ARTICLE IN PRESS

1386-9477/$ - se

doi:10.1016/j.ph

�Correspondifax: +98411334

E-mail addre

Physica E 28 (2005) 491–499

www.elsevier.com/locate/physe

A quasi-two-dimensional charge transport model of AlGaN/GaN high electron mobility transistors (HEMTs)

A. Asgaria,�, M. Kalafia, L. Faraoneb

aCenter for Applied Physics Research, Tabriz University, Tabriz 51664-163, IranbSchool of Electrical, Electronic and Computer Engineering, The University of Western Australia, Crawley, WA 6009, Australia

Received 21 December 2004; accepted 25 May 2005

Available online 18 July 2005

Abstract

A quasi-two-dimensional charge transport model of AlGaN/GaN high electron mobility transistor has been

developed that is capable of accurately predicting the drain current as well as small-signal parameters such as drain

conductance and device transconductance. This model built up with incorporation of fully and partially occupied sub-

bands in the interface quantum well, combined with a numerically self-consistent solution of the Schrodinger and

Poisson equations. In addition, nonlinear polarization effects, self-heating, voltage drops in the ungated regions of the

device are also taken into account. Also, to develop the model, the accurate two-dimensional electron gas mobility and

the electron drift velocity have been used. The calculated model results are in very good agreement with existing

experimental data for AlmGa1�mN/GaN HEMT devices with Al mole fraction within the range from 0.15 to 0.50,

especially in the linear regime of I–V curve.

r 2005 Elsevier B.V. All rights reserved.

PACS: 72.10.�d; 73.20.�r

Keywords: Mobility; AlGaN/GaN; HFET

1. Introduction

The two-dimensional electron gas (2DEG) ob-served in AlGaN/GaN heterostructures is nowunderstood to equate to the difference of the

e front matter r 2005 Elsevier B.V. All rights reserve

yse.2005.05.054

ng author. Tel.:+984113342564;

7050.

ss: asgari@ee.uwa.edu.au (A. Asgari).

surface and substrate charges and the presence oftotal polarization is to facilitate the formation ofthe channel [1]. These polarization fields have beenattributed to the reduced symmetry of the wurtzitecrystal structure and the polar bonding nature ofGaN and its alloys. The AlGaN/GaN materialsystem is unique in that extremely high two-dimensional electron concentrations (41013 cm�2)are readily generated without modulation doping.

d.

ARTICLE IN PRESS

A. Asgari et al. / Physica E 28 (2005) 491–499492

High electron mobility transistors (HEMTs) fab-ricated in the AlGaN/GaN semiconductor systemcan generate large amounts of RF power be-cause of a unique combination of materialcharacteristics. The high breakdown fields(�3� 106V/cm) resulting from the wide band-gaps of GaN and AlGaN enable the use of muchhigher drain biases than can typically be usedin the AlGaAs/GaAs system [2,3]. Togetherwith these high field properties, the high satu-rated electron drift velocity (�1� 107 cm/s) inGaN can be exploited for superior high-frequencyperformance. The potential of AlGaN/GaNHEMTs for applications in microwave powerhas been demonstrated on relatively small de-vices (gate widtho0.2mm), where some deviceshave shown fMAX values as high as 100GHzand minimum noise figures of about 1–2 dB at12GHz [4]. However, the gate peripheries re-ported in these concept studies have been too smallto produce useful amounts of total microwavepower. Furthermore, such devices have yet todemonstrate high efficiency and high associatedgain [4].

More recently, high performance GaN-basedtransistors such as metal-semiconductor field-effect transistors (MESFETs) and AlGaN/GaNheterostructure field effect transistors (HFETs)have been fabricated and reported by severalgroups [5,6]. In spite of this extensive experi-mental work there is much less effort beingexpended on reliable device simulation and mod-eling of GaN-based microelectronic devices. Thedevice simulation models discussed in the openliterature extend from the most general, funda-mental physics based approaches to rather simpleanalytical or charge control methods whichincorporate the results of the electronic bandstructure and carrier transport in an externallyapplied electric field [7,8].

