- Email: [email protected]
Thermal diffusivity of heteroepitaxial diamond films: Experimental setup and measurements
Diamond & Related Materials 19 (2010) 787–791
Contents lists available at ScienceDirect
Diamond & Related Materials j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d i a m o n d
Thermal diffusivity of heteroepitaxial diamond films: Experimental setup and measurements C. Stehl, M. Schreck ⁎, M. Fischer, S. Gsell, B. Stritzker Universität Augsburg, Institut für Physik, D-86135 Augsburg, Germany
a r t i c l e
i n f o
Available online 1 February 2010 Keywords: Laser flash Converging thermal wave Thermal diffusivity Thermal conductivity Heteroepitaxy Iridium Diamond
a b s t r a c t The thermal diffusivity of heteroepitaxial CVD diamond films grown on iridium buffer layers has been measured using a combined laser flash and converging thermal wave setup. Absolute values and anisotropy for a fiber-textured reference sample were in the range of former reports in the literature. The in-plane thermal conductivity for three heteroepitaxial samples grown on Ir/YSZ/Si(001) as deduced from the diffusivity measurements was around 20 W/cm K, similar to high purity large grain polycrystalline films. Laser flash measurements of the perpendicular diffusivity suggest that the defect rich first microns of the heteroepitaxial films represent a thermal series resistance which limits the perpendicular heat transport especially for thin films. For the parallel component of the diffusivity the contribution of this shunt resistance is negligible. The absolute values for the parallel component in the heteroepitaxial films with in-plane angular spread of the crystal lattice below 0.5° were discussed in the framework of the model proposed by Klemens for phonon scattering by grain boundaries. The present data indicate that the remaining defects in heteroepitaxial diamond films with low mosaic spread are significantly less detrimental for the heat transport than large angle grain boundaries. In addition we speculate that the exclusive deposition on the {100} growth sector may also reduce the influence of nitrogen in the gas phase on the heat transport properties. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Within the last two decades the continuous progress in the field of diamond synthesis by chemical vapor deposition (CVD) has led to a large variety of different types of artificial diamond. These range from ultrananocrystalline, nanocrystalline, and polycrystalline material, to high quality single crystals with an extremely low defect density. As a consequence, a large variation of mechanical, optical, and thermal properties can be observed which qualifies the films for different fields of applications. The unmatched thermal conductivity (at room temperature) is one of the extreme material parameters diamond is well-known for. For heat spreaders made from diamond, it represents the essential property. In many other applications like laser windows, detectors, or in electronics, the thermal conductivity has a significant influence on the performance of the particular device. Absolute values for the room temperature conductivity of synthetic diamond cover several orders of magnitude, ranging from less than 0.10 W/cm K in the case of ultrananocrystalline films grown with nitrogen in the gas phase [1] up to more than 23 W/cm K for fibertextured polycrystalline samples with large grain size [2]. The best
⁎ Corresponding author. Tel.: + 49 821 598 3401; fax: + 49 821 598 3425. E-mail address: [email protected] (M. Schreck). 0925-9635/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2010.01.037
natural IIa single crystals reach 25 W/cm K [3] and isotopically enriched (nearly pure) samples can even exceed 30 W/cm K [3,4]. The experimental determination of the thermal conductivity is quite delicate. Various static and dynamic measurement techniques have been developed with different levels of complexity and accuracy [5]. The typically quoted accuracy is in the range of 5–10%. The heated bar technique being probably the most reliable method also allows measurements over a wide temperature range. It is rather laborious especially when the homogeneity of a larger sample is to be checked, and it can only determine the in-plane value. In contrast, the less but still fairly accurate laser flash and converging thermal wave techniques offer more flexibility. They provide the possibility of mapping the sample and determining its anisotropy when they are used in combination. In the present study, these two methods were chosen for the investigation of heteroepitaxial diamond films on iridium. A new setup was built according to the reports in the literature [6–8] including some minor technical improvements. It was then applied to characterize the thermal properties of heteroepitaxial diamond films grown on the multilayer system Ir/YSZ/Si(001) [9]. This new class of diamond films starts growth as a highly oriented ensemble of individual grains and then transforms into a quasi single crystal [10]. The deduced absolute values and the anisotropy of the thermal conductivity were compared with those of a polycrystalline fibertextured reference film. The data indicate that in high quality
788
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
heteroepitaxial films the thermal conductivity is significantly higher and the anisotropy is lower or even inverted relative to fiber-textured polycrystalline films. 