Diamond & Related Materials 14 (2005) 589 – 593 www.elsevier.com/locate/diamond
Thermal conductivity of CVD diamond at elevated temperatures A.V. Sukhadolaua, E.V. Ivakina, V.G. Ralchenkob,*, A.V. Khomichc, A.V. Vlasovb, A.F. Popovichb a
Institute of Physics, Academy of Sciences of Belarus, 70 Skaryna Ave., 220072 Minsk, Belarus b A.M. Prokhorov General Physics Institute RAS, Vavilov str. 38, Moscow 119991, Russia c Institute of RadioEngineering and Electronics RAS, 1 Vvedenskogo sq., 141190 Fryazino, Russia Available online 8 January 2005
Abstract Transient thermal grating and laser flash techniques have been used to measure in-plane (k jj) and perpendicular (k 8) thermal conductivity of 0.3–0.6 mm thick polycrystalline MPCVD diamond films. A small (b20% ) anisotropy in k is revealed, and a correlation of k (8–20 W/cm K at RT) with optical absorption and hydrogen impurity concentration is established. The temperature dependence k(T) between 293 and 460 K follows the relationship k~T n (n=0.17–1.02) depending on the diamond quality. D 2005 Elsevier B.V. All rights reserved. Keywords: Diamond film; Thermal conductivity; Transient thermal grating; Laser flash technique
1. Introduction Due to superior thermal conductivity of diamond, it is ideally suited for heat spreaders for electronic devices, e.g. laser diodes or microwave semiconductor devices. CVD diamond is especially promising for heat dissipation from large size thermal sources such as multichip modules (MCM) , since, unlike to HPHT and natural diamonds, the CVD films can be produced in planar dimensions exceeding 100 mm. The thermal properties are important also for performance of diamond optics of IR and radio frequency ranges. Typically, the thermal conductivity (k) of polycrystalline CVD diamond shows some anisotropy due to columnar crystallite growth . In the present paper, we used the transient thermal grating  and a laser flash  non-contact techniques to measure in-plane and perpendicular thermal conductivity of thick diamond films of different qualities grown in a microwave plasma CVD reactor. The correlation of thermal and optical properties is traced. Since in some cases thermal spreaders must operate at temperatures up to 450–500 K, we measured the
* Corresponding author. Tel.: +7 095 1328229; fax: +7 095 135 7672. E-mail address: ralchenko[email protected]
(V.G. Ralchenko). 0925-9635/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2004.12.002
temperature dependence of thermal conductivity for the diamond films between 293 and 460 K and compared the results with the data of Burgemeister  for natural single crystals, in which nitrogen impurities determine the k value.
2. Experimental The diamond films of different qualities (k=8–20 W/cm K at RT) with thickness in the range of 0.3 to 0.6 mm have been grown by microwave plasma CVD in CH4/H2 mixtures, with methane content varied from 1.5% to 5%, as described elsewhere . The hydrogen and nitrogen impurity concentrations in the films were determined from UV (peak at 270 nm) and IR (stretching C–H vibrations in the range from 2800 to 3100 cm1) of optical absorption spectra, respectively, on the polished free-standing samples . The in-plane thermal conductivity (k jj) was measured with the transient thermal grating (TTG) technique  that is based on the thermal grating recording in the sample by two interfering laser beams, and monitoring the thermal decay of the grating with a probe He–Ne beam diffracting on the TTG. The TTG with the period of 30–120 Am were
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excited in bulk by Nd:YAG laser pulses at 1064 or 266 nm wavelengths. The thermal diffusivity D jj is determined from the exponential decay of the diffraction signal. The laser flash technique (LFT) is based on measurement of travelling time of the thermal wave excited by a laser pulse, from one side of the plate to another [4,8,9]. In this case, the diffusivity D 8 in the direction perpendicular to the sample surface is determined. A pulsed YAG:Nd laser (wavelength 1.06 Am, pulse width 8 ns) was used for sample surface heating, while the temperature kinetics was monitored with a HgCdTe detector. Ti coating was deposited on both sides of the sample to enhance the laser absorption and IR emissivity. The thermal conductivity was found according to relation k=DqC, where q and C are density and the temperaturedependent specific heat of diamond, respectively.
