cryogenic study and modeling of igbts

7/28/2019 Cryogenic Study and Modeling of IGBTs

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CRYOGENICTUDY ANDMODELINGF IGBTSA. Caiafa, X. Wang, J.L. Hudgins, E. Santi, and P.R. Palmer*Department of Electrical EngineeringUniversity of South Carolina

Columbia, SC 29208, USAj.hudgins@,ieee.org

-

Abstract- The switching characteristics (turn-on andturn-off) and forward conduction drop of trench-gate IGBTsare examined over a temperature range of -260 to 25 O C . Aphysics-based model previously developed is modified toincorporate appropriate physical behavior at low junctiontemperatures. Results from the model are compared toexperimental waveforms and discrepancies are discussed.Keywords:L ist of Symbols

Ambipolar diffusion coefficient (cm2/s)Conduction band energy (eV)Donor energy level within the gap (eV)Fermi energy level (eV)Bandgap energy (eV)Valence band energy (eV)Donor degeneracy factorBoltzmanns constant (eV/K )Transconductance S )Transconductance at 300K (S)Electron rest-mass (kg)Electron density of states effective-mass (kg)Hole density of states effective-mass (kg)Electron mobility (cm2Ns)Hole mobility (cm2Ns)Electron concentration (~m - ~)Intrinsic carrier concentration ( ~m - ~)Acceptor impurity doping concentration ( ~m - ~)Effective density of states ( ~m - ~)Donor impurity doping concentration (cm)Ionized acceptor concentration ( ~m - ~)Ionizeddonorconcentration (cm)Recombination center (trap) density (cm)Hole concentration (cm)Time (s)High-level carrier li fetime(s)Absolute temperature(K)Threshold voltage(V)Threshold voltage at 300K (V)Distance along drifthase region (cm)

I. INTRODUCTIONSince the application of superconductor technology, inconjunction with semiconductor devices, is rapidly spreading,new attention to the behavior of semiconductor devices atvery low temperatures should be encouraged. There has beensome previous work on the behavior of power electronicdevices at very low temperatures such as power diodes,

Thiswork wassupportedby thc U.S. OficeofNaval Rcsearch under GrantNO0014-00-1 0131.

*Department of EngineeringUniversity of CambridgeTnunpington StreetCambridge CB2 IPZ, UK

thyristors [l] and 2d generation IGBTs [2]. These studieswere conducted on commercial devices in order to verifytheir applicability to a particular application only. Otherthyristor studies have been performed without achieving theirobjective because of the complexities of the testing at verylow temperatures [3]. There are other studies on the behaviorof semiconductor devices at very low temperatures, but onlyconcerning 1 generation IGBTs or other devices [4]-[7]. Norecent studies at very low temperatures have been performedon the trench-gate technology devices.As shown by the study [3] experimental testing is verydifficult to perform, therefore it would be very helpful todevelop and experimentally validate a mathematical model ofthese devices which can be used in a computer simulation inorder to avoid the complexity of experimental testing. Thepurpose of this work is to present experimental data regardingtrench-gate technology devices, such as IGBTs, andsimulation results using models based on previous work, [8]-[9], to include their behavior at low temperatures. In thepresent work, extensive experimental measurements of thetrench-gate IGBT over a wide temperature range have beenperformed. The device was then simulated using a physics-based model that incorporates temperature dependencies, andsimulation results were compared with the experimentalresults. In the process, some standard empirical formulas fortemperature dependencies of silicon parameters are revisitedand more accurate formulas are derived and implemented inthe simulation. In particular, a formula for the temperaturedependency of ionized impurity-atom concentration isderived. A lmost all of the impurity atoms are ionized attemperatures above 0 OC, but below this temperature, thetemperature dependence of impurity ionization should beaccounted for. Temperature dependencies of the carriermobilities and recombination lifetimes will be discussed indetail in the full paper.11 IGBT PHY SICS-BASEDODEL IT H TEMPERATUREThe behavior of conductivity-modulated devices, such asdiodes and IGBTs, depends heavily on the excess carrier(charge) distribution in the wide drift region. In modemIGBTs, the charge profi le has a ID form over about 90%ofits volume [SI. Thus, a 1D solution is adequate for the bulkof the device. Space-charge neutrality is maintained with themajority carrier profile closely matching the minority carrier

profi le (quasi-neutrali ty). Under these conditions, assuminghigh-level injection, the charge dynamics are described by theambipolar diffusion equation:

