nanomaterials Article Measuring Device and Material ZT in a Thin-Film Si-Based Thermoelectric Microgenerator Pablo Ferrando-Villalba 1,† , Antonio Pablo Pérez-Marín 1 , Llibertat Abad 2 , Gustavo Gonçalves Dalkiranis 1 , Aitor F. Lopeandia 1, * , Gemma Garcia 1 and Javier Rodriguez-Viejo 1 1 Departament de Física, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Spain; pablo.ferrandovillalba@imec.be (P.F.-V.); apperezmarin@gmail.com (A.P.P.-M.); dalkiranis@gmail.com (G.G.D.); gemma.garcia@uab.cat (G.G.); Javier.rodriguez@uab.cat (J.R.-V.) 2 Institut de Microelectrònica de Barcelona-Centro Nacional de Microelectrónica, CSIC, 08193 Cerdanyola del Vallès, Spain; llibertat.abad@imb-cnm.csic.es * Correspondence: aitor.lopeandia@uab.cat; Tel.: +34-935811569 † Current address: IMEC, Kapeldreef 75, 3001 Leuven, Belgium.  Received: 31 March 2019; Accepted: 17 April 2019; Published: 24 April 2019  Abstract: Thermoelectricity (TE) is proving to be a promising way to harvest energy for small applications and to produce a new range of thermal sensors. Recently, several thermoelectric generators (TEGs) based on nanomaterials have been developed, outperforming the efficiencies of many previous bulk generators. Here, we presented the thermoelectric characterization at different temperatures (from 50 to 350 K) of the Si thin-film based on Phosphorous (n) and Boron (p) doped thermocouples that conform to a planar micro TEG. The thermocouples were defined through selective doping by ion implantation, using boron and phosphorous, on a 100 nm thin Si film. The thermal conductivity, the Seebeck coefficient, and the electrical resistivity of each Si thermocouple was experimentally determined using the in-built heater/sensor probes and the resulting values were refined with the aid of finite element modeling (FEM). The results showed a thermoelectric figure of merit for the Si thin films of zT = 0.0093, at room temperature, which was about 12% higher than the bulk Si. In addition, we tested the thermoelectric performance of the TEG by measuring its own figure of merit, yielding a result of ZT = 0.0046 at room temperature. Keywords: thermoelectric characterization; thermoelectric generator; Si thin films 1. Introduction Thermoelectricity is the ability of some materials to produce voltage when exposed to a temperature gradient, and conversely, to produce a temperature gradient when electrons pass through them. The thermoelectric figure of merit of a material establishes the efficiency in energy conversion of the 2 material, and it is defined as ZT = σSk , where σ is the electrical conductivity, S is the Seebeck coefficient and k is the thermal conductivity. As apparent from the formula, increasing σ and S and reducing k leads to a higher figure of merit and thus to a better conversion efficiency. During the last two decades, the interest in thermoelectricity has exponentially grown due to the emergence of nanotechnology. Nanoscale and nanostructured materials show several non-classic transport effects, both thermal and electric, that can be exploited to improve their thermoelectric performance. The most important effect is the enhancement of phonon scattering at boundaries and interfaces, which reduces the thermal conductivity while maintaining a practically unaffected electrical conductivity [1,2]. Additionally, nanomaterials can exhibit electron confinement [3], an increased ZT Nanomaterials 2019, 9, 653; doi:10.3390/nano9040653 www.mdpi.com/journal/nanomaterials Nanomaterials 2019, 9, 653 2 of 9 via electronic band engineering [4], an enhanced Seebeck coefficient via dislocations in nanowires [5], surface states [6] and an enhanced phonon scattering via surface decoration [7], all of which favor ZT. As a result, new thermoelectric generators (TEGs) have been designed and fabricated over the past years, benefitting from the advantages of nanomaterials. To date, various classes of thermoelectric semiconductor compounds have been developed, such as bismuth telluride-based materials for low temperature applications [8–12], or silicon-based materials for higher temperatures [13–15]. These devices can have either a vertical [16] or planar [13] geometry, meaning that the temperature gradient is either set out-of-plane or in-plane with the substrate. Generally, the in-plane geometries allow for higher temperature gradients, owing to their higher dimensions in the direction of the heat flow, and thus achieving an enhanced power output [17]. In addition, top-down fabricated TEGs show a higher yield thanks to their enhanced reproducibility compared with the bottom-up TEGs [16]. On the other hand, these TEGs can be complementary metal-oxide-semiconductor (CMOS)-compatible [13,18] if the active material complies with the technology standards, thus allowing for the integration of generators with low-power consuming devices, such as wearables or body sensors, as well as the integration of microcoolers with microelectronic devices, such as lasers [19]. Several techniques have been developed to evaluate the