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Thermal conductivity of thermoelectric thick films prepared by electrodeposition
Applied Thermal Engineering 51 (2013) 75e83
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Thermal conductivity of thermoelectric thick films prepared by electrodeposition Heng-Chieh Chien a, Chii-Rong Yang c, Li-Ling Liao a, Chun-Kai Liu a, Ming-Ji Dai a, Ra-Min Tain a, Da-Jeng Yao b, d, * a
Electronics and Optoelectronics Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan, ROC Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC Department of Mechatonic Technology, National Taiwan Normal University, Taipei 10610, Taiwan, ROC d Institute of NanoEngineering and MicroSystems, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC b c
h i g h l i g h t s < A novel technique was used to measure the thermal conductivities of thermoelectric thick films. < The thick films are of BieTe and SbeTe compositions and were prepared by electrodeposition. < We used a particular method to prepare a measurable sample. < We compared the thermal conductivities of the films made by different aqueous solutions.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 May 2012 Accepted 3 September 2012 Available online 16 September 2012
Because of a lack of appropriate methods and the difficulties of sample preparation, few direct measurements of the thermal conductivity of thermoelectric materials in thin films have been reported. We prepared thermoelectric thin films of four types containing BieTe and SbeTe by electrodeposition from aqueous solutions with and without added surfactant, and evaluated their intrinsic thermal conductivity with a modified parallel-strip technique. Three thermoelectric materials showed values 0.2e0.5 W m1 K1 of intrinsic thermal conductivity; for the other type problems of sample preparation precluded measurement. According to observations with a scanning electron microscope, the existence of grain boundaries in the thermoelectric thin films is likely the cause of the small values, and their fragile structure causes difficulty in preparation of a test sample. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Thermoelectric Thick film Electrodeposition Thermal conductivity Measurement
1. Introduction The practicality of thermoelectric (TE) devices is limited mainly by the available materials, of which the performance must be improved to compete with conventional cooling and energy-generation systems. The efficiency of TE materials is directly related to a dimensionless figure of merit defined as ZT ¼ S2sT/k; s denotes electrical conductivity, S Seebeck coefficient, k thermal conductivity and T absolute temperature. An enhancement of the TE figure of merit is achievable on increasing the Seebeck coefficient (S) and the electrical conductivity (s), or decreasing the thermal conductivity (k). Among common TE materials, bismuth telluride (Bi2Te3) that serves typically as an n-type material and antimony telluride (Sb2Te3) as a p* Corresponding author. Institute of NanoEngineering and MicroSystems, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC. Tel.: þ886 (0)3 5742850; fax: þ886 (0)3 5745454. E-mail address: [email protected] (D.-J. Yao). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.09.004
type material are reported to show optimal performance near 300 K in bulk form because they have a large thermoelectric figure of merit. Relative to bulk materials, TE film structures are expected to have a significantly smaller thermal conductivity because phonons are strongly scattered at both film interfaces and denser grain boundaries [1e4]; these structures thereby show a feasibility in applications of hot-spot cooling and electric generation operated at small to moderate temperature differences. Among methods to fabricate Bi2Te3 and Sb2Te3 films, electrodeposition [5e8] is simple and cheap relative to dry processes such as molecular-beam epitaxy (MBE) [9], metal-organic chemical-vapor deposition (MOCVD) [10], pulsed laser deposition [11,12], flash evaporation [13] and sputtering [14]. Electrodeposition also enables an easy control of film thickness in a range 0.01e50 mm that shows feasibility and suitability for fabricating the micro-TE devices. Methods to measure the thermal conductivity of thin film with a thickness in the range between 0.01 mm and 1 mm include the 3u
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method [15,16] and others [17,18], but published methods to measure the thermal conductivity of a film of thickness greater than about 5 mm are few because of a strong heat-spreading effect in the in-plane direction of such a thick film. For instance, in a general measurement to determine the thermal conductivity of a film of thickness 10 mm heated with a strip of width 10 mm, the heat diffusing sideways into the film might be about one fifth of the total generated heat. As the thickness increases, so does the heat spreading. The significant lateral heat spreading in a thick film prevents use of Fourier’s law to calculate the thermal conductivity because of inaccurate heat flow and immeasurable temperature of the film/substrate interface. We measured the intrinsic thermal conductivity of TE materials, Bi2Te3 and Sb2Te3, prepared by electrodeposition from the aqueous solutions with and without an added ionic surfactant. The surfactant is anionic sodium dihexyl sulfosuccinate (SDSS) and commonly used in an electrodeposition process to enhance the probability of fabricating a complete micro-TE structure [19]. To prepare the sample, the TE layer (thickness 0.5e3 mm) was deposited on a silicon substrate and spin-coated with a layer of photosensitive epoxy resin (thickness 5e10 mm) that served as a dielectric layer to separate the metallic heating strip from the measured TE layer. We applied a modified parallel-strip method [20,21], an electrical heating and sensing technique, to measure the thermal resistance of such the TE film samples; the measured apparent thermal resistance (Rapp) comprises the film’s intrinsic thermal resistance (Rint ¼ t/kint) and the interfacial resistance (Ri) and is expressed as Rapp ¼ t/kint þ Ri. The correlation between measured thermal resistance and thickness is related to the film’s thermal conductivity; hence, on measurement of TE layers of varied thickness, the measured thermal resistances of the layers could yield their intrinsic thermal conductivity.
The parallel-strip method originates from the analytical solutions of a heater-film-substrate heat conduction problem. Fig. 1 shows the schematic configuration of the two-dimensional steady-state problem. The method assumes a dc current is passed through a heating strip (width ¼ 2a) that deposited upon the measured film (film thickness is t), and thus a constant Joule heat flux (q) is generated from the strip. The designed strip’s length has to be much longer than it’s width for the 2D assumption. The thickness and width of substrate are c and 2b, respectively. The correlated boundary conditions are also shown in Fig. 1; the analytical solutions are expressed as below:
Tf x;d Ta ðqa=hbÞ
$
hc ht hbRiðhf Þ þ þ a ks kf
! þ
N X 1 Ln $tanhðln dÞþ coshðln tÞ ðln aÞ n¼1
! ha kf (1)
2sinðln aÞ $cosðln xÞ $ ðln aÞ X N Ts ðx; cÞ Ta hc ha 1 þ $ $tanhðln cÞ þ 1 ¼ 1þ ks ks ðln aÞ ðqa=hbÞ n¼1 $Fn $cosðln xÞ
Tavgf ¼
2. The modified parallel-strip method Our previous literature [20,21] has described a novel technique, called the parallel-strip method, for measuring the intrinsic thermal conductivity of a dielectric thin film with thickness less than 3 mm. In this job, we would also introduce the parallel-strip method and modify it to measure a thicker laminated film with thickness between 2 mm and 10 mm. The laminated structure comprises a resin layer and a electrodeposited TE layer.
¼ 1þhRiðf sÞ þ
ð2Þ
! ! hc ht hbRiðhf Þ ha þ þ þ a hb ks kf kf ( # ) 2 N X 1 Ln 2sin ðln aÞ $ þ Ta 0 $ $tanhðln dÞ þ 2 ðln aÞ cosh ln t ðln aÞ n¼1 qa
"
1 þ hRiðf sÞ þ
$
(3)
Tavgs ¼
" X N qa hc 1 ha tanhðln cÞ $ 1þ $ þ $ þ1 hb ks a n¼1 ks ðln aÞ # sinðln wÞ þ Ta ð4Þ $Fn $
ln
Fig. 1. Schematic model for the two-dimensional steady-state heat conduction problem of the parallel-strip method.