DEPENDENCIES

(1)--- 2P ( x J )- P(X,t) I aP ( x J ) ,ax2 z atwhereD is the ambipolar diffusion coefficient, z is the high-level carrier lifetime within the drift region and p(x,t) is the0-7803-7754-0/03/$17.0002003IEEE 1897
mailto:j.hudgins@,ieee.orgmailto:j.hudgins@,ieee.org


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excess carrier concentration. A Fourier-based solution forthis equation was proposed for diodes by [9] and extended forIGBTs [8].The IGBT model used in this work implements thisapproach for the representation of the drift region. Themodel contains details of the MOS gate, the depletion layer

capacitances, and the buffer layer (for punch-throughdevices). Moreover, the model includes the temperaturedependencies of parameters such as carrier lifetime,mobilities, intrinsic carrier concentration, MOS thresholdvoltage, and transconductance,so it can correctly reproducethe changes in device behavior as a function of temperature.The model has been verified through experimental testing ofdiodes, and PT and NPT IGBTs with both planar and trench-gate structures, over a temperature range from -1 50to 150"C[8, 10-121. Some typical tum-off waveforms are shown inFigure 1 that compares the experimental and simulatedcurrent and voltage signals for PT and NPT devices. Theresults clearly show the validity of the model in thetemperature range described.

50 0

40 0

300sIg 200amo

00

-mo

500

400

300c00gP-ua

0!- 6

-0 0

600

500

400z300 gS0200 >-

MO

0

-MOFigure 1. Collector current fall and voltageriseof NPT (top) and PT(bottom)-IGBT duringtum-off at temperaturesof- 125 "C (top) and 100"C(bottom). Thesimulated waveforms are blue (voltage)and yellow (current).Figure 1shows an example of the type of experimentalresults that will be used in the paper. These particular

waveforms are for a 600V, 600A trench-gate punch-through(PT) IGBT and a similar NPT device.111. INTRINSICCARRIER AND IONIZED IMPURITYCONCENTRATIONSAT L OW TEMPERATURESA. Intrinsic Carrier Concentration

A detailed derivation of the temperature dependentintrinsic carrier concentration, nh in silicon was done fiomfirst principles and empirical formulations from previouswork [13]-[17]. The oft-quoted expression for ni is given in(2), and is an empirical fi t to data taken in a very hightemperature regime, 450 to 950 K [15]. This temperaturerange is obviously not one typically used for Si devices, iscertainly well above any cryogenic range, and thereforesuspect in its validity at temperatures below 200K .-7020n, =3 . 8 8 ~ 1 0 ' ~ T ~ ' ~ e ~ (2)The new solution introduced here involved three keyimprovements over (2). A series solution to the Fermiintegral was used and the first three terms were kept as theapproximate solution. The traditional solution to the Fermiintegral involves only the first term of a series expansion (or

an approximation to the Fermi-Dirac carrier statistics is usedto simplify the kemel inside the integral). Secondly, thetemperature dependencies of the electron and hole density-of-states effective-masses were included for dopingconcentrations less than 10'' ~m - ~.he electron and holedensity-of-states effective-mass expressions are given inequations(3) and (4), respectively, as derived from data andtheory in [13]. Equations (3) and (4) are polynomialregression fits to the data valid down to 0K and up to 500K.Non-parabolicity of the degenerate valence sub-band andinclusion of the spli t-off valence sub-band are included in thecalculation of the hole effective-mass temperaturedependency [131. Other expressions for the temperaturedependencies of the effective-masses have been proposed,[16], based on [13], but these expressions (particularly therelationship for the hole effective-mass)are inaccurate at verylow and very high temperatures, as shown in Figure 2. Datafrom [131 is included in Figure2 to show the accuracy of thenewly proposed relationships.m =( - 1. 084~10- ~T'7. 580~10- ~T~2. 862x104T+1. 057)m (3)m =(1.872x10- "T4 1.969 xlO *T' +5.857x10"T2+2. 712~1O- ~T+0. 584) m

NormalizedEfiecliveMass1 . 3 1 , I , I I I ,."

