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Thin-film aerogel thermal conductivity measurements via 3ω
Journal of Non-Crystalline Solids 357 (2011) 2960–2965
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Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Thin-film aerogel thermal conductivity measurements via 3ω M.L. Bauer a,⁎, C.M. Bauer a, M.C. Fish a, R.E. Matthews b, G.T. Garner a, A.W. Litchenberger b, P.M. Norris a a b
Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746, USA Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904-4746, USA
a r t i c l e
i n f o
Article history: Received 16 December 2010 Received in revised form 29 March 2011 Available online 30 April 2011 Keywords: Thin-film aerogel; Thermal conductivity; 3ω technique
a b s t r a c t The limiting constraint in a growing number of nano systems is the inability to thermally tune devices. Silica aerogel is widely accepted as the best solid thermal insulator in existence and offers a promising solution for microelectronic systems needing superior thermal isolation. In this study, thin-film silica aerogel films varying in thickness from 250 to 1280 nm were deposited on SiO2 substrates under a variety of deposition conditions. These samples were then thermally characterized using the 3ω technique. Deposition processes for depositing the 3ω testing mask to the sample were optimized and it was demonstrated that thin-film aerogel can maintain its structure in common fabrication processes for microelectromechanical systems. Results indicate that thin-film silica aerogel can maintain the unique, ultra-low thermal conductivity commonly observed in bulk aerogel, with a directly measured thermal conductivity as low as 0.024 W/m-K at temperature of 295 K and pressure between 0.1 and 1 Pa. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Bulk silica aerogel is a two phase porous material with the lowest recorded density and thermal conductivity of any solid. In terms of space occupied, the host material can be as little as 0.01% of the structure with the remainder comprised of air [1,2]. The host, which can be a large variety of materials including silica, alumina [3], clay [4], or carbon nanotubes [5], is a complicated web of interconnects that gives the composite its structure. Since 1934 researchers have studied bulk aerogel thermal properties [6]. Bulk silica aerogels have been shown to have thermal conductivities ranging from as low as 0.006 W/mK [7] (at atmospheric pressure and a temperature of 300 K) to an upper limit approaching the thermal conductivity of amorphous quartz. More recently, aerogels have been successfully manufactured in a variety of forms including microspheres [8], thin films [9], flexible sheets (x-aerogels) [10,11], and photo-luminescent chalcogenides [12], each requiring unique fabrication processes. Integrating thermal insulation into microelectromechanical systems (MEMS) broadens the possible applications of devices that require (or whose performance would be enhanced by) stable elevated temperature. The power needed to maintain a desired component at an elevated temperature is a direct function of the thermal properties of the material thermally insulating it. In general, minimizing the requisite power is advantageous. By incorporating the
⁎ Corresponding author. Tel.: + 1 4342491296. E-mail address: [email protected] (M.L. Bauer). 0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.03.042
insulation directly as part of the die, the area of the MEMS device that needs to be kept at an increased temperature can be separated at the processing stage from that which does not need additional heating. Alternatives include using hybrid dies or complex mounting schemes to thermally isolate components. Extending the integration to include selective or overall thermal insulation would facilitate the manufacture of cheaper, temperature-stabilized devices. Thin-film silica aerogels undergo unique deposition processes [9] to recreate their bulk counterparts with micro or nano-scale dimensions. The most definitive way to understand the effects of these various deposition methods on thermal properties is to directly measure the thermal conductivity of thin film samples. This has proven difficult for a variety of reasons. The ease with which the silica network can collapse increases the difficulty of applying standard microfabrication techniques and decreases the variety of experiments that can be used to characterize such samples. Microscale thermal characterization techniques are not trivial to implement. Thin-film heater techniques have previously been used to measure the thermal properties of bulk aerogels [7]. Steady state techniques, however, are not optimal for thin-film measurements as they offer little sensitivity for characterizing an individual thin film in multilayer samples, and generally they require significant fabrication on the sample. Alternatively, an optical technique such as a pump probe based experiment [13] with a reflective capping layer added to the aerogel may be a viable method for thermally characterizing aerogel films. But great care must be taken to ensure sensitivity to the thermal conductivity of the film of interest independent of other thermal properties such as boundary resistances. Furthermore, quantifying the heat deposited by the perturbating signal can be difficult.
