Diodes for Power Electronic Applications

Lecture Notes Diodes for Power Electronic Applications

William P. Robbins Professor, Dept. of Electrical and Computer Engineering University of Minnesota

OUTLINE

• PN junction power diode construction • Breakdown voltage considerations • On-state losses • Switching characteristics • Schottky diodes • Modeling diode behavior with PSPICE

Diodes - 1 W.P. Robbins Basic Structure of Power Semiconductor Diodes

Anode i 10 P+ 19 -3 microns N = 10 cm A v breakdown 14 -3 voltage N- epi N = 10 cm D dependent

19 -3 N+ substrate N = 10 cm 250 D microns

Cathode anode i 1 i R BV on v BD v

≈ 1 V v

cathode

Diodes - 2 W.P. Robbins Breakdown Voltage Estimate - Step Junction Φ • Non- punch- through diode. Drift W(V) region length Wd > W(BVBD) = length of space charge region at x breakdown. Φc

• W(V) = Wo 1+V/Φc Φ c + V

2εΦc(Na+Nd) • Wo = 4 Φc qNaNd • (E )2 = (E )2 = BV max BD 2 BD Wo 2Φc • Emax = 1 + V/Φc • Solve for W(BVBD) and BVBD Wo to obtain (put in Si values) • Power diode at reverse breakdown: E 2 17 Na >> Nd ; E = EBD ; V = BVBD >> Φc ε BD 1.3x10 BVBD = = ; [V] W 2 BV 2εΦ 2 q Nd Nd 2 o BD 2 c • W (BVBD) = Φ ; Wo = 2 BV c q Nd BD - 5 W(BVBD) = = 10 BVBD ; [µm] EBD • Conclusions 3 15 - 3 1. Large BVBD (10 V) requires Nd < 10 cm 3 - 2. Large BVBD (10 V) requires N drift region > 100 µm Diodes - 3 W.P. Robbins Breakdown Voltage - Punch-Through Step Junction

• Punch-through step junction - W(BVBD) > Wd • At breakdown:

• V1 + V2 = BVBD • E1 + E2 = EBD

2 qNdWd • BV = E W - BD BD d 2ε

ε(EBD)2 • If Nd << (required 2q(BVBD) value of Nd for non-punch-thru diode), then 2 qNdWd qNdWd • E = ; V = • BV ≈ E W and 1 ε 1 2ε BD BD d • Wd(Punch-thru) ≈ 0.5 W (non-punch-thru) • V2 = E2 Wd d

Diodes - 4 W.P. Robbins Effect of Space Charge Layer Curvature diffusing incident acceptor impurities acceptor impurities SiO2 • If radius of curvature is comparable to depletion layer thickness, electric field becomes spatially nonuniform. + P R depletion • Spatially nonuniform electric field layer N - reduces breakdown voltage. + N • R > 6 W(BVBD) in order to limit breakdown voltage reduction to 10% • Impurities diffuse as fast laterally as vertically or less.

• Not feasible to keep R large if • Curvature develops in junction boundary and in BVBD is to be large ( > 1000 V). depletion layer.

Diodes - 5 W.P. Robbins Control of Space Charge Layer Boundary Contour

field plates • Electrically isolated conductors (ﬁeld plates) act as equipotential P+ surfaces. • Correct placement can force depletion layer depletion layer boundary to have boundary - larger radius of curvature and t;hu N s minimize ﬁeld crowding.

SiO2 • Electrically isolated p-regions (guard rings)has depletion regions P P which interact with depletion region P+ of main pn junction. guard ring depletion • Correct placement of guard rings layer - can result in composite depletion boundary N region boundary having large radius N+ of curvature and thus minimize ﬁeld crowding. aluminum Diodes - 6 contact W.P. Robbins Surface Contouring to Minimize Field Crowding

• Large area diodes have depletion • Proper contouring of surface can layers that contact Si surface. mimimize depletion layer curvature and thus field crowding. • Difference in dielectric constant of Si and air causes field crowding at surface. • Use of a passivation layer like SiO2 can also help minimize field crowding and • Electric fields fringing out into air attract also contain fringing fields and thus impurities to surface that can prevent attraction of impurities to lower breakdown voltage. surface. Diodes - 7 W.P. Robbins Conductivity Modulation of Drift Region

• Forward bias injects holes into drift region from P+ layer. Electrons x attracted into drift region from N+ layer. So-called double injection. + + P - + N - N

