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Measurement of thermal conductivity in diamond films using a simple scanning thermocouple technique
Diamond and Related Materials 9 Ž2000. 1312᎐1319
Measurement of thermal conductivity in diamond films using a simple scanning thermocouple technique H.P. HoU , K.C. Lo, S.C. Tjong, S.T. Lee Department of Physics and Materials Science, City Uni¨ ersity of Hong Kong, 83 Tat Chee A¨ enue, Kowloon, Hong Kong Received 24 August 1999; accepted 30 December 1999
Abstract In this paper we present a simple scanning thermocouple technique for measuring the thermal conductivity Ž . of diamond thin films. We first describe the fabrication procedure of the thermocouple tip, which involves first fixing a 10-m-thick tungsten wire inside a glass capillary tube and then coating the exposed tip with gold. The goldrtungsten thermocouple was used to map the temperature distribution on the diamond surface. The measured data are fitted into the solution obtained from solving the steady-state heat conduction equations which also take into account the heat loss from the sample. For our diamond sample, the measured for the temperature range between 299.2 K and 317.4 K is between 5.4 and 6.2 Ž"0.6. W cmy1 Ky1 , which is within the range published elsewhere for ‘dark’ CVD diamond materials. 䊚 2000 Elsevier Science S.A. All rights reserved. Keywords: Diamond films; Scanning thermocouple technique; Thermal conductivity
1. Introduction With a thermal conductivity up to five times higher than that of copper, diamond made by the chemical vapour deposition ŽCVD. technique is well known to be very effective for heat spreading applications. At present, due to their relatively high production costs, CVD diamond heat sinks are only used in selected devices where high-speed heat spreading capability is essential. Currently, nearly all semiconductor heat sinks are made from copper, silicon carbide or aluminium nitride. Since future electronics will operate at higher speed and in higher density, and hence with very high power density, an efficient high-speed heat spreader must be required to ensure acceptable lifetime and speed performance. The continual improvement of CVD diamond production costs will undoubtedly lead to its widespread applications in a range of electronic devices in the future. The increased production volume will also mean that U
Corresponding author. Fax: q852-2-7887830. E-mail address: [email protected] ŽH.P. Ho..
there is the need for a quick and reliable method for characterising the thermal conductivity of the material. The scanning thermocouple technique described in this paper aims particularly to address this issue. The measurement of thermal conductivity of diamond, ranging between a few and more than 20 W cmy1 Ky1 w1x depending on the CVD techniques and conditions, has been reported by several authors w2᎐5x. Measurement methods such as thermocouple arrays, thin films, thermal flash technique and thermoresistor thin film are the common techniques for measuring the temperature distribution in the sample. Up until now all the direct measurement methods involving thermocouples require a number of sample preparation steps including deposition of metal thin films and welding of thermocouple wires to different measurement locations on the sample. This measurement approach may take considerable time and effort. In this paper we present an alternative technique which aims to simplify the temperature measurement process by scanning a thermocouple tip across the sample surface. In our demonstration set-up a resistive heater wire is
0925-9635r00r$ - see front matter 䊚 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 0 . 0 0 2 3 1 - 4
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
used as the heat source. The steady thermal gradient across the sample is measured by a gold᎐tungsten thermocouple. The thermal conductivity can thus be deduced from the measured temperature data. In addition to the measurement of thermal conductivity the new technique can also provide a low-cost alternative for mapping of temperature distributions, which may be important for a range of applications including the optimisation of semiconductor packages.
2.1. The heated-bar technique In our experiment, we fabricate a sharp thermocouple tip and then perform temperature measurement at selected locations on the sample surface. One can then use the data to reconstruct a two-dimensional surface temperature profile. For a simple case, in which the two ends of the sample bar are connected to two constant temperature sources, we use our thermocouple to measure the steady-state temperature gradient along the sample bar. If there is no heat loss, the temperature profile should be a straight line with slope ⌬Tr⌬ x, and the thermal conductivity can be calculated according to the equation: ) A/ ž ⌬T ⌬x
where A is the cross-sectional area of the sample perpendicular to the heat flow direction and Q is the heat power input from the high-temperature end. However, due to the heat loss from the sample surface by radiation and convection, the steady-state heat balance equation is modified to the following form:
⭸2 T Hp y Ts0 A ⭸X 2
where H is the loss heat flux by radiation and convection per unit surface area per degree of temperature difference, and p is the perimeter of the cross section of the bar. One can define s Hpr A as a measure of the importance of surface loss compared to heat conduction within the sample. The solution to the above equation is given by Carslaw and Jaeger w6x as:
'
T Ž x. s
an outward heat flux at the surface. A least-square fitting technique can be used for obtaining an optimum match between this solution and the measured data of T Ž x . by varying T2 and . After differentiation with respect to temperature, the temperature gradient at heater location Ž xs L. becomes ⭸T Ž x . ⭸x
xsL
s
w T2 cosh Ž x . y T1 x . sinh Ž L .