M.L. Bauer et al. / Journal of Non-Crystalline Solids 357 (2011) 2960–2965
Alternatively, the 3ω technique was chosen for this study in which a metal wire serves as a frequency varying heat source and means to measure temperature. This technique was originally used to measure the thermal conductivity of bulk solids over a wide temperature range [14]. It was then adapted to measure thin films deposited on a substrate of known properties [15]. Subsequently the technique was expanded to measure superlattices [16], fluids [17] and carbon nanotube arrays [18].While the 3ω technique has also been utilized to measure properties of porous materials such as bulk xerogels [19] and 55% porous aerogel films with thermal conductivities as low as 0.14 W/mK [20] this study reports the first use of 3ω for determining the thermal conductivity of high porosity silica aerogel films. The 3ω technique was advantageous for this study due to its sensitivity to individual layers in multilayer structures [21,22], high accuracy and repeatability [13], and its ability to eliminate convective as well as radiative error [23]. 2. Materials and methods Resulting aerogel properties are determined largely by the sol–gel process and specifically for thin films by the deposition and drying procedures. Solvent to solute ratios determine the ultimate porosity of the aerogel while reaction time and acid–base catalysts contribute largely to the pore size. Surface modifying agents, as well as temperature and humidity, also play a role in aerogel micro structure formation. For this study, silica aerogel thin films were fabricated using two step acid–base partial hydrolysis/condensation chemistry [24] varying reaction temperature, catalyst type, and catalyst concentration. Several deposition and drying methods were used to prepare the aerogels. Common to each method was the requirement that solvent evaporation be limited during and after gel formation to preserve the tenuous micro structure of the aerogel. 2.1. Sol–gel procedures In the first process the sol–gel precursor solution was made by first combining Tetraethyl orthosilicate (TEOS), EtOH, H2O and HCL in molar ratios of 1.0:4.1:0.9:42 × 10− 6 at 60 °C for ninety minutes to produce prehydrolyzed TEOS solution. Gelation was induced by combining prehydrolyzed TEOS, EtOH, and 0.15 N NH4OH in a volume ratio of 1.0:1.33:2.0. The approximate gelation time of this formulation was tuned to 3.5 h based on the NH4OH catalyst concentration. Samples produced using this technique are referred to as Aerogel A. The second procedure, process B, follows the B2 acid–base catalyzed method outlined by Prakash [9] and has been shown to produce aerogels with 60–90% porosity. To make stock solutions, TEOS, EtOH, H2O, and HCL were combined in molar ratios of 1.0:3.8:1.1:7 × 10− 6 at 60 °C for ninety minutes. Once cooled to room temperature, the stock solution, EtOH, and 0.05 M NH4OH were combined to induce the condensation reaction and gelation in an oven at 50 °C for a minimum of ninety hours. Such samples are referred to as Aerogel B. The third sol–gel method was a much faster process than that used to produce Aerogel A or Aerogel B. The hydrolysis reaction was achieved by combining TEOS, water, and either nitric acid or sulfuric acid and acetic acid in molar ratios of 1.0:4.72:3.6 × 10− 3 and 1.0:4.72:1.25 × 10− 3:0.035 respectively. The solution was stirred vigorously while mixing in order to drive a homogeneous reaction by overcoming the immiscibility at such concentration. After 1.5– 2.0 h, the solution clarified, indicating that the clear sol had been obtained without precipitation of large silica particles. The further hydrolysis reaction was allowed to continue for 2–3 h while stirring and storing in a sealed container. The condensation reaction was induced as the prehydrolyzed TEOS was added to the EtOH and 14.8 N NH4OH, in a volume ratio of 1:3.12:0.046. Gel times of 5–8 min were recorded. The variation was due to the aging of prehydrolyzed TEOS.
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Samples produced using this much faster process are referred to as Aerogel C. 2.2. Thin-film deposition processes Aerogel A and Aerogel C films were deposited using thin film deposition methods of both spin and dip coating [24]. During the condensation reaction, the non-viscous solutions used to prepare Aerogel A and Aerogel C were applied to the silicon dioxide wafers 45 and 4 min, respectively, before gelation and allowed to gel. During deposition onto the wafers, care was taken to prevent solvent evaporation, which would collapse the porous structure. The gel and wafer were then washed in aging solutions to modify the gels, strengthening them and making them hydrophobic. Aerogel A was treated for ambient drying, which included a 30 minute wash in excess EtOH, another 30 minute wash in hexane, a minimum 12 hour wash in 6H4OH, EtOH, and hexamethyldisilazane (HMDS) in a volume ratio of 1:17:3 at 55 °C overnight. The gels were then returned to room temperature and washed for 2 h in excess EtOH before drying. The HMDS modification produced hydrophobic gels. Alternatively, a sonication deposition method developed by Prakash and Brinker [25] was used to deposit Aerogel B. The gel is first washed for three hours in EtOH, then for three hours in hexane, and then reacted with a solution of 6% TMCS or HMDS and 94% hexane by volume to replace the hydroxide groups in the pores with O–Si (Me)3. The six-hour washing process was then repeated. The modified gel was sonicated at an output of 20 Hz for at least 20 min then diluted in EtOH to form a sol–gel suspension. The suspension was then filtered through a 1.1 μm syringe filter and deposited on the wafer to form the aerogel film. Initial samples were not washed in EtOH prior to sonication and were sonicated in 100% excess hexane. This however, produced samples with large roughness which did not allow the subsequently applied capping layer to sufficiently planarize the surface. A subset of the Aeorgel B films was pyrolyzed at 450 °C for 1 h as described by Parkash et al. [9] to increase porosity and lower thermal conductivity (referred to as Aerogel B-Pyrolyzed). 2.3. Microfabrication It is not possible to deposit the well defined thin metal line required by the 3ω experiment directly onto a rough aerogel surface without a capping layer. Otherwise, portions of the line may sink into surface pores and either not connect with the rest of the wire or alter the heat flow away from that of an ideal line-source heater. A rough aerogel surface would also make developing photoresist difficult, as exposing photoresist in crevices made by the rough aerogel would be almost impossible. In order to make these experiments more feasible, silicon dioxide was sputtered as a protective capping layer onto the sample using a RF magnetron sputtering system at 300 W in a 0.533 Pa argon environment. Gold was initially investigated for use as the 3ω heater wire due to its thermoresistive linearity over a specific temperature range. A silicon dioxide capping layer was sputtered on a silicon wafer with a thin-film aerogel, then a thin titanium seed layer and a thicker gold layer (to simulate heater wires) were each sputtered onto the capping layer. A resist test pattern was imaged with a contact mask aligner using a positive photoresist. While the iodine-based gold etch appeared to work properly, the fluorine-based titanium etch destroyed the capping layer and the aerogel underneath it in a matter of seconds. To avoid testing multiple wet etch chemistries, as well as avoid submerging aerogel in potentially damaging solvents for long periods of time, reactive ion etching was used as an alternative and liftoff was discounted as a deposition method. Dry etching of noble metals is accomplished using a physical argon etch, which provides no selectivity between materials. As soon as the metal layer for the 3ω pattern was etched through, the capping layer
M.L. Bauer et al. / Journal of Non-Crystalline Solids 357 (2011) 2960–2965
Dimensions not to scale to exaggerate heat spreading
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z
Nb Heater 200 nm
x
Sputtered Quartz 200 nm Aerogel Film 250-1280 nm Amorphous Quartz Semi-infinite Substrate
y Fig. 1. Schematic demonstrating heat flow in a test sample. Not shown here are the four niobium pads for electrical contact.
