Nanoscale This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online PAPER View Journal | View Issue Quantifying thermal transport in buried Cite this: Nanoscale, 2021, 13, 10829 semiconductor nanostructures via cross-sectional Open Access Article. Published on 19 May 2021. Downloaded on 11/28/2022 3:41:23 PM. scanning thermal microscopy† Jean Spièce,*a Charalambos Evangeli, ‡a Alexander J. Robson,a Alexandros El Sachat,b Linda Haenel,e M. Isabel Alonso, c Miquel Garriga, c Benjamin J. Robinson, a,d Michael Oehme, e Jörg Schulze,e Francesc Alzina,b Clivia Sotomayor Torresb,f and Oleg V. Kolosov *a,d Managing thermal transport in nanostructures became a major challenge in the development of active microelectronic, optoelectronic and thermoelectric devices, stalling the famous Moore’s law of clock speed increase of microprocessors for more than a decade. To find the solution to this and linked pro- blems, one needs to quantify the ability of these nanostructures to conduct heat with adequate precision, nanoscale resolution, and, essentially, for the internal layers buried in the 3D structure of modern semi- conductor devices. Existing thermoreflectance measurements and “hot wire” 3ω methods cannot be effectively used at lateral dimensions of a layer below a micrometre; moreover, they are sensitive mainly to the surface layers of a relatively high thickness of above 100 nm. Scanning thermal microscopy (SThM), while providing the required lateral resolution, provides mainly qualitative data of the layer conductance due to undefined tip–surface and interlayer contact resistances. In this study, we used cross-sectional SThM (xSThM), a new method combining scanning probe microscopy compatible Ar-ion beam exit nano- cross-sectioning (BEXP) and SThM, to quantify thermal conductance in complex multilayer nano- structures and to measure local thermal conductivity of oxide and semiconductor materials, such as SiO2, SiGex and GeSny. By using the new method that provides 10 nm thickness and few tens of nm lateral resolution, we pinpoint crystalline defects in SiGe/GeSn optoelectronic materials by measuring nanoscale Received 10th December 2020, thermal transport and quantifying thermal conductivity and interfacial thermal resistance in thin spin-on Accepted 13th May 2021 materials used in extreme ultraviolet lithography (eUV) fabrication processing. The new capability of DOI: 10.1039/d0nr08768h xSThM demonstrated here for the first time is poised to provide vital insights into thermal transport in rsc.li/nanoscale advanced nanoscale materials and devices. Introduction nanoscale. While scanning and transmission electron micro- scopies (SEM and TEM) provide excellent nanostructural Nanomanufacturing that became a major foundation for characterization, the means for the mapping of materials and modern technological development directly relies on the rapid devices specifically physical properties are lagging well behind. and versatile quantitative characterization of devices on the In particular, one of the most vital characteristics of materials at the nanoscale, their ability to transfer or impede heat, is also one of the most difficult to characterize. The microelec- a Physics Department, Lancaster University, LA1 4YB, UK. tronic industry is struggling to dissipate heat generated by E-mail: o.kolosov@lancaster.ac.uk, spiece.jean@gmail.com nanoscale hot spots in computer processor chips;1,2 the new b Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, nanostructured thermoelectrics rely on suppressing the detri- Campus UAB, Bellaterra, 08193 Barcelona, Spain c mental thermal conductance pathways, the phase change Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193 Bellaterra, Spain memory that strives to replace both flash and dynamic d Material Science Institute, Lancaster University, Lancaster, LA1 4YB, UK memory need improved management of local heat generation e University of Stuttgart, Pfaffenwaldring 47, 70569 Stuttgart, Germany to become a feasible alternative.3 f ICREA, Passeig Lluis Companys 23, E-08010 Barcelona, Spain However, the measurement of thermal conductivity, even in † Electronic supplementary information (ESI) available. See DOI: 10.1039/ a simple geometry, such as a thin film on a substrate, presents d0nr08768h ‡ Current address: Department of Materials, University of Oxford, Oxford, OX1 significant challenges to traditional techniques, if the layer 3PH, UK. thickness is smaller than 100 nm.4 In particular, decoupling This journal is © The Royal Society of Chemistry 2021 Nanoscale, 2021, 13, 10829–10836 | 10829 View Article Online Paper Nanoscale the thermal conductivity and the interfacial resistance between locations and defects via variations in the local heat conduc- the film and the substrate, and accessing the in-plane