Thermal conductivity (W/cmK)
18 16 14 12 10 8 1
Methane concentration (%) Fig. 2. Dependence of thermal conductivities k jj and k 8 on CH4 concentration in CH4/H2 mixture used for diamond deposition with other growth parameters kept constant: microwave power 5 kW, substrate temperature 717 8C, gas flow rate 400 sccm, pressure 100 Torr.
3. Results 3.1. Room temperature measurements A collection of samples grown upon a variety of synthesis conditions has been measured, and an inverse correlation of thermal conductivity and hydrogen impurity in the film has been established . This finding is in a good agreement with the earlier result of Coe and Sussmann . The thermal conductivity at room temperature is controlled by phonon scattering rate on various defects, grain boundaries and phonon–phonon interactions. Since hydrogen decorates the defects, the hydrogen impurity concentration is a convenient indicator of imperfections in CVD diamond [9–11]. Thermal conductivity vs. bonded H content in our diamond samples is shown in Fig. 1. The conductivity varies from 21 to 8 W/cm K when the bonded (C–H) hydrogen concentration ranges from 70 to 1000 ppm. The perpendicular values k 8 are systematically higher by 10–15% than the in-plane values k jj.
Thermal conductivity (W/cmK)
20 18 16 14 12 10 8 0
Bonded hydrogen concentration (ppm) Fig. 1. Thermal conductivities k jj and k 8 vs. concentration of bonded (C–H) hydrogen impurity in diamond films as measured from integrated IR absorption of stretching C–H modes between 2800 and 3100 cm1.
The source of anisotropy is a preferred location of defects at or near boundaries of columnar grains directed perpendicular to the film plane [2,12]. The enhanced concentration of defects, including extended ones, has been revealed along grain boundaries with transmission electron microscopy even in high quality films . The thermal resistance would be less for phonons propagating along the columns than for those crossing the grain boundaries and the defect batmosphereQ around. Indeed, thermal barriers at the grain boundaries have been revealed  by local measurements of thermal diffusivity by photothermal microscopy and TTG. The conductivity is found to decrease with the methane concentration in the source gas, as might be expected, since the supersaturation with hydrocarbons in gas phase leads to more defective material. This is illustrated in Fig. 2 for a set of the films produced at different CH4 percentages in H2, while keeping constant other deposition parameters. The bonded H in the films has been found to increase with CH4 concentration in the gas mixture (not shown here), so the trend in Fig. 2 is in line with that in Fig. 1. As the unpurified hydrogen generated by an electrolyzer has been the H2 source in these particular deposition runs, some nitrogen impurity was present in reaction chamber. While the CH4 content in the gas mixture increased from 1.5% to 5%, the growth rate increased from 2.6 to 5.0 Am/h, however, by the cost of reduced thermal conductivity. Again, the anisotropy in k values is clearly seen for this series of the films. Various point and extended defects impact not only the thermal conductivity, but result in enhanced optical absorption as well. In particular, since the nitrogen is the main impurity in natural diamonds, the correlation between the conductivity and characteristic absorption peaks in infrared region in nitrogen-contaminated natural single crystals of type Ia is well known . Besides the specific absorption peaks, a continuous absorption background may exist in polycrystalline CVD diamond because of disordered regions
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7.9 W/cm K 11.3 12.4 12.5
25 15.3 17.4
Wavelength (nm) Fig. 3. Optical absorption spectra in UV–visible range for a set of polished diamond films with different in-plane thermal conductivity (k jj values are indicated for each sample). Inset: the absorption spectrum for a sample with k=14.6 W/cm K in logarithmic scale.