2. Experimental The laser flash [11] and converging thermal wave [12] techniques are dynamic methods for measuring the thermal diffusivity α of thin slabs. For the laser flash measurement a short-pulsed laser heats a circular area of ca. 9 mm diameter on the front face of the sample. After the incidence of the laser pulse, the heat spreads over the sample and causes a temperature rise on its rear surface, whose transient curve is recorded. The rise time depends on the through-plane (perpendicular) thermal diffusivity αperp and the thickness d of the sample. For the converging thermal wave measurement the pulsed laser heats an annular area of 10 mm diameter and 0.5 mm thickness on the front surface of the sample. Consequently, the heat spreads over the sample and the temperature rise in the center of the annulus is recorded. The rise time of the transient curve depends on the in-plane (parallel) thermal diffusivity αpar of the sample and the radius R of the annulus. By applying both the laser flash and the converging thermal wave technique to the sample one can measure the anisotropy. The setups for both methods are basically the same as previously published by other authors [6–8], incorporating slight improvements. Essentially one single setup is sufficient for performing both types of measurements, as can be seen in Fig. 1. The samples are heated by a Nd:YAG laser with a wavelength of 1064 nm. The pulse width is 17 ns (FWHM) in Q-switched mode, whereas it increases to 100 µs when the Q-switch of the laser is inhibited. The laser delivers up to 800 mJ of energy per pulse. A continuously variable attenuator allows for adjusting the pulse energy to a level that avoids overheating and ablation. The thermal radiation from the rear surface of the sample is focused on an infrared detector by two zinc selenide lenses. The detector is based on mercury cadmium telluride and cooled with liquid nitrogen. It is very sensitive and extremely fast with a rise time of 24 ns. The built-in amplifier has a bandwidth of 20 MHz. The
detector is protected from stray laser radiation by a 250 μm thick germanium slab. A digital storage oscilloscope records the detector voltage. It is triggered by an appropriate signal from the laser in order to record some milli- or microseconds before and after the laser pulse. For the converging thermal wave measurements, a convex lens and an axicon are positioned between the laser and the sample. Another essential component for the converging thermal wave setup is a set of apertures on both sides of the sample, as depicted in Fig. 1, part B. On the front side, a tantalum disc shadows the interior of the laser annulus from stray laser radiation. It is suspended from a crosshair of 25 μm thin tungsten wires. These withstand the high laser power and have a negligible effect on the annular pattern. On the back side of the sample, an aperture limits the temperature detection to a small area in the center of the laser annulus. Design and material of this aperture turned out to be critical for an efficient suppression of infrared stray light reaching the detector. Black plastic which efficiently absorbs IR radiation and a hole with a diameter of 1 mm were ideal to avoid any laser flash contribution to the converging thermal wave signal. The key feature of the presented setup is its high resolution in time and temperature. Measurements on diamond samples thinner than 100 µm and with temperature rises of less than 1 K at the detection spot can be accomplished. To obtain a good signal-to-noise ratio averaging over some hundred transient curves is done. The measurements are evaluated by fitting the theoretical curves to the measured transients, as shown in Fig. 2. For laser flash measurements, the fitting function is given by [11] ( ) h i h i 20 LF n 2 2 ffit ðt; → γ Þ = γ1 1 + 2 ∑ ð−1Þ exp −n π γ2 t−tg exp −γ3 ðt−tg Þ + γ4 n=1
ð1Þ The vector → γ contains the fitting parameters. γ1 denotes the amplitude of the signal and γ4 is added to account for the offset of the detector voltage. The most important fitting parameter is γ2, which contains the thermal diffusivity. Heat losses can be accounted for by the exponential factor, incorporating the heat loss parameter γ3 [13].
Fig. 1. Schematic drawing of the experimental setup. The changes necessary for switching between laser flash and converging thermal wave measurements are emphasized by the dashed boxes A and B.
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
Fig. 2. Typical transient curves (red) and fitting curves (blue) of (a) laser flash and (b) converging thermal wave measurements. In panel (a) noise from the Q-switch can be seen at t = 0.
The time t is shifted by the center of gravity of the laser pulse, tg, in order to consider the finite pulse length. For the converging thermal wave method, another fitting function with similar fitting parameters is used [14]: CTW
ffit
ðt; → γÞ=
" # γ1 1 −γ3 ðt−tg Þ + γ4 : exp − 4γ2 ðt−tg Þ t−tg
ð2Þ
The thermal diffusivity α is obtained from the fitting parameter γ2: 2
αperp = γ2 d for laser flash measurements;
ð3aÞ
2
αpar = γ2 R for converging thermal wave measurements:
ð3bÞ
The propagation of uncertainty in γ2, d and R can be considered according to Gauss. By multiplication with the density ρ and the specific heat capacity c of the sample, one can calculate the thermal conductivity κ [11]: κ = αρc:
ð4Þ
For ρ and c literature values of natural diamond are used.
789
Apart from the finite laser pulse width and heat losses no other distortions of the transient curves need to be considered. These comprise the contribution of the finite heating area for the laser flash measurements as well as lateral dimensions and thickness of sample and heating annulus in the converging thermal wave experiments [13]. In addition, within the small interval of less than 1 K for the temperature rise on the rear face of the sample the detector response can be considered as linear [12]. The accuracy of the setup was tested with reference materials of known thermal diffusivity, namely copper, molybdenum, silicon, and tantalum. The measured values corresponded with the literature values taken from Touloukian et al. [15] to within ±8%, while the accuracy of the literature values themselves was only 4–9%. The accuracy of ±8% was also assumed to apply for diamond samples. Four diamond samples grown by microwave plasma CVD at pressures of 115–180 mbar with methane concentrations of 5–10% were investigated. Their properties are summarized in Table 1. Sample A was polycrystalline, grown on a silicon (001) substrate. This sample was used for the comparison with published values and with the values of the heteroepitaxial films B, C, and D. These were grown on Ir/YSZ/Si(001). All four samples had a size of at least 2 × 2 cm2, so that the sample size had no effect on the converging thermal wave results. Before the measurements, the substrate was removed completely for samples A and B. For the thinner films C and D, the Si was etched only within an area with a diameter of 2 cm, so that the remaining frame stabilized the diamond membrane. Afterwards 200–300 nm of titanium was evaporated onto both surfaces of the diamond membranes by electron beam evaporation in order to provide an absorption and emission layer for the laser and thermal radiation. During all measurements illumination was done on the nucleation side.