thermal tance. Furthermore, by analyzing the SThM signal of the conductivity is difficult, and often not possible.5 Furthermore, wedge-shaped section, and applying an appropriate analytical as nanostructured device architectures are becoming more model, we are able to independently extract the intrinsic This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. complex with increased layer number and innovative three- thermal conductivity of isotropic material layers on a substrate. dimensional (3D) geometries, such as FIN-FET transistors and The ease of use of our approach and the extreme sensitivity to low-k interconnects, new approaches are required to probe the local physical properties renders it suitable for a broad range thermal transport in buried layers and the interlayer inter- of samples and opens new paths for fundamental and applied faces. Existing techniques are mostly limited to either surface research in nanomaterials and devices. or bulk probing, and cannot assess thermal transport in buried nanostructures. Open Access Article. Published on 19 May 2021. Downloaded on 11/28/2022 3:41:23 PM. Scanning probe microscopy (SPM)-based techniques, such Experimental as scanning thermal microscopy (SThM), can provide an efficient solution with lateral resolution on the order of a few SThM compatible nano-cross-sectioning nanometers to a few tens of nanometers.6,7 SThM uses a probe The nano-cross-sectioning (see Fig. 1a) described with a heated thermal sensor and a nanoscale sharp apex that elsewhere19,20 has been used to create an easily accessible is brought in the thermal contact with the sample, and surface section through a 3D structure for the subsurface SPM scanned in a raster pattern over the surface of the probed analysis of the material.17,18 Briefly, it uses three intersecting sample. The electrical resistance of the probe sensor is pro- Ar-ion beams aligned to a single plane that impinge on a portional to its temperature, and is monitored during scan- sample side at a small negative angle (∼−5°) from below the ning. By measuring the probe temperature, heat transfer pro- sample surface. As the beam exits at a glancing angle to the perties of the sample can be deduced.8–10 However, whilst sample surface, we call this technique beam-exit nano-cross- using SThM to quantify the overall thermal conductance of the sectional polishing.18,21 The cross-sectioned surface obtained complex 3D structure remains challenging but possible, asses- has a wedge-like geometry and sub-nm surface roughness, sing thermal conductivities of the individual structure elements making it fully compatible for studies via SPM methods. buried in the 3D device and reliably separating them from the Equally essential, the glancing angle of the ion beam, and the interfacial thermal resistance remains out-of-reach of the tech- nique. Several groups11–16 devoted their studies to temperature and conductance measurements using SThM. While Park et al.13 reported measurements of ErAs/GaAs MBE superlat- tices with 6 nm RMS roughness, Juszczyk et al.14 used craters in photonic structures to access subsurface materials. If the structure allows a cleavage, such as in coherent crystalline materials, these can be probed as demonstrated by Jung et al.,15 where an LED cleavage was used to map the nanoscale temperature distribution during its operation. However, all the methods reported the lack of reproducibility, can only be used to study a small set of structures, and most prominently use ill-defined surfaces, which creates major hurdles for the SThM probe measurements. To address these challenges, here, we demonstrate cross- sectional SThM (xSThM), a new method, which combines SThM with beam-exit nano-cross-sectional polishing (BEXP), a nano-cross-sectioning tool, that creates an easily accessible close to atomically flat section through a 3D structure enabling the SPM analysis of the subsurface layers of the studied material or device.17,18 The cross-sectioned surface has a wedge-like geometry and sub-nm surface roughness and is fully compatible with SThM enabling thermal transport measurements as a function of material thickness, which Fig. 1 (a) Schematic representation of nano-cross-sectioning beam- changes depending on the position of the probe across the exit cross-section polishing (BEXP); Ar ions impinge on the sample edge cut. at a shallow negative angle (ca. – 5°) to its surface creating a SPM com- patible cut adjacent to the intact sample surface. (b) Schematic repre- We demonstrate the capabilities of this new method by sentation of the xSThM measurement; SThM probe scans the cross-sec- exploring the heat transport in the complex buried semi- tioned area of a multilayered material (The sample is presented in the conductor and optoelectronic nanostructures, quantifying