In the present work, a quasi–two-dimensionalmodel is presented that is capable of determiningthe drain current versus drain-source voltage, thedrain current versus gate-source voltage, as well asrelated physical parameters such as transconduc-tance. This is achieved by (i) using a self-consis-tent solution to the Schrodinger and Poissonequations in order to obtain the 2DEG density,

(ii) approximating the simulated electron driftvelocity, (iii) taking into account the 2DEGchannel temperature, (iv) using a more accuratemodel for the electron mobility, and (v) incorpor-ating a simple, realistic model for the ungated areain the AlGaN/GaN HEMT device.

2. Model description

In order to obtain accurate values for the Fermienergy, the energies of quantized levels within the2DEG, the occupancy of the various sub-bands,the intrasub-band and intersub-band couplingcoefficients, Hij, and the sheet carrier concentra-tion for the 2DEG in AlGaN/GaN heterostruc-tures, both the Schrodinger and Poisson equationsmust be solved self-consistently. This has beenachieved by solving Schrodinger’s equation andsimultaneously taking into account the electro-static potential obtained from Poisson’s equation,as well as the image and exchange-correlationpotentials using Numerov’s numerical method. Inthe self-consistent calculation, the nonlinear for-mulism of the polarization-induced field as afunction of Al mole fraction in AlmGa1�mN/GaN heterostructures has been assumed, as wellas taking into account all fully and partiallyoccupied sub-bands within the interface 2DEGpotential well [9,10]. Using such an approach,it is possible to calculate the 2D-electron mobi-lity taking into account the combined contribu-tions from each of the individual electron scatter-ing mechanisms. The details of such calculationshave been reported in a previous publication[11,12].To calculate the current–voltage (I–V) charac-

teristics of AlGaN/GaN HEMTs, a quasi-2Dmodel has been implemented [7,8,15]. The FETmodel used in calculations is shown schematicallyin Fig. 1, where the x-direction is along thechannel, the z-direction is along the growthdirection, the regions I and III represent theungated channel portions of the FET, and regionII represents the gated area of the device. In themodel it has been assumed that the voltage varieslinearly with x direction in the ungated regions:thus, the 2DEG density in each of the three regions

ARTICLE IN PRESS

I II III

Source

AlGaN

GaN

2DEG Channel

Gate Drain

L

x

z

W

LSG

LG

LGD

Fig. 1. Schematic HEMT structure used for model calculations.0 12 15

0

20

40

60

80

100

120

140

2DE

G e

ffec

tive

wid

th (

Å)

2DEG Density (x1012 cm-2)

963

Fig. 2. Calculated variation of the 2DEG effective width,

d2DEG, versus 2DEG density in AlGaN/GaN heterostructures.

A. Asgari et al. / Physica E 28 (2005) 491–499 493

can be calculated as follows:

NSðxÞ ¼

I : NSVGS

LSGx

� ��

�AlGaN�0qðdAlGaN þ d2DEGÞ

V chðxÞ;

II : NSðVGSÞ ��AlGaN�0

qðdAlGaN þ d2DEGÞV chðxÞ;

III : NSVDS � VGS

LGDðx � LG � LSGÞ þ VGS

� ��

�AlGaN�0qðdAlGaN þ d2DEGÞ

V chðxÞ;

8>>>>>>><>>>>>>>:

(1)

where x is the distance along the channel from thesource, VGS and VDS are the applied gate-sourceand drain-source voltage with respect to thegrounded source, �AlGaN and dAlGaN are theAlGaN barrier dielectric constant and thickness,respectively, q is electron charge, and LSG, LG andLGD are the lengths of the ungated distancebetween source and gate, the gate length and theungated distance between gate and drain, respec-tively. The Vch(x) term is the channel potential andd2DEG represents the effective width of the 2DEG

ID ¼

Wqvðx;T ;EÞNSðxÞ � qDðT ;EÞdNSðxÞ

dx; linear regime;

WqvsatðTÞNSðxÞ � qDðTÞdNSðxÞ

dx; saturation regime;

8>><>>:

(2)

channel. The effective width of the 2DEG at eachpoint in the channel in the x direction depends onthe 2DEG density at that point, and can be

calculated from the self-consistent Schrodingerand Poisson equations using d2DEG ¼ ð1=NSÞR

z NSðzÞ dz. The calculated variation of d2DEG

versus 2DEG density for an AlGaN/GaN hetero-structure is shown in Fig. 2. As evident fromthis diagram, with increasing 2DEG density thewidth of the potential well decreases and the2DEG become more confined to the interfaceregion.The drain current, ID, is given by the following

relation:

where the first term is the drift current and thesecond represents the diffusion current, W is thegate width (see Fig. 1), T is the temperature, E is

ARTICLE IN PRESS

Rth CthID VDS

T0

TchTch(f)-T0

frequency

Fig. 4. Equivalent thermal circuit for the self-heating effect

used to model AlGaN/GaN HEMTs.

