EE 5340 Semiconductor Device Theory Lecture 18 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

Test 2 – Tuesday 05Apr11 11 AM Room 129 ERB Covering Lectures 11 to19 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 L18-29Mar2011

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Ideal diode equation for EgN = EgN Js = Js,p + Js,n = hole curr + ele curr Js,p = qni2Dp coth(Wn/Lp)/(NdLp), [cath.] = qni2Dp/(NdWn), Wn << Lp, “short” = qni2Dp/(NdLp), Wn >> Lp, “long” Js,n = qni2Dn coth(Wp/Ln)/(NaLn), [anode] = qni2Dn/(NaWp), Wp << Ln, “short” = qni2Dn/(NaLn), Wp >> Ln, “long” Js,n<<Js,p when Na>>Nd , Wn & Wp cnr wdth ©rlc L18-29Mar2011

Ideal diode equation for heterojunction Js = Js,p + Js,n = hole curr + ele curr Js,p = qniN2Dp/[NdLptanh(WN/Lp)], [cath.] = qniN2Dp/[NdWN], WN << Lp, “short” = qniN2Dp/(NdLp), WN >> Lp, “long” Js,n = qniP2Dn/[NaLntanh(WP/Ln)], [anode] = qniP2Dn/(NaWp), Wp << Ln, “short” = qniP2Dn/(NaLn), Wp >> Ln, “long” Js,p/Js,n ~ niN2/niP2 ~ exp[[EgP-EgN]/kT] ©rlc L18-29Mar2011

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 ©rlc L18-29Mar2011

npn BJT topology x x’ p-Base n-Collector N-Emitter z WB WB+WC -WE x”c Charge Neutral Region Depletion Region x x’ p-Base n-Collector N-Emitter z WB WB+WC -WE x”c x” xB x’E IE IC IB ©rlc L18-29Mar2011

BJT boundary and injection cond (npn) ©rlc L18-29Mar2011

BJT boundary and injection cond (npn) ©rlc L18-29Mar2011

IC npn BJT (*Fig 9.2a) ©rlc L18-29Mar2011

npn BJT bands in FA region q(VbiE-VBE ) q(VbiC-VBC ) qVBE qVBC injection high field ©rlc L18-29Mar2011

Coordinate system - prototype npn BJT (Fig 9.8*) ©rlc L18-29Mar2011

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) tE0, tB0, tC0 minority carrier life- times for E, B, and C regions ©rlc L18-29Mar2011

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 dpE(x’), dnB(x), dpC(x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C ©rlc L18-29Mar2011

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 ©rlc L18-29Mar2011

npn BJT boundary conditions ©rlc L18-29Mar2011

Emitter solution in npn BJT ©rlc L18-29Mar2011

Base solution in npn BJT ©rlc L18-29Mar2011

Collector solution in npn BJT ©rlc L18-29Mar2011

Hyperbolic tangent function ©rlc L18-29Mar2011

npn BJT regions of operation VBC Reverse Active Saturation VBE Forward Active Cutoff ©rlc L18-29Mar2011

npn FA BJT minority carrier distribution (Fig 9.4*) ©rlc L18-29Mar2011

npn RA BJT minority carrier distribution (Fig 9.11a*) ©rlc L18-29Mar2011

npn cutoff BJT min carrier distribution (Fig 9.10a*) ©rlc L18-29Mar2011

npn sat BJT minority carrier distribution (Fig 9.10b*) ©rlc L18-29Mar2011

npn BJT currents in the forward active region ©RLC IC = JCAC IB=-(IE+IC ) JnE JnC IE = -JEAE JRB=JnE-JnC JpE JGC JRE JpC ©rlc L18-29Mar2011

References * Semiconductor Physics and Devices, 2nd ed., by Neamen, Irwin, Boston, 1997. **Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, John Wiley, New York, 1986. ©rlc L18-29Mar2011