the next section). The 3D topography is overlaid with the SThM response. nanoscale gradients in composition, and revealing dis- Image dimensions: 5 × 5 × 0.77 μm. 10830 | Nanoscale, 2021, 13, 10829–10836 This journal is © The Royal Society of Chemistry 2021 View Article Online Nanoscale Paper inert nature of Ar results in negligible surface damage and nature of the sample, making it transversely isotropic. The practically no modification of the measured physical pro- three regions corresponding to the Si substrate, the Ge virtual perties of the studied materials. substrate and the Ge0.9Sn0.1 layer were clearly observed in the The cross-sectioned area was then thermally imaged via thermal image. Fig. 2b shows the dependence of RX and the This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. SThM (see Fig. 1b). Here, SThM measurements were per- topography profile x as a function of the height, t, of the formed in an ambient environment using a commercial sample nano-cross-section as obtained from a profile of the SPM (Bruker MultiMode Nanoscope IIIa controller) and xSThM image (Fig. 2a) and the topography image, respectively. custom-built electronics. Acting as both a sensor and a heater, The height is quantified via topography since the thickness of the SThM probe (Kelvin Nanotechnology, KNT-SThM-01a, 0.3 the layer varies linearly with the position.21 The relatively low N m−1 spring constant, <100 nm tip radius) is based on a SiN and spatially uniform thermal resistance in the Si substrate is cantilever with gold legs connecting to a Pd film evaporated on adjacent to the steep resistance increase as the probe transited Open Access Article. Published on 19 May 2021. Downloaded on 11/28/2022 3:41:23 PM. the tip.22 The SThM probe is one of the Wheatstone to the Si1−xGex and Ge layers with a high density of misfit dis- bridge resistors, thus allowing a precise monitoring of the locations. This is followed by a decrease and roughly constant probe resistance as explained elsewhere.7 In this study, we thermal resistance in what is believed to be a dislocation-free used an excess temperature of 50 K with respect to the environ- Ge layer. Finally, as the tip entered the Ge0.9Sn0.1 layer, the ment. When scanning across the surface of the sample, the heat resistance increased again, continuing to increase probe is biased by a combined AC + DC voltage, and its towards the sample surface, suggesting an increase in the Sn resistance is monitored via a modified Wheatstone bridge.23 When the SThM probe at a temperature difference ΔT above the sample temperature contacts the sample surface, it cools down depending on the heat flux q to the sample and, conse- quently, on the sample local heat transport characteristics. These temperature variations change the electrical resistance of the probe, which was quantified via calibration techniques described elsewhere,7,24 and used to determine the sample thermal properties. By measuring q and ΔT, the tip– sample thermal contact resistance RX = ΔT/q can be found. To achieve this, we processed the acquired data using a calibration methodology that provides compensation for the tip geometry and ambient air conductance,25 and more impor- tantly gives comparable quantitative measurements with the ones performed in a high vacuum environment (see ESI† for details). Results and discussion Measuring anisotropic thermal conductance on the nanoscale In this section, we used the new method to investigate the nanoscale transport in complex anisotropic systems with the predominantly diffusive thermal transport, and qualitatively compare the thermal conductivities in such layers. Fig. 1b shows a 3D topography rendering section that is overlaid with color corresponding to the SThM output of an MBE grown multilayer sample of Si/SixGe1−x/Ge/GeySn1−y. The GeSn materials represent a potential platform for Si manufacturing- based optoelectronics due to the possibility of achieving a direct bandgap.26–28 In this structure, first, a 100 nm Ge layer was grown on a silicon substrate. During the growth, Si atoms diffused inside the Ge layer at high process temperatures,29 Fig. 2 (a) Thermal contact resistance RX image across the cross-sec- and therefore, created an SiGe alloy of decreasing Si concen- tioned Si/GexSi1−x/GeySn1−y layers. Image is a zoom in the area shown in tration, as the distance from the Si–Ge interface increased (see Fig. 1b. (b) RX profile acquired from the image (blue, left axis), as indi- cated by the blue arrow by averaging 100 lines, and topography profile, ESI† for details). Then, another 100 nm Ge layer was grown x, (magenta, right axis) as a function of height, t, across Si/GexSi1−x/ creating a so-called Ge “virtual substrate”. Finally, a 200 nm GeySn1−y layers. The areas of different materials are shown and are