With the values of T2 and found, the gradient at location Ž xs L. will be put back into the initial thermal conductivity equation, s QrwŽ ⌬Tr⌬ x .) A x, for replacing Ž ⌬Tr⌬ x .. The conductivity at temperature T2 will be calculated as w7x:
2. Experimental details
s Qr
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T1 sinh w Ž L y x .x q T2 sinh Ž x . sinh Ž L .
where L is the distance between the steady-state temperature sources T1 and T2 . This equation effectively describes the temperature profile along a sample with its ends at temperature T1 and T2 ŽT1 - T2 . and with
s
Qsinh Ž L . Aw T2 cosh Ž L . y T1 x
In essence, this analysis allows us to include heat losses along the length of the sample and thus modifies the linear thermal conductivity equation, i.e. s QrwŽ ⌬Tr⌬ x .) A x, to become variable gradient along the length of the sample. By extrapolating our curving range to the high-temperature end where the drop of temperature due to heat loss along the sample is small, we can assume the gradient derived at this location fits the linear thermal conductivity equation. Hence we can calculate the thermal conductivity at the high-temperature ŽT2 . point. For this reason, it should be mentioned that this method is accurate only at the high-temperature end of the sample. One further condition we need to impose here is that the thermal conductivity remains constant throughout the temperature range that the experiment is operating in. This means that for real samples, in which the thermal conductivity varies with temperature, small temperature gradients should be used in order to ensure acceptable measurement accuracy. Nevertheless, for the temperature ranges that we used in our experiments, which is approximately 17⬚C at the most, the changes in thermal conductivities for our samples are, respectively, 8%, 0.3% and up to 4% Žsample dependent. for silicon, copper and CVD diamond w4,5,9x. For the present experimental set-up such effect will inevitably introduce further errors to the measured thermal conductivity values. 2.2. Experimental setup The measurement setup is schematically shown in Fig. 1. In order to ensure a steady-state heat flux parallel to a bar-shaped sample, a resistive heater wire is attached at one end of the bar-shaped sample and the other end of the bar is thermally grounded to a metal block with water cooling inside. Within the measurement period we constantly monitor the cooling
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H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 1. Schematic of experimental setup: Ž1. radiation isolation enclosure; Ž2. x-, y- and z-axis micro-scanning stages; Ž3. gold᎐tungsten thermocouple tip; Ž4. aluminium blocks; Ž5. sample; Ž6. resistance heater wire; and Ž7. thermal ground metal block.
water temperature to ensure it does not fluctuate more than "0.1⬚C. A pre-fabricated gold᎐tungsten thermocouple tip is mounted on a micro-scanning stage for measuring the temperature at different locations along the length of the sample. 2.3. Thermocouple fabrication and calibration A cross-sectional view of the thermocouple device is shown in Fig. 2a. The fabrication steps of the thermocouple tip are as follows: Ž1. a tungsten wire Ždiameter 10 m. is inserted halfway along the inner channel of a micro-pipette. Ž2. The tube is heated inside the flame from a micro-burner. As the glass wall melts the pipette is pulled so that a thin layer of glass is collapsed onto the wire. Ž3. After carefully breaking the elongated section at the same location as the tungsten wire end and dipping the glass tip into 1 M sodium hydroxide solution for 5᎐6 min, a tungsten tip protected by a thin layer of glass will be formed. Ž4. Upon sharpening the tip using 1 m diamond polishing paste, a thin layer of gold is sputtered onto the tip region for finally forming the micro-thermocouple. Fig. 2b shows the optical micrograph of the tungsten tip just before the sputtering deposition of the gold film. Connections to the gold film and the tungsten wire are made using copper wire. A nanovoltmeter ŽKeithley, model 2182. is used for measuring the thermocou-
ple output voltage. The two gold᎐copper and tungsten᎐copper junctions are mounted to a large metal block for minimising temperature fluctuations during measurement. We select tungsten for the core material due to its high strength, which makes it very suitable for sharp tips Ždiameter - 10 m., and gold for the coating due to the ease of sputtered deposition. A harder material such as platinum should be better in terms of wear resistance. However, the choice of materials, other than those with low thermal power, should not affect the overall design of the system presented here. The measured thermoelectric power of the thermocouple tip versus temperature is shown in Fig. 3. A type-K thermocouple junction was used as the calibration standard. The thermoelectric power of our thermocouple is slightly lower than that obtained from the literature w8x, especially in the high-temperature region. This may be attributed to impurities in the sputtered gold.