A. Asgari et al. / Physica E 28 (2005) 491–499494

the electric field given by E ¼dV chðxÞ

dx, vðx;T ;EÞ is

the electron drift velocity, vsat is the saturated driftvelocity, D(T,E) is the electron diffusion constantwhich can be assumed to be related to the mobilityvia the classical Einstein relation for low fieldgiven by

D ¼kB T

qmðTÞ, (3)

where kB is Boltzmann’s constant and mðTÞis the2D-electron mobility as a function of temperature.For the dependence of drift velocity on thelongitudinal electric field, simulated results havebeen used. However, if an analytical form isrequired, then the following relation as reportedin literature can be used [7,8,12]:

vðx;TÞ ¼mðTÞ

dV chðxÞdx

1þ dV chðxÞdx

=ECðTÞ

� nh i1=n(4)

where EC(T) is the temperature dependent electricfield in the saturation regime. In comparison withprevious analytical forms and fitting to thesimulated data in Fig. 3, the power term in thedenominator, n, is kept at a value of 2

3, which is 1 in

literature [7,8,12]. Although the calculation ofdrain current is difficult using Eq. (4) as theexpression for the drift velocity in comparison theexpression with n ¼ 1, it does give good agreement

0 50 100 150 200 250 3000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Nor

mal

ized

Vel

ocity

( v

/vsa

t )

Electric Field (kV/cm)

Analytical (n=2/3 in equation (4)) Monte carlo simulation

Fig. 3. Normalized electron drift velocity v=vsat versus electric

field in AlGaN/GaN HEMTs.

with simulated results. Fig. 3 shows the driftvelocity versus electric field E ¼

dV chðxÞdx

as calcu-lated from Eq. (4) and from simulation. It isevident from this figure, that the agreementbetween these two calculations is very good.Consequently, the calculated drain current willbe virtually identical regardless of the method usedto determine vðx; tÞ.As evident from Eqs. (2)–(4), the transport

parameters of the 2DEG are dependent ontemperature. However, the temperature of thedevice is different from the electron gas channeltemperature because of self-heating effects. Thus,in order to accurately calculate mobility, mðTÞ,saturated drift velocity, vsatðTÞ, and electric field inthe saturation regime, EC(T), it is necessary todetermine the channel temperature, which wascalculated by simulating the self-heating effectusing the equivalent thermal circuits shown inFig. 4. In this model, the channel temperaturevaries at each operating point depending on thedevice power [13,14]:

Tch ¼ T0 þ PDSRth

¼ T0 þ ID VDS Rth, ð5Þ

where Tch and T0 are the channel temperature andthe device temperature (ambient temperature),respectively, PDS is the device power, and Rth isthe thermal resistance which is dependent ontemperature and can be calculated from the devicetransconductance [13,14]. The thermal resistancefor AlGaN/GaN HEMTs has been calculatedusing a Monte Carlo simulation, and is shown inFig. 5, which indicates that the thermal resistanceincreases approximately linearly with increasing

ARTICLE IN PRESS

Tch

ID fromEq. 2

VDS, VGS ID

d2DEG

Vch

NS

Converged ID

D(T)v(T)

Fig. 6. The flowchart of simulation algorithm used to

determine the drain current vs. drain-source voltage for

AlGaN/GaN HEMT’s.

290 330 370 410 45024

25

26

27

28

29

30

Rth

(K

.mm

/W)

2DEG Channel Temperature (K)

Fig. 5. Calculated thermal resistance variation with 2DEG

channel temperature in AlGaN/GaN HEMTs.

A. Asgari et al. / Physica E 28 (2005) 491–499 495

2DEG channel temperature. Such an increase inTch will also reduce the 2DEG mobility and carriersaturation velocity, leading to a lower ID for agiven VDS and VGS. The self-heating effect isclearly most severe at high VGS and VDS.

The above equations provide all the parametersneeded in order to calculate the drain current. Theprocedure for undertaking such a calculation isbriefly described as follows:

(i)

Given a set of drain-source and gate-sourcevoltages, 2DEG effective width and draincurrent, the channel temperature can becalculated.