and potential aerogel would be etched at a high rate. Therefore, niobium was selected for the 3ω line heater due to its availability, well-known reactive ion etching chemistries, good adhesion to quartz, and for its thermoresistive linearity over low temperatures. A 200 nm thick, low-stress niobium layer was dc magnetron sputtered at 500 W in a 0.613 Pa argon environment. The niobium layer was patterned with a positive photoresist (AZ Electronic Materials 4110) using a Suss MicroTEC MJB4 Contact Mask Aligner. A custom mask was used to define the 3ω pattern needed: a long metal line 10 μm wide connected to four large pads for electrical measurements. Fig. 1 provides a schematic of the test structure used for this study. An Oxford Instruments PlasmaLab-100 System was used for the reactive ion etching steps. Experimentally, a SF6 + Ar chemistry was selected for its anisotropy and familiarity with the reactive ion etch operators. To minimize physical etching of the underlying capping layer, laser endpoint detection was used to stop the etching process so as to not alter the heater structure and to help maintain the assumption of an ideal line source heater in the testing results. Again, without the sputtered silicon dioxide capping layer, even the small over etching time used to ensure the niobium was completely removed would damage the fragile aerogel. An oxygen ash was used to remove the photoresist after etching.
potentiometer, thereby removing the first harmonic response and allowing for a more precise filter setting. The experimental procedure was validated by measuring an amorphous quartz substrate adhered directly to the wire pattern. Using the slope method described by Cahill and Pohl [14] the thermal conductivity of the substrate at 295 K was measured to be 1.22 W/mK with an experimental uncertainty of less than 6%, which agrees well with literature [14]. Data analysis for multi-layer samples followed the methodology developed by Borca-Tasciuc et al. [22] for relating V3ω to film thermal conductivity, k, in a multilayer sample. Each layer is assumed to be isotropic. Contributions from the niobium heater's thermal mass and thermal boundary resistance were considered trivial and ignored [22]. For multi layer samples, the complex second harmonic temperature response is
3. Experimental
An = −tanh ðBn dn Þ ;
As previously noted, the thermal conductivity of the aerogel samples was tested by applying the 3ω technique. All reported measurements were made at a 295 K temperature and a pressure between 0.1 and 1 Pa. The experiment required a thin metal wire to be adhered to the sample. This metal line served as both an AC heat source and as a thermometer. By tuning the driving frequency, the thermal penetration depth is varied, which provides sensitivity in determining the thermal properties of multilayer samples. Fig. 2 provides a schematic of the circuit used in the experiment. A SR830 digital signal processing lock-in amplifier was used to generate the sinusoidal AC current used to perturb the sample. The input signal was passed through the niobium wire (adhered to the sample) as well as a potentiometer (set to the same electrical resistance as the unperturbed metal wire). This 1ω input signal causes Joule heating at the 2ω frequency. Because the thin line's electrical resistance varies with temperature, the metal's second harmonic electrical resistance oscillations, R2ω, allow the wire to serve as a thermometer due to its thermoresistive response to the perturbation. To acquire this information, the third harmonic voltage oscillations across the niobium wire, V3ω, were measured by the lock-in amplifier. Because the first harmonic signal is thousands of times larger than the third harmonic signal [14] it is necessary to have the lock-in amplifier take the difference of the signal across the niobium wire and the
T2ω =
−p ∞ sin2 ðbλÞ ∫ dλ; πκ1 L 0 A1 B1 b2 λ2
ð1Þ
in which
Ai−1 =
Ai Bi ki −tanh ðBi−1 di−1 Þ Bi−1 ki−1 ; 1− B Ai Bki ki tanh ðBi−1 di−1 Þ i−1 i−1
ð2Þ
s
ð3Þ
Lock-in Amplifier AB
Reference
Digital Multimeter
Digital Multimeter
Fig. 2. Schematic of 3ω experimental layout.
M.L. Bauer et al. / Journal of Non-Crystalline Solids 357 (2011) 2960–2965
changes with respect to temperature changes. This implies that R2ω = T2ω dR where R2ω and T2ω are the metal line's resistance and dT temperature variations from steady state caused by the 2ω response dR to the sinusoidal AC signal. dT is a constant for a given wire, which can be determined by monitoring the metal wire's electrical resistance at various temperatures. Using this information and Ohm's Law it can be shown that [26]
Quartz-Aerogel-Quartz Data
4.0 3.5 3.0 2.5 T2ω[K] 2.0 1.5 1.0 0.5 0 1 10
Quartz Substrate Only Data
2
10
10
3
4
10
Driving Frequency [Hz] Fig. 3. Exemplary raw data converted from phase V3ω to phase T2ω by Eq. (5). This data is fit to Eqs. (1) through (4). At higher frequencies the trend deviates from linearity as a function of the thermal diffusivity. To avoid complications from fitting several unknown quantities, only frequencies insensitive to the thermal penetration depth are considered. Uncertainty in the data is less than 4% which is smaller than the height of the data points shown.
Table 1 Thermal testing results. Aerogel type
Thickness (nm)
kfilm (W/mK)
Estimated error (W/mK)
A B B-pyrol C C
1280 250 370 300 620
0.24 0.067 0.024 0.33 0.29
±0.05 ±0.01 ±0.005 ±0.07 ±0.06
Bi =
i2ω 1 = 2 2 λ + : αi
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V3ω =
1 V1ω dR T 2 R0 2ω dT
ð5Þ
where R0 is the metal line's steady-state resistance. Thus, the procedure for determining the thermal conductivity of each layer of a given sample is to measure the metal line's R0 and dR values, then to dT measure the V3ω response for a supplied V1ω over a range of frequencies, and to relate V3ω to T2ω by Eq. (5). Next, the results of Eqs. (1–4) can be fitted over the entire frequency range. The thermal conductivity of the amorphous quartz substrate is already known from the previously noted validation of the technique using a one layer sample. The sputtered SiO2 is assumed to have a thermal conductivity of 0.94 W/mK [27]. Data was collected using a 1.5 V rms AC source generated by the lock-in amplifier at frequencies between 10 and 10,000 Hz in logarithmic steps. In order to match the sample's R0 resistance, which allows the lock-in to accurately eliminate the first harmonic signal, a potentiometer was autonomously adjusted by a stepper motor until the voltage drop across it was within 0.5% of the sample's voltage drop. Data was collected with the sample under vacuum at 1 mTorr pressure and 295 K temperature.
