PHYSICAL REVIEW APPLIED 12, 014007 (2019) Growth Monitoring With Submonolayer Sensitivity Via Real-Time Thermal-Conductance Measurements P. Ferrando-Villalba,1 D. Takegami,1 Ll. Abad,2 J. Ràfols-Ribé,1 A. Lopeandia,1,* G. Garcia,1 and J. Rodriguez-Viejo1 1 Grup de Nanomaterials i Microsistemes, Dep. Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain 2 Institut de Microelectrònica de Barcelona- Centro Nacional de Microelectrònica − CSIC, Cerdanyola del Vallès, 08193, Spain (Received 20 March 2019; published 3 July 2019) Growth monitoring during the early stages of vapor deposition is of prime importance to understand the growth process, the microstructure, and thus the overall layer properties. We demonstrate that phonons can be used as an extremely sensitive probe to monitor the real-time evolution of film microstructure during growth, from incipient clustering to continuous film formation. For that purpose, a silicon nitride membrane-based sensor is fabricated to measure the in-plane thermal conductivity of thin film (conductive or nonconductive) samples. Operating with the 3ω-Völklein method at low frequencies, the sensor shows an exceptional resolution down to (κ · t) = 0.065 W/m K nm, enabling accurate measurements even in poor conductive samples. Validation of the sensor performance is done by growth characterization of organic and metallic thin films to tackle the low to high thermal-conductivity range. In both cases, at early stages of growth, the extreme sensitivity of the technique has revealed an initial reduction of the effective thermal conductance of the supporting amorphous membrane, K, related to the surface phonon scattering enhanced by the incipient nanoclusters formation. As cluster coalescence advances, K reaches a minimum to rise up upon the percolation threshold. Subsequent island percolation produces a sharp increase of the conductance and once the surface coverage is completed K increases linearly with thickness. The thermal conductivity of the deposited films is also obtained from the slope of K with thickness. DOI: 10.1103/PhysRevApplied.12.014007 I. INTRODUCTION (LEED, MEED) are also reliable tools to monitor two- dimensional (2D) ordering during epitaxial growth [5,6]. Monitoring the first stages of thin-film growth is of Among all, electrical measurements are very powerful key importance to understand and thus tune the prop- since (i) the electrical resistance in metallic thin films erties of the grown layers. Critical microstructure fea- [7] may vary orders of magnitude above the percola- tures, such as grain size, morphology, crystal orientation, tion threshold [8] and (ii) drastic electrical conductiv- nature of grain boundaries, and surface morphology are ity changes during the initial growth stages can identify defined during the early growth process. Real-time mea- phase transformations [9], such as amorphous-to-crystal surements have proven their potentiality to understand the transition in Mo films [10]. Unfortunately, although sim- growth dynamics, either for thin films or nanoparticles ple and accessible, this approach is limited to metallic deposited on surfaces. Actually, in situ diagnostics dur- or highly conductive layers, precluding the analysis of ing growth with monolayer sensitivity have already been organic or insulating materials. In contrast, phonons are performed by a variety of techniques, such as wafer curva- a more generic probe, extremely sensitive to film struc- ture measurements mapping the stress evolution [1], ellip- ture thanks to their larger mean free path compared to sometry [2], x-ray reflectivity [3,4], and resistance-based electrons. However, real-time thermal conductance mea- measurements. Low or medium energy electron diffraction surements during film growth are much scarcer, mainly due to the technical challenges associated with them. * Additionally, the potential application of nanomateri- aitor.lopeandia@uab.cat als, thin films, and nanostructures in heat management Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. and efficient thermoelectric devices has boosted the neces- Further distribution of this work must maintain attribution to the sity to perform accurate thermal-conductivity measure- author(s) and the published article’s title, journal citation, and ments at the nanoscale. In particular, phonon engineering DOI. in low-dimensional materials has appeared as the most 2331-7019/19/12(1)/014007(11) 014007-1 Published by the American Physical Society P. FERRANDO-VILLALBA et al. PHYS. REV. APPLIED 12, 014007 (2019) effective approach to enhance the thermoelectric figure such as In (indium), and an organic conductor, N,N -Bis of merit [11–13] through the reduction of thermal con- (3-methylphenyl)-N,N -diphenylbenzidine (TPD), often ductivity. The implementation of alternative nanomaterials used as a hole injector in organic light-emitting diode designs has encouraged the development of different sen- (OLEDs). Complementary characterization techniques sors and methodologies, enabling accurate determination (SEM, AFM, and electrical measurements) are used to of thermal conductivity in low-dimensional architectures. correlate conductance features with sample morphology Whether based on optical [14] or electrical [15] sig- throughout the growth. nals, these alternative thermal sensors and the associated methodologies have allowed in-plane [16,17] and