W d • If Wd ≤ high level diffusion length La , carrier distributions quite ﬂat with p(x) p(x) = n(x) log scale ≈ n(x) ≈ na. 16 = n a = 10

• For na >> drift region doping Nd, the p (x) resistance of the drift region will be n (x) 14 n p n no = 10 quite small. So-called conductivity p no modulation. n po p = 10 6 no x • On-state losses greatly reduced below those estimated on basis of drift region low-level (Nd) ohmic conductivity. Diodes - 8 W.P. Robbins Drift Region On-State Voltage Estimate

QF q A Wd na • I = = ; Current needed F τ τ to maintain stored charge QF. W d q [µn + µp] na A Vd x • IF = ; Wd Ohm’s Law (J = σE) + + P - + N - N 2 I Wd F • Vd = ; Equate above + V - + V - [µn + µp] τ j d Cross-sectional two equations and solve for V d area = A

• Conclusion: long lifetime τ minimizes Vd.

Diodes - 9 W.P. Robbins Diode On-State Voltage at Large Forward Currents

µ o 17 -3 • µn + µp = ; nb ≈ 10 cm . i na 1 + nb • Mobility reduction due to increased 1 carrier-carrier scattering at large na. R on

v q na A Vd µo ≈ 1 V • IF = ; Ohms Law Wd na 1 + I W nb f d • Vd = with density-dependent mobility. q µo nb A

• Vd = IF Ron • Invert Ohm’s Law equation to find Vd as function IF assuming na >> nb. • V = Vj + Vd Diodes - 10 W.P. Robbins Diode Switching Waveforms in Power Circuits

Q = I t /2 rr rr rr di /dt d i /dt F 0.25 I I F R r r

I rr

diF diR • and determined t t t 3 5 dt dt 4 by external circuit.

V t V on rr FP • Inductances or power semiconductor devices.

t V V t r r R 2 t t 5 1 S = t 4

Diodes - 11 W.P. Robbins Diode Internal Behavior During Turn-on

ε A diF C (V) = V ≈ I R + L sc W(V) FP F d dt W d L = stray or Rd = q µn Nd A wiring inductance

• Injection of excess carriers into drift region greatly

reduces Rd.

Diodes - 12 W.P. Robbins Diode Internal Behavior During Turn-off

• Rd increases as excess carriers are removed via recombination and carrier sweep- out (negative current).

diR • V = I R + L r rr d dt

ts i nte r v al • Insufficient excess carriers remain to support Irr, so P+N- junction becomes reverse- biased and current decreases to zero.

• Voltage drops from Vrr to VR as current decreases to zero. Negative current integrated over its time duration removes a total charge Q . Diodes - 13 rr W.P. Robbins Factors Effecting Reverse Recovery Time

• If stored charge removed mostly diR diR trr • I = t = ; Defined on by sweep-out Qrr ≈ QF ≈ IF τ rr dt 4 dt (S + 1) switching waveform diagram

• Using this in eqs. for Irr and trr 2 and assuming S + 1 ≈ 1 gives Irr trr diR trr • Q = = ; Defined rr 2 dt 2(S + 1) 2 I τ on waveform diagram F trr = and diR dt • Inverting Qrr equation to solve for trr yields diR diR 2Q I = 2 I τ 2Qrr(S+1) rr dt rr F dt trr = and Irr = diR (S + 1) dt

Diodes - 14 W.P. Robbins Carrier Lifetime-Breakdown Voltage Tradeoffs

• Low on-state losses require Conclusions kT L = D τ = τ 1. Higher breakdown voltages q [µ + µ ] n p require larger lifetimes if low -5 L = Wd ≥ W(V) = 10 BVBD on-state losses are to be maintained.

• Solving for the lifetime yields 2. High breakdown voltage devices slower than low W 2 d -12 2 breakdown voltage τ = = 4x10 (BVBD) (kT/q) [µn+µp] devices.

