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Characterization of thermal conductivity in thin film multilayered membranes
Thin Solid Films 484 (2005) 328 – 333 www.elsevier.com/locate/tsf
Characterization of thermal conductivity in thin film multilayered membranes N. Sabate´T, J. Santander, I. Gra`cia, L. Fonseca, E. Figueras, E. Cabruja, C. Cane´ Centre Nacional de Microelectro`nica CNM-IMB, Campus UAB, 08193 Bellaterra, Barcelona, Spain Received 2 April 2004; received in revised form 19 January 2005; accepted in revised form 24 January 2005 Available online 7 March 2005
Abstract In this paper we propose a novel approach for the thermal conductivity determination in thermal membrane-based devices. In the presented methodology, the fitting of experimental and simulated thermal dissipation of two resistive elements is used to characterize both the materials composing the membrane structure and the material used in the heating element patterning. The determination of this parameter, usually disregarded in most of the analysis, leads to a complete characterization of the structure and represents an improvement, as a better accuracy in the thermal properties of the membrane under study can be achieved. To demonstrate its effectiveness, the method has been applied to a already-fabricated flow sensor structure. D 2005 Elsevier B.V. All rights reserved. PACS: 07.10.C Keywords: Thermal conductivity; Membranes; Micromechanical devices; Multilayers
1. Introduction The power consumption of a thermal-effect based sensor depends on the fabrication materials as well as on a proper design. However, the optimisation of the sensor operation features at the design level requires the previous knowledge of the thermal properties of the materials that are going to be implemented in the structure. Due to their low thermal and electrical conductivity and its availability in standard microelectronic fabrication technologies, Si3N4 and SiO2 have been widely used in micromachined structures [1–5]. Nevertheless, the variety of reported values of thermal conductivity of these materials when deposited as thin-film layers provides evidence of their dependence both on the type of deposition process—Low Pressure Chemical Vapour Deposition (LPCVD), Plasma Enhanced Chemical Vapour Deposition (PECVD), etc—and on their processing parameters [6] (temperature, gas concentration, pressure. . .).
T Corresponding author. Tel.: +34 935947700; fax: +34 935801496. E-mail address: [email protected] (N. Sabate´). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.01.085
Values between 1.1 [7] and 1.4 W m1 K1 [8] have been reported for SiO2 whereas values from 2.3 [9] to 25–30 W m1 K1 [8] can be found for Si3N4 in the literature. As a result, if the power consumption of a particular sensor structure is to be optimized at a design level, the strong dependence of thermal conductivity values on the fabrication process raises the need of characterizing the specific implemented layers. In most of the reported studies about thermal conductivity in dielectric and metallic thin films, layers under study have been deposited on silicon substrates [10–12]. Nevertheless, in the Microsystems (MEMS) field, some authors have proposed the fabrication of micromachined test structures, so the thermal dissipation of a thermistor placed on these structures can be approached by means of analytical calculus. However, this method requires the onpurpose fabrication of high isolated structures such as cantilevers beams or suspended bridges with a very particular geometry [13–15]. Alternatively, the determination of physical properties in more complex structures that cannot be solved analytically can also be approached by means of mathematical simulations. Nowadays, a wide
N. Sabate´ et al. / Thin Solid Films 484 (2005) 328–333
Fig. 1. Thermal dissipation mechanisms in a micromachined structure.
range of commercial simulation programs have arisen as a powerful design tool for the MEMS community. In this sense, the physical parameters of a theoretical model reproducing accurately the sensor working conditions can be tuned to fit the experimental thermal behaviour. Examples of this approach can be consulted in recent works, in which some authors have used simulation results from software based on Finite Element (FE) method of calculus to fit the temperature distribution in gas sensor membranes [16 17]. Generally, experimental data is obtained by scanning the sensor membrane with an Atomic Force Microscope (AFM) temperature probe or by recording the temperature distribution with an infrared camera. In this paper, a new method of performing the comparison between experimental and simulation data for obtaining thermal conductivities in a set of sensor membranes is presented. The proposed method is based on the fitting of experimental and simulated thermal dissipation of a calorimetric flow sensor consisting of three resistive elements when working in vacuum conditions. As will be shown, this method not only takes benefit of already-fabricated structures but also simplifies the simulation model and increases the accuracy of the obtained results.