- Equation (3)- - Equation, Ref. [16]X Data, Ref. [13]

0 9: Hoe /-- quation(4)- - Equation,Ret [16]X Data, Ref. [13]6

0 50 1 w 1 5 0 m2 5 0 3 0 0 3 5 0 m4 5 00.5l " " ""Temperature (K)

(4)

0

Figure2. Temperature dependence of the electron (top curves) and the hole(bottom curves) effective-masses, normalized with respect to the electronrest mass.

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Thirdly, the temperature dependence of the bandgap wasincluded in the model. The formulation, (9, for thetemperature dependence of the bandgap, EG, hat is used hereis valid from0to 500 K [17].EG =1.17+1.059x10dT -6.05x10-7T Z forTI 170KEG =1.1785- .025 x 10-T - .05x lo- T2 or T >170K(5)Other expressions have been used to account for thetemperature dependence of the energy bandgap, [14] and[18], but do not provide as good a fit to data from [13] and[17]. These various formulations are il lustrated in Figure 3.The expressions of (5) provide a reasonable fit over the entiretemperature range of interest and are an improvement overthat given by [141 for Tabove 300K.

1.2E g (ev)

1.16

1.14

1.12

1.1

1.06

Eouat lon 15)-\x1.16----

-

-

1.06I

-[095cosh(&) +0.742sinh(& )]cosh[075h[$)]

(6)The two expressions for intrinsic carrier concentration,

equations (2) and (6), are shown at high temperatures (top ofFig. 4), at low temperatures around the boiling point ofnitrogen (middle of Fig. 4), and at extremely lowtemperatures (bottom of Fig. 4). Equations suggested by [13]and [181 are included in the figure for comparison. Note that(2) overestimates the carrier concentration above roomtemperature and underestimates it at low temperatures. It isclear that (2) is inadequate to describe the temperaturevariationofnj . There is, however, agood match between (6)

and the expression proposed by [13] at all temperatures. Theexpression from [13] is shown below as (7). In fact, it can beshown that (6) and (7) are approximately equivalentexpressions when (3)-(5) are used in both. This updatedversion of (7) is also shown in Figure4.

l o i 5 3

// - arber[13] [161- - i ss len e t d . I161/ , ,yhlo*ok, I , , I I , I i

300 320 340 360 380 400 420 440 460 480 500Temperature (K)

75 80 65 90 95Temperature (K )IO

(7)

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B. I onized Donor Impurity ConcentrationSeveral dominant physical parameters associated withsemiconductor devices are sensitive to temperaturevariations; causing their dependent device characteristics tochange dramatically. The most important of these parameters

are: i ) the minority carrier lifetimes (which control the high-level injection l ifetimes), ii ) the hole and electron mobilities,iii) the impact ionization collision cross-sections, and iv) thefree-carrier concentrations (primarily the ionized impurity-atom concentration). A lmost all of the impurity atoms areionized at temperatures above 0 " C, but below thistemperature the incomplete ionization should be accountedfor in the donor concentration. A formula for the ionizeddonor impurity concentration is now derived.Charge neutrality requires the sum of all charge to bezero as described in (8).

p -n+N i -N ,=O (8)Assuming n-type material (8) reduces to n =ND+. Theionized donor concentration in terms of its energy level inthe

gap and the total doping concentration is (assumes uniformdoping density) described by (9).

where go is the donor degeneracy factor (usuallyassumed to be equal to 2 to account for electron spin), and EDis the donor energy level wi thin the gap. Using the standardapproximate solution to the Fermi integral for non-degeneratesemiconductors and the effective density of states, it can beshown that the ratio, n/Nc, s as given in (10).n / N , =e(EF-EC)'kT (10)