ð4Þ
In these expressions the subscript i represents the ith layer starting from the top, with n total layers. For the three layer samples studied, the SiO2 capping layer, the aerogel thin film, and the SiO2 substrate are the 1st, 2nd and 3rd layers respectively. Here, αi corresponds to the specified layer's thermal diffusivity in which α = k/ρc where ρ and c are density and specific heat respectively. The variables L, p, ω, and d are the metal wire length, peak electric power, driving current's angular frequency, and layer thickness, respectively. Depending on the boundary condition at the bottom of the sample, the exponent s is either −1, 0, or 1 corresponding to an isothermal, semi-infinite, or adiabatic assumption. λ is the variable of integration. To apply Eqs. (1–4), V3ω must be related to T2ω. Over moderate temperatures, a metal wire exhibits linear electrical resistance
4. Results By knowing the thermal conductivity of the SiO2 capping layer and substrate and by selecting frequency regions in which the samples are insensitive to thermal diffusivity due to the thermal wavelength being greater than the thickness of the capping layer and aerogel layer, the aerogel's thermal conductivity becomes the only unknown parameter. Data reduction is significantly simplified to fitting a linear trend line. Fig. 3 provides a sample data set from Aerogel B. In this figure, the raw data, V3ω, was converted to T2ω by Eq. (5). The data is compared to best fit thermal conductivity results of Eqs. (1–4). Also shown is the temperature rise for the SiO2 substrate without any additional layers scaled also to the same effective power across the niobium wire as the data from Aerogel B. Thermal spreading caused by the capping layer prevents a direct calculation of the aerogel film's thermal conductivity
Aerogel 788 nm
100 nm Fig. 4. Left: side view SEM image of an aerogel thin film formed through process C. Right: bulk aerogel formed through process C. These images confirm that Aerogel C's porous structure collapsed during deposition.
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Niobium 188 nm
Quartz 186 nm Aerogel 374 nm
10 nm Fig. 5. Left: side view of Aerogel B-Pyrolyzed after deposition of the quartz and niobium layers. Right: high resolution top view of the same sample prior to the deposition of capping layers. Both images show the highly porous structure of the aerogel remained intact after deposition of the gel and of the two capping layers.
by the differential method [15]. Nonetheless, the analysis technique used fully captures the effects of the capping layer. In order to avoid the effects due to uncertainty in the aerogel's specific heat and density (with both contributing to thermal diffusivity and therefore the overall heat equation) frequencies were only considered in the range in which the sample is sufficiently insensitive to the thermal diffusivity of the aerogel film. It has been shown [21] that a significant portion of 3ω data is insensitive to variations in thermal diffusivity depending on sample properties and geometry. More specifically, at low enough frequencies. For the geometries studied, 100–500 Hz signals had a negligible response (less than the V3ω measurement uncertainty) to variations in a best fit thermal diffusivity. With this simplification, the reported aerogel thermal conductivity values were calculated after considering uncertainty propagation in experimental parameters including V3ω ; V1ω ; R0 ; dR , sample geometry including metal heater dimensions dT and capping layer thickness, and also the assumed thermal properties of the two SiO2 layers. The resulting thermal conductivities and uncertainties for each sample measured are shown in Table 1. 5. Discussion While supercritical drying of aerogels is the most common way to preserve their tenuous structure, the high thermal conductivity results from the 3ω testing of Aerogel C indicate that too much solvent evaporation occurred during synthesis causing the structure to collapse. This was verified by comparing SEM images of a bulk version of Aerogel C and a thin film version similar to the samples tested, as shown in Fig. 4. The bulk Aerogel C showed highly porous silica networks while the thin film did not display this features. For this reason, despite being supercritically dried, Aerogel C did not yield the ultra-low thermal conductivity generally found in silica aerogels. Aerogel A had similar problems to Aerogel C. In its deposition, care was taken to limit solvent evaporation during gelation and modification, however, this was not fully successful. A portion of the solvent evaporated and the high porosity structure was partially compromised. The sonication method used on Aerogel B provided the most robust method to combat solvent evaporation and structural collapse due in part to gel modification being completed prior to deposition. Aerogel B yielded a lower conductivity than either A or C. This value was further minimized by the pyrolization heat treatment process. The subset of samples produced using process B which underwent pyrolization yielded thermal conductivity values of 0.024 W/m-K. The 450 °C pyrolization oxidized any remaining organic groups yielding a more porous structure. This was further verified by the top and side view SEM images of Aerogel B-Pyrolyzed shown in Fig. 5.
6. Conclusions In this study we have demonstrated the feasibility of creating silica aerogel films that maintain the ultra-low thermal conductivity found in bulk silica aerogel counterparts. The films were successfully thermally characterized by applying the 3ω technique. Several samples were measured at a temperature of 295 K and pressure between 0.1 and 1 Pa. The lowest aerogel thermal conductivity observed was 0.24 W/m-K. Sonication appears to be the key step in depositing an aerogel film without the structure collapsing. Results indicate that pyrolization can further increase the porosity of an aerogel film. Such processes ensure the films low thermal conductivity and therefore ideal use in insulation applications. Preliminary steps have been taken that demonstrate specific microfabrication processes that the fragile film can endure without causing the network to collapse, thus destroying the microstructure and the material's unique properties. This suggests that aerogels may indeed be a solution to thermal management problems in MEMS devices where thin film insulation is required. Acknowledgments The authors greatly acknowledge the financial support of the Defense Advanced Research Projects Agency (Grant No. N66001-081-2059). The authors thank C. J. Brinker for communications regarding deposition of Aerogel B.
