Examination No. 3 - Tuesday, Nov. 15

Transcription

1 NAME (lease rit) SOLUTIONS ECE 35 - DEVICE ELECTRONICS Fall Semester 005 Examiati N 3 - Tuesday, Nv The time fr examiati is hr 5 mi Studets are allwed t use 3 sheets f tes Please shw yur wrk, artial credit may be give At each rblem state exlicitly all assumtis that yu make i the sluti rcess Shw yur wrk with uits, where alicable Please write the aer rvided Use additial sheets ly if ecessary 0 (0 ts) A Si substrate at T = 300 K ctais a accetr imurity ccetrati f 6 3 Na = 0 a) (0 its) Determie the ccetrati f dr imurity atms that must be added s that the material bees -tye ad its Fermi eergy is 00[ ev ] belw the edge f cducti bad The et dig, uder the assumti f lete iizati, determies the desity f majrity carriers, thus + ( E c E f )/ N kt d Na Nce = This yields + 9 ( 0/ 0059) 6 3 Nd Na = 8 0 e = which, uder the secified assumti yields = 4 0 The required dig is: Nd = Na = 4 0 b) (0 its) Evaluate the resistivity f material The resistivity is ρ = qμ+ qμ Csiderig the established majrity carrier ccetrati we determie the ccetrati f mirity carriers as ( ) i 3 3 = = = / 6 3 Because i much lwer tha the resistivity is determied by the electrs Readig the electr mbility frm the Useful Data with the ttal ccetrati N = N + N = 0 / / = 34 0 / T a d we btai μ = 00 / V s which yields the resistivity ρ = = 0458[ Ω] qμ / V s 4 0

2 (0 its) A slab f -tye Si ket i dark rm begis t be illumiated at time t = 0 The illumiati geerates carriers at the rate, G, which is idetical i the etire slab Assume that the rebiati rate f mirity carriers,, ad the life time,, that is L R, is determied by the rati f excess mirity carriers, R = a) (0 its) Usig the geeral ctiuity equati frmulate the equati gverig the chage f excess carrier desity The ct equati Because ( ) j = + GL t q x = 0 = cst ad because f the sace uifrmity ( d = GL dt r else usig the tati du u + = GL dt u = ( ) x = 0 ) we write b) (0 its) Determie the iitial cditi fr the equati The iitial cditi is u( 0) = ( 0) = 0 because ( 0) =

3 3 (0 its) A -tye material fabricated by dig the itrisic Si with accetr imurity f desity 5 3 N a = 60 frms a ctact with the gld cductr a) (0 its) Sketch the eergy-bad diagram at thermal equilibrium ad idicate the barrier height ad built-i tetial qφ B E f qv bi b) (7 its) Calculate the deleti width, x d 5 9 ( ) [ ] ( ) [ ] E E = ktl 6 0 / = 0 ev f v qφ = qχ + E E E = + = ev Vbi Si Si g f v = =003[ ev ] xd = = [ μm] c) (3 its) Calculate the barrier height, qφ B qφ = qχ + E qφ = = 045[ ev ] B Si g Au 3

4 4 (0 its) A very lg -tye Si cductr with the crss-sectial area A= 00 was fabricated such that the dig level is N 0 7 / 3 a = The cductr remais i rm temerature, T = 300 K At the e ed f the cductr, desigated by x = 0 (x-axis rus alg the cductr), there is a excitati causig ijecti f hles, such that the steady state ccetrati f 5 3 excess hles, Δ, at this ed is Δ = 0 Assume life time f hles t be 0 = [ s] a) (0 its) What is the steady state searati betwee E ad at the distace 0 μm frm the it f excitati x / L = +Δ e ; L D Fr Thus D = = 0059[ V] 300 = 777 V s s = ; D = Vμ t E [ ] we read frm the mbility vs ttal dig grah μ = 300 V s ad 9 L = D = Vtμ = 0059[ V] [ s] 0787 μm = Vs Csequetly fr x = 0[ μm] we btai: ( ) ( Ei Ef ) / kt Because e c = / = e = i we ca write [ ] 7 Ei Ef = ktl = 0059 ev l = [ ev] i 07 0 = + = + = Thus E E E E E ( )[ ev] 09759[ ev] c f g i f b) (0 its) What is the hle curret i the cductr at x 0[ μm] = Usig d d j = qd ad I = Aj we btai I = qad dx dx / Frm the exressi fr the hle ccetrati we btai d x L = Δ e ad thus dx L [ As ] D x/ L s 5 3 0/ 0787 I = qa Δ e = 0 / e = 036 A 4 L [ ] [ ] 4

5 5 (0 its) Give ccise resses t the fllwig (the clarity f yur writig is at remium here): a) (5 its) Defie the ccet f Lw Level Ijecti The LLI assumti meas that the ccetrati f mirity carriers ijected it a material with carriers f site ature (majrity carriers) is egligible with resect t the ccetrati f majrity carries This allws us t assume that the ijecti f mirity carriers des t cause ay ractical chage i the ccetrati f majrity carriers I ther wrds the ccetrati f mirity carriers is rders f magitude lwer tha the ccetrati f majrity carries b) (5 its) Exlai the deleti arximati Deleti arximati meas that there are mbile charges i the deleti regi This meas that the ucvered (t balaced) charge i the deleti regi is immbile The charge desity i the deleti regi is determied by the dig c) (5 its) What is the iterretati f Fermi-Dirac distributi The Fermi-Dirac distributi f( E) = ( f )/ E E kt + e reresets the rbability that the electr eergy, radm variable, e, des t exceed the value f E d) (5 its) Give the mathematical exressi f the Jucti law, list the uderlyig assumtis, defie all quatities ivlved i the exressi The Jucti laws ' Va / Vt ' ( x) = e fr the -side f the jucti at x = x ad ' Va Vt ' x = e fr the -side f the jucti at x = x ( ) / determie the chage i the ccetrati f ijected mirity carriers caused by the bias, The symbls ad rereset ccetrati f mirity carriers i - ad -side resectively i thermal equilibrium V a 5