3. Results and discussions 3.1. n-Type silicon wafer and pure copper As part of the calibration procedures, we used this scanning thermocouple technique to measure the ther-
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 2. Ža. Cross-sectional view of gold᎐tungsten thermocouple tip; and Žb. photo of thermocouple tip before gold sputtering.
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H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 3. Measured thermoelectric power for the gold-sputtered tungsten thermocouple ŽU .. Values obtained from ref. w8x are indicated by open circles.
mal conductivity of n-type silicon and pure copper. Fig. 4 shows the temperature measurements along the 20mm length of the silicon bar, which has a nominal resistivity of 4᎐7 ⍀-cm and dimensions: 5 = 20 = 0.5 Žwidth= length = thickness; with accuracy "0.05 mm.,
for two different values of heating power, Q1 s 0.207" 0.003 W and Q2 s 0.465" 0.007 W. The least-square fitting technique for locating the optimum values of T2 and has been used to obtain the best fit between our experimental results and the theoretical distribution of T Ž x .. Subsequently, the optimum values of T2 and are substituted into the equation s QsinhŽ L.r Aw T2 coshŽ L. y T1 x for calculating the thermal conductivity at T2 . The measured thermal conductivity of our n-type silicon sample at 304.6 K and 316.2 K are, respectively, 1.4" 0.1 W cmy1 Ky1 and 1.3" 0.1 W cmy1 Ky1 . Compared to those reported in literature for these temperatures w9x, which are 1.45 W cmy1 Ky1 and 1.38 W cmy1 Ky1 , our results are approximately 3% and 6% lower than the expected values. For the measurement of the thermal conductivity of the copper bar, which has a purity of 99.9% and dimensions: 4.4 = 22 = 0.25 Žwidth = length = thickness; in mm with accuracy "0.05 mm., a heater power, Qs 0.122" 0.002 W, from the resistance heater was applied. The fitted temperature curve wi.e. T Ž x .x along the length of the copper bar is showed in Fig. 5. This corresponds to a thermal conductivity of 4.3" 0.3 W cmy1 Ky1 at 303.4 K. The measured thermal conductivity is 7.5% higher than the value of 4.01 W cmy1
Fig. 4. Temperature measurement along the n-type silicon bar for two heating levels; Q1 s 0.207" 0.003 W Žlower curve.; Q2 s 0.465" 0.007 W Župper curve..
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 5. Temperature measurement along the pure copper bar for heater power Q1 s 0.122" 0.002 W. y1
K reported in the literature, which is within the error limits of our experiment w9x. With this calibration data using copper, which is the second best material in terms of thermal conductivity after diamond, we believe our system, given its simplicity, should be an acceptable method for measuring the thermal conductivity of CVD diamond. 3.2. CVD diamond The diamond sample had a thickness of 0.4 mm was grown using the conventional microwave plasma-assisted CVD technique. The sample had a characteristic black colour indicating a considerable level of the graphite phase. It was first cut into a rectangular bar using a Nd:YAG laser. The edges were then polished to the size 2.0= 11.0= 0.4 Žwidth = length = thickness in mm; with accuracy "0.05 mm.. Fig. 6 shows the temperature measurements along the sample and the reconstructed temperature profiles using the optimal values of T2 and for five different levels of Q. For each temperature data set, the least-square technique is again used for locating the optimum values of T2 and contained in the equation for T Ž x .. The conductivity value Ž . at temperature T2 is subsequently calculated using the equation involving Ži.e. s QsinhŽ L.r Aw T2 coshŽ L. y T1 x.. The measured thermal conductivity values for our diamond sample are shown in Fig. 7. For the temperature range between 299.2 K and 317.4 K, the measured conductivity values are 5.4᎐6.2 Ž" 0.6. W cmy1 Ky1. These values are considerably smaller than those obtained from typical diamond samples. Since the calibration of our set-up using materials with well-defined materials did not suggest any major problem associated with the measurement technique, we believe that the unexpectedly poor values obtained here are intrinsic to the sample. In Fig. 8, Raman spectroscopy revealed a strong at 1332 cmy1
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Fig. 6. Temperature measurement along the diamond bar for different heated powers, starting from bottom curve: Q1 s 0.291" 0.004 W; Q2 s 0.748" 0.010 W; Q3 s 0.976" 0.014 W; Q4 s 1.417" 0.020 W; Q5 s 1.865" 0.026 W.
Žwith FWHM 10 m. due to the diamond bond and a broad peak at 1500᎐1600 cmy1 due to amorphous carbon and graphite. The Raman spectrum and the dark colour of the sample indicate that the sample contains a high level of non-diamond phase. In addition poor crystal quality with small grain size also significantly reduces the mean free path of phonons and thus the thermal conductivity of the material. Similar values have been reported before w4,5x for ‘dark’ CVD diamond materials. 3.3. Discussions First we consider the temperature measurement accuracy using the present thermocouple tip. In the
Fig. 7. Measured thermal conductivity of diamond bar at different temperatures.
