Electrothermal MoSchottky and Silico

Saeed Jahdi, Stu. Member IEEE, OLi Ran, Senior M

Schoo

Abstract— Schottky diodes are known conduction and switching losses comparedhowever, are prone to ringing in the output cthis paper, analytical models have been develthe turn-off switching energy of SiC Schottkdiodes. The models account for the reverse and diode voltage overshoot in the case of the as the output oscillations for the Schottky dduring turn-off exhibit significant reverseincreases with the switching rate and tempSchottky diodes exhibit output oscillationresonance in the circuit. By combining ththermal networks derived from transient thcurves of the diodes, a fast and accurate metthe temperature transient for different switcand electrical time constants has been developcan be used by application engineers to prdissipation when designing converters and catemperature and switching rate dependencies

Index Terms— Modeling, Switching Energy,Power Devices

NOMENCLUTURE VD On-st

dIRR+/dt Slope of current before peak

dIRR-/dt Slope of current after peak

IRR peak

Δt Time difference between vol

CAK deple

RAK dep

Lstray stray ind

RS

ESW S

T

t

odeling and Characterizaon PiN diodes SwitchingOlayiwola Alatise, Member IEEE, Petros Alexakis, SMember IEEE, Phil Mawby, Senior Member IEEE ol of Engineering of University of Warwick Coventry, CV4 7AL, United Kingdom

S.Jahdi@warwick.ac.uk

to have lower d to PiN diodes, characteristics. In loped to calculate

ky and silicon PiN recovery current PiN diode as well

diodes. PiN diodes e current which perature whereas ns due to RLC hese models with hermal impedance thod of predicting ching frequencies ped. These models redict the energy an take account of

of the diodes.

, Silicon Carbide,

ate voltage drop

reverse recovery

reverse recovery

reverse recovery

ltage rise and IRR

etion capacitance

pletion resistance

ductance parasitic

series resistance

Switching energy

Temperature

Time

I. INTRODUC

Silicon PiN and SiC Schottky das free-wheeling diodes in voltagerequire bi-directional power flow exhibits certain characteristics in thsilicon PiN diode suffers from highdue to the fact that it is a bipolconductivity modulation via charregion [3-5]. Hence, when the diodecharge must first be extracted viaafter the diode starts blocking, trecombine in the diode. Fig. 1(aswitching voltage and current wavediode whereas 1(b) shows the swParasitic inductance and high dI/dt peak diode voltage overshoot, whicreverse recovery current, causes hdissipation in the diode [6].

Fig. 1(a). Measured silicon PiN diode tr

Fig. 1(b). Measured silicon PiN diode in

ation of SiC g Transients

Stu.Member IEEE,

CTION diodes are routinely used e source converters that [1-2]. Each technology

he turn-off transient. The h reverse recovery charge ar device that relies on

rge storage in the drift e is turned off, the stored

a a negative current and the excess charge must a) shows the measured eforms for a 1.2 kV PiN

witching power transient. will contribute to higher

ch coupled with the peak igh instantaneous power

ransient voltage and current

nstantaneous power

978-1-4799-5776-7/14/$31.00 ©2014 IEEE 2817

On the other hand, SiC Schottky dioddevices and hence, do not rely on chargeresulting in no reverse charge. However, the Schottky diode is its tendency to presence of parasitic inductance [7-9]characteristic contributes to the switching enminimized by reducing the switching rate.the measured characteristic of a 1.2 kV whereas Fig. 2(b) shows the instantaneous transient. The following section describes mbeen developed for each technology.

Fig. 2(a). Measured SiC Schottky diode trancurrent waveforms.

Fig. 2(b) Measured SiC Schottky diode instantan

II. MODEL DEVELOPMEN

The switching energy models are baslinearized waveforms of the measured characase of the silicon PiN diode, the waveforminductive voltage overshoot and the reverse as shown in Fig. 1(a). The linearized wavediode switching transients are shown in Fdifferent switching phases have been dividtime segments. In the case of the Schottky output oscillations are modeled by damwaveforms as shown in Fig. 2(a) withamplitude equal to the peak inductive voltagthe attenuation determined by the parasitic Rof the diode's equivalent circuit which is shsection A below, the PiN diode model is dein section B, the Schottky diode's model is d

des are unipolar e storage thereby the drawback of oscillate in the

]. This ringing nergy and can be Fig. 2(a) shows

Schottky diode switching power models that have

nsient voltage and

neous power

NT sed on detailed acteristics. In the

ms account for the recovery current

forms of the PiN Fig. 3, where the ded into different diode model, the mped sinusoidal h the maximum ge overshoot and RLC components

hown in Fig. 4. In escribed whereas described.

