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Temperature sensors based on synthetic diamond films
Diamond & Related Materials 16 (2007) 1652 – 1655 www.elsevier.com/locate/diamond
Temperature sensors based on synthetic diamond films Adenilson J. Chiquito a,⁎, Olívia M. Berengue a , Edgar Diagonel a , José C. Galzerani a , João R. Moro b a
Departamento de Física, Universidade Federal de São Carlos, CEP 13565-905, CP 676, Sao Carlos, São Paulo, Brasil b Lab. de Diamantes, Universidade São Francisco, Itatiba, 13231-900, Brasil Received 14 September 2006; received in revised form 29 January 2007; accepted 19 February 2007 Available online 24 February 2007
Abstract The transport properties of synthetic diamond films were studied and the resulting data were applied to the development of a simple device which was used as a temperature sensor. It has been observed that the electrical resistivity follows the variable range hopping conducting process. The sensibility and reliability of the electrical characteristics presented by the sensor were very good in the investigated range of temperatures (10 to 300 K). The sensor reading was unaffected even in the presence of light illumination or magnetic field. © 2007 Elsevier B.V. All rights reserved.
1. Introduction Chemical vapor-deposited CVD diamond films have attracted great attention due to their unusual electrical, optical, and mechanical properties [1]. For instance, it is chemically inert and resistant to the high temperatures, particularly in an environment without oxygen. It is also resistant to α and γ radiations, ultraviolet light, and to nuclear particles. These characteristics make the diamond films ideal systems for different technologic applications (see, for instance, Refs. [2,3]). Artificially synthesized diamond thin films are usually grown by chemical vapor deposition using hot-filament or microwave-plasma techniques [4]. The diamond lattice exhibits a single characteristic Raman-active mode: the triply degenerated phonon which appears as a sharp line at approximately 1332 cm− 1; then its observation is considered as a definitive evidence of diamond growth. The Raman linewidth of polycrystalline CVD diamond films are typically broader (ranging from 5 to 15 cm− 1) because of disorder due to microstrains or chemical defects and they are frequently found shifted by temperature or lattice strain effects [5]. However the development of practicable diamond sensors for different applications has been restricted by a combination of factors like defects inducing slow time responses (mainly in ⁎ Corresponding author. Fax: +55 16 3361 4835. E-mail address: [email protected] (A.J. Chiquito). 0925-9635/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2007.02.012
low doped samples). These effects are due to a complex interplay between bulk trapping centers in CVD materials and the quality of the metal–diamond ohmic contacts used to fabricate the devices. In a recent paper [6] we have shown a comparative study (using Raman spectroscopy) of CVD diamond films searching for growth parameters that could result in high quality doped films. The films thus grown are now used to study some transport properties and the results were applied to the development of a simple device which in turn, was used as a temperature sensor. The sensibility and reliability of the sensor characteristics were very good in the investigated range (10 to 300 K). The sensor readings were unaffected even in the presence of light illumination or magnetic field. 2. Experiment After the growth (details of the procedures were given in Ref. [6]), the samples were characterized by Raman spectroscopy in order to confirm the formation of the diamond films. A sharp diamond peak at 1332 cm− 1 with little non-sp3 background was observed in the Raman spectra of both samples as shown in Fig. 1. The samples which results were displayed in this figure were grown at the same conditions but at different doping levels. As already observed in the literature [6–8], one of the effects of Boron addition is promoting a decrease of the sp2 bonding band as seen in the higher doped sample (Fig. 1). At the same time, the
A.J. Chiquito et al. / Diamond & Related Materials 16 (2007) 1652–1655
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3. Results and discussion From Hall measurements the hole density of the samples was determined (p = 2.2 × 1018 cm− 3). In addition, the value μh = 120 cm2/V s was found for the hole mobility. In synthetic diamond films the graphitic phases can contribute to the decrease of the resistivity. However, the doped samples used here were obtained at temperatures in which the non-diamond phases were drastically reduced, as verified by the Raman spectra (Fig. 1). Then, the measured conductivity is mainly due to the Boron doping and not due to the graphitic phases as expected in rich-sp2 synthetic diamond films. The temperature dependent transport measurements were depicted in Fig. 2. The conduction mechanism in the diamond doped samples is controlled by the variable range hopping mechanism (VRH) in a wide range of temperatures as reported by several authors [12,13]. The VRH mechanism is described by the well known equation qðT Þ ¼ q0 exp Fig. 1. Raman spectra of the diamond films. The peak at 1332 cm− 1 indicates the presence of sp3 diamond. The Boron doping level is indicated in the figure.