(ii)

Using this value of channel temperature,parameters such as 2DEG mobility, satura-tion velocity, and the other parameters inEq. (2) can be calculated, such that a newvalue for ID can be determined. However, inorder to solve Eq. (2), it is necessary to invokethe following boundary condition at thesource and drain ends of the channel region:

V chð0Þ ¼ VS þ ID RS,

V chðLÞ ¼ VDS � ID RD,

where VS is voltage applied to source which iszero in our calculation and RS and RD are the

source and drain contact resistances, respec-tively [15].

(iii)

Once the new drain current has been deter-mined, the 2DEG channel carrier concentra-tion can be re-calculated from the channelvoltage. Thus, new values for the 2DEGeffective width and 2DEG channel tempera-ture can be obtained self-consistently.

(iv)

The above procedure is repeated until IDconverges to a solution, as presented in Fig. 6which shows a flowchart of this simulationalgorithm.

3. Results and discussion

To assess the validity of the quasi-2D chargetransport model, a comparative study has beenundertaken comparing simulated I– V curves toexperimental results from Refs. [16,17] for threeHEMT devices of differing Al1�mGamN alloycomposition: Al0.15Ga0.85N/GaN, Al0.25Ga0.75N/GaN, and Al0.50Ga0.50N/GaN. The materialand device details for each of the three differ-ent device-types are presented in Table 1, and allother material parameters have been taken fromRef. [11]. The results presented in Figs. 7–9 showthe ID versus VDS characteristics for each of the

ARTICLE IN PRESS

00

100

200

300

400

500

600

VGS=-2 V

m=0.15

I D (

mA

/mm

)

VDS(V)

-1 V

0 V

+1 V

654321

Fig. 7. Drain current versus drain-source voltage character-

istics for the Al0.15Ga0.85N/GaN HEMT. The solid line and the

various symbols represent model calculations and experimental

data taken from Ref. [16], respectively. The gate-source voltage,

VGS, is stepped in 1V steps from �2V to +1V.

Table 1

The material and device details used in simulation

Al mole fraction (m) in AlmGa1�mN barrier: 0.15 0.25 0.50

AlGaN barrier thickness Unintentionally doped capping layer 150 A 20 A 20 A

Doped with Si 220 A 150 A 150 A

Unintentionally doped 30 A 30 A 30 A

AlGaN Si doping density 2� 1018 cm�3 2� 1018 cm�3 2� 1018 cm�3

AlGaN unintentional doping density 1� 1018 cm�3 1� 1018 cm�3 1� 1018 cm�3

Drain-gate & gate-source distance (LGD & LGS) 1mm 1 mm 1 mmGate length (LG) 1mm 0.9 mm 0.7 mmGate width (W) 75mm 25 mm 25 mmContact resistance 0.5Omm 0.5Omm 0.5Omm

00

200

400

600

800

1000

1200+2 V

+1 V

0 V

-1 V

VGS=-2 V

m=0.25

I D (

mA

/mm

)

VDS (V)8642

Fig. 8. Drain current versus drain-source voltage character-

istics for the Al0.25Ga0.75N/GaN HEMT. The solid line and the

various symbols represent model calculations and experimental

data taken from Ref. [17], respectively. The gate-source voltage,

VGS, is stepped in 1V steps from �2V to +2V.

A. Asgari et al. / Physica E 28 (2005) 491–499496

three device-types, and for several different gate-source voltage biases. For any particular voltagebias, the drain current is found to increase withincreasing Al mole fraction in the AlGaN barrierowing to a corresponding increase in the 2DEGdensity combined with relatively constant 2DEGmobility. However, this increase is more pro-nounced up to values of m ¼ 0:25, whereas afterthat nonlinear polarization effects mean that thereis only a minor increase in drain currents forincreasing Al mole fraction in the AlGaN. Asevident from these figures, the agreement between

experimental data and simulation results is verygood especially in the linear regime. Such a goodfit to the experimental data suggests that the linearpotential variation within the ungated regions Iand II (see Fig. 1) is a reasonable approximationthat allows the 2DEG density in that area to beestimated. The effect of self-heating in the simula-tion model correctly accounts for the negativeresistance observed in the saturation regime forhigh drain current, although this negative resis-tance is still relatively small. The decrease indrain current versus drain-source voltage forthe Al0.15Ga0.85N/GaN and Al0.50Ga0.50N/GaN

ARTICLE IN PRESS

-5 -4 -3 -2 -1 0 1 20

200

400

600

800

1000 VDS=5 Vm=0.15m=0.25m=0.50

I D (

mA

/mm

)

VGS (V)

Fig. 10. Drain current versus gate-source voltage transfer

characteristics for the three AlmGa1�mN/GaN HEMTs at

VDS ¼ 5V. The solid lines and various symbols represent

model calculations and experimental data taken from Refs. [16],

and [17], respectively.