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Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Thin-film aerogel thermal conductivity measurements via 3ω M.L. Bauer a,⁎, C.M. Bauer a, M.C. Fish a, R.E. Matthews b, G.T. Garner a, A.W. Litchenberger b, P.M. Norris a a b
Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22904-4746, USA Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904-4746, USA
a r t i c l e
i n f o
Article history: Received 16 December 2010 Received in revised form 29 March 2011 Available online 30 April 2011 Keywords: Thin-film aerogel; Thermal conductivity; 3ω technique
a b s t r a c t The limiting constraint in a growing number of nano systems is the inability to thermally tune devices. Silica aerogel is widely accepted as the best solid thermal insulator in existence and offers a promising solution for microelectronic systems needing superior thermal isolation. In this study, thin-film silica aerogel films varying in thickness from 250 to 1280 nm were deposited on SiO2 substrates under a variety of deposition conditions. These samples were then thermally characterized using the 3ω technique. Deposition processes for depositing the 3ω testing mask to the sample were optimized and it was demonstrated that thin-film aerogel can maintain its structure in common fabrication processes for microelectromechanical systems. Results indicate that thin-film silica aerogel can maintain the unique, ultra-low thermal conductivity commonly observed in bulk aerogel, with a directly measured thermal conductivity as low as 0.024 W/m-K at temperature of 295 K and pressure between 0.1 and 1 Pa. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Bulk silica aerogel is a two phase porous material with the lowest recorded density and thermal conductivity of any solid. In terms of space occupied, the host material can be as little as 0.01% of the structure with the remainder comprised of air [1,2]. The host, which can be a large variety of materials including silica, alumina [3], clay [4], or carbon nanotubes [5], is a complicated web of interconnects that gives the composite its structure. Since 1934 researchers have studied bulk aerogel thermal properties [6]. Bulk silica aerogels have been shown to have thermal conductivities ranging from as low as 0.006 W/mK [7] (at atmospheric pressure and a temperature of 300 K) to an upper limit approaching the thermal conductivity of amorphous quartz. More recently, aerogels have been successfully manufactured in a variety of forms including microspheres [8], thin films [9], flexible sheets (x-aerogels) [10,11], and photo-luminescent chalcogenides [12], each requiring unique fabrication processes. Integrating thermal insulation into microelectromechanical systems (MEMS) broadens the possible applications of devices that require (or whose performance would be enhanced by) stable elevated temperature. The power needed to maintain a desired component at an elevated temperature is a direct function of the thermal properties of the material thermally insulating it. In general, minimizing the requisite power is advantageous. By incorporating the
⁎ Corresponding author. Tel.: + 1 4342491296. E-mail address: [email protected] (M.L. Bauer). 0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2011.03.042
insulation directly as part of the die, the area of the MEMS device that needs to be kept at an increased temperature can be separated at the processing stage from that which does not need additional heating. Alternatives include using hybrid dies or complex mounting schemes to thermally isolate components. Extending the integration to include selective or overall thermal insulation would facilitate the manufacture of cheaper, temperature-stabilized devices. Thin-film silica aerogels undergo unique deposition processes [9] to recreate their bulk counterparts with micro or nano-scale dimensions. The most definitive way to understand the effects of these various deposition methods on thermal properties is to directly measure the thermal conductivity of thin film samples. This has proven difficult for a variety of reasons. The ease with which the silica network can collapse increases the difficulty of applying standard microfabrication techniques and decreases the variety of experiments that can be used to characterize such samples. Microscale thermal characterization techniques are not trivial to implement. Thin-film heater techniques have previously been used to measure the thermal properties of bulk aerogels [7]. Steady state techniques, however, are not optimal for thin-film measurements as they offer little sensitivity for characterizing an individual thin film in multilayer samples, and generally they require significant fabrication on the sample. Alternatively, an optical technique such as a pump probe based experiment [13] with a reflective capping layer added to the aerogel may be a viable method for thermally characterizing aerogel films. But great care must be taken to ensure sensitivity to the thermal conductivity of the film of interest independent of other thermal properties such as boundary resistances. Furthermore, quantifying the heat deposited by the perturbating signal can be difficult.
