Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/ EE5342 – Semiconductor Device Modeling and Characterization Lecture 12 February 26, 2010 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc/

ln ia ln(IKF) ln[(IS*IKF) 1/2] ln(ISR) ln(IS) va= Vext VKF Vext - vd = ia*Rs low level injection ln ia ln(IKF) Effect of Rs ln[(IS*IKF) 1/2] Effect of high level injection ln(ISR) Data ln(IS) va= Vext recomb. current VKF L10 February 17

Static Model Equations for I-V Parameter Extraction In the region where: id ~ ISeff[exp {vd/(NeffVt)} – 1] {did/dvd}/iD = d[ln(id)]/dvd = 1/(NeffVt), so {dvd/d[ln(id)]}/Vt = Neff @ (id,vd), and exp{ln(id) – vd/(NeffVt)} = Iseff @ (id,vd). Note: iD, Vt, etc., are normalized to 1A, 1V, resp. L10 February 17

Static Model Equations for C-V Parameter Extraction The Capacitance-Voltage model eqn. is: Cj = CJO[1 - vd/VJ]-M {dvd/d[ln(Cj)]} = -(1/M)(1 - vd/VJ) Experimentally plot y = {dvd/d[ln(Cj)]} vs. vd The slope estimates -1/M, the vd-axis intercept estimates VJ. On the Cj vs. vd plot, the Cj-axis intercept is CJO L10 February 17

PiN Diode PiN: Na >> Nint (= N-) & Nint << Nd Wi = Intrinsic region (metall.) width Em,P-T = Peak field mag. when xn = Wi Vbi = fi = Vtln(NaNd/ni2) Vbi,int = fi,int = Vtln(NaNint/ni2) VHL = Vtln(Nd/Nint), the offset at N+N- Vbi = Vbi,int + VHL VPT = applied voltage when xn = Wi L12 02/26/10

PiN Diode Depletion Fields Normalized Position, x’ = x/Wi Normalized Field, E/Em,P-T dx’p dx’n x’n -x’p L12 02/26/10

PiN Diode Depletion Conditions

CV data and N(x) calculation

Bipolar junction transistor (BJT) E B C VEB VCB Charge neutral Region Depletion Region The BJT is a “Si sandwich” Pnp (P=p+,p=p-) or Npn (N=n+, n=n-) BJT action: npn Forward Active when VBE > 0 and VBC < 0 L12 02/26/10

BJT coordinate systems z x”c x” WB WB+WC -WE xB x x’E x’ Charge neutral Region Depletion Region Base Collector Emitter L12 02/26/10

BJT boundary and injection cond (npn) L12 02/26/10

BJT boundary and injection cond (npn) L12 02/26/10

IC npn BJT (*Fig 9.2a) L12 02/26/10

npn BJT bands in FA region q(VbiE-VBE ) q(VbiC-VBC ) qVBE qVBC injection high field L12 02/26/10

Coordinate system - prototype npn BJT (Fig 9.8*) L12 02/26/10

Notation for npn & pnp BJTs NE, NB, NC E, B, and C doping (maj) xE, xB, xC E, B, and C CNR widths DE, DB, DC Dminority for E, B, and C LE, LB, LC Lminority for E, B, and C (L2min = Dmin tmin) The minority carrier lifetimes in the E, B, and C regions are tE0, tB0, & tC0 L12 02/26/10

Notation for npn BJTs only pEO, nBO, pCO: E, B, and C thermal equilibrium minority carrier conc pE(x’), nB(x), pC(x’’): positional mathe- matical function for the E, B, and C total minority carrier concentrations The excess carrier concentrations dpE(x’), dnB(x), dpC(x’’) are the positional mathematical functions in the E, B, and C L12 02/26/10

Notation for pnp BJTs only nEO, pBO, nCO: E, B, and C thermal equilibrium minority carrier conc nE(x’), pB(x), nC (x’’): positional mathe- matical function for the E, B, and C total minority carrier concentrations dnE(x’), dpB(x), dnC(x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C L12 02/26/10

npn BJT boundary conditions L12 02/26/10

Emitter solution in npn BJT

Base solution in npn BJT

Collector solution in npn BJT

Hyperbolic sine function

npn BJT regions of operation VBC Reverse Active Saturation VBE Forward Active Cutoff L12 02/26/10

npn FA BJT minority carrier distribution (Fig 9.4*) L12 02/26/10

npn RA BJT minority carrier distribution (Fig 9.11a*) L12 02/26/10

npn cutoff BJT min carrier distribution (Fig 9.10a*) L12 02/26/10

npn sat BJT minority carrier distribution (Fig 9.10b*) L12 02/26/10

Defining currents in FA mode npn BJT (Fig 9.13*) L12 02/26/10

References 1 OrCAD PSpice A/D Manual, Version 9.1, November, 1999, OrCAD, Inc. 2 Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, 1993. * Semiconductor Physics & Devices, by Donald A. Neamen, Irwin, Chicago, 1997. L12 02/26/10