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temperatures are kept below 250 8C, so radiation phenomena can be disregarded without a significant change in thermal isolation. Moreover, as our sample is placed in a vacuum chamber, the effects of heat conduction and convection through air can be discarded. Thus, power dissipation occurs only by means of thermal conduction through the layers to be characterized, that is, the layers composing the micromachined membrane. The restriction of the simulation model to a solid structure decreases the number of unknown quantities. Moreover, the obtained solution from a FE simulation model is very sensitive to the properties of the modelled surrounding air and usually, the setting of realistic boundary conditions is a laborious task. So in this work, the heat dissipation in vacuum of the membrane to be characterized has been measured and fitted to a FE model with the aim of determining the thermal conductivity of the membrane materials. The total heat flow Q through the sensor structure can be expressed as: Q ¼ GS kS ðThot Tref Þ
ð1Þ
where G S accounts for geometrical factors, T hot accounts for the temperature generated in the heating resistor, Tref is the temperature of the silicon rim which usually corresponds to the room temperature, Q is the heat related to the power supplied to the heating resistor and k S is the effective thermal conductivity of the structure. T hot and Tref are measured through the resistance value of the polarized resistor and a reference resistor placed on the silicon rim respectively. In this present case, k S is the unknown parameter of the structure, and it depends of the thermal conductivity of the sensor membrane k mem (that can be composed by a single layer or a multilayer) and the thermal conductivity of the heating resistor material k resis, the contribution of which cannot be disregarded, as there will be also thermal losses along its connection tracks. It is clear that, when fitting the experimental dissipation of the central heating resistor with a FE model, the value of k S will be determined, but it would not be possible to determine the
2. Experimental details When supplying power to a heating resistor placed on a micromachined membrane, the heat generated by the Joule effect is dissipated through three different mechanisms: thermal conduction, convection and radiation. Fig. 1 illustrates the thermal dissipation mechanisms in a micromachined structure. In this way, heat is transferred, on one hand, along the membrane by means of thermal conduction through the solid materials and, on the other hand, to the surrounding air by means of conductive and convective mechanisms. In addition to this, when absolute temperatures are high enough, radiation losses turn to be an important mechanism of heat loss. In this study,
Fig. 2. Top-view photograph of one calorimetric flow sensor used in the measurements.
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Fig. 3. Temperature distribution obtained in the membrane by FE simulation (depicted values are in Kelvin degrees). Left: biasing the central resistor. Right: biasing one of the sensing resistors.
corresponding values of k mem and k resis separately. That is, two unknown quantities cannot be determined from a single equation. In order to eliminate this indeterminacy, a new experimental condition is required. In this sense, the threeelement calorimetric flow sensor has a very convenient layout for this purpose: the thermal dissipation of one of the sensing resistors (R sensing) placed at both sides of the central heating resistor (R central) arises as the new required fitting condition. Fig. 2 shows the position of these resistors in a flow sensor membrane. In the present study, all resistors were patterned in a platinum layer. Fig. 3, in which the thermal distribution in the membrane obtained by FE simulation when polarizing R central and R sensing respectively with 1 mW is shown, corroborates that the thermal dissipation varies depending on the position of the resistor. In both cases, thermal conductivity of platinum and nitride were set to 70.0 and 3.0 W/mK respectively as illustrative values. It can be seen that the temperature reached by R sensing is not as high as R central due to the closer location to the silicon rim of R sensing, which produces a
noticeable increase of heat losses. The heat flux through the structure when R sensing is biased and it reaches a temperature T *hot can be expressed as: Q ¼ GTS kS ðT Thot Tref Þ
ð2Þ
Expression (2) provides the second equation required to discriminate between k mem and k resis. As will be shown in next sections, the determination of the thermal conductivity of a membrane composed of a single layer is straightforward and, once this layer is characterized, it is also possible to find the thermal conductivity of additional layers deposited on top.
3. Composition of the characterized layers In order to determine the thermal conductivity of the dielectric layers mainly used in the fabrication of micromachined structures, three different composed membranes were fabricated.
Fig. 4. Cross-sections and thin film thickness of the different measured samples.
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Fig. 3 shows schematically the cross-sections of the fabricated samples type A, B and C. In sample type A, the membrane consisted of a LPCVD Si3N4 which plays the role of mechanical support. The starting material of the membrane-based sensor fabrication is a 100 mm diameter, 350 Am thick, b100N p-type silicon double side polished wafer. Over this substrate a 300 nm thick LPCVD silicon nitride layer is deposited on a thin pad oxide. After the deposition, performed at 800 8C with a residual pressure between 0.25–0.28 mbar, this nitride layer is implanted with boron 41015 at. cm2 in order to reduce its high intrinsic tensile stress. Then, a layer of 250 nm of sputtered platinum is deposited at room temperature. Platinum needs a previous titanium layer of 25 nm to improve its adherence to the nitride. After the patterning of platinum resistors, the process ends with the silicon micromachining of the substrate, which is performed by means of a back side KOH etching. As can be seen in Fig. 4, an additional layer of PECVD SiO2 has been deposited at 380 8C and a pressure of 2.0 mbar after platinum deposition in sample B. This layer is typically used to provide electrical isolation between heater and electrodes in semiconductor gas sensors. Finally, in the case of sample C, this SiO2 passivation layer has been substituted by a three-layer composition made of a combination of PECVD Si3N4, deposited at 380 8C and 2.0 mbar of residual pressure and PECVD SiO2.
4. Determination of thermal conductivities Before starting the thermal characterization of the structures the measurement of the Temperature Coefficient of Resistance (TCR) was performed accurately. Values from 1600 ppm K1 in the passivated resistors to 1850 ppm K1 in the non-passivated samples were encountered, which is again an evidence of the processing dependence of physical properties in thin deposited layers [18,19]. Once the temperature dependence of the resistance was calibrated, the samples were introduced in a vacuum chamber provided with external electrical connections. Table 1 summarizes the thermal isolation of the membrane depending on the biased resistor and the measured samples (average and error have been determined from measurement of three samples). As expected, thermal isolation of resistors depends, not only on the composition of the membrane but also on its location. Table 1 Experimental values of the thermal isolation of R central and R sensing for the different measured samples Sample
dT/dP (K/mW) R (central resistor)
dT/dP (K/mW) R (lateral resistor)
A B C
89.0F1.5 41.6F0.4 53.1F1.8
80.5F0.7 39.5F0.4 46.3F1.4
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Fig. 5. Thermal dissipation obtained experimentally and by FE simulations for different thermal conductivities of the membrane materials.