out- II. EXPERIMENTAL SECTION of-plane [18,19] thermal-conductivity measurements of nanowires and thin films with outstanding nanometer spa- A. Sensor design and simulation tial resolution [20,21]. A remarkable contribution to the The sensor developed here consists of a long and thin field was achieved by Völklein et al. in 1990 when they Pt line deposited on a suspended SiNx membrane and con- developed a suspended membrane-based sensor using a nected in a four-wire configuration [Figs. 1(a) and 1(b)] long and thin Pt electrical transductor operated in dc to along with an external Pt line. The thermal conductance measure in-plane thermal conductivity of thin films [17]. of the whole membrane is determined with the centered More recently, Sikora et al. went a step further in improv- Pt line (normal operation), while both lines, centered and ing this technology by combining the Völklein method external, are needed to exclusively measure the thermal with the ac 3ω-method, reaching exceptional thermal- conductance of the membrane volume portion between conductance sensitivity, K/K ∼ = 10−3 [22,23]. them. See Fig. S1 in the Supplemental Material [27] for In parallel, ex situ thermal probe studies performed details of the sensor microfabrication. on thin films [24,25] have shown that the thermal con- In normal operation, the thermal conductance is cal- ductivity of a grown material is conditioned by the culated by using the one-dimensional (1D) Fourier law, thermal-conductance loss of the substrate induced both assuming an ideal transversal heat flow from the central by interfacial scattering of phonons in the in-plane mea- Pt line to the substrate toward the Si frame, which yields surements [24] and by thermal boundary resistance in the   out-of-plane measurements [25]. Accordingly, the thermal L K = kSiNx tSiNx 2 , (1) conductivity of the thin layer cannot be simply calculated λ via the differential measurement of the thermal conduc- tance of the whole sample (film + membrane/substrate) where tSiNx and kSiNx are the thickness and the thermal con- and a reference (only membrane/substrate), but must be ductivity of the silicon nitride, respectively, L is the length calculated using a set of thermal-conductance measure- of the Pt strip between the voltage probes, and λ is the ments performed at different film thicknesses. To date, transversal distance between the central Pt strip (linewidth most of these measurements have only been performed ex b = 5 µm) and the Si bulky substrate. situ, evaluating the temperature dependence of the ther- Using the classical diffusive Fourier equations for heat mal conductivity k for each singular thickness. To our transport and FEM with COMSOL software, we model the knowledge, real-time studies during growth at early stages heat transport in several sensor geometries. Considering taking into account the impact of the microstructure on the Joule heating produced by a dc current flowing through phonon scattering have not been previously reported. It is the Pt central strip, the simulated steady-state tempera- worth noting that although Völklein and Starz [26] already ture profiles are obtained. The central part of the strip demonstrated in 1997 that a Völklein-like sensor operating always shows a flatter temperature profile than its bor- in dc mode could perform in situ measurement of thermal ders, information that is used to determine the location of conductance in thin films, those measurements were lim- voltage probes in the central strip to ensure that the sens- ited to metallic films thicker than 1 µm, contrary to the ing area is limited taken with maximizing the temperature sensor presented here. homogeneity. In this paper, we present (i) an improved 3ω-Völklein The optimum sensor (taking into account the resolu- technique allowing highly sensitive conductance mea- tion limits of the available photolithographic system and surements (K/K < 10−3 ), (ii) the sensor optimization the structural stability of the SiNx membrane) consists of through FEM (Finite Element Modeling) thermal analy- a long and narrow SiNx membrane (3 mm × 250 µm × sis, (iii) an innovative study of the thermal evolution of 180 nm) that supports the two Pt sensing strips the sensor during growth, and (iv) real-time measurements (3 mm × 5 µm × 100 nm) with voltage probes separated by of the thermal conductance during growth of both highly 2 mm. The electrical lines of the voltage probes enter the insulating and conductive (electrically and thermally) membrane following in close proximity to the central Pt materials with submonolayer sensitivity. Proof-of-concept strip, minimizing heat leakage and thus temperature drop is achieved by analyzing two different materials: a metal, along the strip. The simulated profile of the longitudinal 014007-2 GROWTH MONITORING WITH SUBMONOLAYER. . . PHYS. REV. APPLIED 12, 014007 (2019) (a) an oscillating current I = I0 sin ωt, the amplitude of the induced temperature oscillations can be calculated with the 1D heat equation (assuming that the sensor is infinitely long), which, after some approximations (see the Supple- mental Material [27] for details of mathematical deriva- tion), yields P0 T2ω =   , (2) 2λ4 4τ λ2 K 1 + ω2 4τ 2 + 3D2 + 3D (b) where P0 = Io2 R/2, D = kSiNx /(ρSiNx cSiNx ), τ = Cp /K, and Cp = bL(ρSiNx cSiNx tSiNx + ρPt cPt tPt ). Here, ρSiNx ,Pt is (c) the density of the SiNx membrane and the Pt strip, cSiNx ,Pt is their specific heat capacity, Cp is the heat capacity of the strip and the portion of SiNx beneath it, τ is the ther- mal time constant of the sensor, D is the thermal diffusivity of SiNx , R is the Pt strip electrical resistance between the voltage probes, and I0 is the current amplitude. From Eq. (2), the apparent thermal conductance can be calculated as K2ω = P0 /T2ω , which resembles K at low frequencies. When a thin-film sample grows on the SiNx membrane, the parameters in Eq. (2) may vary as k, c, and ρ will no longer correspond solely to the SiNx membrane, but to the combination of the deposited film (from now on called “sample”) and the substrate membrane. In this case, an effective value for these magnitudes can be calculated (assuming a vertical growth of the film) by pondering the FIG. 1. (a) Optical micrograph of the sensor consisting on a different values as a function of the film thickness, tsmp suspended rectangular membrane (with a total width of 2λ) a longitudinal strip Pt heater placed on the center with a distance L kSiNx · tSiNx + ksmp · tsmp keff = , (3) between the four wire electrical probes. Red arrows indicated the tSiNx + tsmp ideal heat flow directions. (b) Surface temperature distribution of cSiNx · tSiNx + csmp · tsmp the sensor (brighter is hotter) in a FEM dc study. (c) Longitudinal ceff = , (4) and transversal temperature distributions of the sensor in a FEM tSiNx + tsmp dc study. ρSiNx · tSiNx + ρsmp · tsmp ρeff = , (5) tSiNx + tsmp temperature [black line in Fig. 1(c)] shows a large and flat keff central plateau where the inhomogeneity is lower than 3% Deff = . (6) ρeff · ceff of the total temperature rise. We notice two tiny tempera- ture depressions at ±1000 μm, coinciding with the voltage Here, ksmp , csmp , and ρsmp are the sample thermal con- probe locations. The transversal profile exhibits a constant ductivity, specific heat capacity, and density. In the same slope only perturbed by minimal flat segments correspond- way, the extrinsic values K and Cp will vary as well as the ing with the position of the Pt strips. With this sensor, thermal time constant τ as the thermal conductivity of the SiNx layer can be mea-   L sured with an accuracy of 0.05% in the absence of other K(tsmp ) = (kSiNx · tSiNx + ksmp · tsmp ) 2 , (7) uncertainty sources. See the Supplemental Material [27] λ for more information about the modeling. Cp (tsmp ) = bL(ρSiNx · cSiNx · tSiNx + ρPt · cPt · tPt + ρsmp · csmp · tsmp ), (8) B. Thermal analysis during film deposition Cp (tsmp ) τ = . (9) Based on Sikora et al. developments [22,23], we deduce K(tsmp ) a mathematical expression to extract the thermal con- ductivity from the measured thermal conductance at dif- If the measuring frequency is low (ω  3Deff /8λ2 ), ferent thicknesses. When the central Pt line is fed with then the measured K2ω resembles K and the derivative of 014007-3 P. FERRANDO-VILLALBA et al. PHYS. REV. APPLIED 12, 014007 (2019) Eq. (7) can be used to calculate the thermal conductivity (a) of the sample film by measuring in real time the thermal conductance during growth [K2ω (tsmp )], as shown in Eq. (10).   dK dK L dtsmp = ksmp 2 → ksmp = L . (10) dtsmp λ 2λ However, if a higher current angular frequency ω is used, (b) ksmp can be extracted by fitting the measured K2ω with Eq. (11) using the thickness-dependent parameters (Eqs. (6)–(9))    2λ4 4τ  λ2 K2ω (tsmp ) = K(tsmp ) 1 + ω2 4τ  2 + 2 + . 3Deff 3Deff (11) FIG. 2. (a) Calculated real thermal conductance (black) and apparent thermal conductance modeled at 1 Hz (red) and 3 Hz In Fig. 2(a) the calculated K2ω is plotted for current fre- (blue) during the deposition of a layer. (b) Calculated fre- quencies of 0 Hz (dc), 1 and 3 Hz (the parameters used quency dependence of the temperature oscillations in the sensor are listed in the figure caption). If the conductance is mon- before and after depositing a 250-nm film (the inset is a zoom itored with a current at 1 Hz, the apparent thermal conduc- out).The material properties used in both plots are the follow- tance K2ω is very similar to K throughout the deposition. ing: kSiNx = 2.65 W m−1 K−1 ,cSiNx = 0.7 J K−1 kg−1 , ρSiNx = However, at 3 Hz, there is an evident difference in the slope 3.18 g/cm3 , kPt = 33 W m−1 K−1 , cPt = 0.133 J K−1 kg−1 , ρPt = of the curves: although the absolute value of the appar- 21.45 g/cm3 , ksmp = 0.21 W m−1 K−1 , csmp = 1.05 J K−1 kg−1 , ent thermal conductance only varies from 97% to 93% of and ρsmp = 1.08 g/cm3 . Structural parameters are tSiNx = 180 nm, tPt = 110 nm, λ = 123 μm, b = 5 μm, and L = K [Fig. 2(b))], the slope of K2ω is up to 40% higher than 2000 μm. the one of K [Fig. 2(a)]. Generally, measuring with higher frequencies increases the dependence of K2ω with intrinsic properties of the sample that may not be well known (like sample one) nonsuspended sensor, which produces no self- csmp or ρsmp ), hindering the determination of ksmp . heating and is used to subtract the 1ω component of the sample sensor. Thus, the 3ω component of the differential C. Experimental setup voltage is only produced in the sample sensor and owing to the cancellation of the 1ω voltage, it could be ampli- The sensor is introduced in a high vacuum chamber fied with a gain Gdiff = 75. The main benefit of using a equipped with an effusion cell that enables a good control twin sensor (instead of a variable resistance) as a reference of the evaporation rate to deposit the sample at the back- for the differential measurement is that if the temperature side of the suspended membrane. A previously calibrated of the sample holder varies, the resistance of both sensors quartz crystal microbalance (QCM) is located near the sen- will change hand-in-hand, making it unnecessary to build sor to monitor the layer growth rate with a precision of a control system for the cancellation of the 1ω voltage. The 0.01 Å/s. A set of shutters permits to shadow the deposition exact electronics used in the measurement of the different selectively in the device, in the QCM, or in both. voltage signals are detailed in Fig. S4 of the Supplemental The temperature of the sample is controlled with a Material [27]. custom-made proportional-integral-derivative (PID) con- From the measured voltage signals, the resistance Rsmp troller system that reads the temperature of a Pt100 and and the temperature oscillations T2ω can be calculated as provides heat through a Kapton heater, yielding a temper- ature control with fluctuations smaller than 0.003 K from V1ω 77 K up to 400 K. Rsmp = , (12) I0 · Gsmp The experiment is performed by feeding two sensors (sample and reference) with a current wave of a given 2V3ω T2ω = dR , (13) amplitude and frequency, generating a voltage drop in each I0 dTsmp · Gdiff · Gsmp sensor. The voltage signals from both sensors, as well as the differential voltage between them, are subtracted using where V1ω and V3ω are the 1ω and 3ω voltage components the low-noise amplifiers with gains Gsmp , Gref , and Gdiff , measured in the sample sensor and dRsmp /dT is the slope respectively. The reference sensor is a twin (equal to the of the sample resistance as a function of the temperature. 014007-4 GROWTH MONITORING WITH SUBMONOLAYER. . . PHYS. REV. APPLIED 12, 014007 (2019) III. RESULTS a standard deviation of data equal to 8 and 1.3 nW/K, respectively. This accuracy in the thermal conductance A. Sensor performance test provides an extremely high resolution in the product of Initially, the self-heating of the Pt sensor is determined the thermal conductivity and the thickness, (k · t) = by measuring both the 3ω voltage and the variation of 0.065 W/m K nm. Although there is a decrease in the data the 1ω voltage with ω = 2π rad/s. Since the frequency dispersion for 500 µA, there is also a noticeable reduction is very low, both signals yield identical self-heating, but in the average value of the thermal conductance from 16.91 as can be seen in Fig. 3(a), the self-heating calculated to 16.85 µW/K that may be justified by a small reduc- with the 3ω voltage (T2ω ) is less noisy than the one tion of the sensor dR/dT due to the higher average heater calculated with the 1ω voltage(Tdc ). Also, the slope of temperature. log T2ω vs log I0 has a value very close to 2, demon- The thermal conductivity of the SiNx membrane is eval- strating that the self-heating depends on the square of the uated for temperatures between 80 and 230 K, as shown current. in Fig. 4 (black squares). The results are very similar to T2ω has been measured in a wide frequency range the values found in the out-of-plane direction using the (1–2000 Hz) and compared with finite element simulations 3ω method on a similar SiNx membrane (red circles in in a time-dependent study, as can be seen in Fig. 3(b). The Fig. 4). The latter values are obtained through a differen- high coincidence between both datasets suggests that the tial measurement of two samples with thicknesses of 180 behavior of the sensor is purely driven by heat transport and 450 nm, granting that the thermal boundary resistances physics. This is an important difference from the device between the film and the substrate are cancelled. Thus, the presented by Sikora et al. [22], where the use of a NbN similarity of both the in-plane and the out-of-plane values strip sensor allowed measurements at very low tempera- confirm that there are not substantial phonon size effects, tures, but produced non-negligible electrical effects due to or anisotropy, in our layers. In both cases, the variation of the high electrical impedance of that material. k with temperature shows a similar tendency to data pre- Finally, as shown in Fig. 3(c), the uncertainty of the sented by Sikora et al. [22,23] (continuous line in Fig. 4). conductance measurement is determined at two different The discrepancy in the absolute values may account for current intensities, 300 and 500 µA, which generate tem- density or stoichiometry variations related to the different perature amplitudes of about 2 and 6 K and produced growth film characteristics in each work. Huge differences in k variation with temperature are observed when com- paring our data with the work of Sultan et al. [28] (blue (a) (b) triangles in Fig. 4). We suggest, as will be discussed later, that this difference is probably related to fact that they use a nanocrystalline membrane. The measurements performed in this work have an extremely low variability owing to the high sensitivity of the method. The main source of uncertainty in the in-plane (c) FIG. 3. (a) Self-heating of the sensor measured with the 3ω and 1ω voltages (ω = 1 Hz). (b) Temperature oscillations as a func- tion of the frequency. The measured values are compared with the simulated ones using the COMSOL model. (c) Measurement of the uncertainty in the thermal conductance. K refers to the FIG. 4. Thermal conductivity values measured at different tem- standard deviation of the data. Red circles and black squares cor- peratures with the 3ω-Völklein method (in-plane direction) and respond to data obtained with input currents of 500 and 300 µA, the 3ω method (out-of-plane direction). Data from Sultan et al. respectively, with ω = 1 Hz. [28] and Sikora et al. [23] are also included for comparison. 