performance of a TEG [20,21], measuring the efficiency and the figure of merit (ZT), while avoiding some of the side effects, such as the Thomson effect. However, an alternative means of characterization consists of separately measuring the three extrinsic parameters related ZT: the total heat conductance from the hot side to the cold side, the electrical resistance (produced by the active material plus the contact resistances), and the total Seebeck coefficient produced by all of the TEG legs. This is an advantageous approach when treating with microTEGs, where thermal dynamics are much faster than in bulk systems, the heat fluxes can be better controlled, and the thermal contact resistance between deposited films can be neglected. In this paper, we characterized the performance of a previously reported planar and CMOS-compatible TEG [18], and measured the figure of merit of the active material, which consisted of p- and n-doped 100 nm thin-film Si. The comparison between the ZT of the complete TEG with the zT of the active nanoSi, allowed us to assess the grade of optimization, as well as the amount of room left for increasing the performance of the device. Taking measurements of the three individual parameters composing the figure of merit was made possible by taking advantage of an in-built heating grid that created a known ∆T between the central part (hot side) and the frame (cold side). Experimental measurements were combined with a detailed 3D finite element model (FEM) to extract the contributions of structural materials in the thermal conduction and to calculate the real temperature difference between the Si ends, thus correcting the resulting Seebeck and thermal conductance measurements. A 3D FEM was also developed to subtract the current crowding effect in the electrical conductance measurements. 2. Experimental Methods The characterized device was a planar thin-film TEG, where the active materials are p- and n-doped Si strips, with doping concentrations around 2 × 1019 atoms/cm2 (Figure 1). A 400 nm thick SiO2 film was used as a structural material that held the Si strips and prevented them from breaking throughout the fabrication process. The contact lines were made of a 200 nm thick Au film, and the ohmic contact with the Si was favored by creating a NiSi alloy in the Si open-via, prior to the Au deposition. Since this was a test device, it also includes a grid in the center in order to create controlled temperature gradients in the Si strips. The complete fabrication of this device is explained elsewhere [18]. The measurement of the electrical resistivity was performed by feeding the Si thermocouples with a current of 1 µA and measuring the voltage drop using the offset compensation mode of the source (Keithley 2400, Keithley, Cleveland, OH, USA). In order to extract the resistivity of the material, we created a 3D finite element model (FEM) with COMSOL (Version 4.2, COMSOL AB, Stockholm, Sweden), which accounted for the current crowding effect at the contacts. The following methodology was used. First, the Au resistivity was set to the resistivity being measured in the grid, and the contact resistivity between Au/Si was set from a previous measurement. Next, the electrical resistivity of Nanomaterials 2019, 9, 653 3 of 9 p-Si and n-Si was set equal (ρp−Si = ρn−Si = ρSi ). This resistivity was scanned and the values at which the resistance of the model resembled the resistivities being measured were selected as the real Nanomaterials 2019, 9, x FOR PEER REVIEW 3 of 9 resistivity values. Figure 1. (a) Micrograph of the front of the thermoelectric generator (TEG) being tested, indicating the Figure membrane1. (a)area Micrograph of the heater/sensor and the central front of the thermoelectric generator Au grid locations. (TEG)ofbeing (b) Detail tested, the thin film indicating strips that the conform to the 5 n-p thermocouples that were found in each side of the squared membrane.film membrane area and the central heater/sensor Au grid locations. (b) Detail of the thin strips (c) Image that conform to the 5 n-p thermocouples that of the free-standing membrane take from the back. were found in each side of the squared membrane. (c) Image of the free-standing membrane take from the back. The thermal conductivity was measured by heating up the central grid (by feeding with current) The measurement and measuring the voltageof the electrical in 4-wires resistivity using was 2425. a Keithley performed After theby feeding temperaturethe Sicalibration thermocouples of the with a current of 1 A and measuring the voltage drop using the offset grid as a resistance temperature detector (RTD) was performed, the temperature was measured compensation mode offrom the source (Keithley the change 2400, at in resistance Keithley, each point. Cleveland, The thermalOH,conductance USA). In order to extract was then the as calculated resistivity G = P/∆T, of and the material, we created a 3D finite element model (FEM) with COMSOL (Version the thermal conductivity was found by applying the