In order to determine the values of thermal conductivity, a 3D model of the membrane was built with ANSYSn Software. Special care has been taken in the definition of thermal boundary conditions and aspect ratio of solid elements. As the thickness of the modelled membrane is very small compared to the lateral dimensions, it can be considered that temperature across the z dimension is homogeneous. This assumption is valid as long as in-plane heat transport is higher than transport out of the plane. In vacuum conditions and at temperatures below which radiation effects are noticeable, this condition is fulfilled. According to this, a multilayer membrane can be modelled as a single layer with an effective thermal conductivity K ef, which allows us to work with a simplified structure of thickness h ef: Kef ¼
K 1 d h1 þ K 2 d h2 þ . . . þ K n hn hef
The fact that the sensor is placed in a vacuum chamber plays down the difficulty of setting the thermal boundary conditions. In this case, a silicon rim has been added around the membrane and a reference temperature has been set on its edges. The high conductivity of silicon (150 W/m K) makes it an effective heat sink, and reference temperature is reached in the silicon at a very short distance from the membrane ends (Fig. 3). The minimum lateral dimension of the squared silicon rim is established by performing consecutive simulations in which this parameter is enlarged until the temperature distribution in the membrane does not show any significant variation (below 1%). The fitting of thermal conductivities starts with sample A, in which the membrane consists of a single layer of LPCVD nitride. In a first series of thermal simulations the thermal conductivity of nitride has been varied from 1.0 to 20.0 W/m K and platinum has been set between 40 and 75 W/m K. Values for platinum have been decreased from reported bulk value 72 W/m K until a value as low as 40 W/ m K, which is expected to be a lower limit of thermal conductivity for deposited platinum. Fig. 5 shows the intersection of the experimental thermal isolation of resistor
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R central with the simulated values data set. It is clear from the figure that despite the large variation of platinum conductivities, the upper and lower limits of the intersected lines restrict the possible values of LPCVD nitride thermal conductivity in the range of 2.00–2.75 W/m K. The same procedure was performed with R sensing, which provided values for nitride between 2.05 and 2.65 W/m K. It has to be noted that the influence of the thermal conductivity of platinum on the total thermal conductance of the structure is low due to the narrow tracks of the patterned resistors. Thus, a more detailed scan with ANSYSn optimisation tool of the pair of values (K Pt, K nitride) allowed the fitting of the experimental dissipation of R central and R sensing. The results provided two lines the intersection of which supplied the real thermal conductivity values. In Fig. 6 the intersected lines with the corresponding averaged values of thermal conductivity are depicted. Dispersion of values was calculated with the same fitting procedure for the upper and lower experimental values of thermal conductance giving rise to a value of 2.40F0.25 W/m K for LPCVD Si3N4 and 56F10 W/m K for platinum. The high dispersion encountered in platinum thermal conductivity is due to the low influence of resistors in the total thermal conductance of the structure. In any case, the calculated value for thin-film platinum is lower that its bulk value (72 W/m K). In this sense, it has to be noted that if the determination of the thermal conductivity of the membrane had been performed by setting the thermal conductivity of platinum to the mentioned bulk value and therefore fitting only the thermal dissipation of one resistor (as carried out by other authors [19]), the result for the nitride layer conductivity had yield 2.10 W/m K which is significantly lower. This can be checked in Fig. 6 in which the intersection of k Pt=72 W/m K with the thermal dissipation of R central depicted. Furthermore, effective thermal conductivity of membranes was also calculated for samples type B and C with the proposed methodology, and thermal conductivity values for the single layers was extracted from expression (1).
Fig. 6. Experimental dissipation fitting of R central and R sensing obtained from an ANSYS detailed scan. The intersection point shows the real thermal conductivity values of the nitride and platinum.
Table 2 Experimental thermal conductivity values of the membrane materials Material layer
Thermal conductivity (W/m K)
LPCVD Si3N4 (Boron implanted) PECVD Si3N4 PECVD SiO2 Platinum
2.40F0.25 1.8F0.5 1.55F0.15 56F10
Table 2 shows the results for all the fabrication layers. Note that the error associate to PECVD Si3N4 layer is around 20%. The high dispersion in this value is due to error propagation, since as in the computation of the thermal conductivity of this specific layer the values of the rest of the layers are required, and to the small thickness of the measured layer. 4.1. Validation of reported values The obtaining of the thermal conductivity values of the fabrication materials is of great interest regarding the optimisation of power consumption of sensors based on thermal principles. That is, once the thermal properties are known, they can be introduced in the simulation model in order to, on one hand, validate the values obtained with the presented methodology and, on the other hand, to ensure that our model reproduces real operational conditions of the structure. With the aim of reproducing operation conditions the simulation model was enlarged by the addition of surrounding air (k=0.0264 W/m K). The temperature distribution obtained when a applying 1 mW to the central resistor in sample A is shown in Fig. 7. In Fig. 8, the experimental results and simulation data for the dissipation of the central resistor of sample type A in vacuum and in operation conditions are compared. First of all, it can be observed that there is an important increase in power consumption when the sample is surrounded by air. Secondly, the good agreement of experience and simulation
Fig. 7. Temperature distribution around the central resistor when operated in ambient atmosphere (depicted values are in Kelvin degrees).