C-H concentration (ppm)
both on grain boundaries and in bulk, and possibly due to other extended defects. Optical absorption spectra in the 200–700 nm wavelength range for a set of the films with in-plane values k jj in the range 7.9–17.4 W/cm K are shown in Fig. 3. It is seen that the higher absorption corresponds to lower conductivity. An absorption feature around 270 nm (seen as a shoulder in the spectra) is due to substitutional paramagnetic nitrogen. The 270 nm optical absorption intensity is proportional to concentration of P1 paramagnetic center (dispersed nitrogen) with g=2.0024 as observed in the electron spin resonance spectra measured earlier for our samples . Using the procedure of extracting the 270 nm peak from the original absorption spectrum as described in , the concentration of substitutional nitrogen atoms in the films was determined in the range of 0.8–14 ppm. Spectral photocurrent (PC) measurements in CVD diamond reveal [15,16] a threshold at 2.2 eV due to electron photoionization from substitutional nitrogen donors to the conduction band. However, this threshold is hardly seen in absorption, as it is masked by the monotonously increasing sub-band-gap absorption due to extended defects and disordered regions both on grain boundaries and in bulk. This is illustrated in inset in Fig. 3 where the absorption spectrum for a sample with k=14.6 W/cm K is re-plotted in logarithmic scale with no clear indication of 2.2 eV threshold. Obviously, the absorption and PC spectra reveal different spectral features, because PC detects only those absorption events that generate propagating carriers.
500 400 300 200 100
Substitutional nitrogen concentration (ppm) Fig. 4. Correlation between bonded hydrogen (C–H) and nitrogen impurity concentrations in the diamond films. Hydrogen is assumed to decorate the N-induced growth defects.
The presence of substitutional nitrogen in amount roughly above 50 ppm is required to cause any noticeable reduction in the thermal conductivity , while the N concentration is much lower in our samples. This means that nitrogen does not influence directly the thermal transport in the films considered, rather its action is indirect. Indeed, in CVD growth process, the impurity nitrogen likely promotes defect formation, as supported by a correlation between N and H impurity concentrations  (Fig. 4). Such correlation is though to stem from the tendency for hydrogen to decorate structural imperfections (extended defects) induced by nitrogen. Transmission electron microscopy revealed disordered nanometer-scale regions, in particular on the twin intersections, in N-enriched films . From modeling of experimental data on temperature-dependent thermal conductivity, Woerner et al.  concluded that the addition of small amount (5 ppm to the process gas) nitrogen in MW plasma degenerates grain boundaries (and possibly creates extended defects) resulting in the conductivity decrease. Since besides nitrogen-induced defects there are other structural defects in our films the correlation between H content and k value (Fig. 1) takes place regardless of the N contamination level, at least for the coarse-grained films in our MPCVD conditions. This might be invalid for the films produced using different chemistry such as, for example, for ultrananocrystalline diamond films . The thermal conductivity decrease with the absorption is presented quantitatively in Fig. 5 as the k vs. a plot, where a is absorption coefficient at arbitrary chosen wavelength of 500 nm. Due to variety of defects, the absorption in the visible range is continuous without any specific features; therefore, the choice of the wavelength at which the absorption coefficient is taken is not critical, so similar trends as in Fig. 5 could be obtained for other wavelengths or for integrated absorption. The observed inverse correlation qualitatively is in agreement with the data of Graebner , who measured a spectrally integrated absorption coefficient, rather than the monochromatic value as in our case.
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λ =500 nm
16 14 12 10 8 0
Absorption (cm-1) Fig. 5. The correlation between thermal conductivity k jj at 293 K and absorption coefficient a at 500 nm wavelength for selection of diamond films of a wide range quality.
3.2. Thermal conductivity between 293 and 460 K In dielectric crystals, the dependence of thermal conductivity on temperature shows clear maximum . At low temperatures, the conductivity rises with temperature ~T3, the phonon free pass length being restricted by the sample size (or grain size). At higher temperatures, the phonon– phonon (umklapp) scattering activates leading to the conductivity decrease, so the maximum in k takes place near 100 K for most pure type IIa single crystal diamonds . The presence of defects reduces the absolute value of the conductivity and shifts the maximum towards higher temperatures. Using Callaway’s model, the relative role of different types of the defects in CVD diamond was analysed in broad temperature range (5–500 K) [11,12,19,24], including point defects (impurities, isotopes, vacancies), extended defects (disordered/amorphous regions, voids and microcracks), dislocations and grain boundaries. The thermal resistance of most high quality polycrystalline thick CVD diamond films at room temperature has been shown to be dominated by intrinsic umklapp scattering. For ideal dielectric crystal, this mechanism leads to asymptotic dependence k~T 1 at high T of the order of Debye temperature (1860 K for diamond), while at lower temperatures the conductivity after the maximum drops with T exponentially . The slope changes (decreases) with defect concentration . In the important applications temperature range 300–500 K, the conductivity behavior can be approximated by a relationship k~T n with exponent n dependent on material quality. Extensive studies of natural diamonds between 320 and 450 K performed by Burgemeister  showed that the conductivity decreases with temperature by 20–60% depending on diamond purity. The k values followed the power low with n lowering from 1.26 (averaged for type IIa diamonds) to 0.5 as the nitrogen impurity concentration increased, while conductivity decreased from 20 W/cm K down to 6 W/cm K.