3. Results The results for the diamond samples are summarized in Table 1. Fig. 3 shows a graphical representation. The polycrystalline sample A exhibits a moderate thermal diffusivity of ca. 8–10 cm2/s, which corresponds to a conductivity of ca. 14–17 W/cm K. The anisotropy of the polycrystalline material is evident. Its parallel thermal conductivity is ca. 17% lower than its perpendicular counterpart. The absolute value for αpar is similar to the diffusivity reported by Chae et al. [7], who investigated comparable polycrystalline diamond wafers by the converging thermal wave technique. Sample B was heteroepitaxially grown on Ir/YSZ/Si(001). Its mosaic spread as determined by X-ray diffraction measurements is comparatively high for films on Ir (full width at half maximum of 4.5° for the in-plane angular spread). The anisotropy of its thermal conductivity is significantly lower than for the fiber-textured film A, but still its parallel conductivity is ca. 8% lower than in the direction perpendicular to the film. However, the absolute values are much higher than the values for sample A and come close to natural diamond of type IIa. Samples C and D show a polar and azimuthal mosaic spread in the range of several tenths of a degree as typical for high quality diamond
Table 1 Sample parameters and measured values for thermal diffusivity α and conductivity κ. The N2 concentration refers to the gas phase. Major contributions to the experimental error result from the geometric parameter d (sample thickness) or R (radius of annulus), respectively, and the error of the fit. Sample
Thickness (µm)
Tilt | twist (°)
N2 (ppm)
αperp | αpar (cm2/s)
κperp | κpar (W/cm K)
A (fiber-textured) B (heteroepitaxial) C (heteroepitaxial) D (heteroepitaxial)
300 ± 10 350 ± 10 169 ± 5 60 ± 3
– 1.4 0.18 0.12
0 0 35 40
10.1 ± 9% 12.1 ± 7% 11.3 ± 6% 7.9 ± 14%
18.1 21.7 20.3 14.2
|– | 4.5 | 0.29 | 0.44
| 7.8 ± 9% | 11.2 ± 9% | 11.6 ± 9% | 12.2 ± 9%
| | | |
14.0 20.1 20.8 21.8
790
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
Fig. 3. Graphical representation of the measured thermal diffusivity and conductivity of four diamond films. The lines have been added in order to emphasize the change in anisotropy between samples A and B and samples C and D. The areas highlighted in blue denote typical values for different types of natural diamond according to [15].
films on Ir. In contrast to the other samples, their parallel diffusivities are higher than the corresponding perpendicular values. The difference for sample C is in the range of the experimental error so that it may be considered as isotropic. The thin sample D however, has the lowest thermal diffusivity in perpendicular direction of all four samples, and a 45% higher parallel value. The parallel diffusivities of samples C and D are even close to the values for natural type IIa diamond. 4. Discussion The absolute values and the anisotropic behavior of the polycrystalline sample A are in accordance with former reports on fibertextured CVD diamond samples [6]. The phonons are scattered at the grain boundaries, which are oriented perpendicular to the film. This lowers the parallel thermal diffusivity and conductivity. Due to the columnar internal structure the perpendicular diffusivity is less affected. For the three heteroepitaxial samples (B, C, and D) there is a clear trend for the perpendicular conductivity to increase with film thickness. Absolute values range from 8.45 cm2/s for the thinnest sample D (58 µm) to 12.1 cm2/s for the 350 µm thick sample. To explain this behavior one has to consider the internal structure of heteroepitaxial diamond films on Ir. In the nucleation step an extremely high density (∼ 1011 cm− 2) of nuclei is formed by an ion bombardment process (bias enhanced nucleation (BEN)). Their initial angular spread (at 600 nm film thickness) is normally around 1° [10] which means that a high density of small angle grain boundaries is present. During the subsequent growth the grains merge and coarsen, the angular spread significantly decreases and at a thickness of above 10 µm the grain boundary network dissolves into short isolated defect bands with still an appreciable density of dislocations in the film. For the sake of simplicity we call the whole thickness range in which these drastic changes occur the ‘nucleation layer’. Due to its defective nature we expect a significantly lower thermal conductivity. During the laser flash measurements low and high quality parts of the film form a serial connection of thermal resistors. As a consequence the high thermal resistance of the nucleation layer dominates the result for the thinnest layer stack, e.g. the measured value of αperp for sample D, which is 58 µm thick, is 22% lower than the value for sample C, which is 165 µm thick. The contribution of the nucleation layer decreases with film thickness. Considering the parallel thermal conductivity we first notice that the values for all heteroepitxial layers are nearly 50% higher than the fiber-textured film. The large angle grain boundaries apparently limit the heat transport. Among the heteroepitaxial layers the thickest
sample B grown without nitrogen has the lowest value. Though the effect is of the order of the experimental errors it could indicate that the small angle grain boundaries in this sample with a comparatively high in-plane angular spread of 4.5° still yield a significant contribution to the phonon scattering. For samples C and D with identical growth conditions and similar texture data the in-plane conductivity is rather high. For the converging thermal wave measurement the low quality nucleation layer now forms part of a parallel circuit in which the high conductivity part of the sample should dominate the overall thermal properties. This may explain the strong anisotropy inverse to that of fiber-textured films especially for the thin sample D. The absolute values for the in-plane conductivity of samples C and D are comparable to the values for the best-conducting fiber-textured material, which has extremely large grain sizes of many dozens of micrometers. In contrast, the average distance between the defect bands in heteroepitaxial films is typically in the range of a few micrometers. Consequently, one would expect a much shorter mean free path of the phonons than in coarse grained fiber-textured samples, which would result in a significantly lower thermal conductivity. Since this is not observed, the scattering probability for phonons at the defect bands in heteroepitaxial diamond seems to be significantly smaller than at the large angle grain boundaries of polycrystalline material. In Ref. [16] Klemens considered the scattering of phonons at grain boundaries in dielectric solids. He showed that low angle grain boundaries scatter phonons as the square of the tilt angle which would nicely fit the trends seen in our measurements. However, the low absolute contribution of this effect to phonon scattering forced him to assume that the grain boundaries are thin sheets of disordered material, i.e. they are effectively three-dimensional instead of twodimensional structures. Their thickness was calculated to be in the order of 10–100 nm [16,17]. The disordered material has a lower density than the material inside the grains. When a phonon crosses the sheet, its velocity changes because of the change in density. This leads to phonon scattering. The same should hold for the defect bands in heteroepitaxial diamond films. However, their scattering probability seems to be lower. It is reasonable to assume that this originates from a lower degree of induced disorder as compared to the material at the large angle grain boundaries of polycrystalline samples. In this way the shorter distances between the defect bands could be overcompensated. If we assume that the density of the grain boundary material decreases with increasing tilt angle, the behavior of sample B with a relatively high mosaic spread could also be explained. Its anisotropy properties resemble that of the polycrystalline sample A. Finally we would like to discuss the role of nitrogen impurities in our experiments. It has been known for a long time that nitrogen in HPHT crystals systematically reduces their heat conductivity [18]. It has also been shown in literature that nitrogen in concentrations of several tens of ppm in the gas phase during CVD diamond growth can already markedly decrease the thermal conductivity [19,20]. In polycrystalline CVD films growth involves at least two different growth sectors ({100} and {111}). In the present heteroepitaxial layers growth is restricted to the {100} face. On this face a 3–4 times smaller nitrogen incorporation probability than on {111} has been reported [21]. In addition, Wörner et al. [20] reported that nitrogen in a microwave CVD process apparently degenerated the grain boundaries in their polycrystalline films being without any influence on the concentration of point defects. While further measurements are required to substantiate the observation this could explain the very high parallel conductivity in spite of some nitrogen in the gas phase. Variable temperature measurements down to low temperatures would also help to elucidate the mechanism of phonon scattering at the defect structures in quasi single crystal heteroepitaxial layers as compared to large angle grain boundaries in polycrystalline films.