doping is also shown to provoke the intensity decrease and an asymmetry of the diamond line. These effects have been attributed to a Fano-type interference [9,10] which, in turn, is linked to the increase of free carriers in the structure. The presence of non-diamond bands and other intrinsic defects (as the formation of deep levels and disorder leading to localization of charges) can produce deleterious effects in devices performance. In this way, only the doped sample was used for the transport measurements. Before devices fabrication, the samples were treated with a conventional degrease solution based on trichloroethylene followed by acetone; next, the samples were immersed in a saturated solution of H2SO4/K2CrO4 at 200 °C for 1 h and immediately rinsed in NH4OH/H2O2 solution and deionized water. The electrical contacts were defined by shadow masks and standard lithographic techniques. The metallization (Ti/Au, 50 nm/100 nm) was made in a high vacuum chamber (10− 6 Torr); the devices were then annealed in an inert Ar atmosphere at 600 °C for 10 min. Ohmic electrodes of 100 μm width were also spaced by 100 μm. The films have thicknesses of approximately 20 μm and before the transport experiments the Si substrate was removed by chemical etching in order to avoid current flowing through it [11]. The electrical measurements were made using a standard ac lock-in low frequency (13 Hz) system. The resistivity was measured using the conventional four-probe method and the Van der Pawn geometry was used for Hall measurements. The current in all experiments was limited to 10 μA (when operating as a temperature sensor, the devices were biased with 1 or 10 μA). For temperaturedependent measurements the samples were incorporated to a modified Janis CCS 150 closed cycle cryostat.
m T0 ; T
ð1Þ
where T0 = 2α3 / kBg(EF). Here, g(EF) is the density of states at the Fermi level and α− 1 is the localization length. VRH mechanism normally occurs only in the low temperature region (below room temperature) wherein the energy is insufficient to excite the charge carrier across the Coulomb gap. Hence conduction takes place by hopping of small region (kBT) in the vicinity of the Fermi level where the density of states remains almost a constant (m = 1/4). This condition is fulfilled when the
Fig. 2. Temperature dependence of the resistivity of the samples. The thin solid line shows the fit to the T1/4 law.
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A.J. Chiquito et al. / Diamond & Related Materials 16 (2007) 1652–1655
temperature is sufficiently small or when the energy states are uniformly distributed. Additionally, if one consider the longrange Coulomb interactions, the exponent m in Eq. (1) should be replaced by 1/2 [14]. The fitting of Eq. (1) to the experimental data is shown in Fig. 2. The agreement of both theoretical and experimental curves in a large range of temperatures confirms that the transport in our samples is governed by the variable range hopping process. Also, the fit procedure has provided 6.6 K1/4 for the slope (T0)1/4. The calculated value for the slope is very different [(T0)1/4 = 67 K1/4] when the Bohr radius for Boron atoms is used as the localization length (α− 1 = 0.3 nm). In fact, this is a very naive assumption: the Mott VRH theory [15] is valid when the distance which a carrier moves (hops) is greater than the nearest neighbor distance. If we consider that the energy states are uniformly distributed, the localization length of the wavefunction describing the carriers will exceed the typical Bohr radius and the calculation of T0 will give a wrong result. Using the experimental value, the localization length was found to be ≈ 6 nm which is a reasonable value for the spatial extention of the carrier's wavefunction. After the electrical characterization, the samples were mounted in a special support together to calibrated temperature sensors. Fig. 3 shows four thermal cycles of resistivity obtained for the doped sample with and without external excitations (magnetic field). The curves were shifted up for clearness because they are identical whatever B = 0 or B = 1 T. The reproducibility of the curves were extensively tested, using different cryogenic systems and different excitation currents (1 μA–10 mA). The results presented in Fig. 3 remained
Fig. 4. Sensitivity and resolution of the implemented diamond sensors. In the insert are presented the thermal response time for 77 K and 273 K for the sample.