Substituting (10) into (9) and solving for n gives theresults shown in (11).

where

and (12) makes use of the results from (3)-(7). A comparisonof various formulations for calculating the ionized donordensity in the drift (base) region of an IGBT is shown inFigure 5. It can be seen from the figure that assuming aconstant density-of-states results in a considerableoverestimation of the ionized donor concentration below 50K (top curve in bottom graph). Using the approximation forni from (2) gives results that greatly underestimates theionized donor concentration (bottom curve in each graph).Therefore, it is recommended that the results fiom (3)-(7) and(1 1)-( 12) be utilized when operating at junction temperaturesbelow 100K (-170 "C) . Above lOOK more than 99% of thedopant atoms are ionized and can assumed to be constantwith temperature.

1 0 ' ~1 0 , I I ,

: /- quations (3)+'),(11),(12)..- - Equations (2)-(4),(11),(12)Equation (11) &Constant Density of States

I

50 55 60 65 70 75 80 85 90 95 100Temperature (K )

- quations (3)-(7),(11),(12)- quation (11) &Constant Density of States- - Equations (2)-(4),(11),(12)

I10 15 20 25 30 35 40 45 50Temperature ( K)

Figure5. Ionized donor concentrationas a functionof temperature over tworanges. T he background doping density is assumed to be lO I4 cnY3 andphosphorousasthe dopant species. Note that the top graph hasa linearvertical scale and the bottom graph has a logarithmic vertical scale.

C. MobilityElectron mobility data at temperatures below 300 K wereused to formulate an empirical temperature dependence [19],[20]. The result of a least squares fit to a power regressioncurve is given in (13). The data used was for an impurityconcentration of 4 x ~ m - ~ .

-1.21pe=2.92x103(&)The electron mobility data is plotted in Figure 6along with(13) and the often used temperature dependence given in [8]and [21], as well as the formulation for 77


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Electron Mobil i tv

Equation Ref. [Z?]Data Ref. [19].[20]- - Equatlon Ref. [21],[8]

1 0 2 ~ ' ' " " " ' ' ' " " " ' ' , . , , , . 11 o I O 10' 1o3

Temperature (K)Figure6. Electron mobility as a function of temperatureforT


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0.5;7="(&) (&)"-l1+ 0.6276+149~~42.22x lo4@:- x10-%,,)+ 0.3938

Note that the simplified version in (16) and the completeequation in (15) both predict a slightly higher value of carrierlifetime at temperatures above 350K and below 150K thandoes the simplerE . Threshol dVoltage

It has been shown that the threshold voltage increase atlow temperatures is mainly due to an increase in bandbending because of the temperature dependence of ni [18].Experiments at temperatures down to 77 K have shown thatthe increase is described as

relation generally used.

V,=VTo 1.13~10-~(T-300) (17)This is modified from a slope of -9 mV/K used previously attemperatures above300K [8], [21].F. Transconductance

A new temperature dependence was developed for theproposed model based on the experimental results of a longchannel MOSFET operating in the linear region (belowpinch-off) under low electric fields (such as is the case duringconduction in an IGBT) over a temperature range of 77 to300K [18]. A power regression curve using a least squaresfi t was used to give:

Previously used temperature dependencies for thetransconductance (exponent of -0.8) were based on IGBToperation at 300K or above [SI, [21].IV. IGBT EXPERIMENTALESULTSSIMULATIONAT ACOMPARISON