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
5. Summary The thermal diffusivity and conductivity of heteroepitaxial CVD diamond films grown on iridium buffer layers were measured. For this purpose a combined laser flash and converging thermal wave setup with high sensitivity and time resolution was built, allowing for measurements on samples of a large range of thicknesses with minimal temperature rise. Absolute values and anisotropy for a fiber-textured reference sample were in the range of former reports in literature. The in-plane thermal conductivity for three heteroepitaxial samples grown on Ir/YSZ/Si(001) was around 20 W/cm K and similar to high purity large grain polycrystalline films. The data indicate that only the first microns of these films have a significantly lower quality which results in a series of resistances for laser flash measurements relevant especially for thin samples. For the measurement of the parallel component the contribution of this shunt resistance is negligible. The high absolute values for parallel thermal conductivity in the heteroepitaxial films with in-plane angular spread of the crystal lattice below 0.5° were discussed in the framework of the phonon scattering model proposed by Klemens. According to this model large angle grain boundaries consist of a thin sheet of disordered and therefore less dense material. The present data indicate that the remaining defects in heteroepitaxial diamond films with low mosaic spread are significantly less detrimental for the heat transport. In addition we speculate that the exclusive deposition on the {100} growth sector may also reduce the influence of nitrogen in the gas phase on the thermal properties. Further experiments involving temperature dependent measurements are desirable in order to better understand the heat transport in this new class of diamond materials. Acknowledgement We gratefully acknowledge financial support of this work by the Deutsche Forschungsgemeinschaft DFG within the contract STR361/16-1.
791
References [1] M. Shamsa, S. Ghosh, I. Calizo, V. Ralchenko, A. Popovich, A.A. Balandin, J. Appl. Physiol. 103 (2008) 083538. [2] E. Wörner, in: B. Dischler, C. Wild (Eds.), Low Pressure Synthetic Diamond, Springer, Heidelberg, Germany, 1998, p. 165. [3] J.W. Vandersande, in: G. Davies (Ed.), Properties and Growth of Diamond, INSPEC, London, United Kingdom, 1994, p. 33. [4] J. Hartmann, M. Reichling, in: M.H. Nazaré, A.J. Neves (Eds.), Properties, Growth and Applications of Diamond, INSPEC, London, United Kingdom, 2001, p. 32. [5] J.E. Graebner, in: M.A. Prelas, G. Popovici, L.K. Bigelow (Eds.), Handbook of Industrial Diamonds and Diamond Films, Dekker, New York, USA, 1998. [6] J.E. Graebner, S. Jin, G.W. Kammlott, B. Bacon, L. Seibles, W. Banholzer, J. Appl. Physiol. 71 (1992) 5353. [7] H.-B. Chae, H. Park, J.-S. Hong, Y.-J. Han, Y. Joo, Y.-J. Baik, J.-K. Lee, S.-W. Lee, Int. J. Thermophys. 22 (2001) 645. [8] G. Lu, W.T. Swann, Appl. Phys. Lett. 59 (1991) 1556. [9] S. Gsell, T. Bauer, J. Goldfuß, M. Schreck, B. Stritzker, Appl. Phys. Lett. 84 (2004) 4541. [10] M. Schreck, F. Hörmann, H. Roll, J.K.N. Lindner, B. Stritzker, Appl. Phys. Lett. 78 (2001) 192. [11] W.J. Parker, R.J. Jenkins, C.P. Butler, G.L. Abbott, J. Appl. Phys. 32 (1961) 1679. [12] P. Cielo, L.A. Utracki, M. Lamontagne, Can. J. Physiol. 64 (1986) 1172. [13] C. Stehl, Diploma thesis, University of Augsburg, 2009. [14] F. Murphy, T. Kehoe, M. Pietralla, R. Winfield, L. Floyd, Int. J. Heat Mass Tran. 48 (2005) 1395. [15] Y.S. Touloukian, R.W. Powell, C.Y. Ho, M.C. Nicolaou, Thermal Diffusivity, IFI/ Plenum, New York, USA, 1973. [16] P.G. Klemens, Int. J. Thermophys. 15 (1994) 1345. [17] A.V. Inyushkin, A.N. Taldenkov, V.G. Ral'chenko, V.I. Konov, A.V. Khomich, R.A. Khmel'nitskiĭ, J. Exp. Theor. Phys. 107 (2008) 462. [18] E.A. Burgemeister, Physica 93B (1978) 165. [19] E. Wörner, C. Wild, W. Müller-Sebert, R. Locher, P. Koidl, Diamond Relat. Mater. 5 (1996) 688. [20] E. Wörner, E. Pleuler, C. Wild, P. Koidl, Diamond Relat. Mater. 12 (2003) 744. [21] R. Samlenski, C. Haug, R. Brenn, C. Wild, R. Locher, P. Koidl, Appl. Phys. Lett. 67 (1995) 2798.
