L09 12Feb021 Semiconductor Device Modeling and Characterization EE5342, Lecture 9-Spring 2002 Professor Ronald L. Carter

L09 12Feb022 Diode Switching Consider the charging and discharging of a Pn diode –(N a > N d ) –W d << Lp –For t < 0, apply the Thevenin pair V F and R F, so that in steady state I F = (V F - V a )/R F, V F >> V a, so current source –For t > 0, apply V R and R R I R = (V R + V a )/R R, V R >> V a, so current source

L09 12Feb023 Diode switching (cont.) + + VFVF VRVR D R RFRF Sw R: t > 0 F: t < 0 V F,V R >> V a

L09 12Feb024 Diode charge for t < 0 xnxn x nc x pnpn p no

L09 12Feb025 Diode charge for t >>> 0 (long times) xnxn x nc x pnpn p no

L09 12Feb026 Equation summary

L09 12Feb027 Snapshot for t barely > 0 xnxn x nc x pnpn p no Total charge removed, Q dis =I R t

L09 12Feb028 I(t) for diode switching IDID t IFIF -I R tsts t s +t rr I R

L09 12Feb029 Band model review (approx. to scale) q  m ~ 4 + V EoEo E Fm E Fp E Fn EoEo EcEc EvEv E Fi q  s,n q  s ~ 4 + V EoEo EcEc EvEv E Fi q  s,p metaln-type s/cp-type s/c q  s ~ 4 + V

L09 12Feb0210 Ideal metal to n-type barrier diode (  m >  s,V a =0) E Fn EoEo EcEc EvEv E Fi q  s,n qsqs n-type s/c qmqm E Fm metal q  Bn qV bi q’nq’n No disc in E o E x =0 in metal ==> E o flat  Bn =  m -  s = elec mtl to s/c barr V bi =  Bn -  n =  m -  s elect s/c to mtl barr Depl reg

L09 12Feb0211 Ideal m to n s/c barr diode depletion width xdxd x qN d  Q’ d = qN d x d x  ExEx -E m xdxd (Sheet of neg chg on mtl)= -Q’ d

L09 12Feb0212 Real Schottky band structure* Barrier transistion region,  Interface states above  o acc, p neutrl below  o dnr, n neutrl D it  -> oo, q  Bn  = E g -  o Fermi level “pinned” D it  -> 0, q  Bn  =  m -  Goes to “ideal” case

L09 12Feb0213 Fig 8.4* (a) Image charge and electric field lines at a metal-diel intf (b) Distortion of the potential barrier due to image forces with E=0 and (c) const E field

L09 12Feb0214 Ideal metal to n-type Schottky (V a >0) qV a = E fn - E fm Barrier for electrons from sc to m reduced to q(V bi -V a ) q  Bn the same DR decr E Fn EoEo EcEc EvEv E Fi q  s,n qsqs n-type s/c qmqm E Fm metal q  Bn q(V bi -V a ) q’nq’n Depl reg

L09 12Feb0215 Ideal m to n s/c Schottky diode curr

L09 12Feb0216 DDiode General Form D [area value] Examples DCLAMP 14 0 DMOD D SWITCH 1.5 Model Form. MODEL D [model parameters].model D1N4148-X D(Is=2.682n N=1.836 Rs=.5664 Ikf=44.17m Xti=3 Eg=1.11 Cjo=4p M=.3333 Vj=.5 Fc=.5 Isr=1.565n Nr=2 Bv=100 Ibv=10 0u Tt=11.54n) *$

L09 12Feb0217 Diode Model Parameters Model Parameters (see.MODEL statement) DescriptionUnit Default ISSaturation currentamp1E-14 NEmission coefficient1 ISRRecombination current parameteramp0 NREmission coefficient for ISR1 IKFHigh-injection “knee” currentampinfinite BVReverse breakdown “knee” voltagevoltinfinite IBVReverse breakdown “knee” currentamp1E-10 NBVReverse breakdown ideality factor1 RSParasitic resistanceohm0 TTTransit timesec0 CJOZero-bias p-n capacitancefarad0 VJp-n potentialvolt1 Mp-n grading coefficient0.5 FCForward-bias depletion cap. coef,0.5 EGBandgap voltage (barrier height)eV 1.11

L09 12Feb0218 Diode Model Parameters Model Parameters (see.MODEL statement) DescriptionUnit Default XTIIS temperature exponent3 TIKFIKF temperature coefficient (linear)°C -1 0 TBV1BV temperature coefficient (linear)°C -1 0 TBV2BV temperature coefficient (quadratic)°C -2 0 TRS1RS temperature coefficient (linear)°C -1 0 TRS2RS temperature coefficient (quadratic)°C -2 0 T_MEASUREDMeasured temperature°C T_ABSAbsolute temperature°C T_REL_GLOBALRel. to curr. Temp.°C T_REL_LOCALRelative to AKO model temperature °C For information on T_MEASURED, T_ABS, T_REL_GLOBAL, and T_REL_LOCAL, see the.MODEL statement.

L09 12Feb0219 The diode is modeled as an ohmic resistance (RS/area) in series with an intrinsic diode. is the anode and is the cathode. Positive current is current flowing from the anode through the diode to the cathode. [area value] scales IS, ISR, IKF,RS, CJO, and IBV, and defaults to 1. IBV and BV are both specified as positive values. In the following equations: Vd= voltage across the intrinsic diode only Vt= k·T/q (thermal voltage) k = Boltzmann’s constant q = electron charge T = analysis temperature (°K) Tnom= nom. temp. (set with TNOM option 

L09 12Feb0220 Dinj –N~1, rd~N*Vt/iD –rd*Cd = TT = –Cdepl given by CJO, VJ and M Drec –N~2, rd~N*Vt/iD –rd*Cd = ? –Cdepl =? SPICE Diode Model 

L09 12Feb0221 DC Current I d = area  ( I fwd - I rev) I fwd = forward current = I nrm  Kinj + I rec  Kgen I nrm = normal current = IS  (exp ( Vd/(N  Vt))-1) Kinj = high-injection factor For: IKF > 0, Kinj = (IKF/(IKF+ I nrm)) 1/2 otherwise, Kinj = 1 I rec = rec. cur. = ISR  (exp (Vd/(NR·Vt))- 1) Kgen = generation factor = ((1-Vd/VJ) ) M/2 I rev = reverse current = I rev high + I rev low I rev high = IBV  exp[-(Vd+BV)/(NBV·Vt)] I rev low = IBVL  exp[-(Vd+BV)/(NBVL·Vt)}

L09 12Feb0222 vD= V ext ln iD Data ln(IKF) ln(IS) ln[(IS*IKF) 1/2 ] Effect of R s V KF ln(ISR) Effect of high level injection low level injection recomb. current V ext -V a =iD*R s

L09 12Feb0223 References Semiconductor Device Modeling with SPICE, 2nd ed., by Massobrio and Antognetti, McGraw Hill, NY, MicroSim OnLine Manual, MicroSim Corporation, 1996.