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Electron Beam–Induced Current Investigation of GaN Schottky Diode A. MATOUSSI, 1,4 T. BOUFADEN, 2 S. GUERMAZI, 1 Y. MLIK, 1 B. EL JANI, 2 and A. TOUREILLE 3 1.—Laboratoire LaMaCoP de Sfax, Institut Préparatoire aux études d’Ingénieurs de Sfax, 3000 Sfax, Tunisia. 2.—Laboratoire de Physique de Matériaux, Faculté des Sciences de Monastir, Monastir, Tunisia. 3.—Laboratoire d’Electrotechnique, Université Montpellier II, 34000 Montpel- lier, France. 4.— E-mail: [email protected] In this article, we report the electron beam–induced current (EBIC) measure- ments in a GaN Schottky diode performed in the line-scan configuration. A the- oretical model with an extended generation source was used to accurately extract some minority carrier transport properties of the unintentionally doped n-GaN layer. The minority hole diffusion length is found to increase from 0.35 µm near the junction to 1.74 µm at the bulk regions. This change is at- tributed to an increase of the carrier lifetime caused by the polarization effects, which are preponderant in this component. For depth distances exceeding 0.65 µm, it is shown that the measured current is produced by the reabsorption recombination radiation process. This corresponds to an absorption coefficient of 0.178 µm 1 , in good agreement with the optical absorption measurement. Key words: GaN, charge carriers, generation, recombination, trapping, electron beam–induced current (EBIC) Journal of ELECTRONIC MATERIALS, Vol. 34, No. 7, 2005 Regular Issue Paper 1059 (Received July 15, 2004; accepted January 18, 2005) INTRODUCTION Gallium nitride is an attractive wide band gap semiconductor material for ultraviolet/visible opto- electronics, 1,2 as well as high-power and high-temper- ature electronics. 3,4 Recently, significant progress has been made in the fabrication of III-V nitride–based bipolar and field effects devices. 5 However, the perfor- mance of the design depends not only on the crys- talline quality of the layers, but also on the minority carrier transport properties such as recombination lifetimes and diffusion lengths. 6 It is well known that defects in materials create recombination centers that reduce the local genera- tion/recombination lifetimes of charge carriers affect- ing their diffusion lengths. 7 In the case of bipolar junction transistors and semi- conductor field effect transistors, large defects densi- ties severely deteriorate the performance of majority carriers’ devices by contributing to the subthreshold current and thus degrading their mobilities. 8 In this study, we determined the diffusion lengths and the optical absorption coefficient from electron beam–induced current (EBIC) measurements on n- GaN Schottky diodes. The absorbed or specimen current (SCM) and the backscattered electron emissive modes of the scan- ning electron microscopy (SEM) as well as optical absorption and photoluminescence (PL) measure- ment and high-resolution SEM (HRSEM) are used to characterize the same structure. EXPERIMENTAL The GaN layer was grown at 600°C by the atmos- pheric metal organic vapour-phase epitaxy (MOVPE) method on (100) silicon substrates using porous sili- con (PS) as a buffer layer. Trimethylgallium (TMG) and ammonia (NH 3 ) were used as Ga and N sources. Hydrogen (H 2 ) was used as a carrier gas. The details of growth can be found elsewhere. 9 The Hall measure- ments at room temperature showed n-type electrical conductivity for the sample with electron concentra- tion of 1.23 10 17 cm 3 and carrier mobility of 122 cm 2 /V·s. Analysis of x-ray diffraction spectra shows that the layer is polycrystalline with preferential growth on the (0002) hexagonal structure. Before metallization, the GaN surfaces were cleaned with organic solvents, etched with HF and

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Page 1: Electron beam-induced current investigation of GaN Schottky diode