layer of Ge0.9Sn0.1 was grown on the top of this layer. The z-gra- aligned with the image. The red dotted line denotes an area, where dis- dient in the SixGe1−x and GeySn1−y layers brakes the isotropic location density reduces moving away from the interface. This journal is © The Royal Society of Chemistry 2021 Nanoscale, 2021, 13, 10829–10836 | 10831 View Article Online Paper Nanoscale concentration. We excluded the possibility that the thermal re- sistance variations had their origin at tip–sample contact area variations since we did not observe any significant topography variations in the cross-sectioned area (see ESI note 7† for rele- This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. vant profiles). The most remarkable observation is that the resistance in the GexSi1−x decreased in the middle region (red dotted area in Fig. 2), which is consistent with the thermal conductivity increase of GexSi1−x with the decrease in the Si content.30 This significant continuing drop in the thermal resistance extend- ing to 200 nm thickness can be linked with the reduction of Open Access Article. Published on 19 May 2021. Downloaded on 11/28/2022 3:41:23 PM. the dislocation density as one moves away from the interface. According to second ion mass spectroscopy (SIMS) measure- ments (see ESI note 6†), the Ge content of the GexSi1−x layer quickly increased from 0 to 80% in the first ∼25 nm. This region corresponds to the sharp increase measured in the thermal resistance. Beyond the low thermal conductivity of GexSi1−x alloys with more than 10% Ge (compared to the pure silicon one),30 such drastic changes in the layer composition were also likely to induce phonon scattering processes, and Fig. 3 Thermal resistance (normalized with Si and Ge layer thermal re- created a low thermal conductivity, which translated into a sistance) profile as obtained by averaging 100 lines as a function of high thermal resistance increase. Then, between 25 and height for the as-grown and annealed samples. With dotted lines, the fitted curves of the GeySn1−y region are indicated. For the as-grown 125 nm, the Ge content increased slowly from 80% to 90% in sample, the slope is dy/dx ≈ 5.8 ± 0.2 × 10−4 nm−1, and for the annealed, the remaining of the layer, where the thermal resistance it is dy/dx ≈ 6.9 ± 0.2 × 10−4 nm−1. decrease is observed. The thermal conductivity of the GexSi1−x alloys increases with the Ge content above 80% Ge. We can then attribute the thermal resistance decrease to this increas- ing thermal conductivity with thickness. In the Ge only layer, the as-grown and the annealed samples by the analysis of the our measurement affords an even lower resistance. This can absolute value and the derivative of the thermal resistance in also be linked to the Ge content, which reaches 100% in this these layers. The lower absolute value suggests a higher con- region (see ESI note 6†), and thus provides a higher thermal centration of Ge near the interface. Simultaneously, the higher conductivity. derivative for the annealed sample suggests, similarly to the We then investigated two SiGex/GeSny samples that have Si1−xGex region, a different GeSn crystal quality. Annealing is similar composition, but different processing conditions, likely to create clusters of Sn inside the Ge, which acted as which are known to change the metastable GeSn alloy26–28 phonon scattering elements, hence reducing the thermal composition and crystallinity upon annealing at high tempera- conductivity. tures.31 Sn mobility inside the Ge can also increase drastically For this complex nanostructure, xSThM here allowed for with temperature with Sn atoms tending to form clusters and the first time to directly link the variation of the local thermal segregates.28 To assess these effects, we compared two conductance due to the layer composition, crystalline defects samples: an as grown sample, and a sample that was sub- and the precipitate nanostructuring, via the physical properties sequently annealed at 500 °C prior to the xSThM characteriz- of buried layers, which would be impossible to access other- ation. Fig. 3 shows the thermal resistance for these two wise. The next section addresses the vital question of how to samples. For comparison purposes, we normalized the signals use xSThM for the quantitative thermal measurements in such to both the Si and Ge layers, which should not change due to layers. the annealing process. Here, we observed almost no difference in the thermal transport in the Si1−xGex region between the as- grown and annealed sample, which would be expected, as the Quantitative measurements of thermal conductivity and annealing temperatures were well below ones needed to interfacial thermal resistance anneal the SiGe structures. In the pure Ge region, we obtained Having established