Materials Science and Engineering A 422 (2006) 316–320

The thermodynamic analysis of the driving force forthe Ni/GaN interfacial reaction

Mei Li a, Changrong Li a,∗, Fuming Wang b, Weijing Zhang a

a School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, PR Chinab School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, PR China

Received 25 November 2005; accepted 14 February 2006

Abstract

Based on the optimized thermodynamic data from literature and the phase equilibrium calculation, the contact interfacial reactions and the phaseformation sequences of Ni/GaN joints were analyzed theoretically under the reported experimental conditions. The phase formation sequences andthe apparent spatial phase sequences were obtained. It was revealed that the phase formation sequences and the apparent spatial phase sequenceswere dominated by many factors, such as the temperature range, time period and the amounts of the original layers of the diffusion couples.© 2006 Elsevier B.V. All rights reserved.

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eywords: Ga–N–Ni; Interfacial reaction; Phase formation sequence

. Introduction

Recently, GaN-based materials have been intensively stud-ed for optoelectronic devices as well as high-temperature andigh-power electronic devices. Visible light-emitting diodes [1],ltraviolet (UV) detectors [2] and high-electro-mobility tran-istors (HEMTs) [3] have been demonstrated. Fabrication oflectrical contacts to theses devices requires the deposition ofetals on semiconductors with subsequent annealing. Interfa-

ial reactions between metals and GaN are important since thelectrical properties of such contacts are influenced by the phasesormed directly on the GaN surface because of process annealingr high-temperature service.

As device performance improves, studies on metal/GaN inter-aces have attracted much attention [4]. Since Ni has been usedn Ni/Au ohmic contacts to GaN [5] and has been examined asSchottky barrier to n-type GaN [4,6–8], an understanding of

he metallurgy of the Ni/GaN system is clearly needed.The knowledge of the phase equilibria is of great help to

nderstand the interfacial phenomena of the metal/compound-emiconductor contact. If the system can be described thermo-

In this paper, on the basis of the thermodynamic parametersfrom literature and the phase equilibrium calculation, the inter-facial reaction sequences of the Ni/GaN joints were analyzedtheoretically.

2. Literature results

2.1. Thermodynamics of the Ga–N–Ni ternary system

Grobner et al. [9] prepared the ternary samples from Ni andGaN powders in various ratios, pressed to pellets and annealedbetween 773 and 973 K for 24 h. Phase analyses were carried outby X-ray diffraction (XRD). Experimental results show that thereactions are sluggish, and no ternary compound was reportedin the Ga–N–Ni ternary system. Based on their experiments andthe data from other literature, Grobner et al. assessed thermody-namically the Ga–N–Ni ternary system. The isothermal sectionof Ga–N–Ni system at 773 K [9] was shown in Fig. 1.

2.2. Literature experimental results of interfacial reactions

ynamically, the possible phase sequences can be predicted andhe experimental results can be analyzed.

∗ Corresponding author. Tel.: +86 10 6233 3607; fax: +86 10 6233 3772.

Ni/GaN interfacial reactions were studied by many investi-gators. Guo et al. [7] studied the thermal stability of Ni Schottkycontacts on n-type GaN. Phase identification was performedprimarily by XRD. According to these investigators, Ni3Ga4w

E-mail address: crli@mater.ustb.edu.cn (C. Li).

921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2006.02.017

as identified to be present along with Ni in the as-deposited

M. Li et al. / Materials Science and Engineering A 422 (2006) 316–320 317

Fig. 1. The isothermal section of the Ga–N–Ni system at 773 K.

film. However, no intermixing between Ni and Ga was observedin the corresponding SIMS (secondary-ion mass spectroscopy)spectra. On subsequent annealing in a N2 atmosphere at 473and 673 K, nickel nitrides, Ni3N and Ni4N, were identified byXRD [7]. However, Venugopalan et al. [10,11], Liu et al. [6]and Bermudez et al. [12] observed that a pronounced interfacialreaction occurred upon annealing above 873 K. Grobner et al.[9] suggested that the Ni3N phase starts to form under a pressureof 104 bar. However, this is an external pressure and the internalpressure, exerted by the reaction, cannot exceed 100 bar. Conse-quently, no Ni3N was observed by XRD, the only solid reactionproduct was Ni3Ga. Venugopalan et al. [10] investigated theinterfacial reactions between thin nickel films and GaN. The

Table 1Annealing conditions and the corresponding reaction products in Ni/GaN jointsfrom Ref. [10]