3. Turn-off times shortened • Substituting for τ in Irr and trr equations gives diR by large but Irr is I dt -6 F • trr = 2.8x10 BVBD increased. (diR/dt) diR • I = 2.8x10-6 BV I rr BD F dt Diodes - 15 W.P. Robbins Schottky Diodes

anode aluminum SiO2 contact - Characteristics rectifying

• V(on) = 0.3 - 0.5 volts. P P

• Breakdown voltages guard ≤ 100-200 volts. ring depletion layer depletion layer boundary with N boundary • Majority carrier device - no guard rings without guard stored charge. rings

• Fast switching because of lack of stored charge. N +

aluminum cathode contact - ohmic Diodes - 16 W.P. Robbins Physics of Schottky Diode Operation

• Electrons diffuse from Si to Al because electrons have larger + V - average energy in silicon i(t) Aluminum n-type Si compared to aluminum. Electron Energy • Depletion layer and thus potential barrier set up. Gives rise to E rectifying contact. Si E Al • No hole injection into silicon. No source of holes in aluminum. Thus - + diode is a majority carrier device. Al + N-Si - + • Reverse saturation current much Diffusing Depletion layer larger than in pn junction diode. electrons This leads to smaller V(on) (0.3 - 0.5 volts)

Diodes - 17 W.P. Robbins Schottky Diode Breakdown Voltage

• Breakdown voltage limited to 100-200 volts. anode

• Narrow depletion region widths because of heavier drift region doping needed for P P low on-state losses.

• Small radius of curvature of depletion region where 16 metallization ends on surface N ≈ 10 of silicon. Guard rings help to mitigate this problem. + N • Depletion layer forms right at silicon surface where cathode maximum field needed for breakdown is less because of imperfections, contaminants.

Diodes - 18 W.P. Robbins Schottky Diode Switching Waveforms

• Schottky diodes switch much faster than pn junction diodes. No Current minority carrier storage. I F • Foreward voltage overshoot VFP much smaller in Schottky diodes. t Drift region ohmic resistance R . V Ω FP

• Reverse recovery time trr much smaller in Schottky diodes. No V(on) minority carrier storage. t voltage • Reverse recovery current Irr comparable to pn junction diodes. C(Schottky) ≈ 5 C(PN) space charge capacitance in Schottky diode larger than in pn R (Sch.) << R (pn) junction diode becasue of Ω Ω narrower depletion layer widths resulting from heavier dopings.

Diodes - 19 W.P. Robbins Ohmic Contacts

• Electrons diffuse from Al into p- type Si becasue electrons in Al have higher average energy.

• Electrons in p-type Si form an Electron Energy accumulation layer of greatly E enhanced conductivity. Al

E • Contact potential and rectifying Si junction completely masked by Accumulation layer enhanced conductivity. So-called i(t) - P-Si or Al ohmic contact. - N + -Si

• In N+ Si depletion layer is very Diffusing narrow and electric fields approach electrons impact ionization values. Small voltages move electrons across barrier easily becasue quantum mechanical tunneling occurs.

Diodes - 20 W.P. Robbins PN Vs Schottkys at Large BVBD

• Minority carrier drift region • Desired breakdown voltage relationships 1.3x1017 q [µ + µ ] n A V requires Nd = and n p a d BVBD • I ≈ F W -5 d Wd ≥ 10 BVBD

17 • Maximum practical value of na =1 0 • Large BVBD (1000 V) requires Nd -3 14 -3 cm and corresponding to = 10 cm where µn + µp = 2 µn + µp = 900 cm /(V-sec) 1500 cm2/(V-sec)

• Desired breakdown voltage requires IF Vd -5 • ≈ 3.1x106 Wd ≥ 10 BVBD A 2 [BVBD] IF Vd = 1.4x106 A BVBD • Conclusion: Minority carrier devices have lower on-state • Majority carrier drift region losses at large BVBD. relationships q [µn + µp] Nd A Vd • IF ≈ Wd Diodes - 21 W.P. Robbins PSPICE Built-in Diode Model

• Circuit diagram • Components

• Cj - nonlinear space-charge capacitance + i diode • Cd - diffusion capacitance. Caused by excess + carriers. Based on quasi-static description of v stored charge in drift region of diode. C j C i (v ) v j d dc j diode - • Current source idc(vj) models the exponential R s I-V characteristic. -

• Rs accounts for parasitic ohmic losses at high v = v + R i diode j s diode currents.