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Alternatively, the 3ω technique was chosen for this study in which a metal wire serves as a frequency varying heat source and means to measure temperature. This technique was originally used to measure the thermal conductivity of bulk solids over a wide temperature range [14]. It was then adapted to measure thin films deposited on a substrate of known properties [15]. Subsequently the technique was expanded to measure superlattices [16], fluids [17] and carbon nanotube arrays [18].While the 3ω technique has also been utilized to measure properties of porous materials such as bulk xerogels [19] and 55% porous aerogel films with thermal conductivities as low as 0.14 W/mK [20] this study reports the first use of 3ω for determining the thermal conductivity of high porosity silica aerogel films. The 3ω technique was advantageous for this study due to its sensitivity to individual layers in multilayer structures [21,22], high accuracy and repeatability [13], and its ability to eliminate convective as well as radiative error [23]. 2. Materials and methods Resulting aerogel properties are determined largely by the sol–gel process and specifically for thin films by the deposition and drying procedures. Solvent to solute ratios determine the ultimate porosity of the aerogel while reaction time and acid–base catalysts contribute largely to the pore size. Surface modifying agents, as well as temperature and humidity, also play a role in aerogel micro structure formation. For this study, silica aerogel thin films were fabricated using two step acid–base partial hydrolysis/condensation chemistry [24] varying reaction temperature, catalyst type, and catalyst concentration. Several deposition and drying methods were used to prepare the aerogels. Common to each method was the requirement that solvent evaporation be limited during and after gel formation to preserve the tenuous micro structure of the aerogel. 2.1. Sol–gel procedures In the first process the sol–gel precursor solution was made by first combining Tetraethyl orthosilicate (TEOS), EtOH, H2O and HCL in molar ratios of 1.0:4.1:0.9:42 × 10− 6 at 60 °C for ninety minutes to produce prehydrolyzed TEOS solution. Gelation was induced by combining prehydrolyzed TEOS, EtOH, and 0.15 N NH4OH in a volume ratio of 1.0:1.33:2.0. The approximate gelation time of this formulation was tuned to 3.5 h based on the NH4OH catalyst concentration. Samples produced using this technique are referred to as Aerogel A. The second procedure, process B, follows the B2 acid–base catalyzed method outlined by Prakash [9] and has been shown to produce aerogels with 60–90% porosity. To make stock solutions, TEOS, EtOH, H2O, and HCL were combined in molar ratios of 1.0:3.8:1.1:7 × 10− 6 at 60 °C for ninety minutes. Once cooled to room temperature, the stock solution, EtOH, and 0.05 M NH4OH were combined to induce the condensation reaction and gelation in an oven at 50 °C for a minimum of ninety hours. Such samples are referred to as Aerogel B. The third sol–gel method was a much faster process than that used to produce Aerogel A or Aerogel B. The hydrolysis reaction was achieved by combining TEOS, water, and either nitric acid or sulfuric acid and acetic acid in molar ratios of 1.0:4.72:3.6 × 10− 3 and 1.0:4.72:1.25 × 10− 3:0.035 respectively. The solution was stirred vigorously while mixing in order to drive a homogeneous reaction by overcoming the immiscibility at such concentration. After 1.5– 2.0 h, the solution clarified, indicating that the clear sol had been obtained without precipitation of large silica particles. The further hydrolysis reaction was allowed to continue for 2–3 h while stirring and storing in a sealed container. The condensation reaction was induced as the prehydrolyzed TEOS was added to the EtOH and 14.8 N NH4OH, in a volume ratio of 1:3.12:0.046. Gel times of 5–8 min were recorded. The variation was due to the aging of prehydrolyzed TEOS.
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Samples produced using this much faster process are referred to as Aerogel C. 2.2. Thin-film deposition processes Aerogel A and Aerogel C films were deposited using thin film deposition methods of both spin and dip coating [24]. During the condensation reaction, the non-viscous solutions used to prepare Aerogel A and Aerogel C were applied to the silicon dioxide wafers 45 and 4 min, respectively, before gelation and allowed to gel. During deposition onto the wafers, care was taken to prevent solvent evaporation, which would collapse the porous structure. The gel and wafer were then washed in aging solutions to modify the gels, strengthening them and making them hydrophobic. Aerogel A was treated for ambient drying, which included a 30 minute wash in excess EtOH, another 30 minute wash in hexane, a minimum 12 hour wash in 6H4OH, EtOH, and hexamethyldisilazane (HMDS) in a volume ratio of 1:17:3 at 55 °C overnight. The gels were then returned to room temperature and washed for 2 h in excess EtOH before drying. The HMDS modification produced hydrophobic gels. Alternatively, a sonication deposition method developed by Prakash and Brinker [25] was used to deposit Aerogel B. The gel is first washed for three hours in EtOH, then for three hours in hexane, and then reacted with a solution of 6% TMCS or HMDS and 94% hexane by volume to replace the hydroxide groups in the pores with O–Si (Me)3. The six-hour washing process was then repeated. The modified gel was sonicated at an output of 20 Hz for at least 20 min then diluted in EtOH to form a sol–gel suspension. The suspension was then filtered through a 1.1 μm syringe filter and deposited on the wafer to form the aerogel film. Initial samples were not washed in EtOH prior to sonication and were sonicated in 100% excess hexane. This however, produced samples with large roughness which did not allow the subsequently applied capping layer to sufficiently planarize the surface. A subset of the Aeorgel B films was pyrolyzed at 450 °C for 1 h as described by Parkash et al. [9] to increase porosity and lower thermal conductivity (referred to as Aerogel B-Pyrolyzed). 2.3. Microfabrication It is not possible to deposit the well defined thin metal line required by the 3ω experiment directly onto a rough aerogel surface without a capping layer. Otherwise, portions of the line may sink into surface pores and either not connect with the rest of the wire or alter the heat flow away from that of an ideal line-source heater. A rough aerogel surface would also make developing photoresist difficult, as exposing photoresist in crevices made by the rough aerogel would be almost impossible. In order to make these experiments more feasible, silicon dioxide was sputtered as a protective capping layer onto the sample using a RF magnetron sputtering system at 300 W in a 0.533 Pa argon environment. Gold was initially investigated for use as the 3ω heater wire due to its thermoresistive linearity over a specific temperature range. A silicon dioxide capping layer was sputtered on a silicon wafer with a thin-film aerogel, then a thin titanium seed layer and a thicker gold layer (to simulate heater wires) were each sputtered onto the capping layer. A resist test pattern was imaged with a contact mask aligner using a positive photoresist. While the iodine-based gold etch appeared to work properly, the fluorine-based titanium etch destroyed the capping layer and the aerogel underneath it in a matter of seconds. To avoid testing multiple wet etch chemistries, as well as avoid submerging aerogel in potentially damaging solvents for long periods of time, reactive ion etching was used as an alternative and liftoff was discounted as a deposition method. Dry etching of noble metals is accomplished using a physical argon etch, which provides no selectivity between materials. As soon as the metal layer for the 3ω pattern was etched through, the capping layer
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Dimensions not to scale to exaggerate heat spreading
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z
Nb Heater 200 nm
x
Sputtered Quartz 200 nm Aerogel Film 250-1280 nm Amorphous Quartz Semi-infinite Substrate
y Fig. 1. Schematic demonstrating heat flow in a test sample. Not shown here are the four niobium pads for electrical contact.
