Slide 1Test 2 – Tuesday 05Apr11Slide 3Slide 4Ideal diode equation for EgN = EgNIdeal diode equation for heterojunctionBipolar junction transistor (BJT)npn BJT topologyBJT boundary and injection cond (npn)BJT boundary and injection cond (npn)IC npn BJT (*Fig 9.2a)npn BJT bands in FA regionCoordinate system - prototype npn BJT (Fig 9.8*)Notation for npn & pnp BJTsNotation for npn BJTs onlyNotation for pnp BJTs onlynpn BJT boundary conditionsEmitter solution in npn BJTBase solution in npn BJTCollector solution in npn BJTHyperbolic tangent functionnpn BJT regions of operationnpn FA BJT minority carrier distribution (Fig 9.4*)npn RA BJT minority carrier distribution (Fig 9.11a*)npn cutoff BJT min carrier distribution (Fig 9.10a*)npn sat BJT minority carrier distribution (Fig 9.10b*)npn BJT currents in the forward active region ©RLCReferencesEE 5340Semiconductor Device TheoryLecture 18 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L18-29Mar20112Test 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 L18-29Mar20113©rlc L18-29Mar20114©rlc L18-29Mar20115Ideal diode equation for EgN = EgN Js = Js,p + Js,n = hole curr + ele currJs,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 L18-29Mar20116Ideal diode equationfor heterojunction•Js = Js,p + Js,n = hole curr + ele currJs,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 L18-29Mar20117Bipolar junctiontransistor (BJT)•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 PnpE B CVEBVCBCharge neutral RegionDepletion Region©rlc L18-29Mar20118npn BJT topologyCharge Neutral RegionDepletion Regionxx’p-Base n-CollectorN-Emitterz0WBWB+WC-WE0x”cx”0xB0x’EIEICIB©rlc L18-29Mar20119BJT boundary andinjection cond (npn)    0pp , VVfexppp0pp , VVfexpppCC2iEE2ix"xnCNn0nCtBC0nC0"xnCx'xnENn0nEtBE0nE0'xnE©rlc L18-29Mar201110BJT boundary andinjection cond (npn)  . VVfexpnnn , VVfexpnndependent-inter are BC Base the that NotetBC0pBxBxpBNn0pBtBE0pB0xpBB2i©rlc L18-29Mar201111IC npn BJT(*Fig 9.2a)©rlc L18-29Mar201112npn BJT bands in FA regionqVBCqVBEq(VbiE-VBE )q(VbiC-VBC )injectionhigh field©rlc L18-29Mar201113Coordinate system - prototype npn BJT (Fig 9.8*)©rlc L18-29Mar201114Notation for npn & pnp BJTs•NE, NB, NCE, B, and C doping (maj)•xE, xB, xCE, B, and C CNR widths•DE, DB, DCDminority for E, B, and C•LE, LB, LCLminority for E, B, and C(L2min = Dmin tmin) tE0, tB0, tC0minority carrier life- times for E, B, and C regions©rlc L18-29Mar201115Notation 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 L18-29Mar201116Notation 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 L18-29Mar201117npn BJT boundary conditions      0xp ,1VVexpp0x"p :Cetc. ,Nnn ,1VVexpnxn ,1VVexpn0xn :B1VVexpp0p ,0xx'p :ECCtBC0CCB2i0BtBC0BBBtBE0BBtBE0EEEE©rlc L18-29Mar201118Emitter solution in npn BJT      EEEEtBEE0EEEEEtBEE0EE0EE0EE2E2ELx , x'xx1VVexppx'pLxsinhL"xxsinh1VVexppx'pppp , 0x'px''xpD©rlc L18-29Mar201119Base solution in npn BJT    BtBCBtBEBBBtBCBBtBEBBBxxVVfxxVVfLxLxVVfLxxVVfLxexp1expn when and sinhexpsinhexpsinhnx'nnnn , 0DxnxxnB0B0BB0BB0BB2B2©rlc L18-29Mar201120Collector solution in npn BJT      CCtBCCC0CCCCCtBCC0CC0CC0CCC2C2Lx , VV , L"xpx"pLxsinhL"xxsinh1VVexppx"pppp , 0Dx"px""xp©rlc L18-29Mar201121Hyperbolic tangent function      LxLx0Lx giving,Lx1Lx1Lx1Lx1Lx L, x if so2yy1e , eeeeLx2yLxLxLxLxtanhlimtanh...!tanh////©rlc L18-29Mar201122npn BJT regions of operationVBEVBCForward ActiveReverse ActiveSaturationCutof©rlc L18-29Mar201123npn FA BJT minority carrier distribution (Fig 9.4*)©rlc L18-29Mar201124npn RA BJT minority carrier distribution (Fig 9.11a*)©rlc L18-29Mar201125npn cutoff BJT