A. PiN Diode The total switching energy of theintegration of the switching power as the lower graph in Fig. 3. Tcomprised of 6 areas with algebraicbe integrated in time. The time interms of the switching parameters equation for the switching energy shown below:

∑=

++=5

321

nSWnSWSWSW EEEE

The switching energy components expressed mathematically as shown

⎟⎠⎞⎜

⎝⎛

=+

dtdI

VIERR

DFSW

2

2

1

⎜⎜⎜

⎝

⎛−⎟

⎠⎞

⎜⎝⎛ −=

−

−

dtdI

Idt

dItIVERR

RRRRRR

DSW 12 2

)(2

)(3

1

331

nnnn

nnnn

nnSWn

ttdb

bdatt

caE

−+

⎜⎝

⎛ ++−=

+

+

Where the coefficients in equation dependency of the PiN diodes param

Fig. 3. Linearized power plot withtransients divided into different segmen

B. Schottky Diode Silicon carbide devices are previouadvantages in applications [11-13].known to exhibit oscillations in thTo model the switching energy of

e PiN diode will be the over time. This is shown

The switching energy is c functions that can easily ntervals are expressed in

of the device [10]. The of the Schottky diode is

(1)

ESWn for n=1 to 6 can be n below

(2)

⎟⎟⎟

⎠

⎞Δ− t (3)

)( 221 nn

nn ttcb

−⎟⎠

⎞+

(3) and the temperature meters are given in [10]

the current and voltage

nts.

usly shown to have many . However, they are also he output characteristics. the Schottky diode, it is

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important to first determine the equivalendiode during turn-off transient. Fig. 4 srepresented by a depletion capacitance (Cresistance (RAK), a stray inductance (Lstray)series resistance (RS) [14].

Fig. 4. Clamped inductive switching circuiequivalent circuit. The depletion capacitance is due to the risiwhich depletes the semiconductor undernecontact, the depletion conductance is due tothe capacitance, the stray inductance and due to packaging and wiring of the test ciris a 2nd order circuit which can be solvfrequency domain with expressions for theoscillation frequency and the damping. Tvoltage can be expressed by the equation be

AKAKstray

strayAKSAK

AKstray

AK

Stray

S

GDG

DAK

CRLLCRR

ss

CRLRR

LRs

CsRVV

+⎟⎟⎠

⎞⎜⎜⎝

⎛ ++

++⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

21

Therefore the attenuation and oscillation fdiodes voltage oscillations will be given by

AKAKstray

strayAKSAKV CRL

LCRR2

+=α

AKAKstray

SAK

CRLRR +

=ω

The switching energy of the Schottky dicalculated by integrating the switching characteristic shown in Fig. 5. They aresection for the ease of driving the analyticthe switching energy. The total switching eESW1, ESW2 and ESW3.

nt circuit of the shows the diode CAK), a depletion ) and a parasitic

it showing diode

ing diode voltage eath the Schottky o lossy nature of resistance is be

rcuit. This circuit ved easily in the e attenuation, the The diode output elow:

AKAKstray

SAK

AK

S

CRLRR

CR

+

(4)

frequency of the

(5)

(6)

iode is similarly power transient

e divided into 3 cal equations for energy is sum of

)(4

3

4

3

3

2

3

2

2

1

2

1

3

2

1

dLVeIdtPE

ddIIt

dtdVeIdtPE

dttdt

dIIVdtPE

t

tDC

tPR

t

tSW

t

t

ONtPR

t

tSW

t

t

DSONON

t

tSW

I

I

∫∫

∫∫

∫∫

⎜⎝⎛ +⋅==

⎜⎜

⎝

⎛−⋅==

⎟⎠⎞

⎜⎝⎛ −==

−

−

α

α

Fig. 6(b) shows the switching powillustrating the damped nature ofintervals for the integration (t1, t2, trepresented in terms of the diode shown in [15]. When performing tthe time interval for ESW3 is takenconstant of the decaying sinudependency of the switching characdiode has been outlined in [15].

Fig. 5. Diode circuit model with thshown.