H.-C. Chien et al. / Applied Thermal Engineering 51 (2013) 75e83
where
Ln ¼
coshðl cÞ kf 1 sinhðln cÞ n hRiðf sÞ þ Un $ ha coshðln dÞ ðln aÞ coshðln dÞ kf ðln aÞ hRiðf sÞ þ Un $tanhðln tÞ 1þ ha
ha tanhðln cÞ 1þ $ ks ðln aÞ Un ¼ ks 1þ ðln aÞ$tanhðln cÞ ha 1 coshðln cÞ l l L $ð aÞ$tanhð tÞ n n n 0 C d 2sinðln aÞ B C Bcosh ln Fn ¼ $B C A ks ðln aÞ @ ðln aÞ$tanhðln cÞ 1þ ha 0
ln b ¼ np;
n ¼ 1; 2; 3.
here, k and T denote the thermal conductivity and the temperature respectively with indices “s” for the substrate and “f” for the thin film. h denotes the boundary convective condition, Ta is the ambient temperature. The total interface thermal resistance (Ri) from the metal strip to the substrate is expressed as Ri ¼ Ri(hf) þ Ri(fs), which involved the one at the interface between the metal strip and thin film (Ri(hf)), and the one at the interface between thin film and the substrate (Ri(fs)). Eqs. (3) and (4) give the average temperatures on the top side of the film (Tavg-f) and at the interface between the film and the substrate (Tavg-s), respectively, over the range of 0 x a. With typical substrate thickness (c ¼ 200e2000 mm) and substrate width (2b ¼ 1 cm), a simple 2D simulation result shows the temperature contour is nearly a perfect semicircle in a specific range of r. Also, the analytical solution shows the thermal resistance to a specific range of 50 mm r 120 mm has a logarithmic dependence on r, as shown in Fig. 2. Thus, a semi-empirical correlation is found as
Tavs Ts ðx ¼ rÞ lnðr=ro Þ ; for 50 mm r 120 mm ¼ pks l q$2al
(5)
Fig. 2. The thermal resistance of the substrate within a distance (r) From the location (0, c), expressed as (Tavg-sTs(r,c))/(q$2al), has a logarithmic dependence on r to a specific range of 50 mm r 120 mm.
77
In Eq. (5), the left term is thermal resistance from the interface with Tav-s to the point with Ts in the form of temperature and heat flux; the right term is the same thermal resistance from and to the same positions in the form of substrate’s thermal conductivity and dimensions; in which ro is a fitting parameter. From Eq. (5), the immeasurable temperature, Tav-s, could be deduced by the temperature, Ts (x ¼ r). Because the film is relatively thin compared with the distance r, and the heat flux in the cross-plane direction at x ¼ r is negligible, the Ts (x ¼ r) in Eq. (5) is assumed to equalize the sensing strip temperature Tf (x ¼ r) that can be determined by means of the RTD (Resistance Temperature Detector) principle of operation. To introduce the parallel-strip method mentioned above for measuring a thick TE film prepared by electrodeposition, we need to modify the fitting parameter, ro, by analyzing Eqs. (1)e(4) to suit the thicker measured film. Fig. 3 shows a schematic cross section of the thick-film sample in this job. The typical spacing (r) between the heating strip and the sensing strip is 100 mm; the width of the heating strip is 15 mm and that of the sensing strip is 10 mm. The measured film is a laminated structure which comprises a thicker resin layer and a thinner TE layer. After data analysis with the analytical solutions, Eqs. (3) and (4), we found that ro varies with the thickness (t) and the intrinsic thermal conductivity (kint,f) of the measured film, to be expressed as
ro ¼ hro $a hro ¼ C1 $t C2 þ 0:4381 unit of t : mm C1 ¼ 0:0005$kint;f þ 0:00985 C2 ¼ 0:014638$kint;f þ 1:533166
(6)
Eq. (6) is limited to the ranges 0.1 kint,f 2 (unit: W m1 K1) and 2 t 10 (unit: mm) for accuracy. The limitation was defined as the specific ranges are mainly because the dimension and property of all the measured laminated films are within the ranges. Besides, more limited range usually help the extracted empirical equations to have a higher accuracy. In the use of Eq. (5), parameter kint,f must be initially guessed, and then iteratively improved until the value converges. As the evaluated thermal conductivity (kint,f) is insensitive to parameter ro for such a thick film, we suggest that kint,f can be assigned directly as 1.0, rather than being generated iteratively, and can yield a useful value of the evaluated kint,f (error < 0.1%).
Fig. 3. Schematic diagram of the laminated film structure used for the parallel-strip method. The typical spacing between the heating strip and the sensing strip is 100 mm, the width of the heating strip is 15 mm and of the sensing strip 10 mm.
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Because the immeasurable temperature, Tav-s, has been calculated, we propose another method to measure the thermal conductivity of a thick film as follows: the average temperature on top of the film (Tav-f), also is the heating strip’s temperature, could be measured using the RTD operation principle; the average temperature (Tav-s) could be deduced using Eq. (5), measured sensing strip’s temperature and the calculated parameter ro ð ¼ hro $aÞ. The intrinsic thermal conductivity (kint,f) of the thick film is then calculated with Fourier’s law,
Tavf Tavs 1 t þ Ri $ ¼ hQ $Q 2al kint;f
! (7)
in which Q ¼ q$2al denotes the Joule heat generated from the heating strip. Ri is the total interfacial thermal resistance, for the interfaces between the metal strip and the film and between the thin film and the substrate. Factor (hQ) is introduced to compensate for the inaccuracy induced by the dependence on thickness of the lateral heat spreading within the thick film. This factor is thus modeled herein as a ratio of the Joule heat crossing the regiona x a to the total Joule heat. The infinite-series solution gives
hQ ¼
Qy 1 ¼ ðqaÞ qa (
Za ky 0
vTs ðx;cÞ dx vy
( ! !) 0 N X cosh ln c a 0 0 0 1þ ¼ 0 ln a $Ln $tanh ln t b n¼1 cosh ln d 0 ) 2sin2 ln a $ 2 ðln aÞ
(8)
After an investigation of parameters, an empirical relation replaces the analytical one for convenience, namely
hQ ¼ D1 exp D2 $t þ 0:11
unit of t : mm
D1 ¼ 0:00071$kint;f þ 0:899521
(9)
D2 ¼ 0:000092$kint;f þ 0:047338 As same as Eq. (6), Eq. (9) is also limited to the ranges 0.1 kint,f 2 (unit: W m1 K) and 2 t 10 (unit: mm) for accuracy. For uncertainty estimation, because quite difficult to prepare the laminated film samples, we did not consider the errors comes from manufacturing process, and just dealt with that induced by instrumental resolution and measured properties. On analyses of the uncertainty, Eq. (5) and Eq. (7) should be rewritten as
r Tavs ðTs ðx ¼ rÞ DTs Þ ro Dro ¼ pðks Dks Þl q$2al DQ
ln
! Tavf DTavf Tavs DTavs 1 t Dt þ Ri ¼ $ 2al kint;f hQ DhQ $ Q DQ
(10)
(11)
here, DTs and DTav-f are, respectively, the temperature errors of sensing strip and heating strip by means of RTD principle and using instrumental resolution of electrical resistance; DQ is the generated joule heat error multiplied by instrumental resolution of applied current and voltage. Dks could be generated from the published temperature-dependent property [22] and Dt was defined with the SEM pictures. As for Dro and DhQ, the both fitting errors are very small and equalize about 0.3%.