Diodes - 22 W.P. Robbins Stored Charge in Diode Drift Region - Actual Versus Quasi-static Approximation

- • One dimensional diagram of a + N N + P power diode.

n(x,t) n(x,t) time • Quasistatic view of decay of excess carrier distribution during time time diode turn-off. n(x,t) = n(x=0,t) f(x)

• Redistribution of excess 0 Wd x carriers via diffusion ignored. Equivalent to carriers moving

time with iniﬁnte velocity. time time • Actual behavior of stored charge distribution during turn-off.

x Diodes - 23 W.P. Robbins Example of Faulty Simulation Using Built-in Pspice Diode Model

L stray 50 nH

I D o • Test circuit example - step-down converter. f V + 50 A d • PSPICE diode model parameters - (TT=100ns 100 V - Sw Cjo=100pF Rs=.004 Is=20fA)

Diode Voltage

-100V -200V • Diode voltage transient -300V

-400V

-500V 0s 100ns 200ns 300ns 400ns 500ns time

Diode Current

100A

50A

0A • Diode current transient.

-50A

-100A

0s 100ns 200ns 300ns 400ns 500ns

time Diodes - 24 W.P. Robbins Improved (lumped-charge) Diode Model

- N region • More accurately model distributed nature p(x) = n(x) of excess carrier distribution by dividing it into several regions, each described by + P + N Q Q Q Q a quasi-static function. Termed the region 1 2 3 4 region lumped-charge approach. x δ d

1 i diode • Circuit diagram of improved diode model. Circuit written in + terms of physical equations of the lumped-charge model. D v Gd CJ j - Vsense1 5 6 7 8 + 2 - R s + + + Ee Re Em Rm Edm Cdm 3 - - - Rdm Emo + - 0 4 + Vsense2 - • Detailed equations of model given in subcircuit listing. 9 • Many other even better (but more complicated models available in technical literature.. Diodes - 25 W.P. Robbins Details of Lumped-Charge Model

Subcircuit Listing • Symbolize subcircuit listing into .Subckt DMODIFY 1 9 Params: Is1=1e-6, Ise=1e-40, Tau=100ns, SCHEMATICS using SYMBOL +Tm=100ns,Rmo=Rs=.001, Vta=.0259, CAP=100p, Gde=.5, + Fbcoeff=.5, Phi=1, Irbk=1e20,Vrbk=1e20 WIZARD *Node 1= anodeand Node 9 = cathode Dcj 1 2 Dcap ; Included for space charge capacitance and reverse • Pass numerical values of parameters *breakdown. Tau, Tm, Rmo,Rs, etc. by entering .model Dcap D (Is=1e-25 Rs=0 TT=0 Cjo={CAP} M={Gde} values in PART ATTRIBUTE window +FC={Fbcoeff} Vj={Phi} +IBV={Irbk} BV=Vrbk}) Gd 1 2 Value={(v(5)-v(6))/Tm +Ise*(exp(v(1,2)/Vta)-1)} (called up within SCHEMATICS). *Following components model forward and reverse recovery. Ee 5 0 VALUE = {Is1*Tau*(exp(V(1,2)/(2*Vta))-1)}; Ee=Qe • See reference shown below for Re 5 0 1e6 more details and parameter Em 6 0 VALUE = {(V(5)/Tm-i(Vsense1))*Tm*Tau/(Tm+Tau)} *Em=Qm extraction procedures. Rm 6 0 1e6 Edm 7 0 VALUE = {v(6)};Edm=Qm • Peter O. Lauritzen and Cliff L. Ma, Vsense1 7 8 dc 0 ; i(vsense1)=dQm/dt “A Simple Diode Model with Cdm 8 0 1 Forward and Reverse Recovery”, Rdm 8 0 1e9 IEEE Trans. on Power Electronics, Rs 2 3 4e-3 Emo 3 4 VALUE={2*Vta*Rmo*Tm*i(Vsense2) Vol. 8, No. 4, pp. 342-346, (Oct., +/(v(6)*Rmo+Vta*Tm)}; Vm 1993) Vsense2 4 9 dc 0 .ends Diodes - 26 W.P. Robbins Simulation Results Using Lumped-Charge Diode Model

Diode voltage and current waveforms Simulation Circuit

L stray 10V Diode 50 nH Voltage

0V I 0V . D o + V f d 50 A -10V 410ns 415ns 420ns - 100 V -100V Sw

-200V

0s 100ns 200ns 300ns 400ns 500ns

time Diode Current • Note soft reverse recovery and forward 50A voltage overshoot. Qualitatively matches

0A experimental measurements.

-50A 0s 100ns 200ns 300ns 400ns 500ns time

Diodes - 27 W.P. Robbins