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H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 8. Raman spectrum of the ‘dark’ diamond sample.
experiment the measured thermal power of the goldrtungsten thermocouple tip is about 0.5 V Ky1 . Since the resolution of the nano-voltmeter is 0.001 V, the maximum achievable temperature resolution can be as high as 0.002 K. However, in reality this ultimately resolution level is limited by a number of factors, including the signal-to-noise ratio of the electronics and the temperature fluctuation within the connection wires. Another source of error may come from the thermal resistance between the thermocouple tip and the sample itself. We are relying on the thermal equilibrium between the tip and the sample surface. Heat energy has to first be transmitted into the thermocouple tip via conduction and thereby raise the temperature of the tip. Any unwanted material on the surface may act as a thermal barrier and thus making the measured value lower than the actual temperature in the sample. For this reason we have to ensure that both the thermocouple tip as well as the sample are free from any contaminations. The fact that we use gold coating should help to some extent since its low reactivity should prevent the formation of native oxide on the surface. In addition, the small diameter of the tungsten wire also means that the contact area between the tip and the sample surface must be less than 10 m wide. Since the supporting material for the tip is glass, which is a relatively poor thermal conductor, the unwanted thermal loading introduced by the tip, which inevitably reduces the temperature of the surface, should be fairly small compared to the bulk of the sample. We can therefore safely assume that the errors due to the thermal loading effect from the thermocouple tip are negligible. Nevertheless such errors should be systematic in nature and can be quite readily estimated through calibration procedures. Another source of error may come from the quantification of heat energy produced by the resistance heater. Here we assume that all of the electrical energy
provided by the voltage source is used for heating up the bar. The amount of heat loss directly from the resistor has been ignored. This should be a reasonable assumption in our case since the external surface area of the heater wire is very small compared to the sample bar. For further improvement of measurement accuracy it should be better to use a calibrated diamond sample of known thermal conductivity. This way one can precisely estimate the total error due to the system, including the error due to heat loss from the heater wire. It should be mentioned that our experiment was primarily designed for performing fast measurement of thermal conductivity of diamond. If both the sample surface and the thermocouple tip are clean then the measurement accuracy of this technique should be quite repeatable once the set-up has been calibrated using samples of known parameters.
4. Conclusion A simple scanning thermocouple technique for the measurement of thermal conductivity of CVD diamond films has been demonstrated. It should find application in the CVD diamond production industry for routine characterisation of sample thermal properties. With the thermocouple fabricated through coating gold on a polished tungsten wire tip a spatial resolution of approximately 10 m may be achieved. Using the heatedbar technique we calibrated the measurement setup by performing measurements on n-type silicon and copper samples. The thermal conductivity of a ‘dark’ CVD diamond sample was then measured for the temperature range between 299.2 K and 317.4 K and found to be in the range of 5.4᎐6.2 Ž" 0.6. W cmy1 Ky1. All measured values compare reasonably well with published data and thus demonstrating the capability of our system for fast thermal characterisation of thin-film materials.
Acknowledgements The authors acknowledge the funding support from the City University of Hong Kong under research grant no. 7000747. The authors are also grateful to Dr C.K. Kwong of the Hong Kong Polytechnic University for the laser-cutting of our diamond sample. References w1x J.E. Graebner, M.E. Reis, L. Seibles, T.M. Hartnett, R.P. Miller, C.J. Robinson, Phys. Rev. B 70 Ž1994. 3702. w2x E. Worner, C. Wild, W. Muller-Sebert, R. Locher, P. Koidl, ¨ ¨ Diamond Relat. Mater. 5 Ž1996. 688. w3x K. Plamann, D. Fournier, B.C. Forget, A.C. Boccara, Diamond Relat. Mater. 5 Ž1996. 699.
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319 w4x E. Jansen, O. Dorsch, E. Obermeier, W. Kulisch, Diamond Relat. Mater. 5 Ž1996. 644. w5x C.J.H. Wort, C.G. Sweeney, M.A. Cooper, G.A. Scarsbrook, R.S. Sussmann, Diamond Relat. Mater. 3 Ž1994. 1158. w6x H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959. w7x M.A. Prelas, G. Popovici, L.K. Bigelow, Handbook of Industrial
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Diamonds and Diamond Films, Marcel Dekker Press, New York, 1998, p. 195. w8x D.D. Pollock, Thermocouple Theory and Properties, CRC Press, Boca Raton, FL, 1991, p. 147. w9x D.R. Lide, in: D.R. Lide ŽEd.., CRC Handbook of Chemistry and Physics, 77th ed, CRC Press, Boca Raton, FL, 1997, pp. 12᎐175.