014007-5 P. FERRANDO-VILLALBA et al. PHYS. REV. APPLIED 12, 014007 (2019) measurement is the precise determination of SiNx mem- (a) brane thickness, which is measured throughout the wafer with a contactless optical profilometer, yielding a standard deviation of 1% of the 180-nm averaged thickness. How- ever, wet etchings at the final steps of microfabrication process could slightly reduce this thickness by up to 10 nm, inevitably increasing the uncertainty up to 5%. (b) B. Real-time measurement of thin-film growth: sensor proof of concept 1. Organic thin-film layers We initially measure the thermal conductance of the (c) membrane as a function of the TPD thickness deposited at 267 ± 2 K, as shown in Fig. 5(a). The temperature uncertainty comes from the thermal oscillations produced by the current wave of amplitude 300 µA. The evap- oration is carried out below 10−7 mbar by heating an effusion cell up to 200 °C, which yields a stable depo- sition rate of 0.29 nm/s. From the slope of the curve K2ω (tsmp ) and applying Eq. (8), we calculate the ther- FIG. 5. Thermal conductance versus thickness during TPD mal conductivity of the TPD layer, resulting in ksmp = growth: (a) Tdep = 267 ± 2 K. Growth rate = 0.29 nm/s. (b) Tdep = 267 ± 2 K. Growth rate = 0.02 nm/s. (c) Tdep = 304 ± (0.153 ± 0.001) W m−1 K−1 . However, if the thermal con- 2 K. Growth rate = 0.02 nm/s. In graphs (b) and (c), data are box ductivity is calculated by fitting Eq. (11), we obtain ksmp = averaged with 10 points/box. The main regions of film growth (0.145 ± 0.001)W m−1 K−1 . As discussed previously, both are separated by dashed red lines. Region I located between 0 nm results are comparable due to the low frequency used in the and the first vertical line corresponds to nucleation and isolated measurement. The low value of the thermal conductivity is island formation; region II to island coalescence; region III to an indication of the glassy character of the TPD layers as percolation across the layer, and region IV to vertical growth of confirmed by calorimetric measurements showing a clear a continuous layer. The slight difference in the initial conduc- signature of the glass transition temperature, as can be seen tance between all the graphs is mainly due to the use of different sensors and/or membranes for the experiments. The black down- in Fig. S7 in the Supplemental Material [27]. ward arrow marks the percolation threshold (separation between As clearly seen in Fig. 5(a), at the early stages of the regions II and III). The inset of (b) shows the abrupt variation of deposition, that is, very low thicknesses, we observe a the electrical conductance at the percolation threshold (nominal decrease in the thermal conductance of around 1.2% of its thickness of 2.6 nm) of the TPD film. This value coincides with initial value, while afterward, K2ω roughly increases lin- the minimum of the thermal conductance (black arrow) in graph early with thickness. In this particular measurement, film (b). The uncertainty of the thermal conductance measurement in growth is stopped at 340 nm, yielding a constant value of this measurements is below 0.1%. the thermal conductance after this particular point. Figures 5(b) and 5(c) show in more detail the initial stages of the evolution of K2ω vs thickness for two TPD To understand and interpret the variation of K2ω with films deposited at 267 and 304 K, both with a low growth thickness, we also perform ex situ analysis of the film mor- rate of 0.02 nm/s. In both cases, we identify four differ- phology either by SEM or by AFM, summarized in Fig. ent regions where thermal conductance follows different S5(a) in the Supplemental Material [27]. Complementary trends with different thicknesses. In region I, the overall electrical characterizations are also performed, as shown conductance decreases abruptly following an exponential in Fig. 5(b) inset, to corroborate the hypothesis described behavior, while it decreases slowly in region II until a min- later on. Surface morphology evolution with thickness imum point is reached. Region III covers the thickness show that TPD does not wet the SiNx membrane surface, range where K2ω increases slowly up to a point where a as it grows in 3D islands in the early growth stages. For linear regime of the conductance with thickness is attained films deposited at 267 K and according to the conduc- and labeled as region IV. The extent of each of these tance evolution, island coalescence seems to happen at a regions is represented in Figs. 5(b) and 5(c) by dashed nominal film thickness of 2.6 nm, while complete surface red lines, and as is clearly seen, varies from one sam- coverage seems to take place at 14 nm. Ex situ analysis ple to another, confirming the importance of deposition of growth regimes is precluded by the evidence of dewet- temperature as will be discussed later. ting of TPD at temperatures well below the glass transition 014007-6 GROWTH MONITORING WITH SUBMONOLAYER. . . PHYS. REV. APPLIED 12, 014007 (2019) temperature [29].The fast film dynamics at temperatures requires that phonons slightly larger than the average inter- below the glass transition temperature makes in situ anal- atomic distance at room temperature be involved in heat ysis an indispensable tool to gain a better understanding of transport along the nitride membrane. We can thus tenta- film formation in molecular glasses. tively attribute the initial sharp reduction of the thermal Before relating the large drop observed in region I with conductance to the formation of TPD isolated clusters on film microstructure, we perform a few tests to rule out any top of the nitride membrane surface, modifying the inter- potential experimental artifact that could have led to tem- facial phonon scattering and thus leading to a decrease of perature variations of the sensor. As extra heat originated the thermal conductance. by condensation of molecules on the substrate is not mod- Although we currently lack a complete understanding of ulated at angular frequency ω or any of its harmonics, and the microscopic processes occurring at the interfaces, we therefore, does not affect the 3ω component of the voltage, believe that the growth of new material on top of the mem- the decrease of conductance cannot be attributed to a sen- brane changes the specularity of the surface, resulting in an sor temperature variation due to this phenomenon. We also effective increase in the phonon scattering rate. We foresee rule out any effect of the sample emissivity variations dur- that the future use of crystalline membranes, such as single ing TPD growth on the membrane, since a measurement crystalline Si, will provide a convenient platform to inves- at 81 K, where radiation effects should be substantially tigate nucleation and island growth dynamics during the lower, shows a similar drop in thermal conductance (mea- early stages of film growth with even higher conductance surement shown in Fig. S6 in the Supplemental Material sensitivity. [27]). The reduction of thermal conductance observed in In region II, the thermal conductance still decreases but the early stages of growth seems to be due to phonon- with a lower slope. We believe that in this region, clusters related phenomena, although covering the surface with enlarge and start to coalesce, providing additional paths TPD is not expected to affect the thermal conductance of for heat transfer, which partially compensate the inter- the SiNx membrane since it is already a disordered struc- face scattering until a minimum is reached at the end of ture with an average phonon mean free path of the order the present region. As island coalescence continues and of the interatomic distance. Nevertheless, a previous work percolation builds up new channels across the layer struc- by Sultan et al. [24,28] already showed similar behavior (K ture (region III), providing additional heat flow paths that decreases at early growth stages with a subsequent increase start to exceed the contribution of the interface scattering. for larger thicknesses) by performing ex situ measurements The coincidence of the minimum in thermal conductance of thermal conductance versus thickness of metal and alu- with a percolation phenomenon threshold is demonstrated mina deposited on SiNx . Nonetheless, our data differs from in a separate experiment where electrical conductance is this previous work in several important aspects: (i) the measured as a function of thickness [inset in Fig. 5(b)], magnitude of the conductance drop is much lower and showing a sharp variation of the slope at 2.6 nm due to (ii) our measurements are carried out in situ with a much electrical continuity through the TPD film. higher conductance sensitivity, providing a much clearer As percolation persists, the thermal conductance signature of the various growth regimes. increases, reaching a linear regime that we identify with Our thermal conductance initial drop, although much the formation of a continuous layer with complete cover- higher than the uncertainty of the measurement, only age, and marking the onset of region IV. Thus, region IV amounts to 1.2% compared to 5–10% in Sultan’s work. corresponds to the vertical growth of the continuous film. Those authors estimated that 40%–50% of the total K In this regime, the increase in thermal conductance is lin- was due to long wavelengths with long mean free path ear and proportional to the thickness of the growing layer. phonons. The estimated average λ value for these phonons Compared to the end of region III, there is a small reduc- was around 4.5 nm, much higher than thermal phonons at tion in the slope of the conductance versus thickness since room-temperature that have λ ∼ 0.2 nm. We thus believe the islands are no longer forming new conductive channels. that the main difference between both results arises from Differences in growth dynamics with the deposition tem- a different microstructure of the SiNx membrane in each perature are also studied, as shown in Fig. 5(c), where TPD case. The thermal conductivity value of our SiNx , slightly film is deposited at 304 K. Although the four regions are below Sultan et al. [24,28] values, combined with the tem- evident in both cases, remarkable differences in region lim- perature dependence shown in Fig. 4, clearly indicates that its appear with respect to the sample deposited at 267 K our nitride is fully amorphous while the one used in Sul- [Fig. 5(b)]. At this temperature, the percolation threshold tan et al. work was probably nanocrystalline. Therefore, a (black downward arrows) and film continuity are 2.5 and lower drop of the thermal conductance in fully amorphous 14 nm, respectively. However, a sample grown at 304 K nitride membrane is consistent with a scenario where the shows a higher percolation threshold of 6 nm (probably contribution of long λ phonons is reduced with respect to due to higher molecular mobility taking place at a higher previous nanocrystalline nitride membranes, even though deposition temperature), and the thickness value for film the conductance drop due to enhanced surface scattering continuity is not clearly resolved from the data since the 014007-7 P. FERRANDO-VILLALBA et al. PHYS. REV. APPLIED 12, 014007 (2019) reduction in the slope after region III is not observed. mostly randomly oriented [31]. We have recently demon- Recent work by Fakhraai and coworkers [29] in TPD strated that heat transport along the backbone (the long films grown at 315 K have shown that film continuity axis of the molecule) is strongly preferred with respect was reached for film thicknesses above 20 nm, which is to transport through the perpendicular direction. There- consistent with our results. fore, the higher thermal conductivity value measured at Although a similar behavior of K2ω is observed for Tdep = 267 K compared to the one obtained for sam- both samples, final values of in-plane conductivity deter- ples grown at Tdep = 305 K is related to variations in the mined from the slope in regions IV of Figs. 5(a) and molecular orientation. 5(c) differ considerably:k = 0.145 W m−1 K−1 for films deposited at Tdep = 267 K and k = 0.132 W m−1 K−1 for those deposited at Tdep = 304 K. While the difference only 2. Metallic thin-film layers amounts to 10%, it is substantially larger than the mea- To complete the proof of concept of the sensor, we surement uncertainty. Both films are amorphous at those also analyze growth kinetics of a metallic indium layer. deposition temperatures, as confirmed by clear glass tran- Figure 6 shows the real-time in situ thermal conductance sition signatures shown in the calorimetric traces of Fig. measurement during growth for two deposition temper- S7 in the Supplemental Material [27]. The variations in atures, 315 and 260 K. Conductance values [Figs. 6(a) thermal transport are related to the intrinsic characteris- and 6(b)] follow a similar pattern to the one observed in tics of vapor-deposited glasses, in particular, density and TPD films, but with much larger thickness scales. The molecular orientation, which strongly depend on the depo- conductance regions can be identified and discussed, as sition temperature. As shown in a previous publication in the TPD case, in view of the microstructure evolution [30], the degree of molecular packing anisotropy depends with thickness (see Fig. S5 in Supplemental Material [27] on the deposition temperature and substantially influences for a complete set of microscopy images). As shown in thermal transport, while the small density variations do the inset of Fig. 6(a), the fast decrease of conductance at play a minor role. TPD films grown at 0.80Tg have the very early stages of deposition is also present. In this molecules with the long axis partially aligned paral- thickness range (up to 0.65 nm), tiny isolated clusters are lel to the substrate, while those grown at 0.91Tg are expected to develop on the surface of the SiNx membrane. (a) (b) (c) FIG. 6. (a) Thermal conductance versus thickness during deposition of In films: (a) Tdep = 315 K. The electron microscopy images of films of varying nominal thickness show the microstructural evolution of the In layer. SEM images are acquired with a magnification of 100,000, except the thickest one recorded at 50k. The 1-µm scale is provided inside the graph. The inset of (a) highlights the conductance drop during the early growth stages. (b) Tdep = 250 K. Thickness range is extended to attain complete percolation and total coverage. The uncertainty of the thermal conductance is indicated by the blue shadow underneath the curve. (c) FEM simulation: normalized conductance versus In nominal thickness for representative structures with isolated islands of different sizes and percolated islands, finally forming a continuous layer. The different growth regimes are shown in roman letters. Inset of (c): Image of the 3D model, consisting of an array of 9 × 9 square In islands (gray) on a SiNx thin membrane (green). 