3. Experiments Thick TE films of BieTe (n-type) and SbeTe (p-type) fabricated with electrodeposition were prepared for measurements. Each film was deposited from the electrolyte with or without an added ionictype surfactant, yielding TE materials of four types to be measured: A, BieTe without surfactant; B, SbeTe without surfactant; C, BieTe with surfactant solution, and D, SbeTe with surfactant. The surfactant was anionic sodium dihexyl sulfosuccinate (SDSS) (Cytec Industries, Inc., USA), of ionic type, which is used to complete the fabrication of a micro-TE structure by enhancing the wettability of the electrolyte. The electrolyte compositions for type A were nitric acid (1.0 M), Bi2O3 (7.5 103 M from powder) and TeO2 (1.0 102 M, from powder), and for type B were nitric acid (1.0 M), Sb2O3 (7.5 103 M, from powder), TeO2 (1.0 102 M from powder) and sodium citrate (0.34 M, serving as a complexing agent). For types C and D materials, the electrolytes were the same as for types A and B, respectively, but with added SDSS surfactant (5 mL/L). Energy-dispersive X-ray analysis (EDX) provided the atomic composition of the deposited TE thick films in Table 1. The atomic proportions of the thick films agree with that of the bulk materials (Bi:Te and Sb:Te ¼ 2:3). Elements carbon (C) and oxygen (O) were detected in a considerable proportion from the surface of the materials fabricated with SDSS solutions e C w32% and O w31% in the BieTe film, and C w20% in the SbeTe film. According to an Auger depth profile, carbon was detected anywhere within the films of BieTe or SbeTe; this generation of elemental carbon accompanied the electrodeposition. Oxygen was detected not within the BieTe film but only on its surface; it appeared probably due to oxidation on contact with air while the film samples were taken from the aqueous solution. We measured the intrinsic thermal conductivity of TE films in two batches. For the first batch, we spin-coated photosensitive epoxy resin layers (trade name: WPR-1201, product of JSR Micro, Inc.) of varied thickness on a silicon substrate (P/Boron, 20e 25 U cm, thickness w525 mm), and then deposited a Cr/Au (thickness w 20 nm/200 nm) heating and sensing strip on the resin layer. Because the resin, WPR-1201, that served as a dielectric layer, is a negative photoresist, we used a positive photoresist, AZ P4620 (Clariant Inc.) to pattern and lift off the heating and sensing strip deposited on the resin. The width of the heating strip was 15 mm and of the sensing strip 10 mm; both strips have the same length 1.5 mm, and their spacing is 100 mm. Due to metallic structure, the heating strip and sensing strip could determine themselves working temperature using the RTD principle of operation. This job used a source meter (Keithley 2400) to apply a dc current to the heating strip for generating Joule heat, then measured the strip’s electrical resistance that can be converted into its heating temperature by using a pre-measured TCR (temperature coefficient of the resistance) correlation between the strip’s electrical resistance and bath temperature. With the same
Table 1 Atomic composition of thick deposited films according to EDX analysis. Material
Solution
Bi (at. %)
Sb (at. %)
Te (at. %)
C (at. %)
O (at. %)
Type A (BieTe) Type B (SbeTe) Type C (BieTe) Type D (SbeTe)
Non-added SDSS Non-added SDSS Added SDSS
37.23
e
62.77
e
e
e
40.38
59.62
e
e
14.31
e
21.61
32.78
31.3
Added SDSS
e
34.23
45.61
20.16
e
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Fig. 4. Schematic diagram of the sample chip and measurement system. A dc current is applied to the heating strip to generate joule heat; the measured electrical resistances of the heating strip and the sensing strip converted into their temperatures.
principle, we used a digital multimeter (Keithley 2700) to measured the electrical resistance of the sensing strip, which can be also converted into its temperature that is induced by the heating strip (shown in Fig. 4). In measurements on this batch, we determined the total thermal resistance of the thick resin film that included the thermal resistance of the resin layer and the interfacial thermal resistance of both the Si-resin and the Cr-resin. The total thermal resistance of the resin film, R*, depends on its film thickness (t), expressed as
m2 K W1 R* t ¼ RSiresin þ Rint;resin t þ RCrresin
(12)
For the second batch, we made a laminated film structure to measure the thermal resistance. The laminated film structure was fabricated with the TE film from electrodeposition on a silicon substrate, and then an epoxy resin layer (WPR-1201) was spincoated on the TE film. We used lithography and lift-off process to deposit the Cr/Au heating and sensing strip pattern upon the resin layer (shown in Fig. 3). For this batch, we measured the total thermal resistance of the laminated structure (R**), expressed as
R** t ¼ RSiTE þ Rint;TE t þ RTEresin þ Rint;resin t þ RCrresin m2 K W1
Fig. 6. Depth profile analysis of the BieTe film covered with a SiO2 layer (400 nm) from Auger electron spectra.
Eq. (14) is obtained on subtracting Eq. (12) from Eq. (13), and becomes as
R** R* ¼ Rint;TE t þ ðRSiTE þ RTEresin RSiresin Þ
(14)
The left side of Eq. (14), R** R*, is linearly proportional to the thickness, t, of the TE film through the thermal resistance, Rint,TE(t) ¼ t/kint,TE. The slope thus yields the reciprocal of the intrinsic thermal conductivity, 1/kint,TE independent of thickness. The second term on the right side of the equality is a sum of interfacial resistances that is obtained from the intersection of a curve fitting to the ordinate axis, and is independent of film thickness.
(13)
Fig. 5. SEM image of the unsuccessful sample. The heatereSiO2eTE samples could not be measured because the SiO2 layer lost its insulating property.
Fig. 7. Observed thermal resistance of the epoxy resin layer. The intrinsic thermal conductivity was calculated as a reciprocal of the slope of the curve through a mathematical correlation expressed in Eq. (5) and the expression Rint(t) ¼ t/kint for thermal resistance.
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Our experimental uncertainty arises mainly from instrumental resolution; its estimate was performed for our typical parameters: the electrical resistance of the heating strip is 30 U and that of the sensing strip is 45 U; the applied dc current for heating is 30 mA. The instrumental resolutions were DV ¼ 1 105 V and DI ¼ 1 106 A for the source meter (Keithley 2400) that matched with the heating strip; DU ¼ 5 104 U and DT ¼ 5 103 K for the multimeter (Keithley 2700) that matched with the sensing strip and was used also to measure the bath temperature to determine the temperature coefficient of the resistance (TCR) of both the heating strip and the sensing strip. For a variation 1 K in the controlled bath temperature, the uncertainty of thermal conductivity of the silicon substrate is 0.47% (at 293 K, k of silicon is 153 W m1 K1) [22]. According to Eq. (10) and the measured TCR relation, the error of the temperature is calculated as 0.22 K for Tav-f, 0.018 K for Tav-s; the error of the Joule heat generation is negligible because of its small value. Sequentially, from the expression, (Tav-f Tav-s)/q, for thermal resistance, the calculated error of the
thermal resistance, independent of film thickness, is thus stationary and is 2.25 107 m2 K W1. The film thickness was measured with a scanning electron microscope (SEM); its deviation, about 40 nm, is essential to evaluate the uncertainty of the measured intrinsic thermal conductivity (kint,TE) of the TE films. From Fourier’s law, in Eq. (11), the uncertainty of kint,TE is 11.95% for TE material of type A, 13.15% for type B and 9.24% for type C. Failed experiments for type D material precluded estimate of its uncertainty. 4. Result and discussion As the parallel-strip method, according to an electrical heating and sensing technique, was used to conduct our measurements, a dielectric layer was deposited between the metallic heating and sensing strip and the measured TE film for insulation. We originally tested PECVD SiO2 as the dielectric layer, but those trials failed because the layer lost its insulating characteristic. Many invisible
Fig. 8. Observed thermal resistance of TE films is shown as a linear function of thickness for types A, B and C materials. In the tests of types A and B, we measured samples in two sets from separate fabrications for verification; the obtained intrinsic thermal conductivities are similar. For the test of type D, the data are so irregular that no reasonable intrinsic thermal conductivity was found.
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81
Table 2 Comparison of measured data with published results (Refs. [26e29]). Measured thermal conductivity (W m1 k1) This work n-Type n-Type n-Type n-Type n-Type p-Type n-Type p-Type p-Type n-Type a b c d
Ref. Ref. Ref. Ref.
BieTe (Type A) (t) (film) BieTe (Type C) (t) (film) BieTe (t) (film) Bi2Te3 (bulk) Bi2Te3 (bulk) Bi2Te3 (bulk) Bi2Te3 (//) (single crystal) SbeTe (Type B) (tL) (film) Sb2Te3 (//) (single crystal) Sb2Te3 (t) (single crystal)
M. Takaishia
S. Miurab
G.J. Snyderc
H. Scherrerd
0.234 0.459 1.2 1.75 0.8 0.963 2 0.418 5.6 1.6
[26]. [27]. [28]. [29].
