Slide 1Review the FollowingFirst AssignmentSecond AssignmentSchedule Changes Due to University Weather ClosingsIntrinsic carrier conc. (MB limit)Classes of semiconductorsEquilibrium concentrationsEquilibrium conc (cont.)n-type equilibrium concentrationsPosition of the Fermi Levelp-type equilibrium concentrationsPosition of the Fermi LevelEF relative to Ec and EvEF relative to EfiLocating Efi in the bandgapExample calculationsSample calculationsEquilibrium electron conc. and energiesEquilibrium hole conc. and energiesCarrier MobilityCarrier mobility (cont.)Carrier mobility (cont.)Slide 24Figure 1.16 (cont. M&K)Drift CurrentDrift current resistanceDrift current resistance (cont.)ReferencesReferencesEE 5340Semiconductor Device TheoryLecture 05 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L05-08Feb20112Review the Following•R. L. Carter’s web page:–www.uta.edu/ronc/•EE 5340 web page and syllabus. (Refresh all EE 5340 pages when downloading to assure the latest version.) All links at:–www.uta.edu/ronc/5340/syllabus.htm•University and College Ethics Policies–www.uta.edu/studentaffairs/conduct/•Makeup lecture at noon Friday (1/28) in 108 Nedderman Hall. This will be available on the web.©rlc L05-08Feb20113First Assignment•Send e-mail to [email protected]–On the subject line, put “5340 e-mail”–In the body of message include•email address: ______________________•Your Name*: _______________________•Last four digits of your Student ID: _____* Your name as it appears in the UTA Record - no more, no less©rlc L05-08Feb20114Second Assignment•Submit a signed copy of the document posted at www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf©rlc L05-08Feb20115Schedule Changes Due to University Weather Closings•Make-up class will be held Friday, February 11 at 12 noon in 108 Nedderman Hall.•Additional changes will be announced as necessary.•Syllabus and lecture dates postings will be updated in the next 24 hours.•Project Assignment will be posted in the next 36 hours.©rlc L05-08Feb20116Intrinsic carrierconc. (MB limit)•ni2 = no po = Nc Nv e-Eg/kT•Nc = 2{2pm*nkT/h2}3/2•Nv = 2{2pm*pkT/h2}3/2•Eg = 1.17 eV - aT2/(T+b) a = 4.73E-4 eV/K b = 636K©rlc L05-08Feb20117Classes ofsemiconductors•Intrinsic: no = po = ni, since Na&Nd << ni, ni2 = NcNve-Eg/kT, ~1E-13 dopant level !•n-type: no > po, since Nd > Na•p-type: no < po, since Nd < Na•Compensated: no=po=ni, w/ Na- = Nd+ > 0•Note: n-type and p-type are usually partially compensated since there are usually some opposite- type dopants©rlc L05-08Feb2011Equilibriumconcentrations•Charge neutrality requires q(po + Nd+) + (-q)(no + Na-) = 0•Assuming complete ionization, so Nd+ = Nd and Na- = Na •Gives two equations to be solved simultaneously 1. Mass action, no po = ni2, and 2. Neutrality po + Nd = no + Na8©rlc L05-08Feb20119Equilibriumconc (cont.)