unchanged (current levels greater than 1 mA provoke undesirable heating). The temperature reading was made by a LakeShore 331S temperature controller using two calibrated TG120 GaAlAs sensors (provided by LakeShore Cryogenics). Each curve contains approximately 3000 experimental points taken during the cooldown and the warm-up cycles. The difference between the signal readings for two consecutive cycles is very low (0.4%). These measurements were repeated under white light illumination (halogen lamp, 150 W) and the results were unchanged (not shown). Sensitivity, resolution and time response are fundamental features for thermometry devices and can be presented in a variety of ways. Typically, the sensitivity is given in terms of the signal sensitivity, which is the change in a measured parameter per change in temperature (in our case, V/K). It is interesting to be noted that when comparing different resistance sensors, an useful material parameter to consider is the dimensionless sensitivity, given as S¼
Fig. 3. Voltage response of the diamond sensor for four thermal cycles measured using I = 1 μA. Panel (a) shows the results without applied magnetic field and panel (b) with magnetic field. The arrows indicate cooling or warming processes and the curves were shifted up for clearness.
dðlnV Þ dðlnT Þ
ð2Þ
where the logarithmic derivatives are calculated using the experimental V versus T curves. By the other hand, the temperature resolution is the smallest temperature difference that can be determined by the sensor (in fact, it is a combination of sensor sensitivity and instrument resolution). It can be expressed as the ratio ΔT/T. In Fig. 4 we show the dimensionless sensitivity and the resolution as a function of the temperature. Thermal response times are determined by physical construction material and mass of the temperature-sensing element. The diamond is a good thermal conductor (five times better than cooper [1]), then becoming a very good sensor. We measured the thermal response
A.J. Chiquito et al. / Diamond & Related Materials 16 (2007) 1652–1655
of ours at usual temperatures (77 K, 273 K) and the results were presented as an insert for Fig. 4. The samples presented a relatively fast thermal response [16]. This fact becomes more important if we taking into account that the electrical contacts geometry and the size (and mass) of the sensor were not optimized for the construction of a device ready for use. The wellbehaved dependence for both voltage reading and sensitivity on the temperature demonstrate the viability of the doped diamond films as a temperature sensor even in the presence of light or magnetic fields. 4. Conclusion In conclusion, we have produced reliable temperature sensors based on thin synthetic diamond films. In addition we have described the transport processes which took place in these films, confirming the variable range hopping as the dominant conduction mechanism. The influence of external parameters such as magnetic field and light were not observed. The geometry of the devices (coplanar electrodes), the well known transport mechanism and the reproducibility of the measurements are surely the most interesting aspects of these sensors. Acknowledgements We would like to thank E. Diagonel for your useful help in the patterning process of the sensors. This work was supported in part by the Brazilian Agencies FAPESP and CNPq.