III. MODEL VALIDATION WMEASUREMEN

The switching energy of the diodeclamped inductive switching test pulse technique. The rig consists oDC link bank capacitor, a 7.5 mHsystem, a thermal chamber and thediode is used as a high side deviwith an inductor and commutating

)9()sin(

)8(

)7(

dttedt

dI

dtdtdV

dt

tDS

N

V ⎟⎠⎞

⎟⎟

⎠

⎞

− ωα

wer transient of the diode f the ringing. The time t3 and t4) in Fig. 5 can be switching parameters as

the integration in Fig. 5, n as 5 times of the time usoid. The temperature cteristics of the Schottky

e representation values of

WITH EXPERIMENTAL NTS es was measured using a

set-up and the double of a DC power supply, a H inductor, a gate drive e devices under test. The ce connected in parallel

g current with a low side

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transistor. As the transistor is switched oncharged to a pre-defined current determinedand the inductance. The transistor is then sthe current is commutated to the diode. Figturn-off power of the 1.2 kV silicon PiN dio6(b) shows that of the SiC Schottky dswitched with a gate resistance of 1measurements have been performed at dtemperatures. It can be seen that the PiNincreases with temperature whereas the Soutput ringing characteristic is temperatur6(a) shows the switching power transient odiode at different ambient temperatures whethat the switching power increases with temdue to increased carrier lifetime with temcauses a higher reverse charge. Also an incpower with the switching rate is seen whifact that the peak reverse recovery currevoltage overshoot of the PiN diode both iswitching rate thereby resulting in a high pe

Fig. 6. Measured turn-off power as a function ofsilicon PiN diode and b) SiC Schottky diode Fig. 6(b) shows the switching power transtemperatures in which due to the oscillationvoltage waveforms (as shown in Fig. 2(b)) oschottky diode, the power is also oscillatingis significantley lower than that of PiNdecreasing with increase in temperature undiode. Fig. 7(a) shows the turn-off switchinsilicon PiN diode as a function of the gate rmodulates the switching rate) and the tempFig. 7(b) shows a similar characteristicSchottky diode. It can be seen from Fi

n, the inductor is d by the duration switched off and g. 6(a) shows the ode whereas Fig. diode. Both are 10 Ω and the different ambient N reverse charge Schottky diode's re invariant. Fig. of the silicon PiN ere it can be seen

mperature. This is mperature which rease in the peak ich is due to the nt and the peak increase with the eak of power.

f temperature for a)

sients at different ns of current and of silicon carbide g, while the total N diode and is nlike Silicon PiN ng energy for the resistance (which perature whereas cs for the SiC ig. 7 that under

identical switching conditions, thsignificantly smaller switching enePiN diode. Both diodes show energies at intermediate switcing rrates, the switching energies in boby high voltage overshoots reinductances. In the case of the Pireverse recovery current is an addfor the Schottky diode, oscillationsthe problem. As the gate resistanceof the Schottky diode, the oscdamped and the switching energy re

Fig. 7. Turn-off switching energy as a fdI/dt for a) Silicon PiN diode and b) SiC Fig. 8(a) shows the modeled and mefor the PiN diode as a function of tlow side switching transistor. Fig. 8for the SiC Schottky diode. Fig. 8and modeled switching energy as afor the PiN diode whereas Fig.characteristic for the Schottky dioFig. 8 that the model is capable closely match the experimental mdegree of margin of error. In the nethermal network is combined witemperature information as a funcswitching conditions. This will alsotemperature rise from the switchindiode is lower than that of the silicresult of lower switching energy seen in Fig. 6 and Fig. 7.

he Schottky diode has ergy compared with the their lowest switching

rates. At high switching oth diodes are dominated esulting from parasitic iN diode, the high peak

ditional problem whereas in the diode voltage are

e is increased in the case illations become better educes as a result.

function of temperature and C Schottky diode

easured switching energy the gate resistance of the 8(b) shows a similar plot 8(c) shows the measured a function of temperature 8(d) shows a similar de. It can be seen from of yielding results that

measurements with some ext section of the paper, a ith the model to yield ction of technology and o show that the expected ngs of the SiC Schottky con PiN diode. This is a and switching power as

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Fig. 8(a) Measured and modeled switching enePiN diode as a function of IGBT gate resistance

Fig. 8(b) Measured and modeled switching eSchottky diode as a function of SiC MOSFET ga

Fig. 8(c) Measured and modeled switching enePiN diode as a function of temperature

Fig. 8(d) Measured and modeled switching eSchottky diode as a function of temperature

ergy of the silicon

energy of the SiC ate resistance

ergy of the silicon

energy of the SiC

IV. IMPACT ON TEM

The waveform derived models for the PiN and Schottky diodes will device junction temperature during combining the model with a thermadevice, a fast, accurate and ipredicting temperature profiles frequencies and gate resistances hasby modifying the parameters used of the switching frequency and elethe switching device on the transiencan be assessed. This will be donenetwork of the device from the trancurve and using the results of theinput. The transfer function of the dis derived by curve fitting the trancurve. Fig. 9(a) shows the process whereas Fig. 9(b) shows that of the

Fig. 9. Thermal impedance fitting data u

The thermal resistances and capacifrom the transfer function shown thermal resistances and capacitancnetwork is generated and converted shown in Table.1. Table.2 shows thcapacitance values for the SiC Schothe equivalent Cauer Network.