Electron Beam–Induced Current Investigation of GaNSchottky Diode

A. MATOUSSI,1,4 T. BOUFADEN,2 S. GUERMAZI,1 Y. MLIK,1 B. EL JANI,2and A. TOUREILLE3

1.—Laboratoire LaMaCoP de Sfax, Institut Préparatoire aux études d’Ingénieurs de Sfax, 3000Sfax, Tunisia. 2.—Laboratoire de Physique de Matériaux, Faculté des Sciences de Monastir,Monastir, Tunisia. 3.—Laboratoire d’Electrotechnique, Université Montpellier II, 34000 Montpel-lier, France. 4.— E-mail: [email protected]

In this article, we report the electron beam–induced current (EBIC) measure-ments in a GaN Schottky diode performed in the line-scan configuration. A the-oretical model with an extended generation source was used to accuratelyextract some minority carrier transport properties of the unintentionally dopedn-GaN layer. The minority hole diffusion length is found to increase from0.35 µm near the junction to 1.74 µm at the bulk regions. This change is at-tributed to an increase of the carrier lifetime caused by the polarization effects,which are preponderant in this component. For depth distances exceeding0.65 µm, it is shown that the measured current is produced by the reabsorptionrecombination radiation process. This corresponds to an absorption coefficientof 0.178 µm1, in good agreement with the optical absorption measurement.

Key words: GaN, charge carriers, generation, recombination, trapping,electron beam–induced current (EBIC)

Journal of ELECTRONIC MATERIALS, Vol. 34, No. 7, 2005 Regular Issue Paper

1059

(Received July 15, 2004; accepted January 18, 2005)

INTRODUCTION

Gallium nitride is an attractive wide band gapsemiconductor material for ultraviolet/visible opto-electronics,1,2 as well as high-power and high-temper-ature electronics.3,4 Recently, significant progress hasbeen made in the fabrication of III-V nitride–basedbipolar and field effects devices.5 However, the perfor-mance of the design depends not only on the crys-talline quality of the layers, but also on the minoritycarrier transport properties such as recombinationlifetimes and diffusion lengths.6

It is well known that defects in materials createrecombination centers that reduce the local genera-tion/recombination lifetimes of charge carriers affect-ing their diffusion lengths.7

In the case of bipolar junction transistors and semi-conductor field effect transistors, large defects densi-ties severely deteriorate the performance of majoritycarriers’ devices by contributing to the subthresholdcurrent and thus degrading their mobilities.8

In this study, we determined the diffusion lengthsand the optical absorption coefficient from electron

beam–induced current (EBIC) measurements on n-GaN Schottky diodes.

The absorbed or specimen current (SCM) and thebackscattered electron emissive modes of the scan-ning electron microscopy (SEM) as well as opticalabsorption and photoluminescence (PL) measure-ment and high-resolution SEM (HRSEM) are usedto characterize the same structure.

EXPERIMENTAL

The GaN layer was grown at 600°C by the atmos-pheric metal organic vapour-phase epitaxy (MOVPE)method on (100) silicon substrates using porous sili-con (PS) as a buffer layer. Trimethylgallium (TMG)and ammonia (NH3) were used as Ga and N sources.Hydrogen (H2) was used as a carrier gas. The detailsof growth can be found elsewhere.9 The Hall measure-ments at room temperature showed n-type electricalconductivity for the sample with electron concentra-tion of 1.23 1017 cm3 and carrier mobility of 122cm2/V·s. Analysis of x-ray diffraction spectra showsthat the layer is polycrystalline with preferentialgrowth on the (0002) hexagonal structure.

Before metallization, the GaN surfaces werecleaned with organic solvents, etched with HF and

Page 2: Electron beam-induced current investigation of GaN Schottky diode

(1)

(2a)

(2b)

(2c)

(2d)

where g(x,z) is the projection of the generation rateon the x,z plane of the excess minority carriers; Dp isthe hole diffusion constant; Lp is the hole diffusionlength; w is the right boundary limit of the sample;h is the sample thickness; and Vs, VA, and V1 are therecombination velocities, respectively, at the cleavedsurface, the back face, and the ohmic contact.