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References [1] J.E. Field, The Properties of Diamond, Academic Press, New York, 1979. [2] T. Hantschel, P. Niedermann, T. Trenkler, W. Vandervorstc, Appl. Phys. Lett. 76 (12) (2000) 1603. [3] P.J. Sellina, A. Galbiati, Appl. Phys. Lett. 87 (9) (2005) 093502. [4] K. Kobashi, K. Nishimura, Y. Kawate, T. Horiuchi, Phys. Rev., B 38 (6) (1988) 4067. [5] J.W. Ager III, D.K. Veirs, G.M. Rosenblatt, Phys. Rev., B 43 (8) (1991) 6491. [6] W. Fortunato, A.J. Chiquito, J.C. Galzerani, J.R. Moro, Thin Solid Films 76 (3) (2005) 246. [7] E. Colineau, E. Gheeraert, A. Deneuville, J. Mambou, F. Brunet, J.P. Lagrange, Diamond Relat. Mater. 6 (5–7) (1997) 778. [8] P. Gonon, E. Gheeraert, A. Deneuville, F. Fontaine, L. Abello, G. Lucazeau, J. Appl. Phys. 78 (12) (1995) 7059. [9] Y. Wang, H. Li, Y. Xiong, S. Zhang, Z. Lin, K. Feng, Diamond Relat. Mater. 9 (9–10) (2000) 1708. [10] F. Pruvost, A. Deneuville, Diamond Relat. Mater. 10 (3–7) (2001) 531. [11] J.T. Huang, W.H. Guo, J. Hwang, H. Chang, Appl. Phys. Lett. 68 (26) (1996) 3784. [12] B. Massarini, J.C. Bourgoin, R.M. Chrenko, Phys. Rev., B 17 (4) (1978) 1758. [13] T. Sato, K. Ohashi, H. Sugai, T. Sumi, K. Haruna, H. Maeta, N. Matsumoto, H. Otsuka, Phys. Rev., B 61 (19) (2000) 12970. [14] A.L. Efros, B.I. Shklovskii, J. Phys. C 8 (1975) L49. [15] N.F. Mott, Metal–Insulator Transitions, Taylor and Francis, London, 1990. [16] Typical thermal response times for the TG 120 AlGaAs LakeShore sensor (which was used as a calibrated sensor in our experiments) are 250 ms (77 K) and 3 s (273 K); http://www.lakeshore.com.
Temperature sensors based on synthetic diamond films Adenilson J. Chiquito a,⁎, Olívia M. Berengue a , Edgar Diagonel a , José C. Galzerani a , João R. Moro b a
Departamento de Física, Universidade Federal de São Carlos, CEP 13565-905, CP 676, Sao Carlos, São Paulo, Brasil b Lab. de Diamantes, Universidade São Francisco, Itatiba, 13231-900, Brasil Received 14 September 2006; received in revised form 29 January 2007; accepted 19 February 2007 Available online 24 February 2007
Abstract The transport properties of synthetic diamond films were studied and the resulting data were applied to the development of a simple device which was used as a temperature sensor. It has been observed that the electrical resistivity follows the variable range hopping conducting process. The sensibility and reliability of the electrical characteristics presented by the sensor were very good in the investigated range of temperatures (10 to 300 K). The sensor reading was unaffected even in the presence of light illumination or magnetic field. © 2007 Elsevier B.V. All rights reserved.