The DUT was placed in a double-layered cryostat suchthat liquid nitrogen and helium could be used for cooling.The DUT was cooled to 77 K and stabilized at thattemperature for several hours. The device was then slowlycooled to below 10 K and held there as the temperaturestabilized before measurements were performed.Switching waveforms (VcE and IC as functions of time) at6 K are shown in Figure 9. The forward voltage drop as afunction of conduction current, at various temperatures, is

shown in Figure 10 and compares well to some limitedprevious experimental results [25]. At 7K conduction is notcontrollable by the gate signal, but occurs when the electricfield is sufficient to cause breakdown and maintains a fixedcurrent value as shown in Figure 10. As the junctiontemperature decreases, the impact ionization efficiencyincreases such that the bulk breakdown voltage decreases.This effect is shownin the measured values of F igure 11. Afinal comparison of measured current waveforms during tum-

off is displayed in Figure 12. The turn-off time decreases asthe temperature is decreased to about 70 K. As thetemperature decreases M e r , the turn-off begins to slow.Below 20K, the turn-off time increases above that measuredat 300 K. This corresponds to large changes in the ionizedimpurity concentration as shown in the bottom graph ofFigure 5 . The carrier mobilities also decrease below 90 K(see data in Figure 6), though this has not yet been includedin the modeling.

T 12% 1 .

9 5 E O 8 1ffibffi 115E-05 1E45Tlme (w )Figure9. Experimental GBT turn-off transient at6 K

Forward voltage drop100

80-g 60-5 40U20

00 2 4 6 8 10

Voltage (vlFigure I O. Forward voltage drop as a fi ct i on ofconduction current, atvarious temperatures.

Fowtd Ereet- Vd tq le8m103

6Do5mzE 400

f 3mzm

-

1CQ0 o 50 100 150 2m 250 300 30

Temperalure69Figure 11 . Forward breakdown voltage measured at 7K , 100K and at roomtemperature.

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Collectorcurrenttum o? REFERENCESJ .F. K amer, H.W. L orenzen, and W. Rehm, Semiconductors at lowtemperatures, EPE-MADEP ConfRec.,pp. 500-505, September 1991.F. Rosenbauer, H.W. Lorenzen, Behavior of I GBT modules in thetemperature range from 5 to 300 K , Cryogenic EnpneeringCon. Rec.,J uly 1995.V.A.K . Temple, F.W. H olroyd, Feasibil ity study for low-temperaturethyristor operation, General E lectric Technical Information Series,December 1986.B. L engeler, Semiconductor Devices suitable for use in Cryogenicenvironments,Cryogenics,pp 439-447, 1974.S . M enhart, J.L. Hudgins, and W.M . Portnoy, The low temperaturebehavior of thyristors, IEEE Tran. ED, vol. 39, pp. 1011-1013, April1992.J .L. Hudgins, S. Menhart, W.M . Portnoy, and V.A. Sankaran,Temperature variation effects on the switching characteristics of mos-gate devices, EPE - M D E P Conf: Rec., pp. 262-266, September1991.J .L. Hudgins, C.V. Godbold, W.M. Portnoy, and O.M. M ueller,Temperature effects on GTO characteristics, EEE IAS Annual Mrg.Rec.,pp. 1182-1186,October 1994.P.R. Palmer, J .C. J oyce, P.Y . Eng, J .L. Hudgins, E. Santi, and R.Dougal, Circuit simulator models for the diode and IGBT with fulltemperature dependent features, IEEE PESC Rec., pp. 470-476, June2001.Leturcq, B erraies, Debrie, Gil let, Kallala and M assol, Bipolarsemiconductor device models for computer-aided design in powerelectronics, 6th European ConferenceonPower E lectronics,vol. 2, p.

-T3(10 KT=%KT=IOK

T = 15K7T= 6K.-.T =20 K1ME05 1 06E-m 1OBE45 1 1E-E 1 1E-051 14E05 11E-E 1 18E-05

llme(sec)Figure 12. Measured coll ector current tum-off waveforms at varioustemperatures.