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the thermal conductivity values of the rest of the layers composing the membrane. 6. Conclusions
Fig. 8. Experimental thermal dissipation in vacuum and in air conditions.
of the sensor data in real operation conditions allows for the validation of the thermal conductivity values obtained with this new approach.
5. Discussion In the present paper the feasibility of a novel approach to thermal conductivity characterization has been faced by using an already-fabricated flow sensor structure. However, this method can be exported to any type of membrane-based thermal sensor whenever two dissipating elements are properly placed on the membrane under study. Although the fitting of experimental and simulated data coming from the thermal dissipation of a heating element has been already used by other authors, the present approach allows the determination of not only the thermal conductivity of the membrane but also the thermal conductivity of the material used in the patterning of the heating element, which in some cases cannot be determined by standard methods (i.e. Wiedemann–Franz law) as what happens to be with doped polysilicon [20]. As has been shown, the determination of this parameter leads to a better accuracy of the obtained thermal conductivity values and at the same time, allows the characterization of the total thermal conductance of the sensor structure. As can be observed from the results obtained in this work, the accuracy associated to the thermal conductivity of the thin film layer used in the patterning of sensor resistors (i.e. platinum) is quite poor. However, this value can be determined more accurately by means of a proper variation of the geometrical parameters of the resistors in order to enhance their thermal losses. That is, the greater the influence of the heating element on the total thermal conductance of the structure, the better the accuracy of the obtained results. At the same time, when characterizing a multilayer membrane with this method it must be considered that an increase in the number of layers can lead to a loss of accuracy. This effect, which can be observed for the values obtained in the PECVD Si3N4 layer, is due to the influence of the accumulated error in the determination of
A novel approach for the thermal conductivity determination of a thin film patterned into a membrane or deposited over a membrane is presented. The methodology is based on the fitting between experimental and simulated thermal dissipation under vacuum conditions of two resistors placed on a membrane. In the presented case the proposed methodology has been applied to a calorimetric flow sensor structure. Compared to previous works, the presented method provides not only the thermal conductivity of the membrane materials but also of the metallic layer used in the heating element implementation. The determination of this parameter leads to a better accuracy of the obtained thermal conductivity values and at the same time, allows the characterization of the total thermal conductance of the sensor structure. The method can be generalised to any material patterned into a membrane. Acknowledgment This work has been mainly funded by CICyT Spanish projects (Ref: DPI-2001-3213 and Ref. TIC2001-0554). References [1] N.R. Swart, A. Nathan, Sens. Actuators, A, Phys. 43 (1994) 3. [2] D. Lee, W. Chung, M. Choi, J. Back, Sens. Actuators, B, Chem. 33 (1996) 147. [3] A. Pike, J.W. Gardner, Sens. Actuators, B, Chem. 45 (1997) 19. [4] A. Gftz, I. Gra`cia, C. Cane´, E. Lora-Tamayo, J. Micromechanics Microengineering 7 (1997) 247. [5] I. Simon, N. Baˆrsan, M. Bauer, U. Weimar, Sens. Actuators, B, Chem. 73 (2001) 1. [6] Y.S. Yu, K.E. Goodson, J. Appl. Phys. 85 (10) (1999) 7130. [7] M. Arx, Ph.D. Thesis, ETH Zurich, Switzerland, 1998. [8] M.S. Sze, Physics of Semiconductors Devices, John Wiley and Sons, New York, 1981. [9] W. Lang, IEEE Trans. Electron Devices 17 (4) (1990) 212. [10] D.G. Cahill, T.H. Allen, Appl. Phys. Lett. 65 (3) (1994) 309. [11] S. Lee, D.G. Cahill, J. Appl. Phys. 81 (6) (1997) 2590. [12] M.B. Kleiner, S.A. Kuhn, W. Weber, IEEE Trans. Electron Devices 42 (9) (1996) 1602. [13] A. Irace, P.M. Sarro, Sens. Actuators, A, Phys. 76 (1999) 323. [14] M. Arx, O. Paul, H. Baltes, J. Microelec. Syst. 9 (1) (2000) 136. [15] P. Eriksson, J.Y. Andersson, G. Stemme, J. Microelec. Syst. 6 (1) (1997) 55. [16] C. Calaza, Ph.D.Thesis, Universitat de Barcelona, Spain, 2003. [17] J. Puigcorbe´, D. Vogel, B. Michel, A. Vila`, I. Gra`cia, C. Cane´, J.R. Morante, J. Micromechanics Microengineering 13 (2003) 548. [18] C.I. Popescu, M. Popescu, Thermoresistive Sensors, Thin Film Resistive Sensors, Sensors Series, Institute of Physics Publishing, 1992. [19] F. Mailly, A. Giani, R. Bonnot, P. Temple-Boyer, F. Pascal-Delannoy, A. Foucaran, A. Boyer, Sens. Actuators, A, Phys 94 (1–2) (2001) 32. [20] A.D. Mc Connell, S. Uma, K.E. Goodson, J. Microelec. Syst. 10 (3) (2001) 360.