We measured temperature-dependent in-plane thermal conductivity k jj of our polycrystalline films between 293 and 460 K. The temperature dependence of specific heat C(T), as tabulated in , was used to convert the diffusivity to conductivity values. The results are presented in logarithmic plot (Fig. 6) that confirms that the relationship k~T n holds well for CVD diamond. The n value decreases from 1.02 for the best sample (k jj=18.0 W/cm K) to 0.17 for most defective one (k jj=7.9 W/cm K). Generally, the conductivity decreases with bonded hydrogen content as was observed for wider selection of samples (Fig. 1), yet there are exclusions. The deviation from the strict order based on the H concentration might be due to the fact that the defective fine-grained layer on nucleation side with enhanced H content was polished away for some specimens, but for others not. For comparison, the data for isotope pure synthetic HPHT single crystal diamond taken from  are displayed in Fig. 6 (upper line). They were fitted with n=1.36, the highest slope, to our knowledge, reported for the temperate range considered. The correlation of the n value and the thermal conductivity k jj for CVD films at room temperature is shown in Fig. 7. A similar correlation from the work of Burgemeister  for single crystal type Ia natural diamonds is also given for comparison (his data were recalculated by us from 320 K to 293 K). The high quality films (kN17 W/cm K) exhibit at a given k (293 K) the exponent n very close to those for type IIa
36 isotopically pure 
32 28 24 20
[H] = 150 ppm
Temperature (K) Fig. 6. Logarithmic plot of the in-plane thermal conductivity k jj versus temperature for a batch of diamond films reveals relationship k~T n . The concentration (in ppm) of bonded (C–H) hydrogen impurity is indicated for each sample. For comparison, the data for isotopically pure (enriched in 12C) synthetic HPHT single crystal diamond taken from  are also shown (upper line).
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18 16 14 12 10 8
Type Ia 
6 4 0.2
n Fig. 7. The correlation between exponent n in relationship k~T n and thermal conductivity k at room temperature for CVD diamond (squares) and for single crystal natural diamonds according to Burgemeister  (dashed line). The data for CVD diamond are in-plane k jj values.
and type Ia crystals with low N content. However, the type Ia and CVD diamond with the same, but lower conductivity, have different n values (larger for the former). This is more pronounced for most defective samples, that is the thermal conductivity of CVD diamond decreases slower with temperature than that for the heavily N-doped type Ia diamond. This could be due to the difference in main thermal resistance sources—the point defects in single crystals and probably the extended defects in CVD diamond.
4. Conclusions Transient thermal grating and laser flash techniques have been used to measure in-plane (k jj) and perpendicular (k 8) thermal conductivity of thick polycrystalline MPCVD diamond films. Anisotropy in thermal conductivity (k 8k jj)/k 8 less than 20% is found. The thermal conductivity of the particular set of samples ranges from 8 to 20 W/cm K at room temperature, and inversely correlates with bonded (C– H) hydrogen impurity concentration in diamond. In the temperatures range studied T=293–460 K, the thermal conductivity of CVD diamond follows a relationship k~T n (known for type Ia diamond) with n varied in the range of 0.17–1.02 depending on k value at RT.
Acknowledgements This work was supported in part by the State Science and Technology Committee of Belarus, grant no. M-20, RFBR grant no. 03-03-32396 and INTAS grant no. 01-2173.
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