Growth monitoring with sub-monolayer sensitivity via real time thermal conductance measurements

Growth monitoring during the early stages of film formation is of prime importance to understand the growth process, the microstructure and thus the overall layer properties. In this work, we demonstrate that phonons can be used as sensitive probes to monitor real time evolution of film microstructure during growth, from incipient clustering to continuous film formation. For that purpose, a silicon nitride membrane-based sensor has been fabricated to measure in-plane thermal conductivity of thin film samples. Operating with the 3{\omega}-V\"olklein method at low frequencies, the sensor shows an exceptional resolution down to {\Delta}({\kappa}*t)=0.065 nm*W/(m*K), enabling accurate measurements. Validation of the sensor performance is done with organic and metallic thin films. In both cases, at early stages of growth, we observe an initial reduction of the effective thermal conductance of the supporting amorphous membrane, K, related with the surface phonon scattering enhanced by the incipient nanoclusters formation. As clusters develop, K reaches a minimum at 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 obtained from the variation of K with thickness.


Introduction
Monitoring the first stages of thin film growth is of key importance to understand and thus tune the properties of grown layers. Critical microstructure features such as grain size, morphology, crystal orientation, nature of grain boundaries and surface morphology, are defined during the early growth process. Real-time measurements have proven their potentiality to understand the growth dynamics, either for thin films or nanoparticles deposited on surfaces. Actually, in-situ diagnostics during growth with monolayer sensitivity have already been performed by a variety of techniques such as wafer curvature measurements mapping the stress evolution 1 , ellipsometry 2 , X-ray reflectivity 3,4 and resistance-based measurements. Low or medium energy electron diffraction (LEED, MEED) are also reliable tools to monitor 2D ordering during epitaxial growth 5,6 . Among all, electrical measurements are very powerful since i) the electrical resistance in metallic thin films 7 may vary orders of magnitude above the percolation threshold , and ii) drastic electrical conductivity changes during the initial growth stages can identify phase transformations, such as amorphous-to-crystal transition in Mo films 8 .
Unfortunately, although simple and accessible, this approach is limited to metallic or highly conductive layers, precluding the analysis of organic or insulating materials. In contrast, phonons are a more generic probe, extremely sensitive to film structure thanks to their larger mean free path compared to electrons. However, real-time thermal conductance measurements during film growth are much scarcer, mainly due to the technical challenges associated.
Additionally, the potential application of nanomaterials, thin films and nanostructures in heat management and efficient thermoelectric devices has boosted the necessity to perform accurate the thermal conductivity measurements at the nanoscale. In particular, phonon engineering in low-dimensional materials has appeared as the most effective approach to enhance the thermoelectric figure of merit [9][10][11] through the reduction of thermal conductivity. The implementation of novel nanomaterials designs has encouraged the development of new sensors and methodologies, enabling accurate determination of thermal conductivity in low dimensional architectures. Whether based on optical 12 or electrical 13 signals, these novel thermal sensors and associated methodologies have allowed in-plane 14,15 and out-of-plane 16,17 thermal conductivity measurements, of nanowires and thin films, with outstanding nanometre spatial resolution 18,19 . A remarkable contribution to the field was achieved by Völklein et al. in 1990 who developed a suspended membrane-based sensor using a long and thin Pt electrical transductor operated in DC to measure in-plane thermal conductivity of thin films 15 . More recently, Sikora et al. went a step further in improving this technology by combining the Völklein geometry with the AC 3 -method, reaching exceptional thermal conductance sensitivity, Δ ≅ 10 −320, 21 .
In parallel, ex-situ thermal probe studies performed on thin films 22,23 have shown that the thermal conductivity of a grown material is conditioned by the thermal conductance loss of the substrate induced both by interfacial scattering of phonons in the in-plane measurements 22 and by thermal boundary resistance in the out-of-plane measurements 23 .
Accordingly, the thermal conductivity of the thin layer cannot be simply calculated via the differential measurement of the thermal conductance of the whole sample (film + membrane/substrate) and a reference (only membrane/substrate), but must be calculated using a set of thermal conductance measurements performed at different film thicknesses.

Experimental Section Sensor Design and Simulation
The sensor developed here consists in a long and thin Pt line deposited on a suspended SiNx membrane and connected in a 4-wire configuration (Fig. 1a, In normal operation, the thermal conductance from the central Pt line to the substrate is calculated by using the 1D Fourier law and assuming that the external line is much more conductive than the SiNx beneath, which yields equation 1 where and are the thickness and the thermal conductivity of the silicon nitride respectively, is the length of the Pt strip between the voltage probes, = 4.5 μm is the width of the Pt strip and = 0.002m is the distance between the Pt strip and the substrate. From equation (2), the apparent thermal conductance can be calculated as 2 = 0 /∆ 2 , which resembles at low frequencies.
When a thin-film sample grows on the SiNx membrane, the parameters in equation (2) may vary as , and 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 Here, , and are the sample thermal conductivity, specific heat capacity and density. In the same way, the extrinsic values and will vary, as well as the thermal time constant , as: If the measuring frequency is low ( ≪ 3 8 2 ), then the measured 2 resembles and the derivative of equation (8) can be used to calculate the thermal conductivity of the sample film by measuring in real-time the thermal conductance during growth ( 2 ( )), as shown in equation (11).
However, if a higher current angular frequency is used, can be extracted by fitting the measured 2 with equation (12) using the thickness-dependent parameters (equations (7) -(10)): In Fig. 2a the calculated 2 is plotted for current frequencies of 0 Hz (DC), 1 Hz and 3 Hz (the parameters used are listed in the figure caption). If the conductance is monitored with a current at 1 Hz, the apparent thermal conductance 2 is very similar to throughout the deposition. However, at 3 Hz, there is an evident difference in the slope of the curves: Although the absolute value of the apparent thermal conductance only varies from 97% to 93% of ( Fig.2b), the slope of 2 is up to 40% higher than the one of ( Fig.2a). Generally, measuring with higher frequencies increases the dependence of

Experimental setup
The sensor is introduced in a high vacuum chamber equipped with an effusion cell that enables a good control of the evaporation rate. A previously calibrated quartz crystal microbalance is located nearby the sensor to monitor the layer growth rate with a precision of 0.01 Å/s. The temperature of the sample was controlled with a custom-made PID system that reads the temperature of a Pt100 and provides heat through a Kapton heater, yielding a temperature control with fluctuations smaller than 0.003K, from 77 K up to 400 K.
The experiment is performed by feeding two sensors (sample and reference) with a current wave of a given amplitude and frequency, generating a voltage drop in each sensor. The voltage signals from both sensors, as well as the differential voltage between From the measured voltage signals, the resistance and the temperature oscillations Δ 2 can be calculated as: where 1 and 3 are the 1 and 3 voltage components measured in the sample sensor, and is the slope of the sample resistance as a function of the temperature.

Sensor performance test
Initially, the self-heating of the Pt sensor is determined by measuring both the 3 voltage and the variation of the 1 voltage with = 2 / (Fig.3a). Since the frequency is very low, both signals yield identical self-heating, but as can be seen in Fig. 3a, the selfheating calculated with the 3 voltage (Δ 2 )is less noisy than the one calculated with the 1 voltage (Δ ). Also, the slope of log Δ 2 vs log 0 has a value very close to 2, demonstrating that the self-heating depends on the square of the current. The high coincidence between both datasets suggests that the behaviour of the sensor is purely driven by heat transport physics. This is an important difference from the device presented by Sikora et al. 20 , where the use of a NbN strip sensor allowed measurements at very low temperatures, but produced non-negligible electrical effects due to the high electrical impedance of that material. conductance, from 16.91 W/K to 16.85 W/K that may be justified by a small reduction of the sensor dR/dT due to the higher average heater temperature.
The thermal conductivity of the SiNx membrane was evaluated for temperatures between 80 K and 230 K, as shown in Fig. 4 (black squares). The results are very similar to the values found in the out-of-plane direction using the 3 method on a similar SiNx membrane (red circles in Fig. 4). The latter values were obtained through a differential measurement of two samples with thicknesses of 180 nm and 450 nm, granting that the thermal boundary resistances between the film and the substrate are cancelled. Thus, the similarity of both the in-plane and the out-of-plane values confirm that there are not substantial phonon size effects, or anisotropy, in our layers. In both cases, the variation of with temperature show also a similar tendency than data presented by Sikora et al 20,21 (continuous line in Figure 4). The discrepancy in the absolute values may account for density or stoichiometry variations related to the different growth film characteristics in each work. Huge differences in variation with temperature are observed when comparing our data with Sultan et al. 25 work (blue 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 measurement is the precise determination of SiNx membrane thickness, which was measured throughout the wafer with a contactless optical profilometer, yielding a standard deviation of 1% of the 180 nm averaged thickness. However, wet etchings at the final steps of microfabrication process could slightly reduce this thickness up to 10 nm, inevitably increasing the uncertainty up to 5% .