geometric factor of the 40 Si strips. However, this 4.2, COMSOL AB, Stockholm, experiment Sweden), alone lacks which accounted accuracy for measured since the the currenttemperature crowding effect at the was difference contacts. The following not exactly the one methodology between the Si ends due to the temperature inhomogeneity in the grid, and because not all of thegrid, was used. First, the Au resistivity was set to the resistivity being measured in the heat and flux the wascontact resistivity evacuated through between Au/Si but the Si strips, waspartly set from a previous through the SiO measurement. Next, the electrical 2 and the Au instead. In order to resistivity correct theseof effects, p-Si and n-Si was a second 3DsetFEMequal was(ρcreated=ρ using=COMSOL. ρ ). ThisAfter resistivity was plausible assigning scanned and the thermal values at which the resistance of the model resembled the resistivities being measured conductance values to all of the materials for the different temperatures (see Table 1), the thermal were selected as the real resistivity conductivity value ofvalues. the doped Si was swiped until finding a concordance in thermal conductance with The thatthermal conductivity of the real experimental wasmeasurements. measured by heating up the central grid (by feeding with current) and measuring the voltage in 4-wires using a Keithley 2425. After the temperature calibration of the grid as a resistance Table 1. Values temperature detector of the physical (RTD) was properties usedperformed, in all of thethefinite temperature was measured element modeling (FEM)from the change in resistance simulations. The thermal at conductivity each point.ofThe the thermal conductance gold was calculated fromwas then calculated the measured resistivityas 𝐺 =the using 𝑃/∆𝑇, Wiedemann–Franz and the law withwas thermal conductivity L =found by−8applying 2.44 × 10 W/K. Thethe contact resistivities geometric were factor also40 of the measured atHowever, Si strips. room C = 3.74 temperature ρ −9 m2 (see Appendix A). The data from the references has been extrapolated. × 10accuracy this experiment alone lacks since the measured temperature difference was not exactly the one between the Si ends due to the temperature inhomogeneity in the grid, and because not all of the T ρAu ki−Si,100nm [22] kAu kSiO2 [23] heat flux was evacuated through the Si strips, but partly through the SiO2 and the Au instead. In K Ω·m W/(m·K) W/(m·K) W/(m·K) order to correct these effects, a second−83D FEM was created using COMSOL. After assigning plausible 50 2.821 × 10 53 31.51 0.317 thermal conductance 100 values to all of the materials 3.258 × 10−8 87.5 for the different 54.57 temperatures0.628 (see Table 1), the thermal conductivity 150 value3.680 of the × 10doped Si was −8 86.5swiped until finding a concordance 72.47 0.910 in thermal conductance with that 200 of the 4.067 10−8 real×experimental measurements. 74.1 87.44 1.180 250 The Seebeck coefficient 10−8 was ×measured 4.497 64.75 the central by heating 98.85 grid of the TEG1.335and then measuring 300 4.890 × 10 −8 56 109.08 1.410 the Seebeck voltage created by the temperature difference with a Keithley 2182A. The measured value 350 5.282 × 10−8 50 116.2 1.45 was extracted using S = V /n∆T, where n = 40 (the number of Si legs). Once again, the second 3D FEM model had to be used owing to the non-homogeneous temperature in the grid (see Appendix B in supplementary information). All the measurements were carried out in a He Cryostat at high vacuum conditions (10−5 mbar). For each measurement, the temperature of the sample holder was stabilized with an uncertainty lower than 0.01 K. simulations. The thermal conductivity of the gold was calculated from the measured resistivity using the Wiedemann–Franz law with L = 2.44 × 10−8 W/K. The contact resistivities were also measured at room temperature ρ = 3.74 × 10−9 m2 (see Appendix A in supplementary information). The data from the references has been extrapolated. 𝐓 Nanomaterials 2019,𝛒9, 653 𝐀𝐮 𝐤𝐢 𝐒𝐢,𝟏𝟎𝟎𝐧𝐦 [22] 𝐤 𝐀𝐮 𝐤 𝐒𝐢𝐎𝟐 [23] 4 of 9 K ·m W/(m·K) W/(m·K) W/(m·K) 50 The Seebeck 2.821 ×coefficient 10−8 53 31.51 was measured by heating the central grid of the TEG0.317and then measuring 100 3.258 × 10 −8 87.5 54.57 the Seebeck voltage created by the temperature difference with a Keithley 2182A. 0.628 The measured value 150 extracted was 3.680 × 10−8S = V /n∆T where using, 86.5n = 40 (the number 72.47 of Si legs). Once0.910 again, the second 3D S 200 4.067 × 10 FEM model had to be used owing to the non-homogeneous temperature in the1.180 74.1 87.44 −8 grid (see Appendix B). 250 All the4.497 × 10−8 measurements 64.75 were carried 98.85 out in a He Cryostat at high vacuum1.335conditions (10−5 mbar). 