the high performance of thermal transport an almost flat response, which indicated that the spreading re- mapping in 3D layers, we first used xSThM to quantitatively sistance was not affected by the increase of Ge layer thickness. deduce the thermal properties of relatively simple 3D struc- When entering to the Ge0.9Sn0.1 layer, the resistance increased tures comprised of isotropic layers. The wedge-like cut enables for both samples. This could be expected due to the lower SThM measurements as function of material thickness that thermal conductivity of GeSn alloys32,33 (between 1 and 10 W changes depending on the position of the probe across the cut m−1 K−1) compared to pure Ge (∼20 W m−1 K−1 for 100 nm (see Fig. 4a). As the tip–surface and wedge sample – substrate film32,34). However, a notable difference was observed between thermal resistance are independent of the tip position, using 10832 | Nanoscale, 2021, 13, 10829–10836 This journal is © The Royal Society of Chemistry 2021 View Article Online Nanoscale Paper and the sample, Rc, and the total thermal spreading resistance within the sample, Rs, RX ¼ Rc þ Rs ð1Þ This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. In vacuum, Rc includes solid–solid contact thermal resis- tance, and in ambient environment, also water meniscus con- ductance.40 For the quantitative evaluation of the sample thermal resistance, we treated Rc as an effective probe-sample interface resistance dependent on the contact area and the sample thermophysical properties, and independent of Rs. The Open Access Article. Published on 19 May 2021. Downloaded on 11/28/2022 3:41:23 PM. SThM tip – sample contact area can be approximated7 by a disk of radius a, reflecting the solid–solid contact dimensions, and when in ambient conditions, may increase due to effects of water meniscus, providing an effective radius of the thermal contact. The thermal spreading resistance depends on the nano- scale structure and the material composition of the sample. In the simple case of a bulk isotropic material and a contact radius above the phonon mean free path Λ, the thermal spreading resistance is given by: 1 Rs ¼ ; ð2Þ 4ka where k is the thermal conductivity of the bulk material. In case of the contact radius is much smaller than mean free path, the ballistic approximation can be used.41 Diffusive transport assumption remains valid if the heat source dimen- sion α is bigger than Λ, indicating that the system Knudsen number (Kn = Λ/a) is smaller than 1. In our system, Λ was greatly reduced compared to the bulk values due to interface scattering and impurities.30 Except for dislocation-free Si, where Λ ∼ 300 nm,42 Λ values are usually smaller than 50 nm, the typical effective contact radius.32 In either case, if the contact dimensions or material did not change, the thermal re- Fig. 4 (a) Schematic view of the xSThM scanning along the polished sistance remained constant. sample with an increase in the thickness. The arrows show the heat flow The basic element of any 3D nanostructure is a layer with direction, with their width denoting the increased heat flow. At the limit thermal conductivity k1 on the uniform substrate with thermal of a thick layer, heat flow is mostly lateral within the layer. The top surface was removed from the image because it is not nano-sectioned, conductivity, ks. The angle wedge cut through the layer and the its roughness is very different from the top surface one, and also the top substrate, produced by BEXP nano-cross-sectioning, allowed us surface can be contaminated during the sectioning due to re-deposition to approximate each measurement point as a layer of variable of material, and these measurements should not be compared directly thickness. We then could use an isotropic model for Rs for the with the cross-sectioned area in this case (see ESI Note 8† for the heat spreading within the layer on a substrate as described thermal image including the top surface). (b) Thermal contact resistance, RX, map of the 300 nm SiO2 on Si cross-sectioned sample. (c) RX profile elsewhere:43,44 acquired from the xSThM image by averaging 100 lines as a function 2  3 2ξteff of height across Si/SiO2 layers in the direction shown by the blue ð 1 1 þ K exp  1 6 a 7 dξ arrow at (b). Rs ðtÞ ¼ 6  7 J ðξÞ sinðξÞ 2 ; ð3Þ πkl a 0 4 2ξteff 5 1 ξ 1  K exp  a samples of varied thicknesses therefore allowed to separate the where teff = t + rint × k1 is the effective thickness that depends contribution of the interfacial thermal resistance and sample on the interfacial resistance between the layer and the sub- thermal conductivity in order to deduce the quantitative strate per unit area, rint, and the layer thickness, t, J1 is the first properties.35–39 Bessel function of the first kind, ξ is an integration factor and For the quantification