cracks in the layer destroyed its insulation because of a thin (<500 nm) SiO2 film deposited on a rough TE layer (shown in Fig. 5). As the metallic strip was patterned upon the SiO2 layer with lithography, a large spinning speed (1000 rpm) during photoresist spin coating might have resulted in a porous structure of the SiO2 layer through poor adhesion between the layers of SiO2 and TE, or the fragile structure of the TE film. With a heatereSiO2eTEsubstrate sample, a depth profile analysis from Auger electron spectra (AES) showed the metallic element of the heater (Au) had intruded into the SiO2 layer, and even into the TE layer, because significant Au was detected in these regions (shown in Fig. 6). After several feasibility tests, the photosensitive epoxy resin WPR-1201 was selected to serve as the dielectric layer. This resin layer retained its insulating characteristic because of its thickness (>5 mm) and complete structure. As mentioned above, measurements were conducted in two batches to extract the intrinsic thermal conductivity of TE films. In the first batch, we measured the thermal resistances of the photosensitive epoxy resin layers (trade name: WPR-1201) with varied thickness on a silicon substrate; the measured thermal resistance (shown in Fig. 7) is expressed as
R* ¼ 3:5952$t þ 1:5744 106
m2 K W1
(15)
According to Eq. (12) and the expression Rint, resin(t) ¼ t/kint, resin for thermal resistance, the total interfacial thermal resistance was obtained as the intersection of the fitted curve to the ordinate axis; the intrinsic thermal conductivity (kint, resin) was calculated as the reciprocal of the slope of the fitted curve. Including the uncertainties, the results of the first batch were instinct thermal conductivity kint, resin ¼ 0.278 0.0162 (5.84%) (W m1 K1) and total interfacial thermal resistance RSiresin þ RCrresin ¼ ð1:57 44 0:225Þ 106 ðm2 K W1 Þ. TE samples of four types, deposited on a silicon substrate and covered with an epoxy resin (WPR-1201) layer were measured in the second batch. Subtracting the observed thermal resistance of the first batch (R*) from that of the second batch (R**), we obtained the apparent thermal resistance of the TE layers expressed as the mathematical form of Eq. (14). The calculated thermal resistance and the intrinsic thermal conductivity of the TE films (shown in Fig. 8) follow: type A e BieTe deposited without surfactant e R** ¼ 4.269$t þ Ri,sum 4.5 107 (m2 K W1) and kint,TE ¼ 0.234 0.0279 (11.95%) (W m1 K1) appropriate for a film thickness from 0.48 mm to 1.24 mm; type B e SbeTe without surfactant e R** ¼ 2.394t þ Ri,sum 4.5 107 (m K W1) and kint,TE ¼ 0.418 0.0549 (13.15%) (W m1 K1) appropriate for a thickness from 0.61 mm to 2.0 mm; Type C e BieTe with added
surfactant e R** ¼ 2.18$t þ Ri,sum 4.5 107 (m2 K W1) and kint,TE ¼ 0.459 0.0424 (9.24%) (W m1 K1) appropriate for a thickness from 0.7 mm to 3.4 mm. Here, Ri,sum denotes the sum of the interfacial resistances appearing in Eq. (14). For type D e SbeTe material deposited with added surfactant, the test yielded no credible result of thermal conductivity because we found no reasonable linear correlation between the thermal resistance and the film thickness even though several samples were measured for this material type. Few directly measured thermal conductivities of both BieTe and SbeTe materials have been reported; most literature values were derived on adding the calculated lattice thermal conductivity (kl) and the electron thermal conductivity (ke) converted from the measured electrical conductivity with the WiedemanneFranz law [23e25]. Takaishi et al. [26] reported a thermal conductivity measured by the 3 U method for a n-type BieTe thin film, annealed at 200 C to be 1.20 W m1 K1. Miura et al. [27] reported k ¼ 1.75 W m1 K1 for hot-extruded Bi2Te3 bulk compound. Snyder’s article in handbook [28] reported the measured thermal conductivity of n-type bulk Bi2Te3 to be 0.8 W m1 K1 and that of p-type bulk Bi2Te3 to be 0.963 W m1 K1; the same book [29] elsewhere lists measured values of single-crystal bulk TE materials: k ¼ 2.0 W m1 K1 for Bi2Te3 (in plane); k ¼ 5.6 W m1 K1 for Sb2Te3 (in plane), and 1.6 W m1 K1 for Sb2Te3 (across plane). Table 2 compares the thermal conductivity from this work and from published articles. We found most reported data of bulk materials lie between 0.8 and 2.0 W m1 K1, and our measured intrinsic thermal conductivities are between 0.23 and 0.46 W m1 K1. Our measured values are at least half smaller than that of the aforementioned bulk materials. In theoretical, the thermal conductivity of an amorphous material should be significantly less than that of a bulk material due to severe heat carrier’s scattering. Moreover, the incompact structure like our samples also prevents the electrodeposited film a higher thermal conductivity. For these reasons, we argue the relatively lower intrinsic thermal conductivities of this work are reasonable. Fig. 9 shows SEM images of samples of types A, B and C. According to our observations of all SEM pictures (only some were shown in Fig. 9), the film morphology of each material type coincided within the measured range of film thickness. The significantly small intrinsic thermal conductivities likely resulted from strong scattering of thermal carriers at the evident grain boundaries. For material of type D, as mentioned above, the measurements were unsuccessful because we found no reasonable linear correlation between the thermal resistance and the film thickness. On reviewing the SEM pictures of this material, we found that the interface between the TE layer and the resin layer was blurred
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H.-C. Chien et al. / Applied Thermal Engineering 51 (2013) 75e83
Fig. 10. TEM images of samples of type D for film thicknesses 0.231 and 0.520 mm.
We measured also the Seebeck coefficient (S) and electrical conductivity (s) of these materials at 300 K and calculated their ZT values; S ¼ 40.9 mV K1, s ¼ 6.9686 104 mU1 m1 and ZT ¼ 0.149 for type A; S ¼ 136.4 mV K1, s ¼ 3.2787 104 mU1 m1 and ZT ¼ 0.438 for type B; S ¼ 35.1 mV K1, s ¼ 8.8028 104 mU1 m1 and ZT ¼ 0.071 for type C. The ZT values of types A, B and C are smaller than for the bulk materials, mainly because of their smaller electrical conductivities. 5. Conclusion
Fig. 9. SEM images of samples of types A, B and C for film thicknesses 1.009, 1.034 and 1.462 mm, respectively.
(shown in Fig. 10), perhaps because of the deposition of the resin layer: namely, for spin coating an appropriately thin resin layer on the TE film, a spin speed 5000 rpm and duration 50 s were applied. Such a spinning speed makes the colloidal resin grind the bumpy surface of the fragile TE film such that a thin mixed layer becomes formed between the resin and the TE film. Such a mixed layer of uncertain thickness and undetermined thermal properties was likely the cause of our failed measurements of intrinsic thermal conductivity of these samples.
We implemented a modified parallel-strip technique, appropriate for ranges 0.1 kint,f/W m1 K1 2 and 2 t/mm 10, to measure the intrinsic thermal conductivity of BieTe and SbeTe thermoelectric thin films; the measured results are much smaller than those reported. The smaller values likely resulted from the fragmental grain structure of the films from electrodeposition. Commonly SiO2 or Si3N4 serves as a dielectric layer to separate the metallic heater and the measured film in tests of thin films; the TE films are likely so fragile that the SiO2 dielectric thin layer becomes incompletely insulating because of the photoresist spin coating. We thus replaced the SiO2 layer with a thick layer of epoxy resin as the dielectric, and achieved successful measurements. In the future, with the same method and sample preparation, we plan to measure other thermoelectric thin-film materials, deposited with processes such as sputtering and screen printing, and with electrodeposition with varied parameters, to explore their distinctive physical characteristics.