1. Introduction Chemical vapor-deposited CVD diamond films have attracted great attention due to their unusual electrical, optical, and mechanical properties [1]. For instance, it is chemically inert and resistant to the high temperatures, particularly in an environment without oxygen. It is also resistant to α and γ radiations, ultraviolet light, and to nuclear particles. These characteristics make the diamond films ideal systems for different technologic applications (see, for instance, Refs. [2,3]). Artificially synthesized diamond thin films are usually grown by chemical vapor deposition using hot-filament or microwave-plasma techniques [4]. The diamond lattice exhibits a single characteristic Raman-active mode: the triply degenerated phonon which appears as a sharp line at approximately 1332 cm− 1; then its observation is considered as a definitive evidence of diamond growth. The Raman linewidth of polycrystalline CVD diamond films are typically broader (ranging from 5 to 15 cm− 1) because of disorder due to microstrains or chemical defects and they are frequently found shifted by temperature or lattice strain effects [5]. However the development of practicable diamond sensors for different applications has been restricted by a combination of factors like defects inducing slow time responses (mainly in ⁎ Corresponding author. Fax: +55 16 3361 4835. E-mail address: [email protected] (A.J. Chiquito). 0925-9635/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2007.02.012
low doped samples). These effects are due to a complex interplay between bulk trapping centers in CVD materials and the quality of the metal–diamond ohmic contacts used to fabricate the devices. In a recent paper [6] we have shown a comparative study (using Raman spectroscopy) of CVD diamond films searching for growth parameters that could result in high quality doped films. The films thus grown are now used to study some transport properties and the results were applied to the development of a simple device which in turn, was used as a temperature sensor. The sensibility and reliability of the sensor characteristics were very good in the investigated range (10 to 300 K). The sensor readings were unaffected even in the presence of light illumination or magnetic field. 2. Experiment After the growth (details of the procedures were given in Ref. [6]), the samples were characterized by Raman spectroscopy in order to confirm the formation of the diamond films. A sharp diamond peak at 1332 cm− 1 with little non-sp3 background was observed in the Raman spectra of both samples as shown in Fig. 1. The samples which results were displayed in this figure were grown at the same conditions but at different doping levels. As already observed in the literature [6–8], one of the effects of Boron addition is promoting a decrease of the sp2 bonding band as seen in the higher doped sample (Fig. 1). At the same time, the
A.J. Chiquito et al. / Diamond & Related Materials 16 (2007) 1652–1655
1653
3. Results and discussion From Hall measurements the hole density of the samples was determined (p = 2.2 × 1018 cm− 3). In addition, the value μh = 120 cm2/V s was found for the hole mobility. In synthetic diamond films the graphitic phases can contribute to the decrease of the resistivity. However, the doped samples used here were obtained at temperatures in which the non-diamond phases were drastically reduced, as verified by the Raman spectra (Fig. 1). Then, the measured conductivity is mainly due to the Boron doping and not due to the graphitic phases as expected in rich-sp2 synthetic diamond films. The temperature dependent transport measurements were depicted in Fig. 2. The conduction mechanism in the diamond doped samples is controlled by the variable range hopping mechanism (VRH) in a wide range of temperatures as reported by several authors [12,13]. The VRH mechanism is described by the well known equation qðT Þ ¼ q0 exp Fig. 1. Raman spectra of the diamond films. The peak at 1332 cm− 1 indicates the presence of sp3 diamond. The Boron doping level is indicated in the figure.
doping is also shown to provoke the intensity decrease and an asymmetry of the diamond line. These effects have been attributed to a Fano-type interference [9,10] which, in turn, is linked to the increase of free carriers in the structure. The presence of non-diamond bands and other intrinsic defects (as the formation of deep levels and disorder leading to localization of charges) can produce deleterious effects in devices performance. In this way, only the doped sample was used for the transport measurements. Before devices fabrication, the samples were treated with a conventional degrease solution based on trichloroethylene followed by acetone; next, the samples were immersed in a saturated solution of H2SO4/K2CrO4 at 200 °C for 1 h and immediately rinsed in NH4OH/H2O2 solution and deionized water. The electrical contacts were defined by shadow masks and standard lithographic techniques. The metallization (Ti/Au, 50 nm/100 nm) was made in a high vacuum chamber (10− 6 Torr); the devices were then annealed in an inert Ar atmosphere at 600 °C for 10 min. Ohmic electrodes of 100 μm width were also spaced by 100 μm. The films have thicknesses of approximately 20 μm and before the transport experiments the Si substrate was removed by chemical etching in order to avoid current flowing through it [11]. The electrical measurements were made using a standard ac lock-in low frequency (13 Hz) system. The resistivity was measured using the conventional four-probe method and the Van der Pawn geometry was used for Hall measurements. The current in all experiments was limited to 10 μA (when operating as a temperature sensor, the devices were biased with 1 or 10 μA). For temperaturedependent measurements the samples were incorporated to a modified Janis CCS 150 closed cycle cryostat.