00

200

400

600

800

1000

1200+2 V

+1 V

0 V

-1V

VGS=-3 V

m=0.50

I D (

mA

/mm

)

VDS (V)

-2 V

8642

Fig. 9. Drain current versus drain-source voltage character-

istics for the Al0.50Ga0.50N/GaN HEMT. The solid line and the

various symbols represent model calculations and experimental

data taken from Ref. [17], respectively. The gate-source voltage,

VGS, is stepped in 1V steps from �3V to +2V.

A. Asgari et al. / Physica E 28 (2005) 491–499 497

devices within the regime which is affected by self-heating are �4O�1m�1 and �1.2O�1m�1, respec-tively. It should be noted that this drain current

decrease is greater for devices which have a longerchannel length.Fig. 10 indicates the ID versus VGS transfer

characteristic for each of the three device-types,for a drain-source voltage of +5V. For increas-ingly positive values of gate bias, the depth of thepotential well at the AlGaN/GaN interface in-creases, resulting in an increased 2DEG densityand increased current. For any given gate bias, thedrain current increases appreciably with increasingAl mole fraction, with the increase being moredominant at lower m values. The results presentedin Fig. 10 indicate excellent agreement betweensimulation results and experimental data, espe-cially for lower values of gate-source voltage. Inparticular, the threshold voltage values are vir-tually identical for the experimental and simula-tion results. Such an accurate threshold voltagemodel in AlGaN/GaN heterostructures (especiallyin structures with higher Al mole fraction),requires that the Schrodinger and Poisson equa-tions be solved self-consistently, in addition toconsidering nonlinear polarization effects. Forthe Al0.15Ga0.85N/GaN devices, there is somediscrepancy at high gate-source voltage values.Although there is a relatively small difference incurrent values, it is enough to have a significantimpact on the transconductance, which is given by

gm ¼@ID

@VGS

����VDS¼constant

.

As indicated by the data shown in Fig. 11, thesimulated transconductance for Al0.15Ga0.85N/GaN HEMTs is in good agreement with existingexperimental data for negative gate biases,although there is significant disagreement for0VoVGSo1.5V. However, it is noted that themaximum value for both experimental and mod-eled transconductance is approximately the same.A change in the gate-source voltage bias not onlymodulates the 2DEG density but also the parasiticchannel formed within the doped AlGaN layer.Therefore, as the gate-source voltage increases, themodulation of the 2D channel will be reduced as aresult of the parasitic channel screening the 2DEGfrom the gate-source voltage. Consequently, in theexperimental results, the transconductance for

ARTICLE IN PRESS

-5 -4 -3 -2 -1 0-20

30

80

130

180

230

280

m=0.15m=0.25m=0.50

g m(m

S/m

m)

VGS (V)54321

Fig. 11. The transconductance versus gate-source voltage

characteristics for the three AlmGa1�mN/GaN HEMTs at

VDS ¼ 5V. The various symbols and solid lines represent the

experimental data taken from Refs. [16] and [17], whereas the

dashed lines represent model calculations.

A. Asgari et al. / Physica E 28 (2005) 491–499498

increasing gate biases falls off more rapidly thanexpected since the free carrier concentration withinthe doped AlGaN layer increases to form aparasitic channel [13]. This effect has not beenincluded in the HEMT model used in the presentstudy. Fig. 11 also shows the transconductance ofAl0.25Ga0.75N/GaN and Al0.15Ga0.85N/GaNHEMT structures. It is noted that with increasingAl mole fraction the maximum value of transcon-ductance shifts to more negative gate-sourcevoltages, and the maximum transconductance ofstructures with m ¼ 0:25 is greater than form ¼ 0:50, which can be attributed to the nonlinearpolarization effect. Also, the transconductancepeak occurs at the gate-source voltage that justbegins to cause some noticeable occupation ofionized donors under the gate. At a lower bias,is degraded by the resistive drop through thechannel and, at a higher bias, it is degradedbecause the gate charge fills the AlGaN donorsrather than the channel with electrons. High valuesof transconductance in GaN-based HEMTs areattributed to high peak and saturation velocitiesand high carrier density due to strong polarizationeffects.