In this article, we have used the extended genera-tion profile proposed by Guermazi et al.10,11 that canbe given by the expression

(3a)

(3b)

where x – xo is the lateral position relative to thebeam location; z is the position of beam depth; η isthe electron backscatter coefficient; Eo is the inci-dent energy; Ep 2.8 Eg is the energy of creation ofone electron-hole pair; Rk is the maximum range

of incidents electrons; is the depth function

presented by Kanaya and Okayama;13 Z and ρ arethe atomic number and the density of the target, re-spectively; N is the Avogadro number; and α 1/Lpis the inverse of the diffusion length.

For 20 KeV incident beam energy, the maximumprimary electron range Rk is about 1.24 µm. Withinthe onion-shaped volume is created a density of1.35 1012 ehp/cm3, which is five orders of magnitudesmaller than the background electron concentra-tion. This ensures low injection conditions.

For an elementary source located at the point ofcoordinates (x′,y′) in the onion-shaped generationvolume, the Green’s function associated with Eq. 1and that satisfies the boundary conditions is10–12

(4)

Φ( )z

R k

Dpz

V ppz

s∂∂

==

∆ ∆0

Dpz

V ppz h

A∂∂

= −=

∆ ∆

∆p x) ==0 0

Dp

xV pp

x w

∂∂

==

∆ ∆1

∇ − = −22

1[ ( , )]

( , )( , )∆ ∆

p x zp x zL D

g x zp p

g x x zEE R

zR

eoO

p k k

x xo( , )( )

( )( )− = − − −1 2 2η α

παΦ

RAENZk = 2 389 0

5 3

./

ρ

HCl, rinsed with deionized water, and then blowndry with nitrogen gas. Ohmic contacts were formedby deposition of 150-nm Al followed by an annealingstep at 500°C in nitrogen atmosphere.

The total resistance of the back face of the samplewas 5 Ω. The Schottky contacts were fabricatedby deposition of the 400-nm-thick Au/Ge/Ni layer,followed by lift-off to form dots 2 mm in diameter.From the I-V data, we obtained a barrier heightof 0.88 eV. The investigated device exhibited darksaturation current and high series resistance of2.6 108 A and 8.5 103 Ω, respectively.

Electron beam–induced current (EBIC) measure-ments on the same samples were carried out in situin a JEOL S360 scanning electron microscope (JapanElectron Optics Ltd., Tokyo) using a electronics pre-amplifier followed by a Keithley 428 electrometer.The thickness of the epilayers and the position of thep-n junction inside the structure were monitored bySEM. The backscattered electrons (BSEs) and theSCM as well as optical absorption and PL measure-ments and HRSEM are used to characterize thesame structure.

THEORETICAL ANALYSIS

In these measurements, the electron beam posi-tioned normally to the edge sample at xo scans thecleaved surface along the x-axis from the Schottkybarrier toward the ohmic contact. When the electronbeam is injected into the semiconductor, electron-hole pairs (ehp) will be created within the bulk,as schematically shown in Fig. 1. The interactionvolume is an onion-shaped volume having the inci-dent beam electron direction as a symmetry axisand containing xo. These excess minority carriersthen diffuse toward the device junction where theyare collected and form the induced current in theclosed circuit (Fig. 1).

However, the magnitude of EBIC in the region ncan be calculated using the steady-state continuityequation with appropriate boundary conditions:10

1060 Matoussi, Boufaden, Guermazi, Mlik, El jani, and Toureille

Fig. 1. Schematic EBIC setup on line scan configuration.

G x x z zD l h l h

l z h z h

e k e

e e k

e e

p

k

k k kK

k kw

1w

x x w x x w1

x x w x x

K K

K K

K K

( , ' , , ' )( sin( ))

cos ( / ) cos ( ' / )

(

( ' ) ( ' )

( ' ) (

=+

×

− −+

×

− +[−

− − − − + −

+ − − +

1 l

2 l 2µ

µ µ

µ µ

µ µ '' ) )− ]w

Page 3: Electron beam-induced current investigation of GaN Schottky diode

where and lk is the

wave number determined from the transcendental

equation tan which is deduced

from the boundary condition (2d).The collection probability of the minority carriers,within the GaN layer created at the point source(x′,y′), is defined by