Temperature (K)
As indicates Fig. 5a, at the early stages of the deposition, i.e. very low thicknesses, we observe a decrease in the thermal conductance of around 1.2 % of its initial value, while afterwards 2 roughly increases linearly with thickness. In this particular measurement, film growth was stopped at 340 nm, yielding a constant value of the thermal conductance after this particular point.  Fig. 5b,c by dashed red lines, and as is clearly seen, vary from one sample to another, confirming the importance of deposition temperature as will be discussed later.
To understand and interpret the variation of 2 with thickness, we also performed exsitu analysis of the film morphology either by SEM or by AFM described in Fig. S4a of the SI. Complementary electrical characterizations were also performed, as shown in Fig.   5b inset, to corroborate the hypothesis described later on. Surface morphology evolution with thickness showed that TPD do not wet the SiNx membrane surface, as it grows in 3D islands in the early growth stages. For films deposited at 267K and according to the conductance evolution, island coalescence seems to happen at a nominal film thickness of 2.6 nm while complete surface coverage seems to take place at 14 nm. Ex-situ analysis of growth regimes is precluded by the evidence of dewetting of TPD at temperatures well below the glass transition temperature 26 . The fast film dynamics at temperatures below the glass transition temperature makes in-situ analysis an indispensable tool to gain a better understanding of film formation in molecular glasses. =267±2 K. Growth rate = 0.02 nm/s. c) = 304±2 K. Growth rate = 0.02 nm/s. In graphs b) and c) data is box averaged with 10 points/box. The main regions of film growth are separated by dashed red lines. Region I located between 0 nm and the first vertical line correspond to nucleation and isolated island formation; region II to island coalescence; region III to percolation across the layer and region IV to vertical growth of a continuous layer. The slight difference in the initial conductance between all the graphs is mainly due to the use of different sensors/membranes for the experiments. The black downward arrow marks the percolation threshold (separation between regions II and III). The inset of b) shows the abrupt variation of the electrical conductance at the percolation threshold (nominal thickness of 2.6 nm) of the TPD film. This value coincides with the minimum of the thermal conductance (black arrow) in graph b).
Before relating the large drop observed in region I with film microstructure, we performed few tests to rule out any potential experimental artefact that could have led to temperature variations of the sensor. As extra heat originated by condensation of molecules on the substrate is not modulated at angular frequency or any of its harmonics and therefore, attributed to a sensor temperature variation due to this phenomenon. Also, we ruled out any effect of the sample emissivity variations during TPD growth on the membrane, since a measurement at 81 K, where radiation effects should be substantially lower, showed a similar drop in thermal conductance (Fig. S5 in SI). The reduction of thermal conductance observed in the early stages of growth seems thus to be due to phonon-related phenomena, although covering the surface with TPD is not expected to affect the thermal conductance of the SiNx membrane since it is already a disordered structure with an average phonon mean free path of the order of the interatomic distance.
Nevertheless Our thermal conductance initial drop, although much higher than the uncertainty of the measurement, only amounts 1.2%, compared to 5-10% in Sultan's work. These authors estimated that 40%-50% of the total was due to long-wavelength with long mean free path phonons. The estimated average λ-value for these phonons was around 4.5 nm, much higher than thermal phonons at room-temperature that have λ~0.2nm. We thus believe that the main difference between both results arises from a different microstructure of the used SiNx in each case. The thermal conductivity value of our SiNx, slightly below Sultan et al. 22,25 values combined with the temperature dependence shown in Fig. 4, clearly indicates that our nitride is fully amorphous while the one used in Sultan et al work was probably nanocrystalline. Therefore, a lower drop of the thermal conductance in fully amorphous nitride membrane is consistent with a scenario where the contribution of longλ phonons is reduced with respect to previous nanocrystalline nitride membranes. Even though, the conductance drop due to enhanced surface scattering requires that phonons slightly larger than the average interatomic distance at room temperature have to be involved in heat transport along the nitride membrane. We can thus tentatively attribute the initial sharp reduction of the thermal conductance to the formation of TPD isolated clusters on top of the nitride membrane surface, modifying the interfacial phonon scattering and thus leading to a decrease of the thermal conductance.