Contents lists available at ScienceDirect
Diamond & Related Materials j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / d i a m o n d
Thermal diffusivity of heteroepitaxial diamond films: Experimental setup and measurements C. Stehl, M. Schreck ⁎, M. Fischer, S. Gsell, B. Stritzker Universität Augsburg, Institut für Physik, D-86135 Augsburg, Germany
a r t i c l e
i n f o
Available online 1 February 2010 Keywords: Laser flash Converging thermal wave Thermal diffusivity Thermal conductivity Heteroepitaxy Iridium Diamond
a b s t r a c t The thermal diffusivity of heteroepitaxial CVD diamond films grown on iridium buffer layers has been measured using a combined laser flash and converging thermal wave setup. Absolute values and anisotropy for a fiber-textured reference sample were in the range of former reports in the literature. The in-plane thermal conductivity for three heteroepitaxial samples grown on Ir/YSZ/Si(001) as deduced from the diffusivity measurements was around 20 W/cm K, similar to high purity large grain polycrystalline films. Laser flash measurements of the perpendicular diffusivity suggest that the defect rich first microns of the heteroepitaxial films represent a thermal series resistance which limits the perpendicular heat transport especially for thin films. For the parallel component of the diffusivity the contribution of this shunt resistance is negligible. The absolute values for the parallel component in the heteroepitaxial films with in-plane angular spread of the crystal lattice below 0.5° were discussed in the framework of the model proposed by Klemens for phonon scattering by grain boundaries. The present data indicate that the remaining defects in heteroepitaxial diamond films with low mosaic spread are significantly less detrimental for the heat transport than large angle grain boundaries. In addition we speculate that the exclusive deposition on the {100} growth sector may also reduce the influence of nitrogen in the gas phase on the heat transport properties. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Within the last two decades the continuous progress in the field of diamond synthesis by chemical vapor deposition (CVD) has led to a large variety of different types of artificial diamond. These range from ultrananocrystalline, nanocrystalline, and polycrystalline material, to high quality single crystals with an extremely low defect density. As a consequence, a large variation of mechanical, optical, and thermal properties can be observed which qualifies the films for different fields of applications. The unmatched thermal conductivity (at room temperature) is one of the extreme material parameters diamond is well-known for. For heat spreaders made from diamond, it represents the essential property. In many other applications like laser windows, detectors, or in electronics, the thermal conductivity has a significant influence on the performance of the particular device. Absolute values for the room temperature conductivity of synthetic diamond cover several orders of magnitude, ranging from less than 0.10 W/cm K in the case of ultrananocrystalline films grown with nitrogen in the gas phase [1] up to more than 23 W/cm K for fibertextured polycrystalline samples with large grain size [2]. The best
⁎ Corresponding author. Tel.: + 49 821 598 3401; fax: + 49 821 598 3425. E-mail address: [email protected] (M. Schreck). 0925-9635/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2010.01.037
natural IIa single crystals reach 25 W/cm K [3] and isotopically enriched (nearly pure) samples can even exceed 30 W/cm K [3,4]. The experimental determination of the thermal conductivity is quite delicate. Various static and dynamic measurement techniques have been developed with different levels of complexity and accuracy [5]. The typically quoted accuracy is in the range of 5–10%. The heated bar technique being probably the most reliable method also allows measurements over a wide temperature range. It is rather laborious especially when the homogeneity of a larger sample is to be checked, and it can only determine the in-plane value. In contrast, the less but still fairly accurate laser flash and converging thermal wave techniques offer more flexibility. They provide the possibility of mapping the sample and determining its anisotropy when they are used in combination. In the present study, these two methods were chosen for the investigation of heteroepitaxial diamond films on iridium. A new setup was built according to the reports in the literature [6–8] including some minor technical improvements. It was then applied to characterize the thermal properties of heteroepitaxial diamond films grown on the multilayer system Ir/YSZ/Si(001) [9]. This new class of diamond films starts growth as a highly oriented ensemble of individual grains and then transforms into a quasi single crystal [10]. The deduced absolute values and the anisotropy of the thermal conductivity were compared with those of a polycrystalline fibertextured reference film. The data indicate that in high quality
788
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
heteroepitaxial films the thermal conductivity is significantly higher and the anisotropy is lower or even inverted relative to fiber-textured polycrystalline films. 2. Experimental The laser flash [11] and converging thermal wave [12] techniques are dynamic methods for measuring the thermal diffusivity α of thin slabs. For the laser flash measurement a short-pulsed laser heats a circular area of ca. 9 mm diameter on the front face of the sample. After the incidence of the laser pulse, the heat spreads over the sample and causes a temperature rise on its rear surface, whose transient curve is recorded. The rise time depends on the through-plane (perpendicular) thermal diffusivity αperp and the thickness d of the sample. For the converging thermal wave measurement the pulsed laser heats an annular area of 10 mm diameter and 0.5 mm thickness on the front surface of the sample. Consequently, the heat spreads over the sample and the temperature rise in the center of the annulus is recorded. The rise time of the transient curve depends on the in-plane (parallel) thermal diffusivity αpar of the sample and the radius R of the annulus. By applying both the laser flash and the converging thermal wave