of the thermal properties, we where K is defined as K = (1 − ks/k1)/(1 + ks/k1). Note that this expressed RX as a sum of two main components connected in model can be extended to the orthotropic system45 to describe series: the total contact thermal resistance between the probe thermally anisotropic materials. This thickness varying This journal is © The Royal Society of Chemistry 2021 Nanoscale, 2021, 13, 10829–10836 | 10833 View Article Online Paper Nanoscale thermal spreading resistance is connected with the variation afterwards by simply finding the offset to match the measured in the direction of heat flow as layer thickness crosses from t resistance (see ESI† for more details). The independent deter- ≪ a to t ≫ a, as schematically represented in Fig. 4a. At the mination of several independent thermal parameters in a limit of a thick layer with t ≫ a, the spreading resistance is single experiment became possible, as the measurements were This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. described by eqn (2). performed for the varied thickness of the sample, which was We investigated three films of standard materials currently equivalent to the multiple experiments on the same system.39 widely used in the semiconductor industry46,47 with potential This approach is effective if we assume that the layer thickness for the next generation extreme UV (eUV) lithography: 60 nm does not affect its thermal conductivity, and that layer thermal spin-on carbon, 10 nm spin-on glass, complemented by the conductivity is isotropic (see ESI† for more details). 300 nm thermally grown SiO2 on a Si substrate. In a BEXP In addition, we could use the 300 nm oxide sample as a section, thickness of the layer linearly varied with the position, proxy to an “infinitely thick” calibration sample, allowing to Open Access Article. Published on 19 May 2021. Downloaded on 11/28/2022 3:41:23 PM. and could be precisely quantified via topography.21 Most sig- determine the contact radius a. By assuming literature values nificantly, owing to the perfect near-atomic flatness of the cut, for the SiO2 thermal conductivity (kSiO2 ≈ 1 W m−1 K−1)50,51 the tip–sample thermal resistance as well as the layer-substrate and the interfacial thermal resistance between silicon oxide interfacial thermal resistance were constant, and did not and silicon (rintSiSiO2  1  109 K m2 W1 ),50,52 this value only depend on the layer thickness. This allowed us to perform weakly affects the fitting result given the large thickness of the direct fitting of the RX vs. t dependence using eqn (3), and calibration layer) the only fitting parameter was a. We obtained therefore independently determine k1 and rint. a = 56 nm, which is reasonable for the SThM probe used, with As expected, Fig. 4b shows the xSThM RX map of a 300 nm a good fit quality (see Fig. 4b). It should be noted that all three thermal oxide on Si with thermal resistance of Si area lower samples were thermally imaged sequentially under same geo- than that of SiO2.48 In Fig. 4c, topography and thermal resis- metrical settings and the same SThM probe, and therefore, no tance profiles taken along the blue arrow in Fig. 4b are shown. significant change in a was expected from sample to sample. The thermal resistance of Si is almost stable, while for SiO2, As eqn (3) is valid for all values of layer thickness, the we observed a clear increase with an increase in the thickness power of our method also relies on its ability to measure very corresponding to an increasing spreading resistance. A narrow thin layers. By effectively expanding the thickness scale by 5 dip at the Si–SiO2 interface is attributed to the topographical times, and hence the thickness resolution, it allowed us to variations at the interface that locally changes the contact area study the physical properties of nanoscale layers that were only between the tip apex and the surface. These can occur at the few nm thick. Such thin layers were impossible to be junctions of the very dissimilar materials, but are not present addressed by vertical cross-section due to the SThM tip dia- as we can see in the uniform or smooth gradient materials. meter.21 Applying the same method, and using the calibrated These topographical changes can be readily observed and effective contact radius, we measured thermal conductivities eliminated from the measurements, or compensated by and the interfacial resistances of 60 nm spin-on carbon and special algorithms.49 Note that the difference of Si thermal re- 10 nm spin-on glass (see Table 1). We noted that a general sistance with the sample presented in Fig. 2 is due to the agreement of a trend between the values was obtained, as different tip apex radii of the probe used. When the probe was spin-on carbon was expected to be more thermally