EHP) density of 1E14 cm-3 is generated, which increases to 5E13 cm-3 after 13.9 μs. The initial EHP density does not satisfy the low-level injection condition, and the lifetime of the excess carriers can be calculated using the formula Tn = 1/α(n0 + p0). The discussion also addresses how to express the minority carrier concentration over time.

PREREQUISITES
  • Understanding of semiconductor physics, specifically carrier recombination.
  • Familiarity with low-level injection conditions in semiconductors.
  • Knowledge of excess carrier density calculations and their implications.
  • Proficiency in using equations related to carrier lifetime and generation rates.
NEXT STEPS
  • Study the concept of low-level injection in semiconductors.
  • Learn how to calculate carrier lifetime using Tn and α values.
  • Explore the relationship between excess carrier density and intrinsic carrier concentration.
  • Investigate the mathematical expressions for minority and majority carrier concentrations over time.
USEFUL FOR

Students and professionals in semiconductor physics, electrical engineering, and materials science who are analyzing carrier dynamics in doped silicon and other semiconductor materials.

Marcin H
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Homework Statement


A sample of Si at room temperature is doped with acceptors at a concentration of 3E16 cm^-3. An excess electron hole pair density of 1E14 cm^-3 is generated at some time t = 0. At t = 13.9 μs the excess EHP density is measured and found to be 5E13 cm^-3.(A). Does the initial excess EHP density satisfy the low-level injection condition? From the given information,
calculate the lifetime of the excess carriers.

(B). Given your answer to part (a), how long will it take for the excess minority carrier concentration to equal the
intrinsic carrier concentration?

(C). Give expressions of n and p as a function of t.

Homework Equations


Low Level Injection

Tn = 1/α(no+po)

The Attempt at a Solution



I am not sure how to begin this problem. How is low level injection related to EHP density? I thought we have to look at majority/minority carriers to determine that?

And for the carrier lifetime how do we find Tn without alpha, or the intrinsic carrier concentrations. I'm not sure how EHP densities can help find that.
 
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I can find the generation rate by [(1E14 cm^-3) - (5E13 cm^-3)]/13.9us

but this isn't the equilibrium generation rate right? Or is it?
 

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