Temperature (K) Time Atmosphere Ni–Ga phase incontact with GaN

673 10 min N2 Ni10 min 95%N2 + 5%H2 Ni

873 1 h N2 fcc1 h Ar fcc17 h N2 fcc7 days Sealed in vacuum fcc

1

1

thin Ni films on GaN were annealed at temperatures between673 and 1173 K in N2 or Ar and forming gas, and were analyzedusing glancing angle XRD and Auger depth profiling. The firstindication of an interfacial reaction was found after annealing at873 K for 1 h, showing that Ga was dissolved in the face-centeredcubic Ni film. The extent of dissolution increased with contin-ued annealing. After annealing at 1023 K for 1 h in either N2 orAr, greater intermixing occurred. The different annealing condi-tions and the corresponding reaction products for Ni/GaN joints[10] were shown in Table 1. A trend of increasing Ga content inthe reacted films was observed with increasing temperature.

3. Driving force description

Driving force is the affinity between reacting chemicalspecies in a certain process, for which the process extent isusually represented by the internal variable ξ. In the Thermo-Calc software which is based on Gibbs energy minimization forequilibrium systems, the driving force for a phase � is alwaysevaluated by [13]:

D� = −(

∂G

∂ξ

)T,P,Ni

= −(

∂G

∂N�

)T,P,Ni

The driving force for a stable equilibrated phase is zero, whilstfor an unstable phase is negative. Any phase with positive drivingf

dEPcic

dt

4

fAdpacTNNccpwc

t

023 1 h N2 fcc or Ni3Ga1 h Ar fcc or Ni3Ga4 h N2 fcc or Ni3Ga7 days Sealed in vacuum fcc or Ni3Ga

173 10 min N2 NiGa10 min Ar NiGa30 min Ar NiGa

orce will precipitate from the meta-stable equilibrated system.In the Thermo-Calc software, there are three types of the

efined status for a phase during the equilibrium calculation:NTERED, SUSPEND and DORMANT. ENTERED or SUS-END means that the phase is concluded or excluded in thealculation respectively, while DORMANT means that the phases not considered in the calculation but its driving force for pre-ipitation is calculated.

Based on the thermodynamic data [9] and the experimentalata [9–11], the phase formation sequences were predicted forhe Ni/GaN joints using Thermo-Calc software.

. Driving force analysis

For the Ni/GaN joint, the initial status was set as ENTEREDor fcc(Ni) and GaN phases and DORMANT for other phases.bove 873 K, the reaction at the Ni/GaN interface starts by theiffusion and dissolution of Ga in Ni [10], resulting in the decom-osition of GaN. So, there are a little N2 between Ni and GaNnd the status of gas was changed to be ENTERED. The con-entration of Ga in fcc(Ni) increases with the diffusion of Ga.he starting point of the calculation was supposed to be at thei side, x(Ni) = 0.99 and x(Ga) = 0.01 for the molar fractions ofi and Ga, respectively. The driving force was calculated as the

oncentration of Ga in fcc(Ni) increases with step 0.01 while theoncentration of Ni in fcc(Ni) decreases with the same step. Noositive driving force was obtained until x(Ni) = 0.8, x(Ga) = 0.2,hen the driving force for Ni3Ga precipitation is positive. The

alculation results were shown in Table 2.In Table 2, the third and the fourth columns are respectively

he calculated driving forces for the formation of new precipi-

318 M. Li et al. / Materials Science and Engineering A 422 (2006) 316–320

Table 2Calculated driving forces at 900 K for the Ni/GaN interface at x(Ni) = 0.8 andx(Ga) = 0.2

Phase Status Driving force (J/mol) Mole fraction

fcc ENTERED 0.00000000 1.00000000Gas ENTERED 0.00000000 0.00000000GaN ENTERED −3.56362035 0.00000000Ni3Ga DORMANT 5.24105204 × 10−2

NiGa DORMANT −2.80925178 × 10−1

Ni5Ga3 DORMANT −3.31288701 × 10−1

Ni3Ga2 DORMANT −3.68852545 × 10−1

Liq DORMANT −9.57188872 × 10−1

Ni3Ga4 DORMANT −1.91467142Ni2Ga3 DORMANT −2.29357083Ni3N DORMANT −3.22653309NiGa4 DORMANT −6.09998523Ni4N DORMANT −9.42599631

tates and the calculated mole fractions of the old phases both inthe meta-stable equilibrium system. It is shown in Table 2 thatthe driving force for the formation of Ni3Ga phase is positive andmaximum. The Ni3Ga phase will form at the interface betweenNi/GaN.