conductive solely in contact with the oxide layer, we can assume that the than spin-on glass. Experimental data and fitted curves are total tip–surface contact resistance Rc of eqn (1) is constant as available in the ESI (Note 4†). material and contact area were not varied. We then applied the Finally, it was also possible to quantify thermal conduc- analytical model of eqn (3) using unknown parameters Rc, a, tance anisotropy of more complicated gradient structures with k1 and rint as fitting parameters (see Table 1 for the fitting the use of FEA. In this context, we studied the SixGe1−x gradi- results). In order to further reduce the number of fitting para- ent material, a good candidate for high temperature thermo- meters, and thus increase the accuracy of the fit, we can ana- electrics. We found that as the SThM probe scanned across lytically remove the Rc contribution by defining a new fitting different layers of increased Ge concentration, the thermal re- function f (t − t0) = Rs(t ) − Rs(t0). However, Rc could be obtained sistance at the tip apex increased in good agreement with pre- vious studies on Si1−xGex alloys.30 Modelling the SixGe1−x by FEA enabled us to reproduce experimentally acquired thermal Table 1 Parameters obtained by fitting eqn (1) to experimental data. resistance as a function of the Ge concentration (see ESI For SiO2, literature values are used to obtain a and rint. Grey shaded cells Supporting Note 2† for details). are assumed values with contact radius for the probe for spin-on carbon and spin-on glass taken from the SiOx calibration measurements Fitting 300 nm 60 nm spin-on 10 nm spin-on Conclusions parameters thermal SiOx carbon glass Combining an SPM-compatible nano-cross-sectional tool with k1(W m−1 K−1) 1.0 0.8 ± 0.1 0.3 ± 0.1 SThM, we were able to map and measure with nanoscale rint (10−9 × K m2 W−1) 1.0 4±2 2±2 Rc(106 × K W−1) 9.0 ± 0.1 5.3 ± 0.1 6.0 ± 0.2 resolution the thermal conductivity and interfacial thermal re- a(nm) 56 56 56 sistance of buried layers and interfaces in complex gradient 10834 | Nanoscale, 2021, 13, 10829–10836 This journal is © The Royal Society of Chemistry 2021 View Article Online Nanoscale Paper compound semiconductor nanostructures, which were not support. LTD to ICN2 is supported by the Spanish MINECO accessible previously. We applied a new approach to the inves- (Severo Ochoa Centers of Excellence Program under Grant tigation of the thermal conductance of nanomaterials, provid- SEV-2017-0706 and CEX2019-000917-S) and by the Generalitat ing the depth profiling of thermophysical properties with a de Catalunya (Grants 2017SGR806, 2017SGR488, and the This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. depth resolution below 10 nm. We have directly measured heat CERCA Program). We thank Severine Gomès from CNRS and transport in nano-layered anisotropic systems, such as poten- Harry Hoster from Lancaster Energy for the helpful discus- tial optoelectronic Si/SixGe1−x/Ge/GeySn1−y and thermoelectric sions on the measurements, and Andy Cockburn and Mike SixGe1−x materials, showing an excellent match with the Kocsic from IMEC for the interesting materials and discussion theoretical data with no fitting parameters, and observing of applications. composition variations and dislocation-impeded thermal transport in nanoscale thin layers. Furthermore, using a com- Open Access Article. Published on 19 May 2021. Downloaded on 11/28/2022 3:41:23 PM. plimentary modelling approach, we could deduce the quanti- Notes and references tative values of thermal conductivity in microelectronic thin films and molecular beam epitaxy layers for the next gene- 1 C. A. Mack, IEEE Trans. Semicond. Manuf., 2011, 24, 202– ration optoelectronics and thermoelectrics. 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EP/V00767X/1 and EP/P006973/1 and Faraday 18 O. V. Kolosov, I. Grishin and R. Jones, Nanotechnology, Institution NEXGENNA project for the overall support, and 2011, 22, 185702. Paul Instrument Fund, c/o The Royal Society grant on 19 O. V. Kolosov and I. Grishin, US Patent 9,082,587, “Infrared non-contact atomic force microscopy (ncAFM-IR)” 2015. for the equipment support. We are also grateful to our indus- 20 A. J. Robson, I. Grishin, R. J. Young, A. M. Sanchez, trial collaborators Leica Microsystems, Lancaster Materials O. V. Kolosov and M. Hayne, ACS Appl. Mater. Interfaces, Analysis Ltd and Bruker for the financial and instrumentation 2013, 5, 3241–3245. This journal is © The Royal Society of Chemistry 2021 Nanoscale, 2021, 13, 10829–10836 | 10835 View Article Online Paper Nanoscale 21 A. J. Robson, I. Grishin, R. J. Young, A. M. Sanchez, 36 R. Heiderhoff, H. Li and T. Riedl, Microelectron. Reliab., O. V. Kolosov and M. Hayne, ACS Appl. Mater. 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