Characterization of thermal conductivity in thin film multilayered membranes N. Sabate´T, J. Santander, I. Gra`cia, L. Fonseca, E. Figueras, E. Cabruja, C. Cane´ Centre Nacional de Microelectro`nica CNM-IMB, Campus UAB, 08193 Bellaterra, Barcelona, Spain Received 2 April 2004; received in revised form 19 January 2005; accepted in revised form 24 January 2005 Available online 7 March 2005
Abstract In this paper we propose a novel approach for the thermal conductivity determination in thermal membrane-based devices. In the presented methodology, the fitting of experimental and simulated thermal dissipation of two resistive elements is used to characterize both the materials composing the membrane structure and the material used in the heating element patterning. The determination of this parameter, usually disregarded in most of the analysis, leads to a complete characterization of the structure and represents an improvement, as a better accuracy in the thermal properties of the membrane under study can be achieved. To demonstrate its effectiveness, the method has been applied to a already-fabricated flow sensor structure. D 2005 Elsevier B.V. All rights reserved. PACS: 07.10.C Keywords: Thermal conductivity; Membranes; Micromechanical devices; Multilayers
1. Introduction The power consumption of a thermal-effect based sensor depends on the fabrication materials as well as on a proper design. However, the optimisation of the sensor operation features at the design level requires the previous knowledge of the thermal properties of the materials that are going to be implemented in the structure. Due to their low thermal and electrical conductivity and its availability in standard microelectronic fabrication technologies, Si3N4 and SiO2 have been widely used in micromachined structures [1–5]. Nevertheless, the variety of reported values of thermal conductivity of these materials when deposited as thin-film layers provides evidence of their dependence both on the type of deposition process—Low Pressure Chemical Vapour Deposition (LPCVD), Plasma Enhanced Chemical Vapour Deposition (PECVD), etc—and on their processing parameters [6] (temperature, gas concentration, pressure. . .).
T Corresponding author. Tel.: +34 935947700; fax: +34 935801496. E-mail address: [email protected] (N. Sabate´). 0040-6090/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2005.01.085
Values between 1.1 [7] and 1.4 W m1 K1 [8] have been reported for SiO2 whereas values from 2.3 [9] to 25–30 W m1 K1 [8] can be found for Si3N4 in the literature. As a result, if the power consumption of a particular sensor structure is to be optimized at a design level, the strong dependence of thermal conductivity values on the fabrication process raises the need of characterizing the specific implemented layers. In most of the reported studies about thermal conductivity in dielectric and metallic thin films, layers under study have been deposited on silicon substrates [10–12]. Nevertheless, in the Microsystems (MEMS) field, some authors have proposed the fabrication of micromachined test structures, so the thermal dissipation of a thermistor placed on these structures can be approached by means of analytical calculus. However, this method requires the onpurpose fabrication of high isolated structures such as cantilevers beams or suspended bridges with a very particular geometry [13–15]. Alternatively, the determination of physical properties in more complex structures that cannot be solved analytically can also be approached by means of mathematical simulations. Nowadays, a wide
N. Sabate´ et al. / Thin Solid Films 484 (2005) 328–333
Fig. 1. Thermal dissipation mechanisms in a micromachined structure.
range of commercial simulation programs have arisen as a powerful design tool for the MEMS community. In this sense, the physical parameters of a theoretical model reproducing accurately the sensor working conditions can be tuned to fit the experimental thermal behaviour. Examples of this approach can be consulted in recent works, in which some authors have used simulation results from software based on Finite Element (FE) method of calculus to fit the temperature distribution in gas sensor membranes [16 17]. Generally, experimental data is obtained by scanning the sensor membrane with an Atomic Force Microscope (AFM) temperature probe or by recording the temperature distribution with an infrared camera. In this paper, a new method of performing the comparison between experimental and simulation data for obtaining thermal conductivities in a set of sensor membranes is presented. The proposed method is based on the fitting of experimental and simulated thermal dissipation of a calorimetric flow sensor consisting of three resistive elements when working in vacuum conditions. As will be shown, this method not only takes benefit of already-fabricated structures but also simplifies the simulation model and increases the accuracy of the obtained results.