After Ni3Ga precipitation, two new interfaces, Ni/Ni3Ga andNi3Ga/GaN, will be formed. Thus, the Ni3Ga phase was putinto the equilibrium calculation and its status was changed tobe the ENTERED. And the status of GaN and fcc(Ni) phaseswere changed to be DORMANT for driving forces calculation atinterfaces Ni/Ni3Ga and Ni3Ga/GaN, respectively. The drivingforces at 900 K for the phase formations at interfaces Ni/Ni3Gaand Ni3Ga/GaN were calculated. Because the diffusion of N2generated by the reaction of Ni and GaN is slow [9], there are alittle N2 between Ni3Ga and GaN. Therefore, the status of gaswas changed to be ENTERED. The calculated driving forcesat 900 K for the Ni3Ga/GaN interface were shown in Table 3.Those for Ni/Ni3Ga were not listed since no positive drivingforce was obtained.

It is shown in Table 3 that the driving force of the forma-tion of NiGa phase is positive and maximum. The NiGa phaseturns to precipitate at the interface Ni3Ga/GaN. Again two newinterfaces, Ni3Ga/NiGa and NiGa/GaN, will be formed. Thus,

Table 3Calculated driving forces at 900 K for the Ni3Ga/GaN interface at x(Ni) = 0.74a

P

NGGNNNfLNNNNN

Table 4Calculated driving forces at 900 K for the Ni3Ga/NiGa interface at x(Ni) = 0.74and x(Ga) = 0.25

Phase Status Driving force (J/mol) Mole fraction

Ni3Ga ENTERED 0.00000000 9.77038187 × 10−1

NiGa ENTERED 0.00000000 1.29618134 × 10−2

Gas ENTERED 0.00000000 1.00000000 × 10−2

Ni3Ga2 DORMANT 1.66553498 × 10−1

Ni5Ga3 DORMANT 1.36917552 × 10−1

fcc DORMANT −1.03194150 × 10−2

Liq DORMANT −7.13073270 × 10−1

Ni3Ga4 DORMANT −8.06239946 × 10−1

Ni2Ga3 DORMANT −9.74409372 × 10−1

GaN DORMANT −2.12028420NiGa4 DORMANT −3.99706835Ni3N DORMANT −4.00061168Ni4N DORMANT −1.02516804 × 10

the NiGa phase was put into the equilibrium calculation and itsstatus was changed to be the ENTERED. The status of GaNand Ni3Ga phases were changed to be DORMANT for the driv-ing forces calculation at interfaces Ni3Ga/NiGa and NiGa/GaN,respectively. The driving forces at 900 K for the phase forma-tions at interfaces Ni3Ga/NiGa and NiGa/GaN were calculated.The calculated driving forces at 900 K for the Ni3Ga/NiGa inter-face were shown in Table 4. Those for NiGa/GaN were not listedsince no positive driving force was obtained.

It is shown in Table 4 that the driving force of the Ni3Ga2phase is positive and maximum. So the Ni3Ga2 phase turns toprecipitate at the interface Ni3Ga/NiGa. Again two new inter-faces, Ni3Ga/Ni3Ga2 and Ni3Ga2/NiGa, will be formed. Thus,the Ni3Ga2 phase was put into the equilibrium calculation andits status was changed to be the ENTERED. The status ofNiGa and Ni3Ga phases were changed to be DORMANT forthe driving forces calculation at interfaces Ni3Ga/Ni3Ga2 andNi3Ga2/NiGa, respectively. The driving forces at 900 K for thephase formations at interfaces Ni3Ga/Ni3Ga2 and Ni3Ga2/NiGawere calculated. The calculated driving forces at 900 K for theNi3Ga/Ni3Ga2 interface were shown in Table 5. The calculateddriving forces for the Ni3Ga2/NiGa interface were not listedsince no positive driving force was obtained.