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[15] D.G. Cahill, Thermal conductivity measurement from 30 to 750 K: the 3u method, Review of Scientific Instruments 61 (1990) 802e808. [16] S.M. Lee, D.G. Cahill, Heat transport in thin dielectric films, Journal of Applied Physics 81 (1997) 2590e2595. [17] S. Govorkov, W. Ruderman, M.W. Horn, R.B. Goodman, M. Rothschild, A new method for measuring thermal conductivity of thin films, Review of Scientific Instruments 68 (1997) 3828e3834. [18] O.W. Käding, H. Shurk, K.E. Goodson, Thermal conduction in metallized silicon-dioxide layers on silicon, Applied Physics Letters 65 (1994) 1629e 1631. [19] C.R. Yang, C.H. Yang, P.Y. Chen, Study on anisotropic silicon etching characteristics in various surfactant-added tetramethyl ammonium hydroxide water solutions, Journal of Micromechanics and Microengineering 15 (2005) 2028e2037. [20] H.C. Chien, D.J. Yao, M.J. Huang, T.Y. Chang, Thermal conductivity measurement and interface thermal resistance estimation using SiO2 thin film, Review of Scientific Instruments 79 (2008) 054902. [21] H.C. Chien, D.J. Yao, C.T. Hsu, Measurement and evaluation of the interfacial thermal resistance between a metal and a dielectric, Applied Physics Letters 93 (2008) 231910. [22] Y.S. Touloukian, R.W. Powell, C.Y. Ho, P.G. Klemens, Thermal Conductivity: Metallic Elements and Alloys, IFI/Plenum, New York, USA, 1970. [23] M. Takashiri, K. Miyazaki, S. Tanaka, J. Kurosaki, D. Nagai, H. Tsukamoto, Effect of grain size on thermoelectric properties of n-type nanocrystalline bismuthe telluride based thin films, Journal of Applied Physics 104 (2008) 084302. [24] T. Thonhauser, T.J. Scheidemantel, J.O. Sofo, J.V. Badding, G.D. Mahan, Thermoelectric properties of Sb2Te3 under pressure and uniaxial stress, Physical Review B 68 (2003) 085201. [25] O. Yamashita, K. Satou, H. Odahara, S. Tomiyoshi, Dependence of thermal conductivity on electrical resistivity in bismuthetellurides, Journal of Physics and Chemistry of Solids 66 (2005) 1287e1293. [26] M. Takaishi, S. Tanaka, K. Miyazaki, H. Tsukamoto, Thermal conductivity measurements of bismuth telluride thin films by using the 3 omega method, Thermophysical Properties 27 (2006) 24e26. [27] S. Miura, Y. Sato, K. Fukuda, K. Nishimura, K. Ikeda, Texture and thermoelectric properties of hot-extruded Bi2Te3 compound, Materials Science and Engineering: A 277 (2000) 244e249. [28] G.J. Snyder, in: D.M. Rowe (Ed.), Thermoelectric Handbook: Macro to Nano, CRC Press, Boca Raton, FL, USA, 2006 (chapter 9). [29] H. Scherrer, S. Scherrer, in: D.M. Rowe (Ed.), Thermoelectric Handbook: Macro to Nano, CRC Press, Boca Raton, FL USA, 2006 (Chapter 27).
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Thermal conductivity of thermoelectric thick films prepared by electrodeposition Heng-Chieh Chien a, Chii-Rong Yang c, Li-Ling Liao a, Chun-Kai Liu a, Ming-Ji Dai a, Ra-Min Tain a, Da-Jeng Yao b, d, * a
Electronics and Optoelectronics Research Laboratories, Industrial Technology Research Institute, Hsinchu 31040, Taiwan, ROC Department of Engineering and System Science, National Tsing Hua University, Hsinchu 30013, Taiwan, ROC Department of Mechatonic Technology, National Taiwan Normal University, Taipei 10610, Taiwan, ROC d Institute of NanoEngineering and MicroSystems, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC b c
h i g h l i g h t s < A novel technique was used to measure the thermal conductivities of thermoelectric thick films. < The thick films are of BieTe and SbeTe compositions and were prepared by electrodeposition. < We used a particular method to prepare a measurable sample. < We compared the thermal conductivities of the films made by different aqueous solutions.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 May 2012 Accepted 3 September 2012 Available online 16 September 2012
Because of a lack of appropriate methods and the difficulties of sample preparation, few direct measurements of the thermal conductivity of thermoelectric materials in thin films have been reported. We prepared thermoelectric thin films of four types containing BieTe and SbeTe by electrodeposition from aqueous solutions with and without added surfactant, and evaluated their intrinsic thermal conductivity with a modified parallel-strip technique. Three thermoelectric materials showed values 0.2e0.5 W m1 K1 of intrinsic thermal conductivity; for the other type problems of sample preparation precluded measurement. According to observations with a scanning electron microscope, the existence of grain boundaries in the thermoelectric thin films is likely the cause of the small values, and their fragile structure causes difficulty in preparation of a test sample. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Thermoelectric Thick film Electrodeposition Thermal conductivity Measurement
1. Introduction The practicality of thermoelectric (TE) devices is limited mainly by the available materials, of which the performance must be improved to compete with conventional cooling and energy-generation systems. The efficiency of TE materials is directly related to a dimensionless figure of merit defined as ZT ¼ S2sT/k; s denotes electrical conductivity, S Seebeck coefficient, k thermal conductivity and T absolute temperature. An enhancement of the TE figure of merit is achievable on increasing the Seebeck coefficient (S) and the electrical conductivity (s), or decreasing the thermal conductivity (k). Among common TE materials, bismuth telluride (Bi2Te3) that serves typically as an n-type material and antimony telluride (Sb2Te3) as a p* Corresponding author. Institute of NanoEngineering and MicroSystems, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC. Tel.: þ886 (0)3 5742850; fax: þ886 (0)3 5745454. E-mail address: [email protected] (D.-J. Yao). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.09.004
type material are reported to show optimal performance near 300 K in bulk form because they have a large thermoelectric figure of merit. Relative to bulk materials, TE film structures are expected to have a significantly smaller thermal conductivity because phonons are strongly scattered at both film interfaces and denser grain boundaries [1e4]; these structures thereby show a feasibility in applications of hot-spot cooling and electric generation operated at small to moderate temperature differences. Among methods to fabricate Bi2Te3 and Sb2Te3 films, electrodeposition [5e8] is simple and cheap relative to dry processes such as molecular-beam epitaxy (MBE) [9], metal-organic chemical-vapor deposition (MOCVD) [10], pulsed laser deposition [11,12], flash evaporation [13] and sputtering [14]. Electrodeposition also enables an easy control of film thickness in a range 0.01e50 mm that shows feasibility and suitability for fabricating the micro-TE devices. Methods to measure the thermal conductivity of thin film with a thickness in the range between 0.01 mm and 1 mm include the 3u
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method [15,16] and others [17,18], but published methods to measure the thermal conductivity of a film of thickness greater than about 5 mm are few because of a strong heat-spreading effect in the in-plane direction of such a thick film. For instance, in a general measurement to determine the thermal conductivity of a film of thickness 10 mm heated with a strip of width 10 mm, the heat diffusing sideways into the film might be about one fifth of the total generated heat. As the thickness increases, so does the heat spreading. The significant lateral heat spreading in a thick film prevents use of Fourier’s law to calculate the thermal conductivity because of inaccurate heat flow and immeasurable temperature of the film/substrate interface. We measured the intrinsic thermal conductivity of TE materials, Bi2Te3 and Sb2Te3, prepared by electrodeposition from the aqueous solutions with and without an added ionic surfactant. The surfactant is anionic sodium dihexyl sulfosuccinate (SDSS) and commonly used in an electrodeposition process to enhance the probability of fabricating a complete micro-TE structure [19]. To prepare the sample, the TE layer (thickness 0.5e3 mm) was deposited on a silicon substrate and spin-coated with a layer of photosensitive epoxy resin (thickness 5e10 mm) that served as a dielectric layer to separate the metallic heating strip from the measured TE layer. We applied a modified parallel-strip method [20,21], an electrical heating and sensing technique, to measure the thermal resistance of such the TE film samples; the measured apparent thermal resistance (Rapp) comprises the film’s intrinsic thermal resistance (Rint ¼ t/kint) and the interfacial resistance (Ri) and is expressed as Rapp ¼ t/kint þ Ri. The correlation between measured thermal resistance and thickness is related to the film’s thermal conductivity; hence, on measurement of TE layers of varied thickness, the measured thermal resistances of the layers could yield their intrinsic thermal conductivity.
The parallel-strip method originates from the analytical solutions of a heater-film-substrate heat conduction problem. Fig. 1 shows the schematic configuration of the two-dimensional steady-state problem. The method assumes a dc current is passed through a heating strip (width ¼ 2a) that deposited upon the measured film (film thickness is t), and thus a constant Joule heat flux (q) is generated from the strip. The designed strip’s length has to be much longer than it’s width for the 2D assumption. The thickness and width of substrate are c and 2b, respectively. The correlated boundary conditions are also shown in Fig. 1; the analytical solutions are expressed as below:
Tf x;d Ta ðqa=hbÞ
$
hc ht hbRiðhf Þ þ þ a ks kf
! þ
N X 1 Ln $tanhðln dÞþ coshðln tÞ ðln aÞ n¼1
! ha kf (1)
2sinðln aÞ $cosðln xÞ $ ðln aÞ X N Ts ðx; cÞ Ta hc ha 1 þ $ $tanhðln cÞ þ 1 ¼ 1þ ks ks ðln aÞ ðqa=hbÞ n¼1 $Fn $cosðln xÞ
Tavgf ¼
2. The modified parallel-strip method Our previous literature [20,21] has described a novel technique, called the parallel-strip method, for measuring the intrinsic thermal conductivity of a dielectric thin film with thickness less than 3 mm. In this job, we would also introduce the parallel-strip method and modify it to measure a thicker laminated film with thickness between 2 mm and 10 mm. The laminated structure comprises a resin layer and a electrodeposited TE layer.