Measurement of thermal conductivity in diamond films using a simple scanning thermocouple technique H.P. HoU , K.C. Lo, S.C. Tjong, S.T. Lee Department of Physics and Materials Science, City Uni¨ ersity of Hong Kong, 83 Tat Chee A¨ enue, Kowloon, Hong Kong Received 24 August 1999; accepted 30 December 1999
Abstract In this paper we present a simple scanning thermocouple technique for measuring the thermal conductivity Ž . of diamond thin films. We first describe the fabrication procedure of the thermocouple tip, which involves first fixing a 10-m-thick tungsten wire inside a glass capillary tube and then coating the exposed tip with gold. The goldrtungsten thermocouple was used to map the temperature distribution on the diamond surface. The measured data are fitted into the solution obtained from solving the steady-state heat conduction equations which also take into account the heat loss from the sample. For our diamond sample, the measured for the temperature range between 299.2 K and 317.4 K is between 5.4 and 6.2 Ž"0.6. W cmy1 Ky1 , which is within the range published elsewhere for ‘dark’ CVD diamond materials. 䊚 2000 Elsevier Science S.A. All rights reserved. Keywords: Diamond films; Scanning thermocouple technique; Thermal conductivity
1. Introduction With a thermal conductivity up to five times higher than that of copper, diamond made by the chemical vapour deposition ŽCVD. technique is well known to be very effective for heat spreading applications. At present, due to their relatively high production costs, CVD diamond heat sinks are only used in selected devices where high-speed heat spreading capability is essential. Currently, nearly all semiconductor heat sinks are made from copper, silicon carbide or aluminium nitride. Since future electronics will operate at higher speed and in higher density, and hence with very high power density, an efficient high-speed heat spreader must be required to ensure acceptable lifetime and speed performance. The continual improvement of CVD diamond production costs will undoubtedly lead to its widespread applications in a range of electronic devices in the future. The increased production volume will also mean that U
Corresponding author. Fax: q852-2-7887830. E-mail address: [email protected] ŽH.P. Ho..
there is the need for a quick and reliable method for characterising the thermal conductivity of the material. The scanning thermocouple technique described in this paper aims particularly to address this issue. The measurement of thermal conductivity of diamond, ranging between a few and more than 20 W cmy1 Ky1 w1x depending on the CVD techniques and conditions, has been reported by several authors w2᎐5x. Measurement methods such as thermocouple arrays, thin films, thermal flash technique and thermoresistor thin film are the common techniques for measuring the temperature distribution in the sample. Up until now all the direct measurement methods involving thermocouples require a number of sample preparation steps including deposition of metal thin films and welding of thermocouple wires to different measurement locations on the sample. This measurement approach may take considerable time and effort. In this paper we present an alternative technique which aims to simplify the temperature measurement process by scanning a thermocouple tip across the sample surface. In our demonstration set-up a resistive heater wire is
0925-9635r00r$ - see front matter 䊚 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 0 . 0 0 2 3 1 - 4
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
used as the heat source. The steady thermal gradient across the sample is measured by a gold᎐tungsten thermocouple. The thermal conductivity can thus be deduced from the measured temperature data. In addition to the measurement of thermal conductivity the new technique can also provide a low-cost alternative for mapping of temperature distributions, which may be important for a range of applications including the optimisation of semiconductor packages.
2.1. The heated-bar technique In our experiment, we fabricate a sharp thermocouple tip and then perform temperature measurement at selected locations on the sample surface. One can then use the data to reconstruct a two-dimensional surface temperature profile. For a simple case, in which the two ends of the sample bar are connected to two constant temperature sources, we use our thermocouple to measure the steady-state temperature gradient along the sample bar. If there is no heat loss, the temperature profile should be a straight line with slope ⌬Tr⌬ x, and the thermal conductivity can be calculated according to the equation: ) A/ ž ⌬T ⌬x
where A is the cross-sectional area of the sample perpendicular to the heat flow direction and Q is the heat power input from the high-temperature end. However, due to the heat loss from the sample surface by radiation and convection, the steady-state heat balance equation is modified to the following form:
⭸2 T Hp y Ts0 A ⭸X 2
where H is the loss heat flux by radiation and convection per unit surface area per degree of temperature difference, and p is the perimeter of the cross section of the bar. One can define s Hpr A as a measure of the importance of surface loss compared to heat conduction within the sample. The solution to the above equation is given by Carslaw and Jaeger w6x as:
'
T Ž x. s
an outward heat flux at the surface. A least-square fitting technique can be used for obtaining an optimum match between this solution and the measured data of T Ž x . by varying T2 and . After differentiation with respect to temperature, the temperature gradient at heater location Ž xs L. becomes ⭸T Ž x . ⭸x
xsL
s
w T2 cosh Ž x . y T1 x . sinh Ž L .