m T0 ; T
ð1Þ
where T0 = 2α3 / kBg(EF). Here, g(EF) is the density of states at the Fermi level and α− 1 is the localization length. VRH mechanism normally occurs only in the low temperature region (below room temperature) wherein the energy is insufficient to excite the charge carrier across the Coulomb gap. Hence conduction takes place by hopping of small region (kBT) in the vicinity of the Fermi level where the density of states remains almost a constant (m = 1/4). This condition is fulfilled when the
Fig. 2. Temperature dependence of the resistivity of the samples. The thin solid line shows the fit to the T1/4 law.
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A.J. Chiquito et al. / Diamond & Related Materials 16 (2007) 1652–1655
temperature is sufficiently small or when the energy states are uniformly distributed. Additionally, if one consider the longrange Coulomb interactions, the exponent m in Eq. (1) should be replaced by 1/2 [14]. The fitting of Eq. (1) to the experimental data is shown in Fig. 2. The agreement of both theoretical and experimental curves in a large range of temperatures confirms that the transport in our samples is governed by the variable range hopping process. Also, the fit procedure has provided 6.6 K1/4 for the slope (T0)1/4. The calculated value for the slope is very different [(T0)1/4 = 67 K1/4] when the Bohr radius for Boron atoms is used as the localization length (α− 1 = 0.3 nm). In fact, this is a very naive assumption: the Mott VRH theory [15] is valid when the distance which a carrier moves (hops) is greater than the nearest neighbor distance. If we consider that the energy states are uniformly distributed, the localization length of the wavefunction describing the carriers will exceed the typical Bohr radius and the calculation of T0 will give a wrong result. Using the experimental value, the localization length was found to be ≈ 6 nm which is a reasonable value for the spatial extention of the carrier's wavefunction. After the electrical characterization, the samples were mounted in a special support together to calibrated temperature sensors. Fig. 3 shows four thermal cycles of resistivity obtained for the doped sample with and without external excitations (magnetic field). The curves were shifted up for clearness because they are identical whatever B = 0 or B = 1 T. The reproducibility of the curves were extensively tested, using different cryogenic systems and different excitation currents (1 μA–10 mA). The results presented in Fig. 3 remained
Fig. 4. Sensitivity and resolution of the implemented diamond sensors. In the insert are presented the thermal response time for 77 K and 273 K for the sample.
unchanged (current levels greater than 1 mA provoke undesirable heating). The temperature reading was made by a LakeShore 331S temperature controller using two calibrated TG120 GaAlAs sensors (provided by LakeShore Cryogenics). Each curve contains approximately 3000 experimental points taken during the cooldown and the warm-up cycles. The difference between the signal readings for two consecutive cycles is very low (0.4%). These measurements were repeated under white light illumination (halogen lamp, 150 W) and the results were unchanged (not shown). Sensitivity, resolution and time response are fundamental features for thermometry devices and can be presented in a variety of ways. Typically, the sensitivity is given in terms of the signal sensitivity, which is the change in a measured parameter per change in temperature (in our case, V/K). It is interesting to be noted that when comparing different resistance sensors, an useful material parameter to consider is the dimensionless sensitivity, given as S¼
Fig. 3. Voltage response of the diamond sensor for four thermal cycles measured using I = 1 μA. Panel (a) shows the results without applied magnetic field and panel (b) with magnetic field. The arrows indicate cooling or warming processes and the curves were shifted up for clearness.