technique to the sample one can measure the anisotropy. The setups for both methods are basically the same as previously published by other authors [6–8], incorporating slight improvements. Essentially one single setup is sufficient for performing both types of measurements, as can be seen in Fig. 1. The samples are heated by a Nd:YAG laser with a wavelength of 1064 nm. The pulse width is 17 ns (FWHM) in Q-switched mode, whereas it increases to 100 µs when the Q-switch of the laser is inhibited. The laser delivers up to 800 mJ of energy per pulse. A continuously variable attenuator allows for adjusting the pulse energy to a level that avoids overheating and ablation. The thermal radiation from the rear surface of the sample is focused on an infrared detector by two zinc selenide lenses. The detector is based on mercury cadmium telluride and cooled with liquid nitrogen. It is very sensitive and extremely fast with a rise time of 24 ns. The built-in amplifier has a bandwidth of 20 MHz. The
detector is protected from stray laser radiation by a 250 μm thick germanium slab. A digital storage oscilloscope records the detector voltage. It is triggered by an appropriate signal from the laser in order to record some milli- or microseconds before and after the laser pulse. For the converging thermal wave measurements, a convex lens and an axicon are positioned between the laser and the sample. Another essential component for the converging thermal wave setup is a set of apertures on both sides of the sample, as depicted in Fig. 1, part B. On the front side, a tantalum disc shadows the interior of the laser annulus from stray laser radiation. It is suspended from a crosshair of 25 μm thin tungsten wires. These withstand the high laser power and have a negligible effect on the annular pattern. On the back side of the sample, an aperture limits the temperature detection to a small area in the center of the laser annulus. Design and material of this aperture turned out to be critical for an efficient suppression of infrared stray light reaching the detector. Black plastic which efficiently absorbs IR radiation and a hole with a diameter of 1 mm were ideal to avoid any laser flash contribution to the converging thermal wave signal. The key feature of the presented setup is its high resolution in time and temperature. Measurements on diamond samples thinner than 100 µm and with temperature rises of less than 1 K at the detection spot can be accomplished. To obtain a good signal-to-noise ratio averaging over some hundred transient curves is done. The measurements are evaluated by fitting the theoretical curves to the measured transients, as shown in Fig. 2. For laser flash measurements, the fitting function is given by [11] ( ) h i h i 20 LF n 2 2 ffit ðt; → γ Þ = γ1 1 + 2 ∑ ð−1Þ exp −n π γ2 t−tg exp −γ3 ðt−tg Þ + γ4 n=1
ð1Þ The vector → γ contains the fitting parameters. γ1 denotes the amplitude of the signal and γ4 is added to account for the offset of the detector voltage. The most important fitting parameter is γ2, which contains the thermal diffusivity. Heat losses can be accounted for by the exponential factor, incorporating the heat loss parameter γ3 [13].
Fig. 1. Schematic drawing of the experimental setup. The changes necessary for switching between laser flash and converging thermal wave measurements are emphasized by the dashed boxes A and B.
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
Fig. 2. Typical transient curves (red) and fitting curves (blue) of (a) laser flash and (b) converging thermal wave measurements. In panel (a) noise from the Q-switch can be seen at t = 0.
The time t is shifted by the center of gravity of the laser pulse, tg, in order to consider the finite pulse length. For the converging thermal wave method, another fitting function with similar fitting parameters is used [14]: CTW
ffit
ðt; → γÞ=
" # γ1 1 −γ3 ðt−tg Þ + γ4 : exp − 4γ2 ðt−tg Þ t−tg
ð2Þ
The thermal diffusivity α is obtained from the fitting parameter γ2: 2
αperp = γ2 d for laser flash measurements;
ð3aÞ
2
αpar = γ2 R for converging thermal wave measurements:
ð3bÞ
The propagation of uncertainty in γ2, d and R can be considered according to Gauss. By multiplication with the density ρ and the specific heat capacity c of the sample, one can calculate the thermal conductivity κ [11]: κ = αρc:
ð4Þ
For ρ and c literature values of natural diamond are used.
789
Apart from the finite laser pulse width and heat losses no other distortions of the transient curves need to be considered. These comprise the contribution of the finite heating area for the laser flash measurements as well as lateral dimensions and thickness of sample and heating annulus in the converging thermal wave experiments [13]. In addition, within the small interval of less than 1 K for the temperature rise on the rear face of the sample the detector response can be considered as linear [12]. The accuracy of the setup was tested with reference materials of known thermal diffusivity, namely copper, molybdenum, silicon, and tantalum. The measured values corresponded with the literature values taken from Touloukian et al. [15] to within ±8%, while the accuracy of the literature values themselves was only 4–9%. The accuracy of ±8% was also assumed to apply for diamond samples. Four diamond samples grown by microwave plasma CVD at pressures of 115–180 mbar with methane concentrations of 5–10% were investigated. Their properties are summarized in Table 1. Sample A was polycrystalline, grown on a silicon (001) substrate. This sample was used for the comparison with published values and with the values of the heteroepitaxial films B, C, and D. These were grown on Ir/YSZ/Si(001). All four samples had a size of at least 2 × 2 cm2, so that the sample size had no effect on the converging thermal wave results. Before the measurements, the substrate was removed completely for samples A and B. For the thinner films C and D, the Si was etched only within an area with a diameter of 2 cm, so that the remaining frame stabilized the diamond membrane. Afterwards 200–300 nm of titanium was evaporated onto both surfaces of the diamond membranes by electron beam evaporation in order to provide an absorption and emission layer for the laser and thermal radiation. During all measurements illumination was done on the nucleation side.