With the values of T2 and found, the gradient at location Ž xs L. will be put back into the initial thermal conductivity equation, s QrwŽ ⌬Tr⌬ x .) A x, for replacing Ž ⌬Tr⌬ x .. The conductivity at temperature T2 will be calculated as w7x:
2. Experimental details
s Qr
1313
T1 sinh w Ž L y x .x q T2 sinh Ž x . sinh Ž L .
where L is the distance between the steady-state temperature sources T1 and T2 . This equation effectively describes the temperature profile along a sample with its ends at temperature T1 and T2 ŽT1 - T2 . and with
s
Qsinh Ž L . Aw T2 cosh Ž L . y T1 x
In essence, this analysis allows us to include heat losses along the length of the sample and thus modifies the linear thermal conductivity equation, i.e. s QrwŽ ⌬Tr⌬ x .) A x, to become variable gradient along the length of the sample. By extrapolating our curving range to the high-temperature end where the drop of temperature due to heat loss along the sample is small, we can assume the gradient derived at this location fits the linear thermal conductivity equation. Hence we can calculate the thermal conductivity at the high-temperature ŽT2 . point. For this reason, it should be mentioned that this method is accurate only at the high-temperature end of the sample. One further condition we need to impose here is that the thermal conductivity remains constant throughout the temperature range that the experiment is operating in. This means that for real samples, in which the thermal conductivity varies with temperature, small temperature gradients should be used in order to ensure acceptable measurement accuracy. Nevertheless, for the temperature ranges that we used in our experiments, which is approximately 17⬚C at the most, the changes in thermal conductivities for our samples are, respectively, 8%, 0.3% and up to 4% Žsample dependent. for silicon, copper and CVD diamond w4,5,9x. For the present experimental set-up such effect will inevitably introduce further errors to the measured thermal conductivity values. 2.2. Experimental setup The measurement setup is schematically shown in Fig. 1. In order to ensure a steady-state heat flux parallel to a bar-shaped sample, a resistive heater wire is attached at one end of the bar-shaped sample and the other end of the bar is thermally grounded to a metal block with water cooling inside. Within the measurement period we constantly monitor the cooling
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H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 1. Schematic of experimental setup: Ž1. radiation isolation enclosure; Ž2. x-, y- and z-axis micro-scanning stages; Ž3. gold᎐tungsten thermocouple tip; Ž4. aluminium blocks; Ž5. sample; Ž6. resistance heater wire; and Ž7. thermal ground metal block.
water temperature to ensure it does not fluctuate more than "0.1⬚C. A pre-fabricated gold᎐tungsten thermocouple tip is mounted on a micro-scanning stage for measuring the temperature at different locations along the length of the sample. 2.3. Thermocouple fabrication and calibration A cross-sectional view of the thermocouple device is shown in Fig. 2a. The fabrication steps of the thermocouple tip are as follows: Ž1. a tungsten wire Ždiameter 10 m. is inserted halfway along the inner channel of a micro-pipette. Ž2. The tube is heated inside the flame from a micro-burner. As the glass wall melts the pipette is pulled so that a thin layer of glass is collapsed onto the wire. Ž3. After carefully breaking the elongated section at the same location as the tungsten wire end and dipping the glass tip into 1 M sodium hydroxide solution for 5᎐6 min, a tungsten tip protected by a thin layer of glass will be formed. Ž4. Upon sharpening the tip using 1 m diamond polishing paste, a thin layer of gold is sputtered onto the tip region for finally forming the micro-thermocouple. Fig. 2b shows the optical micrograph of the tungsten tip just before the sputtering deposition of the gold film. Connections to the gold film and the tungsten wire are made using copper wire. A nanovoltmeter ŽKeithley, model 2182. is used for measuring the thermocou-
ple output voltage. The two gold᎐copper and tungsten᎐copper junctions are mounted to a large metal block for minimising temperature fluctuations during measurement. We select tungsten for the core material due to its high strength, which makes it very suitable for sharp tips Ždiameter - 10 m., and gold for the coating due to the ease of sputtered deposition. A harder material such as platinum should be better in terms of wear resistance. However, the choice of materials, other than those with low thermal power, should not affect the overall design of the system presented here. The measured thermoelectric power of the thermocouple tip versus temperature is shown in Fig. 3. A type-K thermocouple junction was used as the calibration standard. The thermoelectric power of our thermocouple is slightly lower than that obtained from the literature w8x, especially in the high-temperature region. This may be attributed to impurities in the sputtered gold.
3. Results and discussions 3.1. n-Type silicon wafer and pure copper As part of the calibration procedures, we used this scanning thermocouple technique to measure the ther-
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 2. Ža. Cross-sectional view of gold᎐tungsten thermocouple tip; and Žb. photo of thermocouple tip before gold sputtering.