Although we currently lack a complete understanding of the microscopic processes occurring at the interfaces, we believe that the growth of new material on top of the membrane changes the specularity of the surface, resulting on an effective increase in the phonon scattering rate. We foresee that the future use of crystalline membranes, such as single crystalline Si, will provide a convenient platform to investigate nucleation and island growth dynamics during the early stages of film growth with even higher conductance sensitivity.
In Region II the thermal conductance still decreases but with a lower slope. We believe that in this region, clusters enlarge and start to coalesce, providing additional paths for heat transfer which partially compensate the interface scattering until a minimum is reached at the end of the present region. As island coalescence continues, percolation builds up new channels across the layer structure (Region III), providing additional heat flow paths that start to exceed the contribution of the interface scattering. The coincidence of the minimum in thermal conductance with a percolation phenomenon threshold was demonstrated in a separate experiment where electrical conductance was measured as a function of thickness (inset in Fig. 5b), showing a sharp variation of the slope at 2.6 nm, due to electrical continuity through the TPD film.
As percolation persists, the thermal conductance increases reaching a linear regime that we identify with the formation of a continuous layer with complete coverage, marking the onset of Region IV. Thus, Region IV corresponds to the vertical growth of the continuous film. In this regime the increase in thermal conductance is linear and proportional to the thickness of the growing layer. Compared to the end of region III, there is a small reduction in the slope of the conductance vs thickness since the islands are no longer forming new conductive channels.
Differences in growth dynamics with the deposition temperature were also studied, as shown in Fig. 5c, where TPD film was deposited at 304K. Although the four regions appear in both cases, remarkable differences in region limits appears compared with sample deposited at 267 K (Fig. 5b). The TPD sample grown at =267 K shows values of the percolation threshold (black downward arrows) and film continuity at 2.5 nm and 14 nm, respectively. However, sample grown at 304 K showed higher percolation threshold, 6 nm (probably due to higher molecular mobility taking place at a higher deposition temperature), and the thickness value for film continuity is not clearly resolved from the data since the reduction in the slope after Region III is not observed. Recent work by Fakhraai and coworkers 26 in TPD films grown at 315K have shown that film continuity was reached for film thickness above 20 nm, which is consistent with our results.
Although similar behaviour of 2 was observed for both samples, final values of inplane conductivity determined form the slope in Regions IV of Fig. 5a Fig. S6 (SI). We thus believe that the variation in thermal properties has to be related to the diverse characteristics of vapourdeposited glasses, in particular density and molecular orientation, which strongly depend on the deposition temperature. It has already been demonstrated that vapour-deposited thin-film organic glasses grown at deposition temperatures slightly below their glass transition develop enhanced kinetic and thermodynamic stability with a maximum at in the vicinity of 0.85 27,28 . Glasses grown in these conditions are coined ultrastable glasses. The glass transition temperature of a conventional TPD glass (this is, a glass cooled from the liquid at 10 K/min) is 333 K. Glasses grown in the region 0.80-0.90 , which is the case for film deposited at 267 K, are stable glasses, as evidenced by the higher onset of their glass transition temperature upon heating (Fig. S6 in SI). However, films grown above 0.90 , which is the case for film grown at 304K, are less stable.
Stability can be directly translated to density, meaning that the sample grown at 267 K (0.80 ) has a slightly higher density that the one vapor-deposited at 304 K (0.91 ).
According to Dalal et al. 29 , the difference in density between the 2 samples should be around 0.3%. Besides, stable glasses embedded with higher density also exhibit higher values of the sound velocity up to 10% [30][31][32] , therefore it is reasonable to expect that more stable glasses will also exhibit an enhancement of the thermal conductivity.
In the same way, vapour-deposited stable glasses show anisotropic molecular packing with a molecular orientation that depends on the deposition temperature. TPD films grown at 0.80 have molecules partially aligned parallel to the substrate while those grown at 0.91 are mostly randomly oriented 29 . Molecular anisotropy can also play a role in heat transport since it could be slightly favoured in the direction of molecular alignment. More studies of the thermal conductivity variation as a function of deposition temperature are under way to disentangle the effects of density and molecular orientation.

