Slide 1Second AssignmentTest 1 – Tuesday 22Feb11Diffused or Implanted IC Resistor (Fig 2.451)An IC Resistor with L = 8W (M&K)1Typical IC doping profile (M&K Fig. 2.441)Mobilities**IC Resistor ConductanceAn IC Resistor with Ns = 8, R = 8Rs (M&K)1The effect of lateral diffusion (M&K1)A serpentine pattern IC Resistor (M&K1)Fermi EnergySlide 13Slide 14Ex-field when Ef - Efi not constantSi and Al and model (approx. to scale)Making contact be- tween metal & s/cEquilibrium Boundary Conditions w/ contactIdeal metal to n-type barrier diode (fm>fs,Va=0)Slide 20Slide 21Slide 22Metal/semiconductor system typesReferencesEE 5340Semiconductor Device TheoryLecture 08 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L08-15Feb20112Second Assignment•Submit a signed copy of the document posted at www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf©rlc L08-15Feb20113Test 1 – Tuesday 22Feb11•11 AM Room 129 ERB•Covering Lectures 1 through 9•Open book - 1 legal text or ref., only.•You may write notes in your book.•Calculator allowed•A cover sheet will be included with full instructions. For examples see http://www.uta.edu/ronc/5340/tests/.©rlc L08-15Feb20114Diffused or ImplantedIC Resistor (Fig 2.451)©rlc L08-15Feb20115An IC Resistor with L = 8W (M&K)1©rlc L08-15Feb20116Typical IC dopingprofile (M&K Fig. 2.441)©rlc L08-15Feb20117Mobilities**©rlc L08-15Feb20118IC Resistor Conductance         g1R dxxnxqgdxxnxqLWGdxLWxnxqdGsx0nx0nnjj,©rlc L08-15Feb20119An IC Resistor with Ns = 8, R = 8Rs (M&K)1©rlc L08-15Feb201110The effect of lateral diffusion (M&K1)©rlc L08-15Feb201111A serpentine patternIC Resistor (M&K1)R = NSRS + 0.65-NCRSnote: RC = 0.65-RS©rlc L08-15Feb201112•The equilibrium carrier concentration ahd the Fermi energy are related as•The potential f = (Ef-Ef)/q•If not in equilibrium, a quasi-Fermi level (imref) is usedFermi EnergykTEEnn and , nnkTEEfifioiofifexpln©rlc L08-15Feb201113Electron quasi-Fermi Energy (n = no + n)kTEEnnn:is density carrier the and , nnnkTEE:defined is (Imref) level Fermi-Quasi Thefifnioiofifnexpln©rlc L08-15Feb201114Hole quasi-Fermi Energy (p = po + p)kTEEnpp:is density carrier the and , nppkTEE:as defined is Imref the holes, Forfpfiioiofpfiexpln©rlc L08-15Feb201115Ex-field when Ef - Ef not constant•Since f = (Ef - Ef)/q = Vt ln(no/ni)•When Ef - Ef = is position dependent,•Ex = -df/dx = -[d(Ef-Ef)/dx] = - Vt d[ln(no/ni)]/dx•If non-equilibrium fn = (Efn-Ef)/q = Vt ln(n/ni), etc•Exn = -[dfn/dx] = -Vt d[ln(n/ni)]/dx©rlc L08-15Feb201116Si and Al and model (approx. to scale)qfm,Al ~ 4.1 eVEoEFmEFpEFnEoEcEvEFiqfs,nqcsi~ 4.05 eVEoEcEvEFiqfs,pmetal n-type s/c p-type s/cqcsi~ 4.05 eV©rlc L08-15Feb201117Making contact be-tween metal & s/c•Equate the EF in the metal and s/c materials far from the junction•Eo(the free level), must be continuous across the jctn.N.B.: qc = 4.05 eV (Si),and qf = qc + Ec - EF EoEcEFEFiEvqc (electron affinity)qfFqf(work function)©rlc L08-15Feb201118Equilibrium Boundary Conditions w/ contact•No discontinuity in the free level, Eo at the metal/semiconductor interface.•EF,metal = EF,semiconductor to bring the electron populations in the metal and semiconductor to thermal equilibrium.•Eo - EC = qcsemiconductor in all of the s/c.•Eo - EF,metal = qfmetal throughout metal.©rlc L08-15Feb201119Ideal metal to n-typebarrier diode (fm>fs,Va=0)EFnEoEcEvEFiqfs,nqcsn-type s/cqfmEFmmetalqfBnqfiqf’nNo disc in EoEx=0 in metal ==> EoflatfBn=fm- cs = elec mtl to s/c barrfi=fBn-fn= fm-fs elect s/c to mtl barr Depl reg©rlc L08-15Feb201120Metal to n-typenon-rect cont (fm<fs)EFnEoEcEvEFiqfs,nqcsn-type s/cqfmEFmmetalqfB,nqfnNo disc in EoEx=0 in metal ==> Eo flatfB,n=fm - cs = elec mtl to s/c barrfi= fBn-fn< 0Accumulation regionAcc regqfi©rlc L08-15Feb201121Ideal metal to p-typebarrier diode (fm<fs)No disc in EoEx=0 in metal ==> EoflatfBn= fm- cs = elec mtl to s/c barr.fBp= fm- (cs + Eg)= hole m to s barr.fi = fm-fs,p = hole s/c to mtl barr.EFpEoEcEvEFiqfs,pqcsp-type s/cqfmEFmmetalqfBnqfiqfp<0Depl regqfBpqfi©rlc L08-15Feb201122Metal to p-typenon-rect cont (fm>fs)No disc in EoEx=0 in metal ==> Eo flatfB,n = fm - cs = elec mtl to s/c barrfBp= fm- (cs + Eg) = hole m to sfi = fm-fs,n = s/c to mtl barr.EFiEoEcEvEfPqfs,nqcsn-type s/cqfmEFmmetalqfBnq(fi)qfpAccum regqfBpqfi©rlc L08-15Feb201123Metal/semiconductorsystem typesn-type semiconductor•Schottky diode - blocking for fm > fs•contact - conducting for fm < fsp-type semiconductor•contact - conducting for fm > fs•Schottky diode - blocking for fm < fs©rlc L08-15Feb201124References1 and M&KDevice Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the m model.2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981.3 and **Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997.Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall,