Strain modulation of epitaxial h-BN on sapphire: the role of wrinkle formation for large-area two-dimensional materials

Strain built-in electronic and optoelectronic devices can influence their properties and lifetime. This effect is particularly significant at the interface between two-dimensional materials and substrates. One such material is epitaxial hexagonal boron nitride (h-BN), which is grown at temperatures often exceeding 1000 °C. Due to the high growth temperature, h-BN based devices operating at room temperature can be strongly affected by strain generated during cooling due to the differences in lattice thermal expansion of h-BN and the substrate. Here, we present results of temperature-dependent Raman studies of the in-plane E2g high phonon mode in the temperature range of 300–1100 K measured for h-BN grown by metalorganic vapor phase epitaxy. We observe a change, by an order of magnitude, in the rate of the temperature-induced frequency shift for temperatures below 900 K, indicating a strong reduction of the effective h-BN/substrate interaction. We attribute this behavior to the creation of h-BN wrinkles which results in strain relaxation. This interpretation is supported by the observation that no change of layer/substrate interaction and no wrinkles are observed for delaminated h-BN films transferred onto silicon. Our findings demonstrate that wrinkle formation is an inherent process for two-dimensional materials on foreign substrates that has to be understood to allow for the successful engineering of devices based on epitaxially grown van der Waals heterostructures.


Introduction
Due to a wide bandgap of around 6 eV [1][2][3], its sp 2 hybridization, and high thermal and chemical stability [4], h-BN is an integral part of many novel electronic and optoelectronic devices.The large electrical resistivity and weak interactions between atomic planes make h-BN a perfect insulating component of van der Waals heterostructures [5,6].A further major advantage of this sp 2 form of BN is that it is an excellent substrate for the growth of other two-dimensional materials [7,8].Encapsulation with h-BN is also known to protect sensitive structures such as transition metal dichalcogenides from degradation and to improve their optical properties [9][10][11].Furthermore, h-BN based devices can be prospective candidates in effective deep ultraviolet lighting Nanotechnology Nanotechnology 35 (2024) 175703 (10pp) https://doi.org/10.1088/1361-6528/ad18e6* Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.[2,[12][13][14] and in the development of future quantum technologies, since point defects in this material can be singlephoton emission sources at room temperature [15][16][17].
In order to fulfill its technological potential, it is necessary to obtain large areas of high-quality two-dimensional h-BN.Since it is difficult to obtain large-area h-BN by mechanical exfoliation, metalorganic vapor phase epitaxy (MOVPE) is considered to be one of the most promising approaches to achieving high-quality material [18,19].Epitaxial growth provides reproducibility of obtained layers as well as enables easy integration of grown h-BN with other materials [8].Apart from the quality of epitaxial h-BN, another important issue is its mechanical interaction with the substrate which determines the properties of the grown material.Extensive research is conducted to find appropriate substrates for the growth of h-BN to obtain the highest qualities and the largest possible areas, [20,21] also by taking into account the substrate modification caused by the growth process itself [22].MOVPE h-BN is grown at high temperatures often exceeding 1000 °C.However, h-BN based devices usually work at much lower temperatures, so differences between the lattice thermal expansion of h-BN and the substrate lead to the generation of strain at the h-BN/substrate interface during cooling down.Such strain can limit the lifetime of devices or even lead to their breakdown.On the other hand, nowadays applying strain to h-BN is intensively studied in terms of changing its band structure properties as well as activating and tuning single photon emission [23][24][25].Interface strain generation can also affect the morphology of h-BN and other two-dimensional materials.The surface morphology in such thin layers is determined by a trade-off between the energy of the elastic bending of the material and the van der Waals interaction between the layer and the substrate.This interplay often leads to wrinkle formation as studied extensively in the case of graphene [26][27][28][29].In fact, the physical mechanism leading to wrinkle formation is similar to the one responsible for the island nucleation in the well-established Stransky-Krastanov growth mode of quantum dots, in which the interplay between the energy of adding a new strained layer and formation of three-dimensional islands plays the crucial role [30].Since the strain generated at the interface between a thin epitaxial layer and a substrate increases with the contact area, wrinkles can be formed only in large-area, continuous material which is weakly attached to the substrate.Therefore, counter-intuitively, the appearance of wrinkles is an indicator of the high quality of the layer.Indeed, in the case of epitaxial h-BN, their presence has been reported for material of good morphology and optical properties [18,31,32].Literature available measurements proved that wrinkles affect strain in h-BN epilayers [33][34][35].
Both of these key aspectsthe quality of the obtained h-BN and strain generated in the grown structure can be studied by the well-established technique-Raman spectroscopy [33,[36][37][38].One can observe two Raman-active phonon modes in h-BN.The first is an interlayer shear mode E 2g low (boron and nitrogen atoms in one plane at opposite sides of a hexagon move in the same direction, but opposite to the atoms in layers above and below) which is more difficult to observe due to its low energy (∼50 cm −1 ).The second is the higher energetic (∼1370 cm −1 ) in-plane phonon mode E 2g high (boron and nitrogen atoms in one plane at the opposite sides of a hexagon move in opposite directions) which is easier to observe [36,39,40].In this report, we present results of temperature-dependent Raman measurements of the in-plane E 2g high phonon mode in bulk and epitaxial h-BN.Based on experimental results we investigated how the phonon energy changes for different temperatures due to differences in thermal expansion of MOVPE h-BN layers and sapphire substrates as well as the optical properties of the epitaxially grown material in the temperature range from room temperature up to around 1100 K. Delaminated h-BN films transferred onto silicon substrates (with 90 nm or 300 nm oxide coating) were also studied to directly compare the properties of our material with literature results for exfoliated h-BN flakes [37,38].To our best knowledge, available Raman studies of epitaxial as-grown (non-transferred) h-BN are limited to temperatures of about 400-500 K [33,35].Results presented in [33] indicate a dramatic change in the rate of variation of the in-plane Raman mode energy with temperature when the h-BN thickness changes, suggesting differences in strain generation and relaxation.This finding indicates the crucial role of processes occurring at the interface between a thin film and a substrate.As described above, the strain generated in layers deposited on other substrates can be relaxed due to effects related to the change of the h-BN morphology such as wrinkling.However, literature available Raman studies of as-grown h-BN at temperatures below 500 K do not reveal any critical point for which the thermomechanical properties of epilayers change.In the case of h-BN grown by MOVPE, the limit of 500 K in literature is due to the defect-related luminescence which is more intense than the Raman signal at higher temperatures.However, we reveal that this disruptive luminescence can be quenched by annealing samples at higher temperatures.Our approach enables us to perform successful Raman studies of the in-plane phonon mode in as-grown h-BN on sapphire up to 1100 K which is much closer to the growth temperature.Measurements at such high temperatures allow us to observe Raman fingerprints of the dramatic change in strain generation in as-grown epitaxial h-BN on sapphire substrate at temperatures close to 900 K.
In order to classify the role of different physical mechanisms which are responsible for the temperature behavior of epitaxial layers, we started with bulk h-BN crystals.In the case of bulk h-BN, the most important mechanisms determining the temperature dependence of the E 2g high mode frequency ω Bulk (T) are the lattice thermal expansion and anharmonic interactions (phonon decay and phonon scattering) [41,42].The contribution of the former to the inplane phonon energy is positive when the temperature increases because the in-plane lattice thermal expansion coefficient in h-BN is negative [43].However, the E 2g high phonon energy in h-BN is known to decrease along with a temperature rise.Thus, anharmonic processes are crucial because only interactions between phonons can explain such behavior.
For epitaxial layers grown by MOVPE, the energy of the E 2g high phonon mode ω(T) is affected by an additional effect.The difference between the lattice thermal expansion coefficients of the h-BN and the substrate leads to the generation of strain at the interface when the temperature changes [44].The phonon shift ω S (T) related to this mechanism is given by: where α Substrate (T′) and α Layer (T′) are the lattices thermal expansion coefficients of the substrate and the layer respectively, T 0 is the layer deposition temperature and the proportionality factor β is the biaxial strain coefficient.For asgrown h-BN layers on a sapphire substrate, T 0 is the growth temperature and for delaminated h-BN films transferred onto silicon, T 0 is room temperature.The β value for h-BN flakes exfoliated from bulk crystals and transferred onto silicon is reported to be around −50 cm −1 /% [37,38] which is similar to the value for graphene of around −70 cm −1 /% [45,46].If we assume that the impact of the lattice thermal expansion and anharmonic processes on the in-plane phonon energy for epitaxial material is the same as for bulk crystal, the E 2g high mode frequency ω(T) is given by: where the added ω Add constant is related to contributions that are difficult to be described analytically such as defects or residual strain.As presented in the following sections, our experimental data indicates that the effective interaction between the h-BN layer and sapphire is strongly reduced below a specific temperature close to 900 K.We want to underline here, that we understand this effective interaction as an impact of the substrate on the strain generated in h-BN.If the expansion of the substrate leads to the generation of large strain in the thin layer deposited on it, then the effective interaction is strong.When the expansion of the substrate weakly affects the strain in the thin layer on top, then this effective interaction is weak.Thus, we interpret this effective interaction between the whole h-BN layer and the whole substrate in analogy to the picture of a thin film on a thick block rather than as of a local, chemical interaction between atoms in BN and atoms in sapphire.We attribute this striking result to the change of the h-BN layer morphology-namely the formation or smoothing of wrinkles.The drop in the temperature leads to a larger lattice mismatch between the grown h-BN and sapphire and therefore induces the strain in the epilayer.At a specific temperature, the total energy is minimized by creating h-BN wrinkles.It is worth mentioning that h-BN does not interact directly with the sapphire.A nonintentional thin AlN layer, which thickness is in the range of 0-2 nm, occurs between them.Since this AlN layer is really thin, its lattice should match up to that of sapphire.Therefore, we assume that the presence of AlN has no significant impact on obtained results.

Material and methods
The reference h-BN sample was a bulk crystal from HQ Graphene.h-BN epitaxial samples were grown on 2-inch sapphire c-plane wafers in a CCS 3 × 2 AIXTRON reactor.Triethylboron (TEB) and ammonia (NH 3 ) were used as precursors of boron and nitrogen, respectively, with hydrogen as carrier gas.Two samples C0 and C1 were grown in continuous flow growth mode (CFG) in the HAHP (high pressure, high ammonia) regime [47].Sample C0 with a large V/III ratio equal to 400, was grown at a temperature of 1315 °C and a pressure of 800 mbar.These growth conditions promote the growth of a thin (about 4 nm), epitaxial layer of high quality.Growth conditions for C1 were changed during the process.The pressure was constant during the growth (600 mbar) but initially, the growth temperature was 1050 °C and the V/III ratio was 200, then 1285 °C and 50, respectively.Such parameters resulted in obtaining about 450 nm thick, polycrystalline, porous material which consists of many freestanding, randomly oriented flakes.The other three samples-F, CF, and CFF were grown mainly using alternating pulses of TEB and ammonia by flow-rate modulation epitaxy (FME) mode.The growth temperature for sample F was 1295 °C, pressure-400 mbar, and V/III ratio in NH 3 to TEB pulses-about 270.Samples CF and CFF were grown by twostage epitaxy [32]-the growth was proceeded under exactly the same conditions as for sample F, however not directly on sapphire substrate, but on a buffer layer similar to C0. CF and CFF differ mainly in the buffer layer growth time and in the number of NH 3 and TEB pulse cycles.There were also modifications in TEB pulse duration.F, CF, and CFF are thin (about 10 nm, 8 nm, and 20 nm respectively) epitaxial layers.For studied layers, the full width at half maximum (FWHM) of the E 2g high phonon mode is about 25 cm −1 which is a low value for epitaxial h-BN indicating the high quality of the grown material [32].The thickness of thin h-BN layers was assessed by Fourier transform infrared (FTIR) measurements [48].FTIR spectra were acquired with a Thermo Scientific Nicolet Continuum Infrared Microscope equipped with 32x Schwarzschild infinity-corrected objective (NA 0.65).The thickness of layer C1 was obtained from the in situ laser reflectometry during the growth.The scanning electron microscope (SEM) images were acquired using FEI Helios NanoLab.
Temperature-dependent Raman measurements were carried out using a Linkam TS1500 heating stage.The excitation source was an Nd:YAG laser operating at 532 nm and the power of the incident light was about 20 mW.The wide bandgap of h-BN results in a low absorption coefficient at this wavelength [49,50] so our samples were transparent for the excitation laser and the signal was collected from the whole sample (in terms of depth), which allows us to study the h-BN/substrate interaction.Spectra were acquired in backscattering geometry with a Renishaw InVia Raman spectrometer using an ×50 objective providing the laser spot size of below 1 μm in diameter.Molecular nitrogen was passed through the Linkam chamber to provide an inert atmosphere that protects the h-BN from potential destruction induced by oxygen or water.To eliminate the sapphire background signal two spectra were collected for every single point-the first with a laser beam focused on the surface of the h-BN layer and the second with a laser beam focused inside the substrate (∼15 μm below).This step is necessary for h-BN layers thinner than a few dozen of nm because h-BN and sapphire Raman peaks overlap.Subtracting the background spectrum allows us to obtain a pure h-BN signal.
To transfer some h-BN films from sapphire to silicon substrates we used the delamination procedure reported in the literature [51].An as-grown h-BN layer was heated on a hot plate at 80 °C.In the next step, it was put onto the surface of the liquid being a mixture of deionized water and isopropanol (8:1 volume ratio).Then the liquid penetrated between the h-BN layer and the sapphire substrate separating them.This enabled the successful transfer of the h-BN film onto the silicon wafer.

Results and discussion
Figure 1(a) shows typical Raman spectra for as-grown h-BN layers on a sapphire substrate (sample F/Sapphire) during annealing up to 1100 K.During increasing temperature, we observe a strong defect-related luminescence which appears around 400 K and hinders the observation of Raman spectra of h-BN like in previous results reported in the literature [33,52].This prevents us from observing the Raman peak associated with the in-plane E 2g high mode.At the beginning, the luminescence intensity increases along with the temperature reaching a maximum at a temperature close to 500-600 K.The luminescence drops for higher temperatures and is completely quenched above 1000 K.When the temperature decreases we no longer observe defect-related luminescence (figure 1(b)) so it is possible to collect Raman spectra of epitaxial h-BN in a broad temperature range that has not been available before.In these spectra, we observe characteristic peaks related to the E 2g high mode in h-BN and phonon modes in sapphire.As mentioned in the Experimental section, for every single point we acquired two spectra-for the h-BN layer on sapphire and for sapphire only (figure 1(c)).This allows us to eliminate the sapphire background and obtain pure MOVPE h-BN spectra (figure 1(d)).Figure 2 shows results for the delaminated h-BN film (sample F/Silicon) transferred onto a silicon substrate (with 300 nm SiO 2 coating).For such films, we also observe strong defect-related luminescence for temperatures higher than about 400 K which is quenched by annealing samples at around 1000 K.As shown in figure 2(a) the luminescence behaves in the same way as for as-grown layers on sapphire.This is clear evidence that light emission originates from defect states in h-BN, not from the sapphire or silicon substrates.According to equation (2), we need the temperature dependence of E 2g high mode frequency for bulk material to study h-BN/sapphire interaction in our MOVPE material.Figure 3 shows this dependence in the temperature range from room temperature up to around 1100 K.The acquired Raman spectra of the bulk h-BN are presented in the inset.The E 2g high phonon energy ω Bulk (T) decreases for higher temperatures.At the same time, the Raman peak broadens as expected [42].Based on some theoretical predictions we fit the red curve in figure 3 that is given by: T 1380.50 13.17 where temperature is in Kelvins and the result is in cm −1 .The term multiplied by −13.17 is related to anharmonic processes (namely phonon decays) [41].The next term originates from the change of the phonon energy due to lattice thermal expansion which in the literature is derived up to around 600 K [42] and was extrapolated here to higher energies.For more details about equation (3) see supplementary materials.The upper panel in figure 4 (as-grown) shows differences between the E 2g high mode energies for MOVPE as-grown layers on sapphire substrates and the bulk crystal.Results of fitting the experimental data by equation (2) are also presented.The lattice thermal expansion coefficients of h-BN and sapphire are adopted from [43,53].For layers C0, F, and CF we observe a change of the slope at temperatures of about 900 K. Therefore for these 3 layers the function described by equation (2) has been fitted for two temperature ranges separately-below and above 900 K. Table 1 contains the fitting parameters.The bottom indexes <900 K and >900 K refer to fitting function equation (2) for temperatures lower and higher than 900 K respectively.Parameter ω Add<900K has no physical meaning since the slope changes at higher temperatures.Temperature 900 K is chosen as an approximation for the critical temperature.Adding a new fitting parameter related to this characteristic temperature leads to larger standard errors of all fitting parameters and does not improve the quality of the fit.
The parameter β is responsible for the rate of the change of the E 2g high mode energy due to the lattice mismatch between the h-BN layer and sapphire substrate.The fitted β <900K parameters are 1-2 orders of magnitude smaller (in terms of  absolute values) than literature values of β for h-BN flakes exfoliated from bulk material onto silicon (around −50 cm −1 /%) [37,38].This finding indicates that the interaction between our MOVPE material and the sapphire substrate is extremely weak (the generated strain reflects the strength of this interaction).For temperatures below 900 K, this interaction seems to be the strongest for the sample C1/Sapphire.However, layer C1 is very thick compared to others (around 450 nm versus a few nm).One would expect that sapphire should have a more significant impact on thin layers because the substrate affects mostly layers in direct contact with it.Therefore β <900K should be the closest to 0 for layer C1.Indeed it is close to 0 (−3.06 cm −1 /% versus the literature value of around −50 cm −1 /%) but its absolute value is higher than for thinner layers.A different effect, which dramatically reduces h-BN/Sapphire interaction, has to be taken into account to explain such low absolute values of β <900K for layers that are a few nanometers thick.This effect is probably dominating at temperatures lower than 900 K so we observe stronger h-BN/sapphire interaction beyond this temperature.
The above conclusion is based on the comparison of values of β <900K for our as-grown epitaxial layers deposited on sapphire and for exfoliated flakes transferred onto silicon studied in the literature.However, the question arises if our epitaxial material really interacts with the sapphire substrates very weakly or maybe thermomechanical properties of epitaxial films and exfoliated flakes cannot be compared.To dispel any doubts, we carried out additional temperaturedependent Raman measurements of delaminated MOVPEgrown h-BN films transferred onto silicon wafers with 90 or 300 nm thick oxide coating.It allowed us to directly compare our MOVPE material and exfoliated flakes reported in the literature on the same substrate (Si/SiO 2 ) which is a key factor, because for this situation all potential differences are not the result of the interaction with different substrates but originate from differences of the material itself (epitaxial versus exfoliated).Experimental points and results of fit equation (2) to the data are shown in the bottom panel in figure 4 (delaminated).Table 2 presents the fitted parameters.The thermal expansion coefficient of silicon was adopted from the literature [54].We did not consider the oxide coating layer in our calculations.According to the literature, its impact on the thermomechanical properties of a silicon wafer should not change the results significantly [37].Indeed, we do Table 1.Parameters obtained from fitting equation (2) to experimental data for MOVPE as-grown h-BN layers on sapphire substrates.not observe a significant difference in results for h-BN exfoliated on silicon with 90 and 300 nm thick layers of SiO 2 .
For these exfoliated h-BN films the strength of the h-BN/ substrate interaction does not change.The absolute values of β are 1-2 orders of magnitude higher in the whole temperature range compared to the case of as-grown h-BN epilayers on sapphire.On the other hand, the obtained β values are just 2-3 times lower than literature values for h-BN flakes exfoliated from bulk crystal [37,38] indicating that thermomechanical properties of our epitaxial material and exfoliated flakes on the same substrates are quite similar.Therefore, the very small values of β <900K obtained for as-grown h-BN on sapphire must really originate from an extremely weak interaction between epilayers and substrates.Also, the constant rate of the change of the energy of the in-plane phonon mode in delaminated h-BN films transferred onto silicon shows that in this case the mechanism, which reduces the h-BN/substrate interaction for as-grown samples on sapphire, is inactive.Our experimental data indicate that the rate of the phonon energy change with temperature (β) changes by more than one order of magnitude close to 900 K for as-grown MOVPE h-BN layers on sapphire.We attribute this change to the presence of wrinkles.Our h-BN layers are grown on sapphire substrates at high temperatures of around 1600 K.After the growth, when the temperature decreases, the sapphire substrate shrinks while h-BN tries to expand due to the negative in-plane lattice thermal expansion coefficient.This leads to the generation of strain at the h-BN/sapphire interface.At some point, this strain is so high that it has to be relaxed by forming h-BN wrinkles.These wrinkles can be observed in SEM images at room temperature (figure 5(a)).The physical origin of this phenomenon is the competition between the elastic energy (dependent on the material volume) and the energy of the layer/substrate interaction (dependent on the material surface area).The appearance of wrinkles allows for the expansion of the h-BN layer which can slide on the substrate thereby leading to strain relaxation.Since the interaction between the h-BN layer and the substrate is weak (van der Waals) the part of the layer being in contact with the substrate can relax and show a behavior similar to what is expected for freestanding layers.Temperature-related changes in the h-BN morphology influence significantly the energy of the E 2g high Raman mode observed in our measurements.Figure 6 schematically explains our interpretation of the obtained results.Our experiment starts at room temperature so at the beginning our as-grown h-BN is wrinkled (figure 6(a)).
With increasing temperature, the sapphire substrate expands while h-BN tries to shrink.Below some critical point (around 900 K) this process requires very small energy because wrinkles act as h-BN reservoir so the in-plane phonon energy is almost constant (figure 6(c)).At higher temperatures wrinkles are flattened so there is no excess of h-BN.The layer is now fully attached to the substrate.Further expansion of the substrate requires stretching of the h-BN layer (figure 6(b)).As a result, we observe a dramatic jump in the rate of the change of the energy of the E 2g high Raman mode with temperature which can be viewed as an enhancement of the effective interaction between the substrate and h-BN epilayer.Such an interpretation explains why we observe high values for the phonon energy change rate β for as-grown h-BN layers C0, F, and CF.Since they are the thinnest, the stretching caused by the substrate affects them the most (elastic strain energy is smaller than the adhesive energy).CFF is thicker than C0, F, and CF so for this layer, the elastic energy is higher and layers slide over the substrate.Thus in the whole temperature range, only one low value for the β parameter is needed to describe the E 2g high phonon energy change.It is also very important to note that this change of the character of the h-BN/sapphire interaction for thinner layers is observed after one temperature 'cycle' (as we needed to anneal h-BN layers to quench luminescence) so it means that the change of the h-BN/sapphire interaction character is available in both directions.It indicates that during the cooling down of our, flattened h-BN on sapphire, wrinkles should form again.We assume also that in such a situation they are formed not immediately after the start of the cooling down process at 1200 K, but rather at a critical temperature close to 900 K. Otherwise, we would expect β to change not at 900 K but at 1200 K during our post-anneal measurements because the excess h-BN in wrinkles would start to accumulate at this temperature.This finding suggests that during the cooling process of as-grown h-BN on sapphire just after the growth in the reactor, wrinkles should form at a similar temperature.Unfortunately, our growth setup does not allow us to follow these changes in situ.The absolute values of β >900K for C0, F, and CF for as-grown samples are high compared to β <900K , but are still 2-4 times smaller than the literature values [37,38].This is not surprising, as the growth temperature was not achieved during annealing so probably the thermomechanical behavior of our samples is not exactly the same as in the case of the material just after the growth.In this temperature range, the energetic minimum is reached for some residual strain and still-existing wrinkles.Furthermore, high temperatures can change the morphology of the substrate.Thus some additional changes of β >900K may occur.Nevertheless, the most significant change in the character of h-BN/sapphire interaction is still observed close to 900 K. Wrinkles are not observed for the thickest as-grown layer C1.They cannot be created due to the crystalline structure and the thickness of around 450 nm (generated strain is not high enough to separate material of the thickness of about a few hundred nm from the substrate).However, the h-BN/ sapphire interaction is still low because freestanding flakes in thick, porous material can adapt to the volume changes of the substrate almost without strain generation.The fact that absolute values of β <900K for thin h-BN layers are smaller than the absolute value of β for C1 indicate that wrinkle formation determines the thermomechanical interaction between h-BN and sapphire and that all other mechanisms are negligible.The non-zero value β for layer C1 suggests that substrate interaction with porous material still generates some strain.
In the case of delaminated films transferred onto silicon, the mechanism involving wrinkles formation is inactive as shown by SEM images in figure 5(b).The crucial difference is that now h-BN is deposited on a new substrate at room temperature (at this temperature there is no strain between h-BN and silicon).When the temperature increases, silicon expands and the delaminated h-BN tries to shrink.Although strain is generated at the interface, wrinkles cannot be created because the h-BN film is stretched, not squeezed.Therefore we observe a continuous change of the E 2g high mode energy without any critical points (figure 4-bottom panel).When the temperature decreases this strain is just reduced.
Our results regarding delaminated MOVPE h-BN films transferred onto silicon are in agreement with literature data for exfoliated h-BN flakes [37,38].A recent work also studies the case of delaminated MOVPE h-BN layers, but the smaller temperature range of 300-420 K in this work did not allow to study the effects that we observe at around 900 K [35].