4. Conclusions

An accurate quasi-two-dimensional model hasbeen developed for the AlGaN/GaN HEMT.Calculations based on the model are able toaccurately predict the drain current as well assmall-signal parameters such as drain outputconductance, and device transconductance. Themodel incorporates (i) the effects of nonlinearpolarization, (ii) the impact of fully and partiallyoccupied sub-bands within the interface quantumwell, (iii) self-consistent solution of the Schrodin-ger and Poisson equations, (iv) the effects of takinginto account device self-heating, (v) linear voltagedrops in the ungated regions of the device, (vi) amore accurate mobility model for the 2DEG, and(vii) an approximate and accurate model for theelectron drift velocity. It is noted that there is verygood agreement between model calculations andexperimental HEMT data taken from the pub-lished literature for three different device-types.

Acknowledgements

The Authors wish to thank the AustralianResearch Council (ARC) for financial support ofthis work.

References

[1] Joagi, J. Appl. Phys. 93 (2003) 1631.

[2] M. Micovic, A. Kurdoghlian, P. Janke, P. Hashimoto, D.

Wong, J.S. Moon, L. McCray, C. Nguyen, IEEE Trans.

Electron Devices 48 (2001) 591.

[3] L.F. Eastman, V. Tilak, J. Smart, B.M. Green, E.M.

Chumbes, R. Dimitrov, K. Hyungtak, O.S. Ambacher, N.

Weimann, T. Prunty, M. Murphy, W.J. Schaff, J.R.

Shealy, IEEE Trans. Electron Devices 48 (2001) 479.

[4] W. Lu, V. Kumar, E.L. Piner, I. Adesida, IEEE Trans.

Electron Devices 50 (2003) 1069.

[5] R. Coffie, D. Buttari, S. Heikman, S. Keller, A. Chini, L.

Shen, U.K. Mishra, IEEE. Electron Device Lett. 23 (2002)

588.

[6] A. Minko, V. Hoel, S. Lepilliet, G. Dambrine, J.C. De

Jaeger, Y. Cordier, F. Semond, F. Natali, J. Massies,

IEEE. Electron Device Lett. 25 (2004) 167.

[7] Rashmi, A. Kranti, S. Haldar, M. Gupta, R.S. Gupta,

IEEE Trans. Microwave Theory Tech. 51 (2003) 607.

[8] A. Rashmi, A. Kranti, S. Haldar, R.S. Gupta, solid-state

Electron 46 (2002) 621.

ARTICLE IN PRESS

A. Asgari et al. / Physica E 28 (2005) 491–499 499

[9] M. Kalafi, A. Asgari, Physica E 19 (2003) 321.

[10] V. Fiorentini, F. Bernardini, O. Ambacher, Appl. Phys.

Lett. 80 (2002) 1204.

[11] A. Asgari, M. Kalafi, L. Faraone, J. Appl. Phys. 95 (2004)

1185.

[12] F. Scconi, A. Di Carlo, P. Lugli, H. Morkoc, IEEE Trans.

Electron Devices 48 (2001) 450.

[13] C. Anghel, A.M. Lonescu, N. Hefyene, R. Gillon,

European Solid-State Device Research, 33rd Conference

on. ESSDERC ‘03, September 16–18, 2003, pp. 449–452.

[14] W. Jin, W. Liu, S.K.H. Fung, P.C.H. Chan, C. Hu, IEEE

Trans. Electron Devices 48 (2001) 730.

[15] T.H. Yu, K.F. Brennan, IEEE Trans. Electron Devices 50

(2003) 315.

[16] Y.-F. Wu, S. Keller, P. Kozodoy, B.P. Keller, P. Parikh,

D. Kapolenek, S.P. Denbaares, U.K. Mishra, IEEE.

Electron Device Lett. 18 (1997) 290.

[17] Y.-F. Wu, B.P. Keller, P. Fini, S. Keller, T.J. Jenkins, L.T.

Kehias, S.P. Denbaares, U.K. Mishra, IEEE. Electron

Device Lett. 19 (1998) 50.