¼ 1þhRiðf sÞ þ
ð2Þ
! ! hc ht hbRiðhf Þ ha þ þ þ a hb ks kf kf ( # ) 2 N X 1 Ln 2sin ðln aÞ $ þ Ta 0 $ $tanhðln dÞ þ 2 ðln aÞ cosh ln t ðln aÞ n¼1 qa
"
1 þ hRiðf sÞ þ
$
(3)
Tavgs ¼
" X N qa hc 1 ha tanhðln cÞ $ 1þ $ þ $ þ1 hb ks a n¼1 ks ðln aÞ # sinðln wÞ þ Ta ð4Þ $Fn $
ln
Fig. 1. Schematic model for the two-dimensional steady-state heat conduction problem of the parallel-strip method.
H.-C. Chien et al. / Applied Thermal Engineering 51 (2013) 75e83
where
Ln ¼
coshðl cÞ kf 1 sinhðln cÞ n hRiðf sÞ þ Un $ ha coshðln dÞ ðln aÞ coshðln dÞ kf ðln aÞ hRiðf sÞ þ Un $tanhðln tÞ 1þ ha
ha tanhðln cÞ 1þ $ ks ðln aÞ Un ¼ ks 1þ ðln aÞ$tanhðln cÞ ha 1 coshðln cÞ l l L $ð aÞ$tanhð tÞ n n n 0 C d 2sinðln aÞ B C Bcosh ln Fn ¼ $B C A ks ðln aÞ @ ðln aÞ$tanhðln cÞ 1þ ha 0
ln b ¼ np;
n ¼ 1; 2; 3.
here, k and T denote the thermal conductivity and the temperature respectively with indices “s” for the substrate and “f” for the thin film. h denotes the boundary convective condition, Ta is the ambient temperature. The total interface thermal resistance (Ri) from the metal strip to the substrate is expressed as Ri ¼ Ri(hf) þ Ri(fs), which involved the one at the interface between the metal strip and thin film (Ri(hf)), and the one at the interface between thin film and the substrate (Ri(fs)). Eqs. (3) and (4) give the average temperatures on the top side of the film (Tavg-f) and at the interface between the film and the substrate (Tavg-s), respectively, over the range of 0 x a. With typical substrate thickness (c ¼ 200e2000 mm) and substrate width (2b ¼ 1 cm), a simple 2D simulation result shows the temperature contour is nearly a perfect semicircle in a specific range of r. Also, the analytical solution shows the thermal resistance to a specific range of 50 mm r 120 mm has a logarithmic dependence on r, as shown in Fig. 2. Thus, a semi-empirical correlation is found as
Tavs Ts ðx ¼ rÞ lnðr=ro Þ ; for 50 mm r 120 mm ¼ pks l q$2al
(5)
Fig. 2. The thermal resistance of the substrate within a distance (r) From the location (0, c), expressed as (Tavg-sTs(r,c))/(q$2al), has a logarithmic dependence on r to a specific range of 50 mm r 120 mm.
77
In Eq. (5), the left term is thermal resistance from the interface with Tav-s to the point with Ts in the form of temperature and heat flux; the right term is the same thermal resistance from and to the same positions in the form of substrate’s thermal conductivity and dimensions; in which ro is a fitting parameter. From Eq. (5), the immeasurable temperature, Tav-s, could be deduced by the temperature, Ts (x ¼ r). Because the film is relatively thin compared with the distance r, and the heat flux in the cross-plane direction at x ¼ r is negligible, the Ts (x ¼ r) in Eq. (5) is assumed to equalize the sensing strip temperature Tf (x ¼ r) that can be determined by means of the RTD (Resistance Temperature Detector) principle of operation. To introduce the parallel-strip method mentioned above for measuring a thick TE film prepared by electrodeposition, we need to modify the fitting parameter, ro, by analyzing Eqs. (1)e(4) to suit the thicker measured film. Fig. 3 shows a schematic cross section of the thick-film sample in this job. The typical spacing (r) between the heating strip and the sensing strip is 100 mm; the width of the heating strip is 15 mm and that of the sensing strip is 10 mm. The measured film is a laminated structure which comprises a thicker resin layer and a thinner TE layer. After data analysis with the analytical solutions, Eqs. (3) and (4), we found that ro varies with the thickness (t) and the intrinsic thermal conductivity (kint,f) of the measured film, to be expressed as
ro ¼ hro $a hro ¼ C1 $t C2 þ 0:4381 unit of t : mm C1 ¼ 0:0005$kint;f þ 0:00985 C2 ¼ 0:014638$kint;f þ 1:533166
(6)
Eq. (6) is limited to the ranges 0.1 kint,f 2 (unit: W m1 K1) and 2 t 10 (unit: mm) for accuracy. The limitation was defined as the specific ranges are mainly because the dimension and property of all the measured laminated films are within the ranges. Besides, more limited range usually help the extracted empirical equations to have a higher accuracy. In the use of Eq. (5), parameter kint,f must be initially guessed, and then iteratively improved until the value converges. As the evaluated thermal conductivity (kint,f) is insensitive to parameter ro for such a thick film, we suggest that kint,f can be assigned directly as 1.0, rather than being generated iteratively, and can yield a useful value of the evaluated kint,f (error < 0.1%).
Fig. 3. Schematic diagram of the laminated film structure used for the parallel-strip method. The typical spacing between the heating strip and the sensing strip is 100 mm, the width of the heating strip is 15 mm and of the sensing strip 10 mm.
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Because the immeasurable temperature, Tav-s, has been calculated, we propose another method to measure the thermal conductivity of a thick film as follows: the average temperature on top of the film (Tav-f), also is the heating strip’s temperature, could be measured using the RTD operation principle; the average temperature (Tav-s) could be deduced using Eq. (5), measured sensing strip’s temperature and the calculated parameter ro ð ¼ hro $aÞ. The intrinsic thermal conductivity (kint,f) of the thick film is then calculated with Fourier’s law,
Tavf Tavs 1 t þ Ri $ ¼ hQ $Q 2al kint;f
! (7)
in which Q ¼ q$2al denotes the Joule heat generated from the heating strip. Ri is the total interfacial thermal resistance, for the interfaces between the metal strip and the film and between the thin film and the substrate. Factor (hQ) is introduced to compensate for the inaccuracy induced by the dependence on thickness of the lateral heat spreading within the thick film. This factor is thus modeled herein as a ratio of the Joule heat crossing the regiona x a to the total Joule heat. The infinite-series solution gives
hQ ¼
Qy 1 ¼ ðqaÞ qa (
Za ky 0
vTs ðx;cÞ dx vy
( ! !) 0 N X cosh ln c a 0 0 0 1þ ¼ 0 ln a $Ln $tanh ln t b n¼1 cosh ln d 0 ) 2sin2 ln a $ 2 ðln aÞ
(8)
After an investigation of parameters, an empirical relation replaces the analytical one for convenience, namely
hQ ¼ D1 exp D2 $t þ 0:11
unit of t : mm
D1 ¼ 0:00071$kint;f þ 0:899521
(9)
D2 ¼ 0:000092$kint;f þ 0:047338 As same as Eq. (6), Eq. (9) is also limited to the ranges 0.1 kint,f 2 (unit: W m1 K) and 2 t 10 (unit: mm) for accuracy. For uncertainty estimation, because quite difficult to prepare the laminated film samples, we did not consider the errors comes from manufacturing process, and just dealt with that induced by instrumental resolution and measured properties. On analyses of the uncertainty, Eq. (5) and Eq. (7) should be rewritten as
r Tavs ðTs ðx ¼ rÞ DTs Þ ro Dro ¼ pðks Dks Þl q$2al DQ
ln
! Tavf DTavf Tavs DTavs 1 t Dt þ Ri ¼ $ 2al kint;f hQ DhQ $ Q DQ
(10)
(11)
here, DTs and DTav-f are, respectively, the temperature errors of sensing strip and heating strip by means of RTD principle and using instrumental resolution of electrical resistance; DQ is the generated joule heat error multiplied by instrumental resolution of applied current and voltage. Dks could be generated from the published temperature-dependent property [22] and Dt was defined with the SEM pictures. As for Dro and DhQ, the both fitting errors are very small and equalize about 0.3%.