329
temperatures are kept below 250 8C, so radiation phenomena can be disregarded without a significant change in thermal isolation. Moreover, as our sample is placed in a vacuum chamber, the effects of heat conduction and convection through air can be discarded. Thus, power dissipation occurs only by means of thermal conduction through the layers to be characterized, that is, the layers composing the micromachined membrane. The restriction of the simulation model to a solid structure decreases the number of unknown quantities. Moreover, the obtained solution from a FE simulation model is very sensitive to the properties of the modelled surrounding air and usually, the setting of realistic boundary conditions is a laborious task. So in this work, the heat dissipation in vacuum of the membrane to be characterized has been measured and fitted to a FE model with the aim of determining the thermal conductivity of the membrane materials. The total heat flow Q through the sensor structure can be expressed as: Q ¼ GS kS ðThot Tref Þ
ð1Þ
where G S accounts for geometrical factors, T hot accounts for the temperature generated in the heating resistor, Tref is the temperature of the silicon rim which usually corresponds to the room temperature, Q is the heat related to the power supplied to the heating resistor and k S is the effective thermal conductivity of the structure. T hot and Tref are measured through the resistance value of the polarized resistor and a reference resistor placed on the silicon rim respectively. In this present case, k S is the unknown parameter of the structure, and it depends of the thermal conductivity of the sensor membrane k mem (that can be composed by a single layer or a multilayer) and the thermal conductivity of the heating resistor material k resis, the contribution of which cannot be disregarded, as there will be also thermal losses along its connection tracks. It is clear that, when fitting the experimental dissipation of the central heating resistor with a FE model, the value of k S will be determined, but it would not be possible to determine the
2. Experimental details When supplying power to a heating resistor placed on a micromachined membrane, the heat generated by the Joule effect is dissipated through three different mechanisms: thermal conduction, convection and radiation. Fig. 1 illustrates the thermal dissipation mechanisms in a micromachined structure. In this way, heat is transferred, on one hand, along the membrane by means of thermal conduction through the solid materials and, on the other hand, to the surrounding air by means of conductive and convective mechanisms. In addition to this, when absolute temperatures are high enough, radiation losses turn to be an important mechanism of heat loss. In this study,
Fig. 2. Top-view photograph of one calorimetric flow sensor used in the measurements.
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Fig. 3. Temperature distribution obtained in the membrane by FE simulation (depicted values are in Kelvin degrees). Left: biasing the central resistor. Right: biasing one of the sensing resistors.
corresponding values of k mem and k resis separately. That is, two unknown quantities cannot be determined from a single equation. In order to eliminate this indeterminacy, a new experimental condition is required. In this sense, the threeelement calorimetric flow sensor has a very convenient layout for this purpose: the thermal dissipation of one of the sensing resistors (R sensing) placed at both sides of the central heating resistor (R central) arises as the new required fitting condition. Fig. 2 shows the position of these resistors in a flow sensor membrane. In the present study, all resistors were patterned in a platinum layer. Fig. 3, in which the thermal distribution in the membrane obtained by FE simulation when polarizing R central and R sensing respectively with 1 mW is shown, corroborates that the thermal dissipation varies depending on the position of the resistor. In both cases, thermal conductivity of platinum and nitride were set to 70.0 and 3.0 W/mK respectively as illustrative values. It can be seen that the temperature reached by R sensing is not as high as R central due to the closer location to the silicon rim of R sensing, which produces a
noticeable increase of heat losses. The heat flux through the structure when R sensing is biased and it reaches a temperature T *hot can be expressed as: Q ¼ GTS kS ðT Thot Tref Þ
ð2Þ
Expression (2) provides the second equation required to discriminate between k mem and k resis. As will be shown in next sections, the determination of the thermal conductivity of a membrane composed of a single layer is straightforward and, once this layer is characterized, it is also possible to find the thermal conductivity of additional layers deposited on top.
3. Composition of the characterized layers In order to determine the thermal conductivity of the dielectric layers mainly used in the fabrication of micromachined structures, three different composed membranes were fabricated.
Fig. 4. Cross-sections and thin film thickness of the different measured samples.
N. Sabate´ et al. / Thin Solid Films 484 (2005) 328–333
Fig. 3 shows schematically the cross-sections of the fabricated samples type A, B and C. In sample type A, the membrane consisted of a LPCVD Si3N4 which plays the role of mechanical support. The starting material of the membrane-based sensor fabrication is a 100 mm diameter, 350 Am thick, b100N p-type silicon double side polished wafer. Over this substrate a 300 nm thick LPCVD silicon nitride layer is deposited on a thin pad oxide. After the deposition, performed at 800 8C with a residual pressure between 0.25–0.28 mbar, this nitride layer is implanted with boron 41015 at. cm2 in order to reduce its high intrinsic tensile stress. Then, a layer of 250 nm of sputtered platinum is deposited at room temperature. Platinum needs a previous titanium layer of 25 nm to improve its adherence to the nitride. After the patterning of platinum resistors, the process ends with the silicon micromachining of the substrate, which is performed by means of a back side KOH etching. As can be seen in Fig. 4, an additional layer of PECVD SiO2 has been deposited at 380 8C and a pressure of 2.0 mbar after platinum deposition in sample B. This layer is typically used to provide electrical isolation between heater and electrodes in semiconductor gas sensors. Finally, in the case of sample C, this SiO2 passivation layer has been substituted by a three-layer composition made of a combination of PECVD Si3N4, deposited at 380 8C and 2.0 mbar of residual pressure and PECVD SiO2.
4. Determination of thermal conductivities Before starting the thermal characterization of the structures the measurement of the Temperature Coefficient of Resistance (TCR) was performed accurately. Values from 1600 ppm K1 in the passivated resistors to 1850 ppm K1 in the non-passivated samples were encountered, which is again an evidence of the processing dependence of physical properties in thin deposited layers [18,19]. Once the temperature dependence of the resistance was calibrated, the samples were introduced in a vacuum chamber provided with external electrical connections. Table 1 summarizes the thermal isolation of the membrane depending on the biased resistor and the measured samples (average and error have been determined from measurement of three samples). As expected, thermal isolation of resistors depends, not only on the composition of the membrane but also on its location. Table 1 Experimental values of the thermal isolation of R central and R sensing for the different measured samples Sample
dT/dP (K/mW) R (central resistor)
dT/dP (K/mW) R (lateral resistor)
A B C
89.0F1.5 41.6F0.4 53.1F1.8
80.5F0.7 39.5F0.4 46.3F1.4
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Fig. 5. Thermal dissipation obtained experimentally and by FE simulations for different thermal conductivities of the membrane materials.