•For Nd > Na (taking the + root)no = (Nd-Na)/2 + {[(Nd-Na)/2]2+ni2}1/2•For Nd >> Na and Nd >> ni, can use the binomial expansion, givingno = Nd/2 + Nd/2[1 + 2ni2/Nd2 + … ]•So no = Nd, and po = ni2/Nd in the limit of Nd >> Na and Nd >> ni©rlc L05-08Feb201110n-type equilibriumconcentrations•N ≡ Nd - Na , n type  N > 0•For all N, no = N/2 + {[N/2]2+ni2}1/2•In most cases, N >> ni, sono = N, and po = ni2/no = ni2/N, (Law of Mass Action is al-ways true in equilibrium)©rlc L05-08Feb201111Position of theFermi Level•Ef is the Fermi level when no = po•Ef shown is a Fermi level for no > po •Ef < Ef when no < po•Ef < (Ec + Ev)/2, which is the mid-band©rlc L05-08Feb201112p-type equilibriumconcentrations•N ≡ Nd - Na , p type  N < 0 •For all N, po = |N|/2 + {[|N|/2]2+ni2}1/2•In most cases, |N| >> ni, sopo = |N|, and no = ni2/po = ni2/|N|, (Law of Mass Action is al-ways true in equilibrium)©rlc L05-08Feb201113Position of theFermi Level•Ef is the Fermi level when no = po•Ef shown is a Fermi level for no > po •Ef < Ef when no < po•Ef < (Ec + Ev)/2, which is the mid-band©rlc L05-08Feb201114EF relative to Ec and Ev•Inverting no = Nc exp[-(Ec-EF)/kT] gives Ec - EF = kT ln(Nc/no) For n-type material: Ec - EF =kTln(Nc/Nd)=kTln[(Ncpo)/ni2]•Inverting po = Nv exp[-(EF-Ev)/kT] gives EF - Ev = kT ln(Nv/po) For p-type material: EF - Ev = kT ln(Nv/Na)©rlc L05-08Feb201115EF relative to Ef•Letting ni = no gives  Ef = Ef ni = Nc exp[-(Ec-Ef)/kT], so Ec - Ef = kT ln(Nc/ni). Thus EF - Ef = kT ln(no/ni) and for n-type EF - Ef = kT ln(Nd/ni) •Likewise Ef - EF = kT ln(po/ni) and for p-type Ef - EF = kT ln(Na/ni)©rlc L05-08Feb201116Locating Ef in the bandgap •Since Ec - Ef = kT ln(Nc/ni), and Ef - Ev = kT ln(Nv/ni) •The 1st equation minus the 2nd gives Ef = (Ec + Ev)/2 - (kT/2) ln(Nc/Nv)•Since Nc = 2.8E19cm-3 > 1.04E19cm-3 = Nv, the intrinsic Fermi level lies below the middle of the band gap©rlc L05-08Feb201117Examplecalculations•For Nd = 3.2E16/cm3, ni = 1.4E10/cm3no = Nd = 3.2E16/cm3po = ni2/Nd , (po is always ni2/no)= (1.4E10/cm3)2/3.2E16/cm3= 6.125E3/cm3 (comp to ~1E23 Si)•For po = Na = 4E17/cm3,no = ni2/Na = (1.4E10/cm3)2/4E17/cm3= 490/cm3©rlc L05-08Feb201118Samplecalculations•Ef = (Ec + Ev)/2 - (kT/2) ln(Nc/Nv), so at 300K, kT = 25.86 meV and Nc/Nv = 2.8/1.04, Ef is 12.8 meV or 1.1% below mid-band•For Nd = 3E17cm-3, given thatEc - EF = kT ln(Nc/Nd), we haveEc - EF = 25.86 meV ln(280/3), Ec - EF = 0.117 eV =117meV ~3x(Ec - ED) what Nd gives Ec-EF =Ec/3©rlc L05-08Feb201119Equilibrium electronconc. and energiesov2ivofioffffiococfcfcopNlnkTnNnlnkTEvE and;nnlnkTEE or ,kTEEexpnn;NnlnkTEE or ,kTEEexpNn©rlc L05-08Feb201120Equilibrium hole conc. and energiesoc2icofcioffffiovofvfvvonNlnkTnNplnkTEE and;nplnkTEE or ,kTEEexpnp;NplnkTEE or ,kTEEexpNp©rlc L05-08Feb201121Carrier Mobility•In an electric feld, Ex, the velocity (since ax = Fx/m* = qEx/m*) is vx = axt = (qEx/m*)t, and the displx = (qEx/m*)t2/2•If every tcoll, a collision occurs which “resets” the velocity to <vx(tcoll)> = 0, then <vx> = qExtcoll/m* = mEx©rlc L05-08Feb201122Carrier mobility (cont.)•The response function m is the mobility.•The mean time between collisions,