Table 5Calculated driving forces at 900 K for the Ni3Ga/Ni3Ga2 interface at x(Ni) = 0.74a

P

NNGNfNLNNGNNN

nd x(Ga) = 0.25

hase Status Driving force (J/mol) Mole fraction

i3Ga ENTERED 0.00000000 9.86666667 × 10−1

aN ENTERED 0.00000000 6.66666661 × 10−3

as ENTERED 0.00000000 6.66666673 × 10−3

iGa DORMANT 1.33928839i3Ga4 DORMANT 1.09623592i2Ga3 DORMANT 1.01446718

cc DORMANT 1.00452255iq DORMANT 9.15408106 × 10−1

i3Ga2 DORMANT 8.15408497 × 10−1

i5Ga3 DORMANT 4.48206499 × 10−1

iGa4 DORMANT −8.87318187 × 10−1

i3N DORMANT −5.05269039i4N DORMANT −1.13824984 × 10

nd x(Ga) = 0.25

hase Status Driving force (J/mol) Mole fraction

i3Ga2 ENTERED 0.00000000 1.66666667 × 10−2

i3Ga ENTERED 0.00000000 9.73333333 × 10−1

as ENTERED 0.00000000 1.00000000 × 10−2

i5Ga3 DORMANT 3.67475387 × 10−3

cc DORMANT −7.12130939 × 10−2

iGa DORMANT −1.89516858 × 10−1

iq DORMANT −9.18473903i3Ga4 DORMANT −1.06838740i2Ga3 DORMANT −1.36303420aN DORMANT −2.53666795iGa4 DORMANT −3.79241981i3N DORMANT −4.60776451i4N DORMANT −1.00296088 × 10

M. Li et al. / Materials Science and Engineering A 422 (2006) 316–320 319

Fig. 2. The phase formation sequence at the Ni/GaN couple at 900 K.

It is shown in Table 5 that the driving force of the Ni5Ga3phase is positive and maximum. The Ni5Ga3 phase turns toprecipitate at the interface Ni3Ga/Ni3Ga2. Again two new inter-faces, Ni3Ga/Ni5Ga3 and Ni3Ga2/Ni5Ga3, will be formed. Thelocal equilibrium states are reached at the interfaces betweenNi/Ni3Ga, Ni3Ga/Ni5Ga3, Ni5Ga3/Ni3Ga2, Ni3Ga2/NiGa andNiGa/GaN, respectively.

The above-mentioned phase formation sequence is illustratedin Fig. 2. As for the Ni/GaN joint at 900 K, the newly formedphases in the phase formation sequence are Ni3Ga at the Ni/GaNinterface, NiGa at the Ni3Ga/GaN interface, Ni3Ga2 at theNi3Ga/NiGa interface and Ni5Ga3 at the Ni3Ga/Ni3Ga2 inter-face. The apparent spatial phase sequence is the bottom linein Fig. 2, Ni/Ni3Ga/Ni5Ga3/Ni3Ga2/NiGa/GaN. The apparent

Fs

spatial phase sequence is drawn in the isothermal section ofGa–N–Ni system in Fig. 3.

5. Discussion and summary

Based on the thermodynamic data and the driving force analy-sis, the phase formation sequences were analyzed for the Ni/GaNjoints. The apparent spatial phase sequence was obtainedfor the Ni/GaN joint at 900 K, i.e. Ni/Ni3Ga/Ni5Ga3/Ni3Ga2/NiGa/GaN.

Since the reactions between Ni and GaN are slow [9], the spa-tial phase sequence is different at different temperature range anddifferent time period. For example, the spatial phase sequence isNi/Ni3Ga/GaN at 1023 K, 4 h as shown in the dash line box ofFig. 2, while the spatial phase sequence is Ni/Ni3Ga/NiGa/GaNat 1173 K, 10 min as shown in the dot dash line box of Fig. 2.So the spatial phase sequences depend on the temperature andtime.

The spatial phase sequences depend on not only the tem-perature and time, but also the amounts of Ni and GaN.If the Ni forms thin-film, the spatial phase sequence isNi3Ga/Ni5Ga3/Ni3Ga2/NiGa/GaN after the thin-film Ni is con-sumed. If the Ni film is very thin, the reaction between Ni3Gaand NiGa may not occur.

These theoretical analyses explain the experimental observa-ttid

A

tTNN2

R

ig. 3. The isothermal section of the Ga–N–Ni system at 900 K and the phaseequence of the Ni/GaN couple.

ions well. The different phase formation sequences and hencehe different apparent spatial phase sequences are mainly dom-nated by the temperature, time and the relative amounts of theiffusion couples.

cknowledgements

The authors would like to express their appreciation tohe Royal Institute of Technology Sweden for supplying thehermo-Calc software. This work was supported by the Nationalatural Science Foundation of China (No. 50371008) and theational Educational Committee for the Doctorate program (No.0030008016).

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