300 4.890 × 10 −8 56 109.08 1.410 For each measurement, the temperature of the sample holder was stabilized with an uncertainty lower 350 0.01 K.5.282 × 10−8 than 50 116.2 1.45 3. Results and Discussion 3. Results and Discussion The results The of the electrical results resistivity of the electrical of the Siofare resistivity theshown Si are in Figure shown in 2. The measured Figure values of 2. The measured ρ values of ρ were calculated by multiplying were calculated the measured by multiplying resistance the measured (R) by the resistance (R)section by theofsection the strip × 0.1 m (50 strip of the (50 ×2) 0.1 m2 ) and dividing it by the and dividing distance it by between the distance the centers between of the the centers contacts of the (200 contacts m). (200 m). Nevertheless, the thecurrent currentcrowding crowdingeffect effectproduced produced a higher a higher density density of current of current nearnear the the border border of contact, of the the contact, which which reduced the reduceddistance the distance traveled traveled by theby the carriers carriers inside inside the SiFurthermore, the Si strip. strip. Furthermore, the contact the contact resistance resistance was enhanced was enhanced duereduction due to the to the reduction of the effective of the effective section. section. As theseAs thesewere effects effects were considered considered in the in the simulation, the simulation, the FEM-corrected FEM-corrected ρ values ρ values were morewere more precise precise than thandirectly the ones the ones directly measured. measured. It is also It is also worth noting that worth noting that theas the Si behaves Siabehaves as a the metal, since metal, since the resistance resistance grows with thegrows with thethus temperature, temperature, confirmingthusthe correct confirming the of doping correct doping of the strips. the strips. Figure 2. (a) Image of the voltage distribution in the modeled thermocouples. (b) Comparison between Figure 2. (a) Image of the voltage distribution in the modeled thermocouples. (b) Comparison the measured resistivity (calculated using the distance between centers of the contacts as thermocouple between the measured resistivity (calculated using the distance between centers of the contacts as length) and the modeled resistance. thermocouple length) and the modeled resistance. The thermal conductivity was measured and then corrected using the second model developed The thermal conductivity was measured and then corrected using the second model developed with COMSOL (Figure 3). In Figure 3b, both results of the thermal conductivity can be seen. The two with COMSOL (Figure 3). In Figure 3b, both results of the thermal conductivity can be seen. The two effects mentioned in the methods section have the following implications. First, the structural materials effects mentioned in the methods section have the following implications. First, the structural (mainly the SiO2 ) and the Au lines were responsible for a considerable part of the heat flow from the materials (mainly the SiO2) and the Au lines were responsible for a considerable part of the heat flow center to the substrate. Subtracting this effect, reduced the thermal conductivity of the Si. On the other from the center to the substrate. Subtracting this effect, reduced the thermal conductivity of the Si. hand, the inhomogeneity in the temperature of the heating grid produced a higher temperature in the center than in the limits of the grid. Thus, the measured ∆T was higher than the ∆T occurring along the silicon strips. Correcting this effect increased the Si thermal conductivity. The two effects discussed neutralized each other quite well, and the corrected thermal conductivity did not substantially differ from the raw measured value. The FEM-corrected values show the peak characteristic of crystalline On the other hand, the inhomogeneity in the temperature of the heating grid produced a higher temperature in the center than in the limits of the grid. Thus, the measured ∆𝑇 was higher than the ∆𝑇 occurring along the silicon strips. Correcting this effect increased the Si thermal conductivity. The two effects discussed neutralized each other quite well, and the corrected thermal conductivity did not substantially differ Nanomaterials 2019, 9, 653from the raw measured value. The FEM-corrected values show the peak 5 of 9 characteristic of crystalline materials, slightly shifted to higher temperatures compared to the intrinsic bulk Si, and the resulting values fit well with the literature data [24–29]. materials, slightly shifted to higher temperatures compared to the intrinsic bulk Si, and the resulting values fit well with the literature data [24–29]. Figure 3. (a) Temperature distribution in the TEG (white is hot). (b) Comparison between the measured Figurethermal 3. (a) conductivity Temperaturek,distribution the modeled in onethe andTEG an intrinsic (white Si isfilm. hot).