3. Experiments Thick TE films of BieTe (n-type) and SbeTe (p-type) fabricated with electrodeposition were prepared for measurements. Each film was deposited from the electrolyte with or without an added ionictype surfactant, yielding TE materials of four types to be measured: A, BieTe without surfactant; B, SbeTe without surfactant; C, BieTe with surfactant solution, and D, SbeTe with surfactant. The surfactant was anionic sodium dihexyl sulfosuccinate (SDSS) (Cytec Industries, Inc., USA), of ionic type, which is used to complete the fabrication of a micro-TE structure by enhancing the wettability of the electrolyte. The electrolyte compositions for type A were nitric acid (1.0 M), Bi2O3 (7.5 103 M from powder) and TeO2 (1.0 102 M, from powder), and for type B were nitric acid (1.0 M), Sb2O3 (7.5 103 M, from powder), TeO2 (1.0 102 M from powder) and sodium citrate (0.34 M, serving as a complexing agent). For types C and D materials, the electrolytes were the same as for types A and B, respectively, but with added SDSS surfactant (5 mL/L). Energy-dispersive X-ray analysis (EDX) provided the atomic composition of the deposited TE thick films in Table 1. The atomic proportions of the thick films agree with that of the bulk materials (Bi:Te and Sb:Te ¼ 2:3). Elements carbon (C) and oxygen (O) were detected in a considerable proportion from the surface of the materials fabricated with SDSS solutions e C w32% and O w31% in the BieTe film, and C w20% in the SbeTe film. According to an Auger depth profile, carbon was detected anywhere within the films of BieTe or SbeTe; this generation of elemental carbon accompanied the electrodeposition. Oxygen was detected not within the BieTe film but only on its surface; it appeared probably due to oxidation on contact with air while the film samples were taken from the aqueous solution. We measured the intrinsic thermal conductivity of TE films in two batches. For the first batch, we spin-coated photosensitive epoxy resin layers (trade name: WPR-1201, product of JSR Micro, Inc.) of varied thickness on a silicon substrate (P/Boron, 20e 25 U cm, thickness w525 mm), and then deposited a Cr/Au (thickness w 20 nm/200 nm) heating and sensing strip on the resin layer. Because the resin, WPR-1201, that served as a dielectric layer, is a negative photoresist, we used a positive photoresist, AZ P4620 (Clariant Inc.) to pattern and lift off the heating and sensing strip deposited on the resin. The width of the heating strip was 15 mm and of the sensing strip 10 mm; both strips have the same length 1.5 mm, and their spacing is 100 mm. Due to metallic structure, the heating strip and sensing strip could determine themselves working temperature using the RTD principle of operation. This job used a source meter (Keithley 2400) to apply a dc current to the heating strip for generating Joule heat, then measured the strip’s electrical resistance that can be converted into its heating temperature by using a pre-measured TCR (temperature coefficient of the resistance) correlation between the strip’s electrical resistance and bath temperature. With the same
Table 1 Atomic composition of thick deposited films according to EDX analysis. Material
Solution
Bi (at. %)
Sb (at. %)
Te (at. %)
C (at. %)
O (at. %)
Type A (BieTe) Type B (SbeTe) Type C (BieTe) Type D (SbeTe)
Non-added SDSS Non-added SDSS Added SDSS
37.23
e
62.77
e
e
e
40.38
59.62
e
e
14.31
e
21.61
32.78
31.3
Added SDSS
e
34.23
45.61
20.16
e
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79
Fig. 4. Schematic diagram of the sample chip and measurement system. A dc current is applied to the heating strip to generate joule heat; the measured electrical resistances of the heating strip and the sensing strip converted into their temperatures.
principle, we used a digital multimeter (Keithley 2700) to measured the electrical resistance of the sensing strip, which can be also converted into its temperature that is induced by the heating strip (shown in Fig. 4). In measurements on this batch, we determined the total thermal resistance of the thick resin film that included the thermal resistance of the resin layer and the interfacial thermal resistance of both the Si-resin and the Cr-resin. The total thermal resistance of the resin film, R*, depends on its film thickness (t), expressed as
m2 K W1 R* t ¼ RSiresin þ Rint;resin t þ RCrresin
(12)
For the second batch, we made a laminated film structure to measure the thermal resistance. The laminated film structure was fabricated with the TE film from electrodeposition on a silicon substrate, and then an epoxy resin layer (WPR-1201) was spincoated on the TE film. We used lithography and lift-off process to deposit the Cr/Au heating and sensing strip pattern upon the resin layer (shown in Fig. 3). For this batch, we measured the total thermal resistance of the laminated structure (R**), expressed as
R** t ¼ RSiTE þ Rint;TE t þ RTEresin þ Rint;resin t þ RCrresin m2 K W1
Fig. 6. Depth profile analysis of the BieTe film covered with a SiO2 layer (400 nm) from Auger electron spectra.
Eq. (14) is obtained on subtracting Eq. (12) from Eq. (13), and becomes as
R** R* ¼ Rint;TE t þ ðRSiTE þ RTEresin RSiresin Þ
(14)
The left side of Eq. (14), R** R*, is linearly proportional to the thickness, t, of the TE film through the thermal resistance, Rint,TE(t) ¼ t/kint,TE. The slope thus yields the reciprocal of the intrinsic thermal conductivity, 1/kint,TE independent of thickness. The second term on the right side of the equality is a sum of interfacial resistances that is obtained from the intersection of a curve fitting to the ordinate axis, and is independent of film thickness.
(13)
Fig. 5. SEM image of the unsuccessful sample. The heatereSiO2eTE samples could not be measured because the SiO2 layer lost its insulating property.
Fig. 7. Observed thermal resistance of the epoxy resin layer. The intrinsic thermal conductivity was calculated as a reciprocal of the slope of the curve through a mathematical correlation expressed in Eq. (5) and the expression Rint(t) ¼ t/kint for thermal resistance.
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Our experimental uncertainty arises mainly from instrumental resolution; its estimate was performed for our typical parameters: the electrical resistance of the heating strip is 30 U and that of the sensing strip is 45 U; the applied dc current for heating is 30 mA. The instrumental resolutions were DV ¼ 1 105 V and DI ¼ 1 106 A for the source meter (Keithley 2400) that matched with the heating strip; DU ¼ 5 104 U and DT ¼ 5 103 K for the multimeter (Keithley 2700) that matched with the sensing strip and was used also to measure the bath temperature to determine the temperature coefficient of the resistance (TCR) of both the heating strip and the sensing strip. For a variation 1 K in the controlled bath temperature, the uncertainty of thermal conductivity of the silicon substrate is 0.47% (at 293 K, k of silicon is 153 W m1 K1) [22]. According to Eq. (10) and the measured TCR relation, the error of the temperature is calculated as 0.22 K for Tav-f, 0.018 K for Tav-s; the error of the Joule heat generation is negligible because of its small value. Sequentially, from the expression, (Tav-f Tav-s)/q, for thermal resistance, the calculated error of the
thermal resistance, independent of film thickness, is thus stationary and is 2.25 107 m2 K W1. The film thickness was measured with a scanning electron microscope (SEM); its deviation, about 40 nm, is essential to evaluate the uncertainty of the measured intrinsic thermal conductivity (kint,TE) of the TE films. From Fourier’s law, in Eq. (11), the uncertainty of kint,TE is 11.95% for TE material of type A, 13.15% for type B and 9.24% for type C. Failed experiments for type D material precluded estimate of its uncertainty. 4. Result and discussion As the parallel-strip method, according to an electrical heating and sensing technique, was used to conduct our measurements, a dielectric layer was deposited between the metallic heating and sensing strip and the measured TE film for insulation. We originally tested PECVD SiO2 as the dielectric layer, but those trials failed because the layer lost its insulating characteristic. Many invisible
Fig. 8. Observed thermal resistance of TE films is shown as a linear function of thickness for types A, B and C materials. In the tests of types A and B, we measured samples in two sets from separate fabrications for verification; the obtained intrinsic thermal conductivities are similar. For the test of type D, the data are so irregular that no reasonable intrinsic thermal conductivity was found.
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Table 2 Comparison of measured data with published results (Refs. [26e29]). Measured thermal conductivity (W m1 k1) This work n-Type n-Type n-Type n-Type n-Type p-Type n-Type p-Type p-Type n-Type a b c d
Ref. Ref. Ref. Ref.