(5)

Then, the collected current is obtained from the vol-ume integral of the product of the minority carriercollection probability by the Green’s function associ-ated with the generation profile:10–12

(6)

For an impulse located in the junction plane (x 0),we suppose that the junction field yields to a minor-ity collection probability equal to 1. Hence, the ana-lytical expression of the collected induced currentwithin the depletion layer for vertical junction is ofthe form

(7)

where Io is the maximum of the collected current atthe Schottky junction, and α is the inverse of the dif-fusion length of the minority carrier (holes). Equa-tion 7 yields a straight-line relationship for a plot ofln(I/Io) versus x2

o. The diffusion length can be thenobtained directly as the inverse square root of theslope (1/slope). The different parameters usedhere are summarized in Table I.

( ) ,lw V

l Dk1

k p2=

µ αµ

k k

k

l k

V1

Dp= + =−

µ kV 1

Dp+

2 21,

RESULTS AND DISCUSSION

Figure 2 shows the BSE/SCM profiles acrossthe GaN structure. According to the BSE and thespecimen current signal, no significant porous sili-con buffer was found at the GaN/Si boundary. Thethickness of the epitaxial n-GaN layer obtained was1.03 µm. The space charge region was about 0.25 µmfrom the Au/GaN junction centered at xo 0. Wenote also that the absorbed signal is the opposite ofthe BSE profile. Figure 3 shows the EBIC line-scanprofile as a function of the incident beam position at20 KV beam voltage. The curve has a decreasing ex-ponential shape. However, the change in slope of theEBIC curve to the theoretical one as the distance xoincreased indicates different values of the diffusionlength in the layer, as shown in Fig. 4. The gener-ated minority carrier diffusion lengths have beendeduced from the inverse square root of the slope ofα2. So, we obtain the following.• From the linear part (1) of the curve, the inverse

square root of the slope gives Lp 0.35 µm.• In the centered region (II), the linear part gives

Lp 1.74 µm.As the junction-source distance increases (more

than xN 0.65 µm), the deviation of the theoreticalcurve from the experimental one is about 17%. Thismay be due to the contribution of the reabsorbedrecombination radiation current (IRRR) to the mea-sured one that is preponderant in such a struc-ture.12,14 Note that the distance between origin Oand M is about 0.18 µm2, and its square root is xo 0.245 µm (Fig. 4). This width corresponds to thedepletion layer thickness 0.25 µm as determined bythe BSE and absorbed emissive mode of SEM.

Electron Beam–Induced Current Investigation of GaNSchottky Diode 1061

H x zl h l h

l h l z h

e k e

e k e

kK

k kw

1w

x w1

x w

k k

k k

( ' , ' )sin ( )

sin ( / ) cos ( ' / )

( ' ) ( ' )

=+

×

−+

×

+[ ]

− − −

2

2 2µ µ

µ µ

k

I eE 1

E Rl h

l h l h

e k e

e k e e dx

zR

l z h dz

EBICo

P k

k

k kK

w w

x w1

x w x xw

kk

R

K K

K K

k

=−

+

×

− − − − −

( ) sin ( / )sin ( )

( )

( ) cos ( / )

( ) ( ) ( )

η απ

µ µ

µ µ α

2 2

1

2

1

2

0

0

2o

Φ∫∫

I x e g x z dx dz I eDL o ox

V( ) ( ' , ' ) ' '= ≈ −∫∫ α 2

02

Table I. Physical Parameters Used in Calculation

Eo (KeV) Ep (eV) η Rk (µm) Vs(cm/s) VA (cm/s) V1(cm/s) H (µm)

20 9.54 0.16–0.22 1.24 106 104 103 500

Fig. 2. Cross section of the Au/GaN junction and BSE and SCM pro-files across the cleaved surface of the undoped GaN Schottky diode.This is obtained at an acceleration voltage of 15 KeV and beam current of 2 nA.

Page 4: Electron beam-induced current investigation of GaN Schottky diode

However, the minority carrier diffusion lengthmay be affected by the degradation in crystallinequality of the GaN film, as suggested by Ref. 15.Figure 5 shows the cross section of the HRSEMimage that is processed to enhance contrast for bet-ter visibility of defects. One may observe that theGaN film grows on the polycrystalline form and theaverage spacing between two adjacent columns is inthe range 0.28–0.4 µm. Here, the column size isin the same order of magnitude as the measured

diffusion length Lp 0.35 µm. Hence, if we assumethat the carrier recombination occurs at the colum-nar edges, these sites constitute depletion lines thatthen limit the mobility of the minority carrier acrossthe layer, which reduces the diffusion length.

In our case, we ascribe the observed increase ofthe diffusion length to an increase of the carrierlifetime. Let us estimate the minority hole lifetimein such an n-GaN sample.

A calculation of the minority carrier lifetime atroom temperature was performed using the relationL Dτ. The diffusivity D and hole mobility µp arerelated via the Einstein equation. Because of thelowest values of µp in almost all MOCVD p-GaNepilayers, which do not exceed 100 cm2/V·s, we haveassumed a hole mobility of 15 cm2/V·s in this study.With this value, the lifetime constant was estimatedat 2 ns for Lp 0.35 µm to 0.25 108 sec for Lp 1.74 µm. Several recombination mechanisms couldbe responsible for the increase of Lp and the lifetimeconstant.

Chernyak et al.16,17 have shown in p-GaN andAlGaN films that electron-beam injection (up to 1500sec) increases the minority carrier diffusion lengthand lifetime. They attribute this change to the trap-ping of electrons on deep levels associated with Mgacceptors. According to Ref. 18, the increase of Lpcould be related to the high internal electric field(up to 1 MV/cm) caused by spontaneous and piezo-electric polarization. These effects are now emergingas a dominant factor for the optical and electricalproperties of nitride heterostructures. In wurtziteInGaN/GaN structures, Gotoh and Fabio19,20 as-signed the blue shift of luminescence and the de-crease in the PL decay time to the piezoelectriceffects. Strassburg et al.21 have demonstrated inAlGaN quantum wells that the piezoelectric fieldslead to a strong reduction of the oscillator strengthand to a stark red shift of the PL. In a previouspaper,22 we have observed a spatial inhomogeneity

1062 Matoussi, Boufaden, Guermazi, Mlik, El jani, and Toureille

Fig. 4. Normalized induced current versus squared incident beamposition on logarithmic scale.

Fig. 5. HRSEM cross section of the sample. The columns with sizein the range 0.28–0.4 µm are visible.

Fig. 3. A typical EBIC current as a function of electron beam posi-tion. The circular dots correspond to the measured EBIC current; thesimulated current is indicated by a solid line. By fitting the curve fromthe model, a hole diffusion length of 0.35 µm was obtained near thedepletion region.

Page 5: Electron beam-induced current investigation of GaN Schottky diode

and blue shift of the near-band-edge WZ emission. At5 K, the PL spectrum of the studied sample was dom-inated by sharp peaks at 3.306 and 3.364 eV, while atroom temperature, it is dominated by a large peaklocated around 3.24 eV (Fig. 6). These peaks were at-tributed to localized excitons induced by piezoelectricfields. By means of thermal step method, we havefound in this layer a space charge density up to3·106 C/cm2,23 in good agreement with the calcula-tion of Bernardini et al.24 This is an argument infavor of the implication of the piezoelectric effects onthe transport carrier properties in GaN, as suggestedby Harris et al.25

On the other hand, the increase in the diffusionlength can be due to the reabsorption recombinationradiation (RRR) processes.12,15 Recently, it wasfound by Pavesi and Guzzi26 that the RRR effectsare significant as long as the AlGaAs has a directgap and the Al concentration increases in the alloy.They showed in GaAs/AlGaAs structures that theinner layer of GaAs was excited by reabsorption ofphotons emitted by the cap layer AlGaAs, whichgenerate other e-h pairs and contributes conse-quently to the increase of the measured carrier life-time and diffusion length. Akamatsu et al.14 andGuermazi et al.12 pointed out by means of EBIC ex-periments that the diffusion length of the minoritycarrier is deduced from the collected current nearthe junction, but in the regions located very far fromthe junction, the measured current is produced bythe RRR process.

These processes produce an additional photocur-rent with magnitude described by exp (–apxo), whereap is the optical absorption coefficient. Hence, fordistance xo greater than xN 0.65 µm, the observedchange in the slope of the curve might be due tothese processes. From the linear part (3) of the

curve (Fig. 4), the square root of the slope givesap 0.178 µm1. Figure 7 shows the absorption co-efficient measured at room temperature by an ultra-violet-infrared spectrometer. It appears here thatthe above value is an average coefficient measuredat photon energy above 3.4 eV.

This is likely a result of the photons emitted at3.24 eV, which are related to excitons localized nearthe PS/GaN interface.22 Note that the value of mea-sured ap is about 0.15 µm1 for photon energy of3.24 eV. According to Von Roos,27 the carrier lifetimedue to the reabsorption of the emitted light can be

calculated using the formula , where

D 2.6 cm2/s is the hole diffusivity.For a measured absorption coefficient of 0.15 µm1,

corresponding to the most emitted photons at 3.24 eV,the formula gives a hole lifetime of 5 · 108 s in thebulk material. This proves that the RRR processesmight be a possible explanation for the increase ofthe carrier lifetime in this component. In summery,the results allow us to attribute the change in the ob-served Lp to the polarization effects and the RRRprocess. Then, it is shown that the EBIC measure-ments could be used to determine the diffusion lengthand the absorption coefficient in the III-nitrides–based structures.

CONCLUSIONS

In this article, we have determined some trans-port properties of the undoped MOVPE GaN Schot-tky diode using an induced-current EBIC model ofthe form exp(–xo

2/L2) within the depletion layer. Aminority diffusion length Lp of 0.35 µm was foundfor holes near the depletion region, but very far fromthe junction was increased to 1.74 µm in the bulk

= ap−2

3/ D

Electron Beam–Induced Current Investigation of GaNSchottky Diode 1063

Fig. 6. PL spectra of the same sample at room and low temperature(5 K). The excitation power is 10 mW.

Fig. 7. Optical absorption coefficient versus photon energy, mea-sured at room temperature.

Page 6: Electron beam-induced current investigation of GaN Schottky diode

regions. This change is attributed to an increaseof the carrier lifetime caused probably by the RRRprocesses and the polarization effects. Near theGaN/PS interface, the collected current seems toresult from the RRR, which implies an additionalphotocurrent to the EBIC current. Based on theabsorption measurement, this corresponds to an ab-sorption coefficient of 0.178 µm1 in the sample.

ACKNOWLEDGEMENTS

This work was supported by the Tunisian Secre-tary of State for Research Science and Technologyand CMCU Project No. 01 F13 10. Thanks go to E.Saless for the device processing and Dr. C. Grill forhis assistance in SEM/EBIC characterizations.

REFERENCES1. S. Nakamura, T. Mukai, and M. Senoh, Appl. Phys. Lett.

64, 1687 (1994).2. S. Nakamura et al., Jpn. J. Appl. Phys. 38, L1578 (1997).3. N. Mohammad and H. Morkoç, Progr. Quantum Electron.

20, 361 (1996).4. S.J. Pearton, J.C. Zolper, R.J. Shul, and F. Ren, J. Appl.