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H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 3. Measured thermoelectric power for the gold-sputtered tungsten thermocouple ŽU .. Values obtained from ref. w8x are indicated by open circles.
mal conductivity of n-type silicon and pure copper. Fig. 4 shows the temperature measurements along the 20mm length of the silicon bar, which has a nominal resistivity of 4᎐7 ⍀-cm and dimensions: 5 = 20 = 0.5 Žwidth= length = thickness; with accuracy "0.05 mm.,
for two different values of heating power, Q1 s 0.207" 0.003 W and Q2 s 0.465" 0.007 W. The least-square fitting technique for locating the optimum values of T2 and has been used to obtain the best fit between our experimental results and the theoretical distribution of T Ž x .. Subsequently, the optimum values of T2 and are substituted into the equation s QsinhŽ L.r Aw T2 coshŽ L. y T1 x for calculating the thermal conductivity at T2 . The measured thermal conductivity of our n-type silicon sample at 304.6 K and 316.2 K are, respectively, 1.4" 0.1 W cmy1 Ky1 and 1.3" 0.1 W cmy1 Ky1 . Compared to those reported in literature for these temperatures w9x, which are 1.45 W cmy1 Ky1 and 1.38 W cmy1 Ky1 , our results are approximately 3% and 6% lower than the expected values. For the measurement of the thermal conductivity of the copper bar, which has a purity of 99.9% and dimensions: 4.4 = 22 = 0.25 Žwidth = length = thickness; in mm with accuracy "0.05 mm., a heater power, Qs 0.122" 0.002 W, from the resistance heater was applied. The fitted temperature curve wi.e. T Ž x .x along the length of the copper bar is showed in Fig. 5. This corresponds to a thermal conductivity of 4.3" 0.3 W cmy1 Ky1 at 303.4 K. The measured thermal conductivity is 7.5% higher than the value of 4.01 W cmy1
Fig. 4. Temperature measurement along the n-type silicon bar for two heating levels; Q1 s 0.207" 0.003 W Žlower curve.; Q2 s 0.465" 0.007 W Župper curve..
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 5. Temperature measurement along the pure copper bar for heater power Q1 s 0.122" 0.002 W. y1
K reported in the literature, which is within the error limits of our experiment w9x. With this calibration data using copper, which is the second best material in terms of thermal conductivity after diamond, we believe our system, given its simplicity, should be an acceptable method for measuring the thermal conductivity of CVD diamond. 3.2. CVD diamond The diamond sample had a thickness of 0.4 mm was grown using the conventional microwave plasma-assisted CVD technique. The sample had a characteristic black colour indicating a considerable level of the graphite phase. It was first cut into a rectangular bar using a Nd:YAG laser. The edges were then polished to the size 2.0= 11.0= 0.4 Žwidth = length = thickness in mm; with accuracy "0.05 mm.. Fig. 6 shows the temperature measurements along the sample and the reconstructed temperature profiles using the optimal values of T2 and for five different levels of Q. For each temperature data set, the least-square technique is again used for locating the optimum values of T2 and contained in the equation for T Ž x .. The conductivity value Ž . at temperature T2 is subsequently calculated using the equation involving Ži.e. s QsinhŽ L.r Aw T2 coshŽ L. y T1 x.. The measured thermal conductivity values for our diamond sample are shown in Fig. 7. For the temperature range between 299.2 K and 317.4 K, the measured conductivity values are 5.4᎐6.2 Ž" 0.6. W cmy1 Ky1. These values are considerably smaller than those obtained from typical diamond samples. Since the calibration of our set-up using materials with well-defined materials did not suggest any major problem associated with the measurement technique, we believe that the unexpectedly poor values obtained here are intrinsic to the sample. In Fig. 8, Raman spectroscopy revealed a strong at 1332 cmy1
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Fig. 6. Temperature measurement along the diamond bar for different heated powers, starting from bottom curve: Q1 s 0.291" 0.004 W; Q2 s 0.748" 0.010 W; Q3 s 0.976" 0.014 W; Q4 s 1.417" 0.020 W; Q5 s 1.865" 0.026 W.
Žwith FWHM 10 m. due to the diamond bond and a broad peak at 1500᎐1600 cmy1 due to amorphous carbon and graphite. The Raman spectrum and the dark colour of the sample indicate that the sample contains a high level of non-diamond phase. In addition poor crystal quality with small grain size also significantly reduces the mean free path of phonons and thus the thermal conductivity of the material. Similar values have been reported before w4,5x for ‘dark’ CVD diamond materials. 3.3. Discussions First we consider the temperature measurement accuracy using the present thermocouple tip. In the
Fig. 7. Measured thermal conductivity of diamond bar at different temperatures.