BieTe (Type A) (t) (film) BieTe (Type C) (t) (film) BieTe (t) (film) Bi2Te3 (bulk) Bi2Te3 (bulk) Bi2Te3 (bulk) Bi2Te3 (//) (single crystal) SbeTe (Type B) (tL) (film) Sb2Te3 (//) (single crystal) Sb2Te3 (t) (single crystal)
M. Takaishia
S. Miurab
G.J. Snyderc
H. Scherrerd
0.234 0.459 1.2 1.75 0.8 0.963 2 0.418 5.6 1.6
[26]. [27]. [28]. [29].
cracks in the layer destroyed its insulation because of a thin (<500 nm) SiO2 film deposited on a rough TE layer (shown in Fig. 5). As the metallic strip was patterned upon the SiO2 layer with lithography, a large spinning speed (1000 rpm) during photoresist spin coating might have resulted in a porous structure of the SiO2 layer through poor adhesion between the layers of SiO2 and TE, or the fragile structure of the TE film. With a heatereSiO2eTEsubstrate sample, a depth profile analysis from Auger electron spectra (AES) showed the metallic element of the heater (Au) had intruded into the SiO2 layer, and even into the TE layer, because significant Au was detected in these regions (shown in Fig. 6). After several feasibility tests, the photosensitive epoxy resin WPR-1201 was selected to serve as the dielectric layer. This resin layer retained its insulating characteristic because of its thickness (>5 mm) and complete structure. As mentioned above, measurements were conducted in two batches to extract the intrinsic thermal conductivity of TE films. In the first batch, we measured the thermal resistances of the photosensitive epoxy resin layers (trade name: WPR-1201) with varied thickness on a silicon substrate; the measured thermal resistance (shown in Fig. 7) is expressed as
R* ¼ 3:5952$t þ 1:5744 106
m2 K W1
(15)
According to Eq. (12) and the expression Rint, resin(t) ¼ t/kint, resin for thermal resistance, the total interfacial thermal resistance was obtained as the intersection of the fitted curve to the ordinate axis; the intrinsic thermal conductivity (kint, resin) was calculated as the reciprocal of the slope of the fitted curve. Including the uncertainties, the results of the first batch were instinct thermal conductivity kint, resin ¼ 0.278 0.0162 (5.84%) (W m1 K1) and total interfacial thermal resistance RSiresin þ RCrresin ¼ ð1:57 44 0:225Þ 106 ðm2 K W1 Þ. TE samples of four types, deposited on a silicon substrate and covered with an epoxy resin (WPR-1201) layer were measured in the second batch. Subtracting the observed thermal resistance of the first batch (R*) from that of the second batch (R**), we obtained the apparent thermal resistance of the TE layers expressed as the mathematical form of Eq. (14). The calculated thermal resistance and the intrinsic thermal conductivity of the TE films (shown in Fig. 8) follow: type A e BieTe deposited without surfactant e R** ¼ 4.269$t þ Ri,sum 4.5 107 (m2 K W1) and kint,TE ¼ 0.234 0.0279 (11.95%) (W m1 K1) appropriate for a film thickness from 0.48 mm to 1.24 mm; type B e SbeTe without surfactant e R** ¼ 2.394t þ Ri,sum 4.5 107 (m K W1) and kint,TE ¼ 0.418 0.0549 (13.15%) (W m1 K1) appropriate for a thickness from 0.61 mm to 2.0 mm; Type C e BieTe with added
surfactant e R** ¼ 2.18$t þ Ri,sum 4.5 107 (m2 K W1) and kint,TE ¼ 0.459 0.0424 (9.24%) (W m1 K1) appropriate for a thickness from 0.7 mm to 3.4 mm. Here, Ri,sum denotes the sum of the interfacial resistances appearing in Eq. (14). For type D e SbeTe material deposited with added surfactant, the test yielded no credible result of thermal conductivity because we found no reasonable linear correlation between the thermal resistance and the film thickness even though several samples were measured for this material type. Few directly measured thermal conductivities of both BieTe and SbeTe materials have been reported; most literature values were derived on adding the calculated lattice thermal conductivity (kl) and the electron thermal conductivity (ke) converted from the measured electrical conductivity with the WiedemanneFranz law [23e25]. Takaishi et al. [26] reported a thermal conductivity measured by the 3 U method for a n-type BieTe thin film, annealed at 200 C to be 1.20 W m1 K1. Miura et al. [27] reported k ¼ 1.75 W m1 K1 for hot-extruded Bi2Te3 bulk compound. Snyder’s article in handbook [28] reported the measured thermal conductivity of n-type bulk Bi2Te3 to be 0.8 W m1 K1 and that of p-type bulk Bi2Te3 to be 0.963 W m1 K1; the same book [29] elsewhere lists measured values of single-crystal bulk TE materials: k ¼ 2.0 W m1 K1 for Bi2Te3 (in plane); k ¼ 5.6 W m1 K1 for Sb2Te3 (in plane), and 1.6 W m1 K1 for Sb2Te3 (across plane). Table 2 compares the thermal conductivity from this work and from published articles. We found most reported data of bulk materials lie between 0.8 and 2.0 W m1 K1, and our measured intrinsic thermal conductivities are between 0.23 and 0.46 W m1 K1. Our measured values are at least half smaller than that of the aforementioned bulk materials. In theoretical, the thermal conductivity of an amorphous material should be significantly less than that of a bulk material due to severe heat carrier’s scattering. Moreover, the incompact structure like our samples also prevents the electrodeposited film a higher thermal conductivity. For these reasons, we argue the relatively lower intrinsic thermal conductivities of this work are reasonable. Fig. 9 shows SEM images of samples of types A, B and C. According to our observations of all SEM pictures (only some were shown in Fig. 9), the film morphology of each material type coincided within the measured range of film thickness. The significantly small intrinsic thermal conductivities likely resulted from strong scattering of thermal carriers at the evident grain boundaries. For material of type D, as mentioned above, the measurements were unsuccessful because we found no reasonable linear correlation between the thermal resistance and the film thickness. On reviewing the SEM pictures of this material, we found that the interface between the TE layer and the resin layer was blurred
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Fig. 10. TEM images of samples of type D for film thicknesses 0.231 and 0.520 mm.
We measured also the Seebeck coefficient (S) and electrical conductivity (s) of these materials at 300 K and calculated their ZT values; S ¼ 40.9 mV K1, s ¼ 6.9686 104 mU1 m1 and ZT ¼ 0.149 for type A; S ¼ 136.4 mV K1, s ¼ 3.2787 104 mU1 m1 and ZT ¼ 0.438 for type B; S ¼ 35.1 mV K1, s ¼ 8.8028 104 mU1 m1 and ZT ¼ 0.071 for type C. The ZT values of types A, B and C are smaller than for the bulk materials, mainly because of their smaller electrical conductivities. 5. Conclusion
Fig. 9. SEM images of samples of types A, B and C for film thicknesses 1.009, 1.034 and 1.462 mm, respectively.
(shown in Fig. 10), perhaps because of the deposition of the resin layer: namely, for spin coating an appropriately thin resin layer on the TE film, a spin speed 5000 rpm and duration 50 s were applied. Such a spinning speed makes the colloidal resin grind the bumpy surface of the fragile TE film such that a thin mixed layer becomes formed between the resin and the TE film. Such a mixed layer of uncertain thickness and undetermined thermal properties was likely the cause of our failed measurements of intrinsic thermal conductivity of these samples.
We implemented a modified parallel-strip technique, appropriate for ranges 0.1 kint,f/W m1 K1 2 and 2 t/mm 10, to measure the intrinsic thermal conductivity of BieTe and SbeTe thermoelectric thin films; the measured results are much smaller than those reported. The smaller values likely resulted from the fragmental grain structure of the films from electrodeposition. Commonly SiO2 or Si3N4 serves as a dielectric layer to separate the metallic heater and the measured film in tests of thin films; the TE films are likely so fragile that the SiO2 dielectric thin layer becomes incompletely insulating because of the photoresist spin coating. We thus replaced the SiO2 layer with a thick layer of epoxy resin as the dielectric, and achieved successful measurements. In the future, with the same method and sample preparation, we plan to measure other thermoelectric thin-film materials, deposited with processes such as sputtering and screen printing, and with electrodeposition with varied parameters, to explore their distinctive physical characteristics.
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