3. Results The results for the diamond samples are summarized in Table 1. Fig. 3 shows a graphical representation. The polycrystalline sample A exhibits a moderate thermal diffusivity of ca. 8–10 cm2/s, which corresponds to a conductivity of ca. 14–17 W/cm K. The anisotropy of the polycrystalline material is evident. Its parallel thermal conductivity is ca. 17% lower than its perpendicular counterpart. The absolute value for αpar is similar to the diffusivity reported by Chae et al. [7], who investigated comparable polycrystalline diamond wafers by the converging thermal wave technique. Sample B was heteroepitaxially grown on Ir/YSZ/Si(001). Its mosaic spread as determined by X-ray diffraction measurements is comparatively high for films on Ir (full width at half maximum of 4.5° for the in-plane angular spread). The anisotropy of its thermal conductivity is significantly lower than for the fiber-textured film A, but still its parallel conductivity is ca. 8% lower than in the direction perpendicular to the film. However, the absolute values are much higher than the values for sample A and come close to natural diamond of type IIa. Samples C and D show a polar and azimuthal mosaic spread in the range of several tenths of a degree as typical for high quality diamond
Table 1 Sample parameters and measured values for thermal diffusivity α and conductivity κ. The N2 concentration refers to the gas phase. Major contributions to the experimental error result from the geometric parameter d (sample thickness) or R (radius of annulus), respectively, and the error of the fit. Sample
Thickness (µm)
Tilt | twist (°)
N2 (ppm)
αperp | αpar (cm2/s)
κperp | κpar (W/cm K)
A (fiber-textured) B (heteroepitaxial) C (heteroepitaxial) D (heteroepitaxial)
300 ± 10 350 ± 10 169 ± 5 60 ± 3
– 1.4 0.18 0.12
0 0 35 40
10.1 ± 9% 12.1 ± 7% 11.3 ± 6% 7.9 ± 14%
18.1 21.7 20.3 14.2
|– | 4.5 | 0.29 | 0.44
| 7.8 ± 9% | 11.2 ± 9% | 11.6 ± 9% | 12.2 ± 9%
| | | |
14.0 20.1 20.8 21.8
790
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
Fig. 3. Graphical representation of the measured thermal diffusivity and conductivity of four diamond films. The lines have been added in order to emphasize the change in anisotropy between samples A and B and samples C and D. The areas highlighted in blue denote typical values for different types of natural diamond according to [15].
films on Ir. In contrast to the other samples, their parallel diffusivities are higher than the corresponding perpendicular values. The difference for sample C is in the range of the experimental error so that it may be considered as isotropic. The thin sample D however, has the lowest thermal diffusivity in perpendicular direction of all four samples, and a 45% higher parallel value. The parallel diffusivities of samples C and D are even close to the values for natural type IIa diamond. 4. Discussion The absolute values and the anisotropic behavior of the polycrystalline sample A are in accordance with former reports on fibertextured CVD diamond samples [6]. The phonons are scattered at the grain boundaries, which are oriented perpendicular to the film. This lowers the parallel thermal diffusivity and conductivity. Due to the columnar internal structure the perpendicular diffusivity is less affected. For the three heteroepitaxial samples (B, C, and D) there is a clear trend for the perpendicular conductivity to increase with film thickness. Absolute values range from 8.45 cm2/s for the thinnest sample D (58 µm) to 12.1 cm2/s for the 350 µm thick sample. To explain this behavior one has to consider the internal structure of heteroepitaxial diamond films on Ir. In the nucleation step an extremely high density (∼ 1011 cm− 2) of nuclei is formed by an ion bombardment process (bias enhanced nucleation (BEN)). Their initial angular spread (at 600 nm film thickness) is normally around 1° [10] which means that a high density of small angle grain boundaries is present. During the subsequent growth the grains merge and coarsen, the angular spread significantly decreases and at a thickness of above 10 µm the grain boundary network dissolves into short isolated defect bands with still an appreciable density of dislocations in the film. For the sake of simplicity we call the whole thickness range in which these drastic changes occur the ‘nucleation layer’. Due to its defective nature we expect a significantly lower thermal conductivity. During the laser flash measurements low and high quality parts of the film form a serial connection of thermal resistors. As a consequence the high thermal resistance of the nucleation layer dominates the result for the thinnest layer stack, e.g. the measured value of αperp for sample D, which is 58 µm thick, is 22% lower than the value for sample C, which is 165 µm thick. The contribution of the nucleation layer decreases with film thickness. Considering the parallel thermal conductivity we first notice that the values for all heteroepitxial layers are nearly 50% higher than the fiber-textured film. The large angle grain boundaries apparently limit the heat transport. Among the heteroepitaxial layers the thickest
sample B grown without nitrogen has the lowest value. Though the effect is of the order of the experimental errors it could indicate that the small angle grain boundaries in this sample with a comparatively high in-plane angular spread of 4.5° still yield a significant contribution to the phonon scattering. For samples C and D with identical growth conditions and similar texture data the in-plane conductivity is rather high. For the converging thermal wave measurement the low quality nucleation layer now forms part of a parallel circuit in which the high conductivity part of the sample should dominate the overall thermal properties. This may explain the strong anisotropy inverse to that of fiber-textured films especially for the thin sample D. The absolute values for the in-plane conductivity of samples C and D are comparable to the values for the best-conducting fiber-textured material, which has extremely large grain sizes of many dozens of micrometers. In contrast, the average distance between the defect bands in heteroepitaxial films is typically in the range of a few micrometers. Consequently, one would expect a much shorter mean free path of the phonons than in coarse grained fiber-textured samples, which would result in a significantly lower thermal conductivity. Since this is not observed, the scattering probability for phonons at the defect bands in heteroepitaxial diamond seems to be significantly smaller than at the large angle grain boundaries of polycrystalline material. In Ref. [16] Klemens considered the scattering of phonons at grain boundaries in dielectric solids. He showed that low angle grain boundaries scatter phonons as the square of the tilt angle which would nicely fit the trends seen in our measurements. However, the low absolute contribution of this effect to phonon scattering forced him to assume that the grain boundaries are thin sheets of disordered material, i.e. they are effectively three-dimensional instead of twodimensional structures. Their thickness was calculated to be in the order of 10–100 nm [16,17]. The disordered material has a lower density than the material inside the grains. When a phonon crosses the sheet, its velocity changes because of the change in density. This leads to phonon scattering. The same should hold for the defect bands in heteroepitaxial diamond films. However, their scattering probability seems to be lower. It is reasonable to assume that this originates from a lower degree of induced disorder as compared to the material at the large angle grain boundaries of polycrystalline samples. In this way the shorter distances between the defect bands could be overcompensated. If we assume that the density of the grain boundary material decreases with increasing tilt angle, the behavior of sample B with a relatively high mosaic spread could also be explained. Its anisotropy properties resemble that of the polycrystalline sample A. Finally we would like to discuss the role of nitrogen impurities in our experiments. It has been known for a long time that nitrogen in HPHT crystals systematically reduces their heat conductivity [18]. It has also been shown in literature that nitrogen in concentrations of several tens of ppm in the gas phase during CVD diamond growth can already markedly decrease the thermal conductivity [19,20]. In polycrystalline CVD films growth involves at least two different growth sectors ({100} and {111}). In the present heteroepitaxial layers growth is restricted to the {100} face. On this face a 3–4 times smaller nitrogen incorporation probability than on {111} has been reported [21]. In addition, Wörner et al. [20] reported that nitrogen in a microwave CVD process apparently degenerated the grain boundaries in their polycrystalline films being without any influence on the concentration of point defects. While further measurements are required to substantiate the observation this could explain the very high parallel conductivity in spite of some nitrogen in the gas phase. Variable temperature measurements down to low temperatures would also help to elucidate the mechanism of phonon scattering at the defect structures in quasi single crystal heteroepitaxial layers as compared to large angle grain boundaries in polycrystalline films.