Metallic thin-film layers
To complete the proof of concept of the sensor, we also analyse growth kinetics of a metallic indium layer. Fig.6 shows the real-time in-situ thermal conductance measurement during growth, also for two deposition temperatures, 315 K and 260 K. Conductance values (Fig. 6a,b)follow a similar pattern to the one observed in TPD films but with much larger thickness scales. The conductance regions can be identified and discussed, as in the TPD case, in view of microstructure evolution with thickness (see Fig. S4 for a complete set of microscopy images). As shown in the inset of Fig. 6a, the fast decrease of conductance at the very early stages of deposition is also present. In this thickness range (up to 0.65 nm), tiny isolated clusters are expected to develop on the surface of the SiNx membrane. The observed conductance drop of 1.5% is again an indication that phonons with mean-free-paths slightly larger than those typically accounted for in disordered solids are being scattered by the In/SiNx interface. Nevertheless, the minimum conductance found in this case cannot be correlated with a percolation threshold, as we considered in TPD, since individual In islands are much more conductive than the TPD ones and they can contribute significantly to the thermal conduction, even though they are still physically disconnected at this stage.
Interestingly, neither percolation threshold nor complete coverage of In grown on SiNx are reached for metallic layer as thick as 120 nm (nominal thickness), as clearly evidenced in the SEM images. As shown in Fig.6b, where growth characterization is performed up to 450 nm, percolation starts to play a significant role at thicknesses around 200 nm, where the conductance sharply increases due to continuous channels formation.
Subsequently, the thermal conductance increase slows down becoming linear with thickness. The corresponding fitting line (red line in Fig. 6b) Fig.6a and SI Fig.S4b), we approximate the coverage ratio and the mean island area, as specified in SI.
As indicated in Fig. 6a,b we can differentiate four growth regimes: I: nucleation and initial small island growth. II: growth of islands, divided in IIa (with small isolated circular islands) and IIb (with larger islands irregularly shaped forming a bimodal island size distribution). III: island percolation forming continuous channels and IV: vertical growth of a continuous film.
Since the conductance evolution is slightly different (region II is divided in two stages) than the one previously observed for TPD layers, we conduct finite element modelling using the structural information provided by the electron microscopy images. We use a simplified representation of our sample by building an array of 9x9 In square islands on a 180 nm thick SiNx film. Changing the nominal thickness of the layer implies modulating the size and separation of the islands to match the island size and coverage ratio observed by SEM (Table S2 in SI). The thermal conductance was monitored by imposing a heat flow and measuring the temperature difference arising on the simulated structure. The results of the simulation are shown in Fig.6c. The simulation closely predicts the increase of the slope of the curve 2 ( ) deposited at 315 K in a thickness range around 30-50 nm. In this thickness range and up to the percolation threshold above 200 nm In islands are still isolated from one another and the increased conductance is due to the formation of larger islands as In evaporation proceeds. At around 200 nm the sudden increase in the slope is related to island percolation (Region III starts). At the end of the percolation regime a continuous film forms and the conductance is heavily dominated by the In film (Region IV). Then, the conductance increases linearly with a slope given by the thermal conductivity of the film. =260 K. Thickness range is extended to attain complete percolation and total coverage. c) FEM simulation: normalized conductance vs. 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 on an array of 9x9 square In islands (grey) on a SiNx thin membrane(green).

Conclusions
We have developed a universal sensor with extreme accuracy and methodology able to perform real-time thermal conductance measurements during film growth. The technique is adapted for any kind of material and thickness. Large sensitivity allows disentangling the evolution of film microstructure with thicknesses. By analysing changes in the apparent thermal conductance versus thickness, differentiated growth stages could be identified giving rise to a complete comprehension of the growth process for several materials. At early stages, the fast drop of the thermal conductance was related to nucleation and isolated clusters formation. This step is followed by a regime where clusters grow to form islands through coalescence and absorption of atoms/molecules In an intermediated stage the percolation threshold was revealed by a conductance rise while final mode, where the thermal conductance changes linearly with thickness, corresponded to the formation and growth of a continuous film. In this regime, the thermal conductivity of the film can be directly derived from the slope of the conductance versus thickness plot.
The methodology ad-hoc, presented here, is easily extensible to devices with other substrate materials compatibles with epitaxial growth. Using single crystalline membranes, the conductance reduction within the first stages of growth will be enhanced increasing the sensitivity. The extreme sensitivity will pave the way to apply the technique to interesting phenomena such as phase changes during growth, size effects or molecular orientation and density in organic glasses films, among others. .