014007-8 GROWTH MONITORING WITH SUBMONOLAYER. . . PHYS. REV. APPLIED 12, 014007 (2019) The observed conductance drop of 1.5% is again an indi- percolation threshold above 200 nm, In islands are still cation that phonons with mean free paths slightly larger isolated from one another and the increased conductance than those typically accounted for in disordered solids are is due to the formation of larger islands as In evaporation being scattered by the In/SiNx interface. Nevertheless, the proceeds. At around 200 nm, the sudden increase in the minimum conductance found in this case cannot be corre- slope is related to island percolation (region III starts). At lated with a percolation threshold as we considered in TPD, the end of the percolation regime, a continuous film forms since individual In islands are much more conductive than and the conductance is heavily dominated by the In film the TPD ones and they can contribute significantly to the (region IV). Then, the conductance increases linearly with thermal conduction even though they are still physically a slope given by the thermal conductivity of the film. disconnected at this stage. Interestingly, neither percolation threshold nor complete IV. CONCLUSIONS coverage of In grown on SiNx are reached for a metallic layer as thick as 120 nm (nominal thickness), as clearly We develop a universal sensor with extreme accu- evidenced in the SEM images. As shown in Fig. 6(b), racy and methodology able to perform real-time thermal- where growth characterization is performed up to 450 nm, conductance measurements during film growth. The percolation starts to play a significant role at thicknesses technique is adaptive for any kind of material and thick- around 200 nm, where the conductance sharply increases ness. Large sensitivity allows disentangling the evolution due to continuous channel formation. Subsequently, the of film microstructure with thicknesses. By analyzing thermal conductance increase slows down, becoming lin- changes in the apparent thermal conductance versus thick- ear with thickness. The corresponding fitting line [red line ness, differentiated growth stages can be identified, giving in Fig. 6(b)] is proportional to the thickness, meaning that rise to a complete comprehension of the growth process the In layer is already continuous and the thermal conduc- for several materials. At early stages, the fast drop of tivity can be evaluated from the slope of the conductance the thermal conductance is related to nucleation and iso- versus thickness. The value of k for the continuous In lated clusters formation. This step is followed by a regime layer deposited at 260 K is 47 W m−1 K−1 , substantially where clusters grow to form islands through coalescence lower than the tabulated value for In, k = 83 W m−1 K−1 , and absorption of atoms or molecules from the gas phase, probably due to smaller grain size and enhanced bound- which dominates the variation of the heat conductance ary scattering. From the images taken by SEM of the In with thickness. In an intermediated stage, the percolation layer at different thicknesses (insets of Fig. 6(a) and Fig. threshold is revealed by a conductance rise, while the final S5(b) in the Supplemental Material [27]), we approximate mode, where the thermal conductance changes linearly the coverage ratio and the mean island area. with thickness, corresponds to the formation and growth As indicated in Figs. 6(a) and 6(b), we can differentiate of a continuous film. In this regime, the thermal conduc- four growth regimes: I: nucleation and initial small island tivity of the film can be directly derived from the slope of growth, II: growth of islands, divided into IIa (with small the conductance versus thickness plot. isolated circular islands) and IIb (with larger islands irreg- The ad-hoc methodology presented here is easily exten- ularly shaped forming a bimodal island size distribution), sible to devices with other substrate materials compatible III: island percolation forming continuous channels, and with epitaxial growth. Using single crystalline membranes, IV: vertical growth of a continuous film. the conductance reduction within the first stages of growth Since the conductance evolution is slightly different will be enhanced, increasing the sensitivity. The extreme (region II is divided into two stages) than the one previ- sensitivity will pave the way to apply the technique ously observed for TPD layers, we conduct FEM using the to interesting phenomena such as phase changes during structural information provided by the electron microscopy growth, size effects, or molecular orientation and density images. We use a simplified representation of our sam- in organic glass films, among others. ple by building an array of 9 × 9 In square islands on a 180-nm thick SiNx film. Changing the nominal thickness ACKNOWLEDGMENTS of the layer implies modulating the size and separation of the islands to match the island size and coverage ratio We acknowledge financial support from the Minis- observed by SEM (see the Supplemental Material [27] for terio de Economía y Competitividad through Grants details on coverage calculations). The thermal conductance No. CSD2010-00044 (ConsoliderNANOTHERM), No. is monitored by imposing a heat flow and measuring the FIS2013-50304-EXP, and No. MAT2016-79579-R. P. temperature difference arising on the simulated structure. Ferrando-Villalba and J. Ràfols-Ribé were in receipt of an The results of the simulation are shown in Fig. 6(c). The FPU grant from the Spanish Ministry of Education, Cul- simulation closely predicts the increase of the slope of the ture and Sports. Ll. Abad was supported by the “Ramón y curve K2ω (tsmp ) deposited at 315 K in a thickness range Cajal” program (Grant No. RyC-2013-12640) from Span- around 30–50 nm. In this thickness range and up to the ish Government. This work made use of the Spanish 014007-9 P. FERRANDO-VILLALBA et al. PHYS. REV. APPLIED 12, 014007 (2019) IMB-CNM-CSIC clean room (ICTS Network MICRO- [13] M. Hong, Z.-G. Chen, L. Yang, and J. 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