Pis’ma v ZhETF, vol. 112, iss. 2, pp. 112 - 113

High thermal conductivity of bulk GaN single crystal:

An accurate experimental determination

A. V. Inyushkin⁺¹⁾, A. N. Taldenkov⁺, D. A. Chernodubov⁺, V. V. Voronenkov^∗, Yu. G. Shreter^∗×1)

⁺National Research Center Kurchatov Institute, 123182 Moscow, Russia

^∗Ioffe Institute, 194021 St. Petersburg, Russia

^×Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia

Submitted 19 May 2020

Resubmitted 1 June 2020

Accepted 2

June 2020

DOI: 10.31857/S1234567820140086

In recent decades, GaN crystals attract a lot of at-

substrate. After the growth upon cooling, the plate self-

tention, both experimental and theoretical, due to its

separated from the substrate [14]. The bar-shaped sam-

unique physical properties, including thermal conduc-

ple with the cross-section of 1.38 × 3.24 mm² and the

tivity. In pure and lightly doped GaN, the heat is trans-

length of 6.5 mm was made from the plate. We employed

ported practically solely by phonons.

a steady-state longitudinal heat flow technique for ther-

Experiments demonstrate that defects may reduce

mal conductivity measurements within the basal plane

strongly the thermal conductivity of GaN crystals

(see [15] for details).

in a wide temperature range [1-8]. Oxygen substitu-

From the measured Raman spectra, the free elec-

tional atoms, gallium vacancies, and their complexes

tron concentration n_e was estimated to be (2.7 ± 0.2) ×

are the most common point defects in unintention-

× 10¹⁷ cm^-3 for our sample. This value is very close

ally doped GaN. The oxygen atoms at concentration

to the concentration of spin 1/2 paramagnetic defects,

above 10¹⁸ cm^-3 produce substantial decrease in κ at

(2-3) × 10¹⁷ cm^-3, that was determined by DC magne-

room temperature, and in heavily oxygen doped GaN

tization measurements using SQUID magnetometer. We

(> 10¹⁹ cm^-3) an additional scattering process owing

suppose that impurity oxygen and silicon, the shallow

to the phonon interaction with free electrons supplied

donors in GaN, are responsible for the paramagnetism

by oxygen donors becomes important [5].

in our GaN crystal at low temperature when being in

The impact of point defects on thermal conductiv-

the neutral charge state, whereas they supply with free

ity of GaN crystals was investigated by employing the

charge carriers at room temperature.

phenomenological models [1, 3, 5-9] and first-principles

The measured k(T ) for our GaN crystal is presented

approaches [10, 11]. For the GaN crystal studied in [1],

in Fig. 1. Here, plotted are the experimental data for

the contribution of point-defect scattering toward ther-

bulk GaN of other works [1, 2, 4, 5, 16]. In general,

mal resistivity was estimated in [9] to be as high as 90 %

there is a good agreement between results of differ-

around the peak of κ(T) at ∼30 K and about 11 % at

ent measurements. Some essential discrepancies, how-

300 K. Lindsay et al. have shown by ab-initio calcula-

ever, emerge at close inspection. We have found that

tions [12, 13] that the strong effect of impurities is due to

κ(T ) ∝ T-n with n = 1.367 ± 0.002 in the range

small contribution of anharmonic phonon-phonon scat-

80 < T < 300 K, but Slack et al. have observed a weaker

tering processes to the phonon relaxation. This is a con-

dependence κ(T ) ∝ T^-1.22. According to the experi-

sequence of large gap between acoustic and optic modes’

mental results of [7] the slope decreases with increasing

frequencies in the phonon spectra of GaN, which arises

doping from n = 1.3 for the undoped sample to n = 0.55

due to the high mass ratio of Ga and N atoms.

for the highest Si-doped sample.

To clarify the effect of defects in the heat transport

At lowest temperatures of our experiment, below

of GaN we performed an accurate measurements of GaN

about 5.5 K, the measured values of κ(T) are close to

single crystal over a wide temperature range.

the calculated ones, shown as the violet line in Fig. 1.

The wurtzite GaN single crystal plate was grown

The calculations were performed assuming only the dif-

by hydride vapor-phase epitaxy (HVPE) on a sapphire

fuse scattering from sample boundaries and taking into

account the phonon focusing effect. The measured κ(T)

¹⁾e-mail: Inyushkin_AV@nrcki.ru; Y.Shreter@mail.ioffe.ru

at 5 K is about 13 % lower than the calculated value.

112

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2020

High thermal conductivity of bulk GaN single crystal. . .

113

crease above 200 K likely indicates the rising importance

of four-phonon scattering processes in thermal conduc-

tivity.

Thermal conductivity, Raman, and magnetic mea-

surements were carried out in the Resource Cen-

ter funded by National Research Center

“Kurcha-

tov Institute”. The authors are thankful to D. R.