1()1( /(2

)/(1

21 ττ ttth eReRZ −− −×+−×=

MPERATURE the turn-off transients in be used to estimate the repetitive switching. By

al network derived for the nexpensive method of for different switching s been developed. Simply in the model, the impact ectrical time constant of nt thermal characteristics

e by deriving the thermal nsient thermal impedance e electrical model as an device’s thermal network

nsient thermal impedance for the silicon PiN diode SiC Schottky diode.

using MATLAB

tances are then extracted in equation (14) . The

ces of a Forster thermal into a Cauer Network as

he thermal resistance and ottky and PiN diodes for

)1() )/(3

) 32 τteR −−×+ (10)

2821

1 2

R 0.8407 K/W 0.2929 K/W 0

τ 33.43 s 0.0036 s

Table. 1. Foster thermal networ

1 2

R 0.3208 K/W 0.1587 K/W 0

C 0.01172 J/K 0.285 J/K

Table. 2. Cauer thermal networ

The thermal circuit simulation is shown in Flayer Cauer thermal network is used. The inis comprised of the turn-on loss, the conducturn-off loss. For both the SiC Schottky andturn-off loss is the dominant component of ththe case of the silicon PiN diode, this is durecovery charge, whereas in the case of tdiode, this is due to electromagnetic oscillatvoltage during turn-off. Fig. 11(a) showpower pulse for the SiC Schottky diode whshows that of the PiN diode. It is assumed thof the diode is 50% and that the leakage loff-state are small enough to be neglected.

Fig. 10. The Thermal simulation circuit in PLECS

3

0.1841 K/W

0.0469 s

rk

3

0.8382 K/W

39.59 J/K

rk

Fig. 10 where a 3 nput power pulse ction loss and the d PiN diodes, the the total losses. In ue to the reverse the SiC Schottky tions in the diode

ws the switching hereas Fig. 11(b) hat the duty cycle losses during the

S

Fig. 11. Power waveforms for (a) SilicSchottky Diode The results of the simulation are shojunction, case and heatsink tempeplotted against time for the PiN diodFig. 12, the switching frequency resistance of the bottom side trancommutation is 10 Ω. It can be seSchottky diode has a significantemperature compared to the PiN dlower instantaneous switching poSchottky diode. Increasing the switcconverters is a well-known techniqdensity because smaller passive coHowever, this can be at the expensjunction temperature of the powerThe impact of higher switching temperatures can be estimated qmodel. Fig. 13 shows the temperaswitching frequency of 30 kHz. It cato 15 kHz, the operating temperatu50%. This is because the switchingcomponent of the total power losseconduction losses. The advantage ofas can be seen from Fig. 13, thtemperature at higher switching frelower compared to the PiN diode.

Fig. 12. PiN Diode Temperature rise at 1

con PiN Diode and (b) SiC

own in Fig. 12 where the erature profile has been de and Schottky diode. In is 15 kHz and the gate nsistor used for current

een from Fig 12, that the ntly lower steady state diode. This is due to the ower losses in the SiC ching frequency in power que of increasing power omponents can be used. se of increased operating r semiconductor devices. frequencies on junction

quantitatively using the ature profiles at a higher an be seen that compared

ure has increased by over g losses are a significant es even more so than the f the SiC Schottky diode, hat maximum operating equencies is significantly

15 kHz switching

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Fig. 13. Schottky Diode temperature rise at 30 kH

Fig. 14 shows the steady state junction tfunction of the gate resistance of the lowtransistor for the SiC Schottky diode and silThe switching frequency used is 15 kHz temperature is 25 ⁰C. The results show a sijunction temperature for the SiC Schottky with the silicon PiN diode. Furthermore, verrates can be avoided to obviate the probleringing in the Schottky diode and excessiovershoots and peak reverse recovery currenthe PiN diode.

Fig. 14. Steady state junction temperature at 15function of gate resistance.

V. CONCLUSION Waveform based switching models and thehave been presented for silicon PiN andiodes. By linearizing the voltage and cuand integrating them, the switching energy cfor different switching rates and temswitching behavior of PiN diodes is afferecovery while that of the Schottky diode bdiode voltage. The switching power is useda thermal network, which then generates transient profile of the diode. This can be the operating temperatures of the devices the gate resistance and switching rate. Thisreliability and converter design.

Hz switching

temperature as a w side switching licon PiN diodes. and the ambient gnificantly lower diode compared

ry high switching ems of excessive ive peak voltage nts in the case of

5 kHz switching as

ermal simulations nd SiC Schottky urrent waveforms can be calculated

mperatures. The ected by reverse by ringing of the d as an input into

the temperature used to estimate as a function of

s is important for

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