C. Stehl et al. / Diamond & Related Materials 19 (2010) 787–791
5. Summary The thermal diffusivity and conductivity of heteroepitaxial CVD diamond films grown on iridium buffer layers were measured. For this purpose a combined laser flash and converging thermal wave setup with high sensitivity and time resolution was built, allowing for measurements on samples of a large range of thicknesses with minimal temperature rise. Absolute values and anisotropy for a fiber-textured reference sample were in the range of former reports in literature. The in-plane thermal conductivity for three heteroepitaxial samples grown on Ir/YSZ/Si(001) was around 20 W/cm K and similar to high purity large grain polycrystalline films. The data indicate that only the first microns of these films have a significantly lower quality which results in a series of resistances for laser flash measurements relevant especially for thin samples. For the measurement of the parallel component the contribution of this shunt resistance is negligible. The high absolute values for parallel thermal conductivity in the heteroepitaxial films with in-plane angular spread of the crystal lattice below 0.5° were discussed in the framework of the phonon scattering model proposed by Klemens. According to this model large angle grain boundaries consist of a thin sheet of disordered and therefore less dense material. The present data indicate that the remaining defects in heteroepitaxial diamond films with low mosaic spread are significantly less detrimental for the heat transport. In addition we speculate that the exclusive deposition on the {100} growth sector may also reduce the influence of nitrogen in the gas phase on the thermal properties. Further experiments involving temperature dependent measurements are desirable in order to better understand the heat transport in this new class of diamond materials. Acknowledgement We gratefully acknowledge financial support of this work by the Deutsche Forschungsgemeinschaft DFG within the contract STR361/16-1.
791
References [1] M. Shamsa, S. Ghosh, I. Calizo, V. Ralchenko, A. Popovich, A.A. Balandin, J. Appl. Physiol. 103 (2008) 083538. [2] E. Wörner, in: B. Dischler, C. Wild (Eds.), Low Pressure Synthetic Diamond, Springer, Heidelberg, Germany, 1998, p. 165. [3] J.W. Vandersande, in: G. Davies (Ed.), Properties and Growth of Diamond, INSPEC, London, United Kingdom, 1994, p. 33. [4] J. Hartmann, M. Reichling, in: M.H. Nazaré, A.J. Neves (Eds.), Properties, Growth and Applications of Diamond, INSPEC, London, United Kingdom, 2001, p. 32. [5] J.E. Graebner, in: M.A. Prelas, G. Popovici, L.K. Bigelow (Eds.), Handbook of Industrial Diamonds and Diamond Films, Dekker, New York, USA, 1998. [6] J.E. Graebner, S. Jin, G.W. Kammlott, B. Bacon, L. Seibles, W. Banholzer, J. Appl. Physiol. 71 (1992) 5353. [7] H.-B. Chae, H. Park, J.-S. Hong, Y.-J. Han, Y. Joo, Y.-J. Baik, J.-K. Lee, S.-W. Lee, Int. J. Thermophys. 22 (2001) 645. [8] G. Lu, W.T. Swann, Appl. Phys. Lett. 59 (1991) 1556. [9] S. Gsell, T. Bauer, J. Goldfuß, M. Schreck, B. Stritzker, Appl. Phys. Lett. 84 (2004) 4541. [10] M. Schreck, F. Hörmann, H. Roll, J.K.N. Lindner, B. Stritzker, Appl. Phys. Lett. 78 (2001) 192. [11] W.J. Parker, R.J. Jenkins, C.P. Butler, G.L. Abbott, J. Appl. Phys. 32 (1961) 1679. [12] P. Cielo, L.A. Utracki, M. Lamontagne, Can. J. Physiol. 64 (1986) 1172. [13] C. Stehl, Diploma thesis, University of Augsburg, 2009. [14] F. Murphy, T. Kehoe, M. Pietralla, R. Winfield, L. Floyd, Int. J. Heat Mass Tran. 48 (2005) 1395. [15] Y.S. Touloukian, R.W. Powell, C.Y. Ho, M.C. Nicolaou, Thermal Diffusivity, IFI/ Plenum, New York, USA, 1973. [16] P.G. Klemens, Int. J. Thermophys. 15 (1994) 1345. [17] A.V. Inyushkin, A.N. Taldenkov, V.G. Ral'chenko, V.I. Konov, A.V. Khomich, R.A. Khmel'nitskiĭ, J. Exp. Theor. Phys. 107 (2008) 462. [18] E.A. Burgemeister, Physica 93B (1978) 165. [19] E. Wörner, C. Wild, W. Müller-Sebert, R. Locher, P. Koidl, Diamond Relat. Mater. 5 (1996) 688. [20] E. Wörner, E. Pleuler, C. Wild, P. Koidl, Diamond Relat. Mater. 12 (2003) 744. [21] R. Samlenski, C. Haug, R. Brenn, C. Wild, R. Locher, P. Koidl, Appl. Phys. Lett. 67 (1995) 2798.