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H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319
Fig. 8. Raman spectrum of the ‘dark’ diamond sample.
experiment the measured thermal power of the goldrtungsten thermocouple tip is about 0.5 V Ky1 . Since the resolution of the nano-voltmeter is 0.001 V, the maximum achievable temperature resolution can be as high as 0.002 K. However, in reality this ultimately resolution level is limited by a number of factors, including the signal-to-noise ratio of the electronics and the temperature fluctuation within the connection wires. Another source of error may come from the thermal resistance between the thermocouple tip and the sample itself. We are relying on the thermal equilibrium between the tip and the sample surface. Heat energy has to first be transmitted into the thermocouple tip via conduction and thereby raise the temperature of the tip. Any unwanted material on the surface may act as a thermal barrier and thus making the measured value lower than the actual temperature in the sample. For this reason we have to ensure that both the thermocouple tip as well as the sample are free from any contaminations. The fact that we use gold coating should help to some extent since its low reactivity should prevent the formation of native oxide on the surface. In addition, the small diameter of the tungsten wire also means that the contact area between the tip and the sample surface must be less than 10 m wide. Since the supporting material for the tip is glass, which is a relatively poor thermal conductor, the unwanted thermal loading introduced by the tip, which inevitably reduces the temperature of the surface, should be fairly small compared to the bulk of the sample. We can therefore safely assume that the errors due to the thermal loading effect from the thermocouple tip are negligible. Nevertheless such errors should be systematic in nature and can be quite readily estimated through calibration procedures. Another source of error may come from the quantification of heat energy produced by the resistance heater. Here we assume that all of the electrical energy
provided by the voltage source is used for heating up the bar. The amount of heat loss directly from the resistor has been ignored. This should be a reasonable assumption in our case since the external surface area of the heater wire is very small compared to the sample bar. For further improvement of measurement accuracy it should be better to use a calibrated diamond sample of known thermal conductivity. This way one can precisely estimate the total error due to the system, including the error due to heat loss from the heater wire. It should be mentioned that our experiment was primarily designed for performing fast measurement of thermal conductivity of diamond. If both the sample surface and the thermocouple tip are clean then the measurement accuracy of this technique should be quite repeatable once the set-up has been calibrated using samples of known parameters.
4. Conclusion A simple scanning thermocouple technique for the measurement of thermal conductivity of CVD diamond films has been demonstrated. It should find application in the CVD diamond production industry for routine characterisation of sample thermal properties. With the thermocouple fabricated through coating gold on a polished tungsten wire tip a spatial resolution of approximately 10 m may be achieved. Using the heatedbar technique we calibrated the measurement setup by performing measurements on n-type silicon and copper samples. The thermal conductivity of a ‘dark’ CVD diamond sample was then measured for the temperature range between 299.2 K and 317.4 K and found to be in the range of 5.4᎐6.2 Ž" 0.6. W cmy1 Ky1. All measured values compare reasonably well with published data and thus demonstrating the capability of our system for fast thermal characterisation of thin-film materials.
Acknowledgements The authors acknowledge the funding support from the City University of Hong Kong under research grant no. 7000747. The authors are also grateful to Dr C.K. Kwong of the Hong Kong Polytechnic University for the laser-cutting of our diamond sample. References w1x J.E. Graebner, M.E. Reis, L. Seibles, T.M. Hartnett, R.P. Miller, C.J. Robinson, Phys. Rev. B 70 Ž1994. 3702. w2x E. Worner, C. Wild, W. Muller-Sebert, R. Locher, P. Koidl, ¨ ¨ Diamond Relat. Mater. 5 Ž1996. 688. w3x K. Plamann, D. Fournier, B.C. Forget, A.C. Boccara, Diamond Relat. Mater. 5 Ž1996. 699.
H.P. Ho et al. r Diamond and Related Materials 9 (2000) 1312᎐1319 w4x E. Jansen, O. Dorsch, E. Obermeier, W. Kulisch, Diamond Relat. Mater. 5 Ž1996. 644. w5x C.J.H. Wort, C.G. Sweeney, M.A. Cooper, G.A. Scarsbrook, R.S. Sussmann, Diamond Relat. Mater. 3 Ž1994. 1158. w6x H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford, 1959. w7x M.A. Prelas, G. Popovici, L.K. Bigelow, Handbook of Industrial
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Diamonds and Diamond Films, Marcel Dekker Press, New York, 1998, p. 195. w8x D.D. Pollock, Thermocouple Theory and Properties, CRC Press, Boca Raton, FL, 1991, p. 147. w9x D.R. Lide, in: D.R. Lide ŽEd.., CRC Handbook of Chemistry and Physics, 77th ed, CRC Press, Boca Raton, FL, 1997, pp. 12᎐175.