and potential aerogel would be etched at a high rate. Therefore, niobium was selected for the 3ω line heater due to its availability, well-known reactive ion etching chemistries, good adhesion to quartz, and for its thermoresistive linearity over low temperatures. A 200 nm thick, low-stress niobium layer was dc magnetron sputtered at 500 W in a 0.613 Pa argon environment. The niobium layer was patterned with a positive photoresist (AZ Electronic Materials 4110) using a Suss MicroTEC MJB4 Contact Mask Aligner. A custom mask was used to define the 3ω pattern needed: a long metal line 10 μm wide connected to four large pads for electrical measurements. Fig. 1 provides a schematic of the test structure used for this study. An Oxford Instruments PlasmaLab-100 System was used for the reactive ion etching steps. Experimentally, a SF6 + Ar chemistry was selected for its anisotropy and familiarity with the reactive ion etch operators. To minimize physical etching of the underlying capping layer, laser endpoint detection was used to stop the etching process so as to not alter the heater structure and to help maintain the assumption of an ideal line source heater in the testing results. Again, without the sputtered silicon dioxide capping layer, even the small over etching time used to ensure the niobium was completely removed would damage the fragile aerogel. An oxygen ash was used to remove the photoresist after etching.
potentiometer, thereby removing the first harmonic response and allowing for a more precise filter setting. The experimental procedure was validated by measuring an amorphous quartz substrate adhered directly to the wire pattern. Using the slope method described by Cahill and Pohl [14] the thermal conductivity of the substrate at 295 K was measured to be 1.22 W/mK with an experimental uncertainty of less than 6%, which agrees well with literature [14]. Data analysis for multi-layer samples followed the methodology developed by Borca-Tasciuc et al. [22] for relating V3ω to film thermal conductivity, k, in a multilayer sample. Each layer is assumed to be isotropic. Contributions from the niobium heater's thermal mass and thermal boundary resistance were considered trivial and ignored [22]. For multi layer samples, the complex second harmonic temperature response is
3. Experimental
An = −tanh ðBn dn Þ ;
As previously noted, the thermal conductivity of the aerogel samples was tested by applying the 3ω technique. All reported measurements were made at a 295 K temperature and a pressure between 0.1 and 1 Pa. The experiment required a thin metal wire to be adhered to the sample. This metal line served as both an AC heat source and as a thermometer. By tuning the driving frequency, the thermal penetration depth is varied, which provides sensitivity in determining the thermal properties of multilayer samples. Fig. 2 provides a schematic of the circuit used in the experiment. A SR830 digital signal processing lock-in amplifier was used to generate the sinusoidal AC current used to perturb the sample. The input signal was passed through the niobium wire (adhered to the sample) as well as a potentiometer (set to the same electrical resistance as the unperturbed metal wire). This 1ω input signal causes Joule heating at the 2ω frequency. Because the thin line's electrical resistance varies with temperature, the metal's second harmonic electrical resistance oscillations, R2ω, allow the wire to serve as a thermometer due to its thermoresistive response to the perturbation. To acquire this information, the third harmonic voltage oscillations across the niobium wire, V3ω, were measured by the lock-in amplifier. Because the first harmonic signal is thousands of times larger than the third harmonic signal [14] it is necessary to have the lock-in amplifier take the difference of the signal across the niobium wire and the
T2ω =
−p ∞ sin2 ðbλÞ ∫ dλ; πκ1 L 0 A1 B1 b2 λ2
ð1Þ
in which
Ai−1 =
Ai Bi ki −tanh ðBi−1 di−1 Þ Bi−1 ki−1 ; 1− B Ai Bki ki tanh ðBi−1 di−1 Þ i−1 i−1
ð2Þ
s
ð3Þ
Lock-in Amplifier AB
Reference
Digital Multimeter
Digital Multimeter
Fig. 2. Schematic of 3ω experimental layout.
M.L. Bauer et al. / Journal of Non-Crystalline Solids 357 (2011) 2960–2965
changes with respect to temperature changes. This implies that R2ω = T2ω dR where R2ω and T2ω are the metal line's resistance and dT temperature variations from steady state caused by the 2ω response dR to the sinusoidal AC signal. dT is a constant for a given wire, which can be determined by monitoring the metal wire's electrical resistance at various temperatures. Using this information and Ohm's Law it can be shown that [26]
Quartz-Aerogel-Quartz Data
4.0 3.5 3.0 2.5 T2ω[K] 2.0 1.5 1.0 0.5 0 1 10
Quartz Substrate Only Data
2
10
10
3
4
10
Driving Frequency [Hz] Fig. 3. Exemplary raw data converted from phase V3ω to phase T2ω by Eq. (5). This data is fit to Eqs. (1) through (4). At higher frequencies the trend deviates from linearity as a function of the thermal diffusivity. To avoid complications from fitting several unknown quantities, only frequencies insensitive to the thermal penetration depth are considered. Uncertainty in the data is less than 4% which is smaller than the height of the data points shown.
Table 1 Thermal testing results. Aerogel type
Thickness (nm)
kfilm (W/mK)
Estimated error (W/mK)
A B B-pyrol C C
1280 250 370 300 620
0.24 0.067 0.024 0.33 0.29
±0.05 ±0.01 ±0.005 ±0.07 ±0.06
Bi =
i2ω 1 = 2 2 λ + : αi
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V3ω =
1 V1ω dR T 2 R0 2ω dT
ð5Þ
where R0 is the metal line's steady-state resistance. Thus, the procedure for determining the thermal conductivity of each layer of a given sample is to measure the metal line's R0 and dR values, then to dT measure the V3ω response for a supplied V1ω over a range of frequencies, and to relate V3ω to T2ω by Eq. (5). Next, the results of Eqs. (1–4) can be fitted over the entire frequency range. The thermal conductivity of the amorphous quartz substrate is already known from the previously noted validation of the technique using a one layer sample. The sputtered SiO2 is assumed to have a thermal conductivity of 0.94 W/mK [27]. Data was collected using a 1.5 V rms AC source generated by the lock-in amplifier at frequencies between 10 and 10,000 Hz in logarithmic steps. In order to match the sample's R0 resistance, which allows the lock-in to accurately eliminate the first harmonic signal, a potentiometer was autonomously adjusted by a stepper motor until the voltage drop across it was within 0.5% of the sample's voltage drop. Data was collected with the sample under vacuum at 1 mTorr pressure and 295 K temperature.
