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Semiconductor Devices

by: Cassidy Casper

Semiconductor Devices ECE 30500

Cassidy Casper
GPA 3.59

Michael Melloch

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Michael Melloch
Class Notes
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This 3 page Class Notes was uploaded by Cassidy Casper on Saturday September 19, 2015. The Class Notes belongs to ECE 30500 at Purdue University taught by Michael Melloch in Fall. Since its upload, it has received 41 views. For similar materials see /class/207901/ece-30500-purdue-university in Electrical Engineering & Computer Science at Purdue University.

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Date Created: 09/19/15
Constants q 16 X 10 19 C Charge electron m0 911 X 10 31 Kg mass electron so 885 X 10 14FCm permittivity free space k 8617 x 105 eVK Boltzmann h 663 x 10 3415 Planck h h 10552 x 1034 27 kT 00259eV Thermal energy at T 2 300K kTq 0025911 Thermal voltage at T 300K n 1010Cm3 for silicon at 300K Miller Indices 1 Note intercepts of desired plane with coordinate axes 2 Divide each intercept by unit cell length 3 Take reciprocals of values 4 Use appropriate multiplier to convert to smallest possible set ofwhole numbers 5 Enclose in Bohr Model 4 135 E 2 m0q eVn123 H 24neohn quot2 EH is electron binding energy within hydrogen atom Ehwa27rfcf tphL n number electrons cm3 p number holes cm3 n p n in intrinsic semiconductor under equilibrium assuming room temperature n 2 X 105Cm3 in GaAs n 1 X 1010Cm3 in Si n 2 X 1013Cm3 in Ge ECE305 Reference Sheet Yangorang Donors electron increasing P As Sb Acceptors hole increasing B Ga n Al Density of States at energy level E l 2 2 5 55 yea m E 2 EC m 2mE E 91215 E S EU 4 l nzh Fermi Function fE 11 6EEFkT where Epis the Fermi energy or level Probably that state is not filled at given energy E is 1 f E Intrinsic Fermi level is slightly above the middle ofthe bandgap if effective hole mass is greater than the effective electron mass Equilibrium Carrier Concentrations 3kT 1 EF here Degenerate EC EF here Nondegenerate l EV EF here Degenerate 3kT M 32 NC 2 27th M 32 NV 2 2 i anz n NCeltEF Eckr p NVeEVEFkT n nieEFEikT p niem mm Where E is the Fermi level for an intrinsic semiconductor p Tl l39ND NAZO N N N N nng N N N N pniz E 1 3 Ei len 2 4 mn Carrier Action vd drift velocity vdisat z 107for Si at 300K jpldnft drift current density A qpvd holes Jpldrift llmpg I X A qpvdA mom me IOH 0395 I0 It illquot N or ND 1cm p and up electron mobilities at room temp in fig p resistivity a conductivity 2 p 1 a s 1 P 611er pp 1dEc 1dEv 8 3dx de JP 1Pdrift Pdiff llmpg qDPVP 11v Ndrift Ndiff llmm qDan ECE305 Reference Sheet Yangorang Einstein Relationship DNkT DPkT unqupq Photogeneration I Ioe x 10 2 light intensityjust inside material a material dependent absorption coefficient 6n GLOCIA 0041 at light G L is photogeneration rate cm393sec RG Analysis Parameters n0 p0 2 carrier concentrations under equilibrium n p 2 carrier concentrations under arbitrary conditions An n n0Ap p p0 deviations in carrier concentrations from equilibrium values NT 2 number of R G centerscm3 Low Level Injection Conditions Ap ltlt n0 n 3 n0 for n type material An ltlt p0p 3 p0 for p type material I 2 39 39r 2 wherec andc are electron and p cpNT 39 n anT p n hole capture coefficients the average time an excess minority carrier will live in a sea of majority carriers 6 A pl 2 p In n type materIal at i thermal R G Tr 6n An In p type materIal at i thermal R G Tn ECE305 Reference Sheet Yangorang Minority Carrier Diffusion Equations Mn 62An An I7 P P D 0 at N 6x2 n L 6A 62A A pn N n GL at 6x rp Table 31 Common Di 39usion Equtitiun Simphticatium Silnply imtian Steady state No concentration gradient or no dt usion current No drift current or E 0 N0 thermal R G No light TabiQZ v u i s U f y An H 39i in 7 39 M iv DN 4 0 Di No further sinipliiitution i r 2 0 Is isnnncx in the derivation Ea0 lt 3 F GL tO minim Sim itl ist Dilltismn liqtllttii39ifl Snluliuns s39uiuliun rm I t39 Blunt niulu no light A39l l IJI ILIU NIH IjV SUIMIIUII 1111 s ViV SArli39l 39139 III3 int i iii SOLUTIONquot 1M Alp Sultuitm rm 3 GIVEN lczuly llillL no umrcniimiu gradient S39IMI LIYED 3 DIN Iz39QN o T J g 1 Th SOLUTION Anp GI 7quot Solution nu 4 GIVEN Steady state no lLG no light SIMPLIFIED a 2 IAu I An DIII39Iv39I EQN o DNl 5d l I or SOLUTION AIIPX A B Minority Carrier Diffusion Lengths LP 2 1Dp L39p 39 LN 1IDATn Represents the average distance minority carriers can diffuse int annihilate o a sea of majority carriers before being d


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