Conclusions
We present a comprehensive study of the interaction between epitaxial h-BN layers and substrates by means of temperaturedependent Raman spectroscopy.We succeeded in quenching the commonly observed luminescence that hinders Raman spectroscopy above 400 K by introducing an annealing step at high temperatures.This procedure allowed us to measure the Raman signal for temperatures of up to 1100 K. Results obtained for delaminated h-BN films transferred onto silicon indicate that our epitaxial material is similar to bulk material in terms of thermomechanical behavior.The β temperature rate of the E 2g high phonon energy, which is a measure of the strength of the interaction between the h-BN film and silicon, is just 2 times lower (in terms of absolute value) than the literature value for h-BN flakes exfoliated from bulk crystal.However, the temperature-dependent Raman measurements show that asgrown epitaxial h-BN on sapphire behaves completely differently.For temperatures above 900 K the strength of the interaction of h-BN with the sapphire substrate is similar to the one present for delaminated samples on silicon (absolute values of β 2-5 times smaller).However, this interaction almost vanishes for temperatures below 900 K.This finding indicates that the difference in thermal expansion of h-BN and sapphire does not lead to a strain generation in epitaxial material below 900 K.We attribute this effect to wrinkles formation.Creating wrinkles minimizes the total energy of the system in a similar way as island nucleation is energetically favorable during the Stransky-Krastanov growth mode of quantum dots.During MOVPE growth of h-BN, epitaxial material is deposited on the sapphire substrate at a high temperature of around 1600 K.When the temperature is lower, the difference in thermal expansion of sapphire and h-BN leads to strain generation at the interface between them.Below 900 K wrinkles are created and h-BN/substrate interaction is reduced.Decreasing the temperature below 900 K does not generate additional strain but leads to creating new wrinkles.The described mechanism is universal for all two-dimensional materials grown at high temperatures.The creation of wrinkles indicates that the grown layer is continuous, uniform, and weakly interacts with the substrate.Therefore, wrinkle formation constitutes an additional challenge for the growth of van der Waals heterostructures based on high-quality two-dimensional materials.

Figure 1 .
Figure 1.Results of temperature-dependent Raman measurements of the sample F/Sapphire (∼10 nm thickness): (a) Raman spectra of asgrown h-BN for different temperatures during annealing (increasing temperature).(b) Integrated intensities of optical response (Raman signal + luminescence) during and after annealing for different temperatures (blue squares and red circles-experimental points, dashed linesguide to the eye).(c) Raman spectra of the annealed as-grown h-BN layer on sapphire and the substrate at 423 K-the green curve represents the pure h-BN Raman signal.(d) Background-corrected h-BN spectra for different temperatures after annealing.Black lines-Lorentzian curve fits.

Figure 2 (
b) shows signals from the h-BN film on silicon and the bare silicon substrate.Pure h-BN spectra are presented in figure 2(c).

Figure 2 .
Figure 2. Temperature-dependent Raman measurements of the sample F/Silicon (∼10 nm thickness).(a) Integrated intensities of optical response (Raman signal + luminescence) during and after annealing for different temperatures (blue squares and red circles-experimental points, dashed lines-guide to the eye).(b) Raman spectra of the annealed h-BN layer on silicon and the substrate only at 303 K. (c) Background-corrected h-BN spectra for different temperatures after annealing.Black lines-Lorentzian curve fits.

Figure 3 .
Figure 3. Temperature dependence of the E 2g high mode frequency in bulk h-BN (blue circles-experimental points, red line-values obtained from equation (3)).Inset-Raman spectra of E 2g high phonon in bulk h-BN at different temperatures.

Figure 4 .
Figure 4. Differences between E 2g high mode frequencies in the bulk crystal and MOVPE as-grown h-BN on sapphire (upper panel) or delaminated h-BN films transferred onto silicon (bottom panel).Results of fitting equation (2) to the experimental data are also presented.

Figure 5 .
Figure 5. SEM images of h-BN grown by two-stage epitaxy: (a) as-grown h-BN on sapphire, (b) delaminated h-BN film transferred onto silicon at room temperature.

Figure 6 .
Figure 6.Schematic drawing illustrating the behavior of our h-BN layers during temperature-dependent Raman measurements.(a) At low temperature h-BN is wrinkled.During increasing temperature sapphire expands flattening the h-BN epilayer.This process does not consume much energy since wrinkles act as reservoir of the h-BN.Therefore, in this temperature range, the in-plane phonon energy is almost constant.(b) At high temperature, h-BN is flattened so further expansion of the substrate require the stretching of h-BN which changes the energy of the phonon significantly.(c) Impact of the h-BN layer morphology on measured Raman shift (Sample C0/Sapphire).

Table 2 .
Parameters obtained from fitting equation (2) to experimental data for MOVPE delaminated h-BN films transferred onto silicon.