EE 5340 Semiconductor Device Theory Lecture 18 – Spring 2011 Professor Ronald L. Carter

©rlc L18-29Mar20112 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

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5 Ideal diode equation for E gN = E gN J s = J s,p + J s,n = hole curr + ele curr J s,p = qn i 2 D p coth(W n /L p )/(N d L p ), [cath.] = qn i 2 D p /(N d W n ), W n > L p, “long” J s,n = qn i 2 D n coth(W p /L n )/(N a L n ), [anode] = qn i 2 D n /(N a W p ), W p > L n, “long” J s,n >N d, W n & W p cnr wdth

©rlc L18-29Mar20116 Ideal diode equation for heterojunction J s = J s,p + J s,n = hole curr + ele curr J s,p = qn iN 2 D p /[N d L p tanh(W N /L p )], [cath.] = qn iN 2 D p /[N d W N ], W N > L p, “long” J s,n = qn iP 2 D n /[N a L n tanh(W P /L n )], [anode] = qn iP 2 D n /(N a W p ), W p > L n, “long” J s,p /J s,n ~ n iN 2 /n iP 2 ~ exp[[E gP -E gN ]/kT]

©rlc L18-29Mar20117 Bipolar junction transistor (BJT) The BJT is a “Si sandwich” Pn  (P=p +,  =p - ) or Np  (N=n +, =n - ) BJT action: npn Forward Active when V BE > 0 and V BC < 0 P n  EBC V EB V CB Charge neutral Region Depletion Region

©rlc L18-29Mar20118 npn BJT topology Charge Neutral Region Depletion Region x x’ p-Base -CollectorN-Emitter z 0 WBWB W B +W C -W E 0 x” c x” 0 xBxB 0 x’ E IEIE ICIC IBIB

©rlc L18-29Mar20119 BJT boundary and injection cond (npn)

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

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

©rlc L18-29Mar npn BJT bands in FA region qV BC qV BE q(V biE -V BE ) q(V biC -V BC ) injection high field

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

©rlc L18-29Mar Notation for npn & pnp BJTs N E, N B, N C E, B, and C doping (maj) x E, x B, x C E, B, and C CNR widths D E, D B, D C D minority for E, B, and C L E, L B, L C L minority for E, B, and C (L 2 min = D min  min )  E0,  B0,  C0 minority carrier life- times for E, B, and C regions

©rlc L18-29Mar Notation for npn BJTs only p EO, n BO, p CO : E, B, and C thermal equilibrium minority carrier conc p E (x’), n B (x), p C (x’’): positional mathe- matical function for the E, B, and C total minority carrier concentrations  p E (x’),  n B (x),  p C (x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C

©rlc L18-29Mar Notation for pnp BJTs only n EO, p BO, n CO : E, B, and C thermal equilibrium minority carrier conc n E (x’), p B (x), n C (x’’): positional mathe- matical function for the E, B, and C total minority carrier concentrations  n E (x’),  p B (x),  n C (x’’): positional ma- thematical function for the excess minority carriers in the E, B, and C

©rlc L18-29Mar npn BJT boundary conditions

©rlc L18-29Mar Emitter solution in npn BJT

©rlc L18-29Mar Base solution in npn BJT

©rlc L18-29Mar Collector solution in npn BJT

©rlc L18-29Mar Hyperbolic tangent function

©rlc L18-29Mar npn BJT regions of operation V BE V BC Forward Active Reverse Active Saturation Cutoff

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

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

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

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

npn BJT currents in the forward active region ©RLC ©rlc L18-29Mar I C = J C A C I B =-(I E +I C ) J nE J nC I E = -J E A E J RB =J nE -J nC J pE J GC J RE J pC

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