Streltsov for Raman measurements. A. V. Inyushkin,

A. N. Taldenkov, and D. A. Chernodubov acknowledge

financial support from the Russian Foundation for Basic

Research (Grant # 19-07-00229).

Full text of the paper is published in JETP Letters

journal. DOI: 10.1134/S0021364020140039

G. A. Slack, L. J. Schowalter, D. Morelli, and J. A. Fre-

itas, Jr., J. Cryst. Growth 246, 287 (2002).

Fig. 1. (Color online) Thermal conductivity of GaN single

A. JeŻowski, B. A. Danilchenko, M. Boćkowski, I. Grze-

crystals as a function of temperature. Pink circles indi-

gory, S. Krukowski, T. Suski, and T. Paszkiewich, Solid

cate measurement data of this work, the violet line is a

State Commun. 128, 69 (2003).

calculated T³-dependence in the diffuse boundary scatter-

A. JeŻowski, O. Churiukova, J. Mucha, T. Suski,

ing regime. The published results of other experiments -

I. A. Obukhov and B. A. Danilchenko, Mater. Res.

Slack et al. [1] (cyan circles), JeŻowski et al. [2] (yellow

Express 2, 085902 (2015).

circles), Mion et al. [4] (violet squares), Simon et al. [5]

(olive diamonds), and Zheng et al. [16] (blue triangles) -

C. Mion, J. F. Muth, E. A. Preble, and D. Hanser, Appl.

Phys. Lett. 89, 092123 (2006).

and calculations by Lindsay et al. [12] (the solid blue line)

are also shown

R. B. Simon, J. Anaya, and M. Kuball, Appl. Phys. Lett.

105, 202105 (2014).

M. Slomski, P. P. Paskov, J. H. Leach, J. F. Muth, and

This suggests that even at this temperature the point

T. Paskova, Phys. Status Solidi B 254, 1600713 (2017).

defect scattering sizably reduces the conductivity in our

P. P. Paskov, M. Slomski, J. H. Leach, J. F. Muth, and

sample. The experimental curve κ(T) progressively de-

T. Paskova, AIP Advances 7,095302 (2017).

viates from the calculated one with the temperature

R. Rounds, B. Sarkar, T. Sochacki, M. Bockowski,

M. Imanishi, Yu. Mori, R. Kirste, R. Collazo, and

rise reflecting the increasing contribution of the point

Z. Sitar, J. Appl. Phys. 124, 105106 (2018).

defect scattering as compared with boundary scatter-

A. AlShaikhi, S. Barman, and G. P. Srivastava, Phys.

ing strength. The κ(T ) for our GaN sample reaches the

Rev. B 81, 195320 (2010).,

maximum of 3770 W m^-1 K^-1 at 28 K. Here, the value of

10.

J. Ma, X.-J. Wang, B. Huang, and X. Luo, J. Appl.

κ(T ) is determined by the combined effect of the bound-

Phys. 114, 074311 (2013).

ary, point-defect, and anharmonic scattering.

11.

A. Katre, J. Carrete, T. Wang, G. K. H. Madsen, and

There is a very weak dip in the κ(T ) curve centered

N. Mingo, Phys. Rev. Materials 2, 050602 (2018).

near T ≈ 7 K (see Fig. 1). This dip can be ascribed to

12.

L. Lindsay, D. A. Broido, and T. L. Reinecke, Phys. Rev.

the effect of the phonon scattering from electrons bound

Lett. 109, 095901 (2012).

to the neutral donors.

13.

L. Lindsay, D. A. Broido, and T. L. Reinecke, Phys. Rev.

Comparing our measured κ(T ) with the calculated

B 88, 144306 (2013).

dependence of Lindsay et al. [12] for pure GaN (the

14.

V. Voronenkov, A. Leonidov, Yu. Lelikov, A. Zubrilov,

blue solid line in Fig. 1), we find a very good quantita-

and Yu. Shreter, Thick GaN film stress-induced

tive agreement at temperatures from 100 to 200 K: the

self-separation,

e-print

arXiv:cond-mat.mtrl-

calculated values are higher than experimental ones by

sci/1902.03463v2"(2019).

4-5 %. This suggests the overwhelming dominance of

15.

A. V. Inyushkin, A.N. Taldenkov, V. G. Ralchenko,

A. P. Bolshakov, A.,V. Koliadin, and A. N. Katrusha,

three-phonon processes in the phonon scattering. The

Phys. Rev. B 97, 144305 (2018).

phonon scattering from the lattice imperfections and

16.

Q. Zheng, C. Li, A. Rai, J. H. Leach, D. A. Broido, and

charge carriers both contribute small at these and higher

D. G. Cahill, Phys. Rev. Materials 3, 014601 (2019).

temperatures. The rising deviation upward of the theo-

retical κ(T) from experimental one with temperature in-

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2020