Phys. 86, 1 (1999).5. A.T. Ping, Q. Chen, J.W. Yang, M.A. Khan, and I. Adesida,

IEEE Electron. Dev. Lett. 19, 54 (1998).6. Z.Z. Bandic, E.C. Piquette, P.M. Bridger, T.F. Kuech, and

T.C. McGill, Mater. Res. Soc. Symp. Proc. 483, 399 (1998).7. T. Sugahara, H. Sato, M. Hoo, Y. Naoi, S. Kurai, S. Tottori,

K. Yamashita, K. Nishino, L.T. Romano, and S. Sakai, Jpn.J. Appl. Phys. 37, L389 (1998).

8. P. Hacke, H. Nakayama, T. Detchyrohm, K. Hiramatsu,and N. Sawaki, Appl. Phys. Lett. 68, 1362 (1996).

9. A. Matoussi, T. Boufaden, A. Missaoui, S. Guermazi, B.Bessaïs, Y. Mlik, and B. ElJani, Microelectron. J. 32, 995(2001).

10. S. Guermazi, A. Toureille, C. Grill, B. Eljani, and N. Lakhoua,J. Phys. III France 6, 481 (1996).

11. S. Guermazi, A. Toureille, C. Grill, B. Eljani, and N. Lakhoua,Eur. Phys. J. Appl. 9, 43 (2000).

12. S. Guermazi, H. Guermazi, Y. Mlik, B. Eljani, C. Grill, andA. Toureille, Eur. Phys. J. Appl. 16, 45 (2001).

13. K. Kanaya and S. Okayama, J. Phys. D: Appl. Phys. 5, 43(1972).

14. B. Akamatsu, J. Henoc, and P. Henoc, J. Appl. Phys. 52,7245 (1981).

15. S.J. Rosner, E.C. Carr, M.J. Ludowise, G. Girolami, andH.I. Erikson, Appl. Phys. Lett. 70, 794 (1996); J.S. Speckand S.J. Rosner, Physica B 273–274, 24 (1999).

16. L. Chernyak, A. Osinsky, H. Teurkin, J.W. Yang, Q. Chen,and M.A. Khan, Appl. Phys. Lett. 69, 2531 (1996).

17. L. Chernyak, A. Schulte, A. Osinsky, J. Graff, and E.F.Schubert, Appl. Phys. Lett. 80, 926 (2002).

18. C. Monier, A. Freundlich, and M.F. Vilela, J. Appl. Phys. 85,2713 (1999); E.L. Waldron, E.F. Schubert, J.W. Graff,A. Osinsky, W.F. Schoff, and L.F. Eastman (Presentation atthe 6th Annual Wide Bandgap III-Nitride Workshop, Rich-mond, VA, 12–15 March 2000).

19. H. Gotoh, T. Tawara, Y. Kobayashi, and T. Saitoh, Appl.Phys. Lett. 83, 4791 (2003).

20. F.D. Sala, A.D. Carlo, P. Lugli, F. Bernardini, V. Fiorentini,R. Scholz, and J.M. Jancu, Appl. Phys. Lett. 74, 2002(1999).

21. M. Strassburg, A. Hoffmann, J. Holst, J. Christen, T. Rie-mann, F. Bertram, and P. Fischer, Phys. Status Solidi (c).p. 1835 (2003).

22. T. Boufaden, A. Matoussi, S. Guermazi, S. Guillaguet, A.Toureille, Y. Mlik, and B. El jani, Phys. Status Solidi (a)201, 582 (2004).

23. A. Toureille, J. Electrostat. 32, 277 (1994); A. Matoussi,S. Bergaoui, T. Boufaden, S. Guermazi, S. Agnel, Y. Mlik,B. El jani, and A. Toureille (Paper presented at 5th Int.Conf. on Electric Charge in Solid Insulators, Tunisia 22–26November 2004).

24. F. Bernardini, V. Fiorentini, and D. Vanderbilt, Phys. Rev.B 56, R10024 (1997).

25. J.J. Harris, K.J. Lee, J.B. Bebb, H. Tang, I. Harrison, L.B.Flannery, T.S. Cheng, and C.T. Foxon, Semicond. Sci. Tech-nol. 15, 413 (2000).

26. L. Pavesi and M. Guzzi, J. Appl. Phys. 75, 4794 (1994).27. O. Von Roos, J. Appl. Phys. 54, 1390 (1983).

1064 Matoussi, Boufaden, Guermazi, Mlik, El jani, and Toureille