In order to determine the values of thermal conductivity, a 3D model of the membrane was built with ANSYSn Software. Special care has been taken in the definition of thermal boundary conditions and aspect ratio of solid elements. As the thickness of the modelled membrane is very small compared to the lateral dimensions, it can be considered that temperature across the z dimension is homogeneous. This assumption is valid as long as in-plane heat transport is higher than transport out of the plane. In vacuum conditions and at temperatures below which radiation effects are noticeable, this condition is fulfilled. According to this, a multilayer membrane can be modelled as a single layer with an effective thermal conductivity K ef, which allows us to work with a simplified structure of thickness h ef: Kef ¼
K 1 d h1 þ K 2 d h2 þ . . . þ K n hn hef
The fact that the sensor is placed in a vacuum chamber plays down the difficulty of setting the thermal boundary conditions. In this case, a silicon rim has been added around the membrane and a reference temperature has been set on its edges. The high conductivity of silicon (150 W/m K) makes it an effective heat sink, and reference temperature is reached in the silicon at a very short distance from the membrane ends (Fig. 3). The minimum lateral dimension of the squared silicon rim is established by performing consecutive simulations in which this parameter is enlarged until the temperature distribution in the membrane does not show any significant variation (below 1%). The fitting of thermal conductivities starts with sample A, in which the membrane consists of a single layer of LPCVD nitride. In a first series of thermal simulations the thermal conductivity of nitride has been varied from 1.0 to 20.0 W/m K and platinum has been set between 40 and 75 W/m K. Values for platinum have been decreased from reported bulk value 72 W/m K until a value as low as 40 W/ m K, which is expected to be a lower limit of thermal conductivity for deposited platinum. Fig. 5 shows the intersection of the experimental thermal isolation of resistor
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R central with the simulated values data set. It is clear from the figure that despite the large variation of platinum conductivities, the upper and lower limits of the intersected lines restrict the possible values of LPCVD nitride thermal conductivity in the range of 2.00–2.75 W/m K. The same procedure was performed with R sensing, which provided values for nitride between 2.05 and 2.65 W/m K. It has to be noted that the influence of the thermal conductivity of platinum on the total thermal conductance of the structure is low due to the narrow tracks of the patterned resistors. Thus, a more detailed scan with ANSYSn optimisation tool of the pair of values (K Pt, K nitride) allowed the fitting of the experimental dissipation of R central and R sensing. The results provided two lines the intersection of which supplied the real thermal conductivity values. In Fig. 6 the intersected lines with the corresponding averaged values of thermal conductivity are depicted. Dispersion of values was calculated with the same fitting procedure for the upper and lower experimental values of thermal conductance giving rise to a value of 2.40F0.25 W/m K for LPCVD Si3N4 and 56F10 W/m K for platinum. The high dispersion encountered in platinum thermal conductivity is due to the low influence of resistors in the total thermal conductance of the structure. In any case, the calculated value for thin-film platinum is lower that its bulk value (72 W/m K). In this sense, it has to be noted that if the determination of the thermal conductivity of the membrane had been performed by setting the thermal conductivity of platinum to the mentioned bulk value and therefore fitting only the thermal dissipation of one resistor (as carried out by other authors [19]), the result for the nitride layer conductivity had yield 2.10 W/m K which is significantly lower. This can be checked in Fig. 6 in which the intersection of k Pt=72 W/m K with the thermal dissipation of R central depicted. Furthermore, effective thermal conductivity of membranes was also calculated for samples type B and C with the proposed methodology, and thermal conductivity values for the single layers was extracted from expression (1).
Fig. 6. Experimental dissipation fitting of R central and R sensing obtained from an ANSYS detailed scan. The intersection point shows the real thermal conductivity values of the nitride and platinum.
Table 2 Experimental thermal conductivity values of the membrane materials Material layer
Thermal conductivity (W/m K)
LPCVD Si3N4 (Boron implanted) PECVD Si3N4 PECVD SiO2 Platinum
2.40F0.25 1.8F0.5 1.55F0.15 56F10
Table 2 shows the results for all the fabrication layers. Note that the error associate to PECVD Si3N4 layer is around 20%. The high dispersion in this value is due to error propagation, since as in the computation of the thermal conductivity of this specific layer the values of the rest of the layers are required, and to the small thickness of the measured layer. 4.1. Validation of reported values The obtaining of the thermal conductivity values of the fabrication materials is of great interest regarding the optimisation of power consumption of sensors based on thermal principles. That is, once the thermal properties are known, they can be introduced in the simulation model in order to, on one hand, validate the values obtained with the presented methodology and, on the other hand, to ensure that our model reproduces real operational conditions of the structure. With the aim of reproducing operation conditions the simulation model was enlarged by the addition of surrounding air (k=0.0264 W/m K). The temperature distribution obtained when a applying 1 mW to the central resistor in sample A is shown in Fig. 7. In Fig. 8, the experimental results and simulation data for the dissipation of the central resistor of sample type A in vacuum and in operation conditions are compared. First of all, it can be observed that there is an important increase in power consumption when the sample is surrounded by air. Secondly, the good agreement of experience and simulation
Fig. 7. Temperature distribution around the central resistor when operated in ambient atmosphere (depicted values are in Kelvin degrees).