(c)(b) Comparison between Comparison the measured between the Seebeck coefficient k and the modeled coefficient. measured thermal conductivity k, the modeled one and an intrinsic Si film. (c) Comparison between the measured Seebeck coefficient k and the modeled coefficient. In the case of the Seebeck coefficient, only the effect of the temperature inhomogeneity on the In the case ofa role grid played in the corrected the Seebeck value, coefficient, only andthesince effect the ∆T theofreal along the Si temperature strips was lower inhomogeneity than the on the measured value, the S increased by a factor of around 1.5 (Figure 3c). grid played a role in the corrected value, and since the real ∆𝑇 along the Si strips was lower than the measuredWithvalue, these the corrected 𝑆 increased parameters, by a factor theofzT of the material around 1.5 (Figurewas calculated (Figure 4), showing a value 3c). of 0.0093 at 300 K, which upgrades the bulk Si values With these corrected parameters, the 𝑧𝑇 of the material was calculated [30]. Although this(Figure value was expecteda to be 4), showing much higher due to the reduction of the thermal conductivity in thin films, value of 0.0093 at 300 K, which upgrades the bulk Si values [30]. Although this value was expected the power factor S2 /ρ was to benot as high much higher as expected. due to theNonetheless, reduction offabricating the thermal a device with even conductivity thinner in thin films films, theshould powerincrease factor the performance of the material. It is worth noting that this strategy will 𝑆 /𝜌 was not as high as expected. Nonetheless, fabricating a device with even thinner films shouldencounter technical difficulties when increase thetrying to fabricate performance thinner of the doped material. It isfilms, worth and alternative noting doping that this techniques strategy should technical will encounter be considered. In addition, nucleation in extremely thin Si films due to the high temperatures difficulties when trying to fabricate thinner doped films, and alternative doping techniques should used in the fabrication process should be prevented. be considered. In addition, nucleation in extremely thin Si films due to the high temperatures used The figure in the fabrication of merit process of the should beSi strips (zT) could now be compared to that of the whole device (ZT ). prevented. This ZT is calculated as: The figure of merit of the Si strips (𝑧𝑇) could now be2 compared to that of the whole device (𝑍𝑇). SDevice This 𝑍𝑇 is calculated as: ZT = RDevice GDevice where SDevice is the Seebeck coefficient of the whole generator, RDevice is the measured resistance of the thermocouples (including the contact resistances) and GDevice is the measured thermal conductance. This was the practical figure of merit of the generator, which was related to the maximum efficiency that it can perform at. Nanomaterials 2019, 9, 653 6 of 9 The comparison of ZT to the Si zT revealed how optimized the generator was. ZT should always be smaller than zT since a complete device performs worse than the material itself, due to side effects Nanomaterials such 2019,resistance as contact 9, x FOR PEER or REVIEW 6 of 9 extra thermal conductance. In our case, the coefficient zT/ZT was always between 1.9 and 2 (in all of the temperatures measured), meaning that the efficiency of the generator was about two times lower than the optimal 𝑆 𝑍𝑇 = design. In order to improve this value, the structural thermal conductance must be suppressed by reducing 𝑅 𝐺the thickness and width of the supporting SiO 2 where 𝑆 is the Seebeck coefficient of the whole generator, 𝑅 is the measured resistance of structure, as already stated for the microcoolers’ performance [19]. However, since a final use TEG the thermocouples (including the contact resistances) and 𝐺 is the measured thermal device does not require the inclusion of an Au grid, the performance will improve in any case. On the conductance. This was the practical figure of merit of the generator, which was related to the other hand, reducing the electrical contact resistance will likely slightly increase the TEG performance. maximum efficiency that it can perform at. The easiest way of achieving contact resistance reduction will be to enlarge the width of the contacts, as increasing the height may not produce any improvement due to the current crowding effect. 0,014 . 0,012 . zT Si 0,010 . ZT device Figure of merit 0,008 . 0,006 . 0,004 . 0,002 . 0,000 . 50 100 150 200 250 300 350 T (K) Figure 4. Comparison of the zT of the Si and the ZT of the device. Figure 4. Comparison of the 𝑧𝑇 of the Si and the ZT of the device. 4. Conclusions The comparison of 𝑍𝑇 to the Si 𝑧𝑇 revealed how optimized the generator was. 𝑍𝑇 should We always be characterized smaller thana micro-TEG, in which device 𝑧𝑇 since a complete the active materials performs were worse p-Sithe than and n-Si thin material films. itself, The due to performance of the active material was characterized by measuring the individual side effects such as contact resistance or extra thermal conductance. In our case, the coefficient z𝑇/𝑍𝑇 parameters of the wasfigure alwaysof between merit. Two1.9 FEM and 2models were (in all of thedeveloped temperatures to correct the crowding measured), meaningeffect in the that the electrical efficiency of contacts and the temperature inhomogeneity in the grid, as well as to subtract the the generator was about two times lower than the optimal design. In order to improve this value, the heat flow in the structural structural materials. The figure of must thermal conductance merit beof the TEG was compared suppressed by reducingto that the of the activeand thickness nanoSi, width showing of the asupporting three-fold SiO reduction. It is noted that further optimization can be attempted by limiting 2 structure, as already stated for the microcoolers’ performance [19]. However, since heat flow lost through theTEG a final use structural device materials. does not require the inclusion of an Au grid, the performance will improve in any case. On the other hand, reducing the Author Contributions: Conceptualization, A.L.electrical contact and J.R.V.; resistance Experimental will likely slightly measurements, increase and P.F.-V., A.P.P.-M. the TEG performance. G.G.D.; The easiest COMSOL Multiphysics FEMway of achieving software, contact P.F.-V. and G.G.D.;resistance reduction Microfabrication will design andbesupervision, to enlargeL.A.;the data widthcuration, of the P.F.-V. and as contacts, A.P.P.-M.; writing—original increasing the height may draftnot preparation, produceP.F.-V. and A.P.P.-M.; writing—review any improvement due to the current and editing, A.L.F., G.G.A., L.A. and J.R.V.; project administration, J.R.-V. and L.A.; funding acquisition, A.L., J.R.-V. crowding and L.A. effect. Funding: This research was funded by the Spanish Ministerio de Economía y Competitividad through Grants 4. Conclusions CSD2010-00044 (ConsoliderNANOTHERM), FIS2013-50304-EXP and MAT2016-79579-R. Ll. Abad was supported by theWe “Ramón y Cajal” program characterized (RyC-2013-12640) a micro-TEG, fromactive in which the the Spanish government. materials were p-Si and n-Si thin films. The performance of theP.F.-V. Acknowledgments: activeacknowledges material wasthe Spanish Ministry characterized of Education, by measuring the Culture and parameters individual Sports for theofFPU the grant that supported his PhD thesis. G.G.D. acknowledges the Brazilian National Council for Scientific and figure of merit. Two FEM models were developed to correct the crowding effect in the electrical Technological Development (CNPq) for his doctoral fellowship of SwB. This work made use of the Spanish contacts and the IMB-CNM-CSIC temperature clean room (ICTSinhomogeneity in the grid, as well as to subtract the heat flow in the Network MICRONANOFABS). structuralof materials. Conflicts The Interest: The figure authors of merit declare of theof TEG no conflict was compared to that of the active nanoSi, interest. showing a three-fold reduction. It is noted that further optimization can be attempted by limiting heat flow lost through the structural materials. Appendix A: Measurement of the Contact Resistivity The contact resistivity was measured in n-Si and p-Si using the transmission line model. This model consisted of measuring the resistance of the material being tested by using increasingly separated metallic lines. This way, the electrical resistance of the material could be ruled out by fitting the resistance measurements with a line and achieving a value at length 0. This value is twice that of Nanomaterials 2019, 9, 653 7 of 9 Appendix A. Measurement of the Contact Resistivity The contact resistivity was measured in n-Si and p-Si using the transmission line model. This model consisted of measuring the resistance of the material being tested by using increasingly separated metallic 2019, Nanomaterials lines.9, xThis way,REVIEW FOR PEER the electrical resistance of the material could be ruled out by fitting 7 of 9the resistance measurements with a line and achieving a value at length 0. This value is twice that of thethe contact resistance contact resistance (2𝑅(2R). CIn ). order In orderto calculate thethe to calculate electrical conductivity, electrical conductivity,a formula a formula waswas derived derived thatthat took intointo took account account thethe electron crowding electron crowding effect at the effect borders at the bordersof the electrodes. of the electrodes.In this sense, In this thethe sense, point at which point at whichthe the fitted lineline fitted crossed the the crossed abscissa equals abscissa −2𝐿−2L equals , where T , 𝐿 where L(the T transfer (the transferlength) is length) the is the average averagedistance distancethatthat an an electron electron travels in the travels semiconductor in the semiconductor beneath beneaththethe metallic lines. metallic TheThe lines. formula formula forfor acquiring acquiringthethe contact contactresistivity resistivity is: is: 𝜌 ρ=C 𝑅= 𝐿RC𝑊LT W where where 𝑊Wisisthethewidth widthofofthe thecontact. contact. TheThethermal contact resistance thermal contact resistance ononp-Si p-Siwaswasnot notmeasured measuredwith with the the actual actual doping level level used usedininthe theTEG. TEG.After Afterthe thefirst firsttest, test,depicted depictedininFigure Figure A1,A1, thethe implantation implantation dose dose of of thethe p-Si p-Si was was increased increased three three times times in order in order to achieve to achieve the the samesame doping doping levellevel as inasthe inn-Si. the n-Si. The contact The contact resistance resistance measured measured at room at room was ρwas temperature temperature 𝜌 =×3.74 C = 3.74 × 10 10−9 −9 ·m Ω·m 2. Thus, and according to the literature, we can assume 2 . Thus, and according to the literature, we can assume that thatthe thecontact contactresistivity resistivityto tobe be similar similar in both both n- n-and andp-Si p-Si[31] [31]and andthat they that theyhave a weak have a weak temperature temperature dependence, especially for samples with high doping levels. Since the weight dependence, especially for samples with high doping levels. Since the weight of the contact resistances of the contact resistances compared with the total Si strip resistance was smaller than 1.5%, we can assume the measuredthe compared with the total Si strip resistance was smaller than 1.5%, we can assume value measured withoutvalue withoutlarge introducing introducing errors inlarge errors in the simulation. the simulation. 400 350 n-Si p-Si 300 250 Resistance (Ω) 200 150 100 2RC 50 -2LT 0 -30 -20 -10 0 10 20 30 40 50 60 70 80 Length (μm) Figure A1. Contact resistance measurements using the transmission line method. Figure A1. Contact resistance measurements using the transmission line method. Appendix B. COMSOL Model Appendix Two B:3DCOMSOL models wereModel developed using COMSOL Multiphysics. In the first model, Two 3D models were developed the physics described using COMSOLby the Multiphysics. partial differential equations (PDE) was based on the Inmodule the firstofmodel, Electrical the currents, and the study physics described by thewas performed partial in steady differential state. The equations modeled (PDE) system was based was one fourth of the Si strips circuit with the corresponding gold contacts. on the module of Electrical currents, and the study was performed in steady state. The modeled The contact area of 25 × 25 system was one fourth of the Si strips circuit with the corresponding gold contacts. The contact areathe microns was respected. The simulation consisted of feeding the circuit with a current, and probing voltage of 25 to calculate × 25 microns wasthe effectiveThe respected. resistance. simulationThisconsisted was doneoffor the different feeding temperatures the circuit by changing with a current, and the material properties accordingly. probing the voltage to calculate the effective resistance. This was done for the different temperatures by changingIn thethe second model, material the physics properties described by the PDE was based on the module of Joule Heating, accordingly. and In the thestudy secondwasmodel, performed in the steady the physics state. by described For the calculating PDE was thebased thermalonconductivity the moduleofofthe doped Joule Heating, and the study was performed in the steady state. For calculating the thermal conductivity of Si, first the heater was fed with a current and the temperature was probed throughout it. The value the doped of the thermalSi,conductivity first the heaterwaswasscanned, andathe fed with correct current value and was selected was the temperature as that whichthroughout probed produces the same measured thermal conductance as in the real experiment. it. The value of the thermal conductivity was scanned, and the correct value was selected as that which produces the same measured thermal conductance as in the real experiment. In order to measure the real Seebeck coefficient, the simulation consisted of feeding a current to the heater using the same parameters as in the previous simulation, plus the correct value for the thermal conductivity of the doped Si. The temperature was probed both throughout the heater and between the ends of the exposed region of the Si strips. The real Seebeck coefficient was calculated as Nanomaterials 2019, 9, 653 8 of 9 In order to measure the real Seebeck coefficient, the simulation consisted of feeding a current to the heater using the same parameters as in the previous simulation, plus the correct value for the thermal conductivity of the doped Si. The temperature was probed both throughout the heater and between the ends of the exposed region of the Si strips. The real Seebeck coefficient was calculated as follows: ∆T Sreal = Smeasured · measured FEM ∆Tstrips FEM References 1. Dresselhaus, M.S.; Chen, G.; Tang, M.Y.; Yang, R.G.; Lee, H.; Wang, D.Z.; Ren, Z.F.; Fleurial, J.-P.; Gogna, P. New Directions for Low-Dimensional Thermoelectric Materials. Adv. Mater. 2007, 19, 1043–1053. [CrossRef] 2. Li, D.; Wu, Y.; Kim, P.; Shi, L.; Yang, P.; Majumdar, A. Thermal conductivity of individual silicon nanowires. Appl. Phys. Lett. 2003, 83, 2934–2936. [CrossRef] 3. Hicks, L.D.; Dresselhaus, M.S. Thermoelectric figure of merit of a one-dimensional conductor. Phys. Rev. B 1993, 47, 16631–16634. [CrossRef] 4. Pei, Y.; Wang, H.; Snyder, G.J. Band engineering of thermoelectric materials. Adv. Mater. 