V. DISCUSSIONModifi cationof many of the silicon material and IGBTdevice parameters is necessary to correctly capture thephysical behavior for operating temperatures below 200K. Ithas been shown that in particular, operation of IGBTs below100 K requires careful consideration of the materialparameter relationships and their dependencies ontemperature. The parameters of special interest include thedensity-of-states effective-masses or electrons and holes, theenergy bandgap, the resulting intrinsic carrier concentration,the hole and electron mobilities, and the high-level carrierlifetime. It has been shown that extrapolationof commonlyused relationships for temperature dependencies becomesinadequate below 200K and the margin of error dramaticallyincreases below 80K when compared to available data. Thisis primarily due to the fact that the original relationships were

based on data obtained at 300K or above. This necessitates are-examination of the low-temperature data and creation ofcorrected relationships for all these parameters and quantities.Several experimental and simulated switchingwaveforms were provided that indicated the validity of theproposed IGBT model in a temperature range of -260 to 150C (6to425 K). The experimental and simulated waveformswere compared at many operating junction temperatures tohelp validate the changes in the model parameter temperaturedependencies as given by (3)-(6) and (11)-(18). Furthersimulations and corresponding experimental data areexpected to corroborate the proposed model changes forcryogenic operation of IGBTs, particularly after comparingresults fromPT and NPT devices.

84, Sept. 1995.[IO] X. Kang, A. Caiafa, E. Santi, J.L . Hudgins, and P.R. Palmer,Parameter extraction for a power diode circuit simulator modelincluding temperature dependent effects, IEEE APEC Rec., pp. 452-458, March 2002.[ l l ] X. Kang, A. Caiafa, E. Santi, J .L. Hudgins, and P.R. Palmer, Lowtemperature characterization and modeling of IGBTs, IEEE PESCRec., pp., J une 2002.[12] X. Kang, A. Caiafa, E. Santi, J.L. Hudgins, and P.R. Palmer,Characterization and modeling of high-voltage field-stop IGBTs,IEEE IASAnn. Mtg. Rec.,pp. ,October 2002.[I31 H.D. Barber, Effective mass and intrinsic concentration in silicon,Solid-state E lectronics,vol. 10,pp. 1039-1051, 1967.[14] C.D. Thurmond, The standard thermodynamic function for theformation of electrons and holes in Ge, Si, GaAs, and Gap, J .Elecfrochem. Soc., vol 122, pp. 1133-1 141, August, 1975.[15] F.J . Morin and J .P. M aita, Electrical properties of silicon containingarsenic and boron, Physical Rev., vol. 96, no. 1, pp. 28-35, October1954.[16] F.H . Gaensslen and R.C. J aeger, Temperature dependent thresholdbehavior of depletion mode MOSFETs, Solid-Stute Electronics, vol.22, pp. 423-430, 1979.[I71 W Bludau, A. Onton, and W. Heinke, T emperature dependenceofbandgap of silicon, . Appl. Phys.,vol. 45, pp. 1846-1848, 1974.[I81 F.H. Gaensslen, V.L. R ideout, E.J . Walker, and J .J . Walker, Verysmall M OSF ETs for low temoerature oDeration. IEEE Trans. ED. vol.24,pp.218-229, March 1977.[I91 C. J acoboni,C. Canali , G. Ottaviani, and A.A. Quaranta, A review ofsome charge tranmort moperties of si licon,Solid-State E lec., vol. 20,- 1pp. 7749,7977.[20] P. Norton, T. Braggins, and H. Levinstein,Phys. Rev.,vol. B8, p. 5632,1973.[21] A.R. Hefner, A dynamic electro-thermal model for the IGBT, IEEETrans. A, vol. 30, no. 2, pp. 394-405, MarcWApril 1994.[22] R . Singh and B.J . Baliga, Ciyogenic Operation of Silicon PowerDevices,p. 18, K luwer Academic, B oston, 1998.[23] R.A . Logan and A.J. Peters,J . Appl. Phys.,vol. 31, p. 122, 1960.r241 D.B.M. K laassen. A unified mobilitv model for device simulation-11.1 Temperature dependence of camer mobility and li fetime, Solid-state

Elec.,vol. 35, pp. 961-967, 1992.r251 F. Rosenbauer and H.W. Lorenzen, Behavior of IGBT modules in thetemperature range fiom 5 to 300 K , Ciyogenic Engineering Con$Rec.,Columbus, OH, July 1995.

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cryogenic study and modeling of igbts

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