ECE340_L8_S14_Distribution

# 6x1018 cm 3 na91x1017 cm 3 the common rule of thumb

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Unformatted text preview: * n no = N c • e 3/2 − ( Ec − E f )/ kT 16 &gt;&gt; 1 Hole Concentra`on po in a p- type Semiconductor at Equilibrium no(K)= ni2/po , minority carrier Ec Ef e e e ee e e EA e e e e ee ee e e ∫ [1 − f ( E )] • N (E )dE −∞ Ei Ev po = Ev po = N v ( Ev ) • [1 − f ( Ev )] f ( E ) = Fermi Distribution Function N ( E ) = Density of States (cm −3 ) N v ( Ev ) = Effective Density of States (located at valence band edge) e e po(K)= NA, majority carrier f ( Ev ) = 1 − f ( Ev ) = e 1 1+ e − ( E f − Ev )/ kT ( Ev − E f )/ kT if e ( E f − Ev )/ kT ⎛ 2π • m kT ⎞ N v ( Ev ) = 2 ⎜ ⎟ h2 ⎝ ⎠ * p po = N v • e &gt;&gt; 1 3/2 − ( E f − Ev )/ kT 17 Approxima`ng the Fermi Integral: Further Comments •  The approxima`ons to the Fermi integral are valid for non- degenerate semiconductors –  In a non- degenerate semiconductor, the Fermi Level is well within the forbidden gap (several kT away in energy) –  From a prac`cal perspec`ve, the implica`on is that the doping density is not too high –  For Si at room temperature: •  ND&lt;1.6x1018 cm- 3 •  NA&lt;9.1x1017 cm- 3 •  The common rule of thumb is that (Ec- Ef) &gt; ~3kT for the approxima`on to be valid ∞ no = Ec no = N c ( Ec ) • f ( Ec ) f ( E ) = Fermi Function Distribution N ( E ) = Density...
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## This note was uploaded on 03/06/2014 for the course ECE 340 taught by Professor Leburton during the Spring '11 term at University of Illinois, Urbana Champaign.

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