2012, 24, 6125–6135. [CrossRef] [PubMed] 5. Bennett, N.S.; Byrne, D.; Cowley, A. Enhanced Seebeck coefficient in silicon nanowires containing dislocations. Appl. Phys. Lett. 2015, 107, 013903. [CrossRef] 6. Kim, J.; Lee, S.; Brovman, Y.M.; Kim, P.; Lee, W. Diameter-dependent thermoelectric figure of merit in single-crystalline Bi nanowires. Nanoscale 2015, 7, 5053–5059. [CrossRef] [PubMed] 7. Markussen, T.; Jauho, A.-P.; Brandbyge, M. Surface-decorated silicon nanowires: a route to high-ZT thermoelectrics. Phys. Rev. Lett. 2009, 103, 55502. [CrossRef] [PubMed] 8. Snyder, G.J.; Lim, J.R.; Huang, C.-K.; Fleurial, J.-P. Thermoelectric microdevice fabricated by a MEMS-like electrochemical process. Nat. Mater. 2003, 2, 528–531. [CrossRef] [PubMed] 9. Vizel, R.; Bargig, T.; Beeri, O.; Gelbstein, Y. Bonding of Bi2Te3-Based Thermoelectric Legs to Metallic Contacts Using Bi0.82Sb0.18 Alloy. J. Electron. Mater. 2016, 45, 1296–1300. [CrossRef] 10. Kim, I.-H. (Bi,Sb)2(Te,Se)3-based thin film thermoelectric generators. Mater. Lett. 2000, 43, 221–224. [CrossRef] 11. Beeri, O.; Rotem, O.; Hazan, E.; Katz, E.A.; Braun, A.; Gelbstein, Y. Hybrid photovoltaic-thermoelectric system for concentrated solar energy conversion: Experimental realization and modeling. J. Appl. Phys. 2015, 118, 115104. [CrossRef] 12. Venkatasubramanian, R.; Siivola, E.; Colpitts, T.; O’Quinn, B. Thin-film thermoelectric devices with high room-temperature figures of merit. Nature 2001, 413, 597–602. [CrossRef] 13. Dávila, D.; Tarancón, A.; Calaza, C.; Salleras, M.; Fernández-Regúlez, M.; San Paulo, A.; Fonseca, L. Monolithically integrated thermoelectric energy harvester based on silicon nanowire arrays for powering micro/nanodevices. Nano Energy 2012, 1, 812–819. [CrossRef] 14. Strasser, M.; Aigner, R.; Lauterbach, C.; Sturm, T.F.; Franosch, M.; Wachutka, G. Micromachined CMOS thermoelectric generators as on-chip power supply. Sensors Actuators A Phys. 2004, 114, 362–370. [CrossRef] 15. Wang, Z.; Leonov, V.; Fiorini, P.; Van Hoof, C. Micromachined Polycrystalline Sige-Based Thermopiles for Micropower Generation on Human Body. CMP-TIMA 2007, 284–289. 16. Curtin, B.M.; Fang, E.W.; Bowers, J.E. Highly Ordered Vertical Silicon Nanowire Array Composite Thin Films for Thermoelectric Devices. J. Electron. Mater. 2012, 41, 887–894. [CrossRef] 17. Fan, P.; Zheng, Z.; Cai, Z.; Chen, T.; Liu, P.; Cai, X.; Zhang, D.; Liang, G.; Luo, J. The high performance of a thin film thermoelectric generator with heat flow running parallel to film surface. Appl. Phys. Lett. 2013, 102, 033904. [CrossRef] 18. Perez-Marín, A.P.; Lopeandía, A.F.; Abad, L.; Ferrando-Villaba, P.; Garcia, G.; Lopez, A.M.; Muñoz-Pascual, F.X.; Rodríguez-Viejo, J. Micropower thermoelectric generator from thin Si membranes. Nano Energy 2014, 4, 73–80. [CrossRef] 19. Rowe, D.M.; Volklein, F. Integrated thin film thermoelectric cooler. Electron. Lett. 1998, 34, 222. 20. Min, G.; Rowe, D.M.; Kontostavlakis, K. Thermoelectric figure-of-merit under large temperature differences. J. Phys. D. Appl. Phys. 2004, 37, 1301–1304. [CrossRef] Nanomaterials 2019, 9, 653 9 of 9 21. Min, G.; Singh, T.; Garcia-Canadas, J.; Ellor, R. Evaluation of Thermoelectric Generators by I–V Curves. J. Electron. Mater. 2015, 45, 1700–1704. [CrossRef] 22. Chantrenne, P.; Barrat, J.L.; Blase, X.; Gale, J.D. An analytical model for the thermal conductivity of silicon nanostructures. J. Appl. Phys. 2005, 97, 104318. [CrossRef] 23. Asheghi, M.; Touzelbaev, M.N.; Goodson, K.E.; Leung, Y.K.; Wong, S.S. Temperature-Dependent Thermal Conductivity of Single-Crystal Silicon Layers in SOI Substrates. J. Heat Transfer 1998, 120, 30–36. [CrossRef] 24. Ju, Y.S. Phonon heat transport in silicon nanostructures. Appl. Phys. Lett. 2005, 87, 1–3. [CrossRef] 25. Ju, Y.S.; Goodson, K.E. Phonon scattering in silicon films with thickness of order 100 nm. Appl. Phys. Lett. 1999, 74, 3005. [CrossRef] 26. Asheghi, M.; Leung, Y.K.; Wong, S.S.; Goodson, K.E. Phonon-boundary scattering in thin silicon layers. Appl. Phys. Lett. 1997, 71, 1798. [CrossRef] 27. Asheghi, M.; Kurabayashi, K.; Kasnavi, R.; Goodson, K.E. Thermal conduction in doped single-crystal silicon films. J. Appl. Phys. 2002, 91, 5079. [CrossRef] 28. Liu, W.; Asheghi, M. Thermal conductivity measurements of ultra-thin single crystal silicon layers. J. Heat Transfer 2006, 128, 75–83. [CrossRef] 29. Zhang, H.; Lu, Z.; Tian, L.; Tan, Z.; Liu, L.; Li, Z. Measurement of thermal conductivity of ultra-thin single crystal silicon film using symmetric structure. Bandaoti Xuebao(Chinese J. Semicond. 2006, 27, 1961–1965. 30. Bux, S.K.; Blair, R.G.; Gogna, P.K.; Lee, H.; Chen, G.; Dresselhaus, M.S.; Kaner, R.B.; Fleurial, J.-P. Nanostructured Bulk Silicon as an Effective Thermoelectric Material. Adv. Funct. Mater. 2009, 19, 2445–2452. [CrossRef] 31. Stavitski, N.; van Dal, M.J.H.; Lauwers, A.; Vrancken, C.; Kovalgin, A.Y.; Wolters, R.A.M. Systematic TLM measurements of NiSi and PtSi specific contact resistance to n- and p-type Si in a broad doping range. IEEE Electron Device Lett. 2008, 29, 378–381. [CrossRef] © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).