ð4Þ
In these expressions the subscript i represents the ith layer starting from the top, with n total layers. For the three layer samples studied, the SiO2 capping layer, the aerogel thin film, and the SiO2 substrate are the 1st, 2nd and 3rd layers respectively. Here, αi corresponds to the specified layer's thermal diffusivity in which α = k/ρc where ρ and c are density and specific heat respectively. The variables L, p, ω, and d are the metal wire length, peak electric power, driving current's angular frequency, and layer thickness, respectively. Depending on the boundary condition at the bottom of the sample, the exponent s is either −1, 0, or 1 corresponding to an isothermal, semi-infinite, or adiabatic assumption. λ is the variable of integration. To apply Eqs. (1–4), V3ω must be related to T2ω. Over moderate temperatures, a metal wire exhibits linear electrical resistance
4. Results By knowing the thermal conductivity of the SiO2 capping layer and substrate and by selecting frequency regions in which the samples are insensitive to thermal diffusivity due to the thermal wavelength being greater than the thickness of the capping layer and aerogel layer, the aerogel's thermal conductivity becomes the only unknown parameter. Data reduction is significantly simplified to fitting a linear trend line. Fig. 3 provides a sample data set from Aerogel B. In this figure, the raw data, V3ω, was converted to T2ω by Eq. (5). The data is compared to best fit thermal conductivity results of Eqs. (1–4). Also shown is the temperature rise for the SiO2 substrate without any additional layers scaled also to the same effective power across the niobium wire as the data from Aerogel B. Thermal spreading caused by the capping layer prevents a direct calculation of the aerogel film's thermal conductivity
Aerogel 788 nm
100 nm Fig. 4. Left: side view SEM image of an aerogel thin film formed through process C. Right: bulk aerogel formed through process C. These images confirm that Aerogel C's porous structure collapsed during deposition.
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Niobium 188 nm
Quartz 186 nm Aerogel 374 nm
10 nm Fig. 5. Left: side view of Aerogel B-Pyrolyzed after deposition of the quartz and niobium layers. Right: high resolution top view of the same sample prior to the deposition of capping layers. Both images show the highly porous structure of the aerogel remained intact after deposition of the gel and of the two capping layers.
by the differential method [15]. Nonetheless, the analysis technique used fully captures the effects of the capping layer. In order to avoid the effects due to uncertainty in the aerogel's specific heat and density (with both contributing to thermal diffusivity and therefore the overall heat equation) frequencies were only considered in the range in which the sample is sufficiently insensitive to the thermal diffusivity of the aerogel film. It has been shown [21] that a significant portion of 3ω data is insensitive to variations in thermal diffusivity depending on sample properties and geometry. More specifically, at low enough frequencies. For the geometries studied, 100–500 Hz signals had a negligible response (less than the V3ω measurement uncertainty) to variations in a best fit thermal diffusivity. With this simplification, the reported aerogel thermal conductivity values were calculated after considering uncertainty propagation in experimental parameters including V3ω ; V1ω ; R0 ; dR , sample geometry including metal heater dimensions dT and capping layer thickness, and also the assumed thermal properties of the two SiO2 layers. The resulting thermal conductivities and uncertainties for each sample measured are shown in Table 1. 5. Discussion While supercritical drying of aerogels is the most common way to preserve their tenuous structure, the high thermal conductivity results from the 3ω testing of Aerogel C indicate that too much solvent evaporation occurred during synthesis causing the structure to collapse. This was verified by comparing SEM images of a bulk version of Aerogel C and a thin film version similar to the samples tested, as shown in Fig. 4. The bulk Aerogel C showed highly porous silica networks while the thin film did not display this features. For this reason, despite being supercritically dried, Aerogel C did not yield the ultra-low thermal conductivity generally found in silica aerogels. Aerogel A had similar problems to Aerogel C. In its deposition, care was taken to limit solvent evaporation during gelation and modification, however, this was not fully successful. A portion of the solvent evaporated and the high porosity structure was partially compromised. The sonication method used on Aerogel B provided the most robust method to combat solvent evaporation and structural collapse due in part to gel modification being completed prior to deposition. Aerogel B yielded a lower conductivity than either A or C. This value was further minimized by the pyrolization heat treatment process. The subset of samples produced using process B which underwent pyrolization yielded thermal conductivity values of 0.024 W/m-K. The 450 °C pyrolization oxidized any remaining organic groups yielding a more porous structure. This was further verified by the top and side view SEM images of Aerogel B-Pyrolyzed shown in Fig. 5.
6. Conclusions In this study we have demonstrated the feasibility of creating silica aerogel films that maintain the ultra-low thermal conductivity found in bulk silica aerogel counterparts. The films were successfully thermally characterized by applying the 3ω technique. Several samples were measured at a temperature of 295 K and pressure between 0.1 and 1 Pa. The lowest aerogel thermal conductivity observed was 0.24 W/m-K. Sonication appears to be the key step in depositing an aerogel film without the structure collapsing. Results indicate that pyrolization can further increase the porosity of an aerogel film. Such processes ensure the films low thermal conductivity and therefore ideal use in insulation applications. Preliminary steps have been taken that demonstrate specific microfabrication processes that the fragile film can endure without causing the network to collapse, thus destroying the microstructure and the material's unique properties. This suggests that aerogels may indeed be a solution to thermal management problems in MEMS devices where thin film insulation is required. Acknowledgments The authors greatly acknowledge the financial support of the Defense Advanced Research Projects Agency (Grant No. N66001-081-2059). The authors thank C. J. Brinker for communications regarding deposition of Aerogel B.
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