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the thermal conductivity values of the rest of the layers composing the membrane. 6. Conclusions
Fig. 8. Experimental thermal dissipation in vacuum and in air conditions.
of the sensor data in real operation conditions allows for the validation of the thermal conductivity values obtained with this new approach.
5. Discussion In the present paper the feasibility of a novel approach to thermal conductivity characterization has been faced by using an already-fabricated flow sensor structure. However, this method can be exported to any type of membrane-based thermal sensor whenever two dissipating elements are properly placed on the membrane under study. Although the fitting of experimental and simulated data coming from the thermal dissipation of a heating element has been already used by other authors, the present approach allows the determination of not only the thermal conductivity of the membrane but also the thermal conductivity of the material used in the patterning of the heating element, which in some cases cannot be determined by standard methods (i.e. Wiedemann–Franz law) as what happens to be with doped polysilicon [20]. As has been shown, the determination of this parameter leads to a better accuracy of the obtained thermal conductivity values and at the same time, allows the characterization of the total thermal conductance of the sensor structure. As can be observed from the results obtained in this work, the accuracy associated to the thermal conductivity of the thin film layer used in the patterning of sensor resistors (i.e. platinum) is quite poor. However, this value can be determined more accurately by means of a proper variation of the geometrical parameters of the resistors in order to enhance their thermal losses. That is, the greater the influence of the heating element on the total thermal conductance of the structure, the better the accuracy of the obtained results. At the same time, when characterizing a multilayer membrane with this method it must be considered that an increase in the number of layers can lead to a loss of accuracy. This effect, which can be observed for the values obtained in the PECVD Si3N4 layer, is due to the influence of the accumulated error in the determination of
A novel approach for the thermal conductivity determination of a thin film patterned into a membrane or deposited over a membrane is presented. The methodology is based on the fitting between experimental and simulated thermal dissipation under vacuum conditions of two resistors placed on a membrane. In the presented case the proposed methodology has been applied to a calorimetric flow sensor structure. Compared to previous works, the presented method provides not only the thermal conductivity of the membrane materials but also of the metallic layer used in the heating element implementation. The determination of this parameter leads to a better accuracy of the obtained thermal conductivity values and at the same time, allows the characterization of the total thermal conductance of the sensor structure. The method can be generalised to any material patterned into a membrane. Acknowledgment This work has been mainly funded by CICyT Spanish projects (Ref: DPI-2001-3213 and Ref. TIC2001-0554). References [1] N.R. Swart, A. Nathan, Sens. Actuators, A, Phys. 43 (1994) 3. [2] D. Lee, W. Chung, M. Choi, J. Back, Sens. Actuators, B, Chem. 33 (1996) 147. [3] A. Pike, J.W. Gardner, Sens. Actuators, B, Chem. 45 (1997) 19. [4] A. Gftz, I. Gra`cia, C. Cane´, E. Lora-Tamayo, J. Micromechanics Microengineering 7 (1997) 247. [5] I. Simon, N. Baˆrsan, M. Bauer, U. Weimar, Sens. Actuators, B, Chem. 73 (2001) 1. [6] Y.S. Yu, K.E. Goodson, J. Appl. Phys. 85 (10) (1999) 7130. [7] M. Arx, Ph.D. Thesis, ETH Zurich, Switzerland, 1998. [8] M.S. Sze, Physics of Semiconductors Devices, John Wiley and Sons, New York, 1981. [9] W. Lang, IEEE Trans. Electron Devices 17 (4) (1990) 212. [10] D.G. Cahill, T.H. Allen, Appl. Phys. Lett. 65 (3) (1994) 309. [11] S. Lee, D.G. Cahill, J. Appl. Phys. 81 (6) (1997) 2590. [12] M.B. Kleiner, S.A. Kuhn, W. Weber, IEEE Trans. Electron Devices 42 (9) (1996) 1602. [13] A. Irace, P.M. Sarro, Sens. Actuators, A, Phys. 76 (1999) 323. [14] M. Arx, O. Paul, H. Baltes, J. Microelec. Syst. 9 (1) (2000) 136. [15] P. Eriksson, J.Y. Andersson, G. Stemme, J. Microelec. Syst. 6 (1) (1997) 55. [16] C. Calaza, Ph.D.Thesis, Universitat de Barcelona, Spain, 2003. [17] J. Puigcorbe´, D. Vogel, B. Michel, A. Vila`, I. Gra`cia, C. Cane´, J.R. Morante, J. Micromechanics Microengineering 13 (2003) 548. [18] C.I. Popescu, M. Popescu, Thermoresistive Sensors, Thin Film Resistive Sensors, Sensors Series, Institute of Physics Publishing, 1992. [19] F. Mailly, A. Giani, R. Bonnot, P. Temple-Boyer, F. Pascal-Delannoy, A. Foucaran, A. Boyer, Sens. Actuators, A, Phys 94 (1–2) (2001) 32. [20] A.D. Mc Connell, S. Uma, K.E. Goodson, J. Microelec. Syst. 10 (3) (2001) 360.