dðlnV Þ dðlnT Þ
ð2Þ
where the logarithmic derivatives are calculated using the experimental V versus T curves. By the other hand, the temperature resolution is the smallest temperature difference that can be determined by the sensor (in fact, it is a combination of sensor sensitivity and instrument resolution). It can be expressed as the ratio ΔT/T. In Fig. 4 we show the dimensionless sensitivity and the resolution as a function of the temperature. Thermal response times are determined by physical construction material and mass of the temperature-sensing element. The diamond is a good thermal conductor (five times better than cooper [1]), then becoming a very good sensor. We measured the thermal response
A.J. Chiquito et al. / Diamond & Related Materials 16 (2007) 1652–1655
of ours at usual temperatures (77 K, 273 K) and the results were presented as an insert for Fig. 4. The samples presented a relatively fast thermal response [16]. This fact becomes more important if we taking into account that the electrical contacts geometry and the size (and mass) of the sensor were not optimized for the construction of a device ready for use. The wellbehaved dependence for both voltage reading and sensitivity on the temperature demonstrate the viability of the doped diamond films as a temperature sensor even in the presence of light or magnetic fields. 4. Conclusion In conclusion, we have produced reliable temperature sensors based on thin synthetic diamond films. In addition we have described the transport processes which took place in these films, confirming the variable range hopping as the dominant conduction mechanism. The influence of external parameters such as magnetic field and light were not observed. The geometry of the devices (coplanar electrodes), the well known transport mechanism and the reproducibility of the measurements are surely the most interesting aspects of these sensors. Acknowledgements We would like to thank E. Diagonel for your useful help in the patterning process of the sensors. This work was supported in part by the Brazilian Agencies FAPESP and CNPq.
1655
References [1] J.E. Field, The Properties of Diamond, Academic Press, New York, 1979. [2] T. Hantschel, P. Niedermann, T. Trenkler, W. Vandervorstc, Appl. Phys. Lett. 76 (12) (2000) 1603. [3] P.J. Sellina, A. Galbiati, Appl. Phys. Lett. 87 (9) (2005) 093502. [4] K. Kobashi, K. Nishimura, Y. Kawate, T. Horiuchi, Phys. Rev., B 38 (6) (1988) 4067. [5] J.W. Ager III, D.K. Veirs, G.M. Rosenblatt, Phys. Rev., B 43 (8) (1991) 6491. [6] W. Fortunato, A.J. Chiquito, J.C. Galzerani, J.R. Moro, Thin Solid Films 76 (3) (2005) 246. [7] E. Colineau, E. Gheeraert, A. Deneuville, J. Mambou, F. Brunet, J.P. Lagrange, Diamond Relat. Mater. 6 (5–7) (1997) 778. [8] P. Gonon, E. Gheeraert, A. Deneuville, F. Fontaine, L. Abello, G. Lucazeau, J. Appl. Phys. 78 (12) (1995) 7059. [9] Y. Wang, H. Li, Y. Xiong, S. Zhang, Z. Lin, K. Feng, Diamond Relat. Mater. 9 (9–10) (2000) 1708. [10] F. Pruvost, A. Deneuville, Diamond Relat. Mater. 10 (3–7) (2001) 531. [11] J.T. Huang, W.H. Guo, J. Hwang, H. Chang, Appl. Phys. Lett. 68 (26) (1996) 3784. [12] B. Massarini, J.C. Bourgoin, R.M. Chrenko, Phys. Rev., B 17 (4) (1978) 1758. [13] T. Sato, K. Ohashi, H. Sugai, T. Sumi, K. Haruna, H. Maeta, N. Matsumoto, H. Otsuka, Phys. Rev., B 61 (19) (2000) 12970. [14] A.L. Efros, B.I. Shklovskii, J. Phys. C 8 (1975) L49. [15] N.F. Mott, Metal–Insulator Transitions, Taylor and Francis, London, 1990. [16] Typical thermal response times for the TG 120 AlGaAs LakeShore sensor (which was used as a calibrated sensor in our experiments) are 250 ms (77 K) and 3 s (273 K); http://www.lakeshore.com.