Growth Monitoring With Submonolayer Sensitivity Via Real-Time Thermal-Conductance Measurements

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 $3\omega$-Völklein method at low frequencies, the sensor shows an exceptional resolution down to $\mathrm{\Delta }(\kappa \cdot t)=0.065\mathrm{W/m}\mathrm{K}\mathrm{nm}$, 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.

Figure 1

(a) Optical micrograph of the sensor consisting on a suspended rectangular membrane (with a total width of $2\lambda$) a longitudinal strip $\mathrm{Pt}$ heater placed on the center with a distance L between the four wire electrical probes. Red arrows indicated the ideal heat flow directions. (b) Surface temperature distribution of the sensor (brighter is hotter) in a FEM dc study. (c) Longitudinal and transversal temperature distributions of the sensor in a FEM dc study.

Figure 2

(a) Calculated real thermal conductance (black) and apparent thermal conductance modeled at 1 Hz (red) and 3 Hz (blue) during the deposition of a layer. (b) Calculated frequency dependence of the temperature oscillations in the sensor before and after depositing a 250-nm film (the inset is a zoom out).The material properties used in both plots are the following: $k_{\mathrm{Si}{\mathrm{N}}_x}=2.65\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$,$c_{\mathrm{Si}{\mathrm{N}}_x}=0.7\mathrm{J}{\mathrm{K}}^{-1}\mathrm{k}{\mathrm{g}}^{-1}$, ${\rho }_{\mathrm{Si}{\mathrm{N}}_x}=3.18\mathrm{g/c}{\mathrm{m}}^3$, $k_{\mathrm{Pt}}=33\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, $c_{\mathrm{Pt}}=0.133\mathrm{J}{\mathrm{K}}^{-1}\mathrm{k}{\mathrm{g}}^{-1}$, ${\rho }_{\mathrm{Pt}}=21.45\mathrm{g/c}{\mathrm{m}}^3$, $k_{\mathrm{smp}}=0.21\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, $c_{\mathrm{smp}}=1.05\mathrm{J}{\mathrm{K}}^{-1}\mathrm{k}{\mathrm{g}}^{-1}$, and ${\rho }_{\mathrm{smp}}=1.08\mathrm{g/c}{\mathrm{m}}^3$. Structural parameters are $t_{\mathrm{Si}{\mathrm{N}}_x}=180\mathrm{nm}$, $t_{\mathrm{Pt}}=110\mathrm{nm}$, $\lambda =123\mu \mathrm{m}$, $b=5\mu \mathrm{m}$, and $L=2000\mu \mathrm{m}$.

Figure 3

(a) Self-heating of the sensor measured with the $3\omega$ and $1\omega$ voltages $(\omega =1\mathrm{Hz)}$. (b) Temperature oscillations as a function 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. $\mathrm{\Delta }K$ refers to the standard deviation of the data. Red circles and black squares correspond to data obtained with input currents of 500 and 300 µA, respectively, with $\omega =1\mathrm{Hz}$.

Figure 4

Thermal conductivity values measured at different temperatures with the $3\omega$-Völklein method (in-plane direction) and the $3\omega$ method (out-of-plane direction). Data from Sultan et al. [28] and Sikora et al. [23] are also included for comparison.

Figure 5

Thermal conductance versus thickness during TPD growth: (a) $T_{\mathrm{dep}}=267\pm 2\mathrm{K}$. Growth rate = 0.29 nm/s. (b) $T_{\mathrm{dep}}=267\pm 2\mathrm{K}$. Growth rate = 0.02 nm/s. (c) $T_{\mathrm{dep}}=304\pm 2\mathrm{K}$. Growth rate = 0.02 nm/s. In graphs (b) and (c), data are 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 corresponds 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 and/or 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). The uncertainty of the thermal conductance measurement in this measurements is below 0.1%.

Figure 6

(a) Thermal conductance versus thickness during deposition of In films: (a) $T_{\mathrm{dep}}=315\mathrm{K}$. The electron microscopy images of films of varying nominal thickness show the microstructural evolution of the $\mathrm{In}$ 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) $T_{\mathrm{dep}}=250\mathrm{K}$. 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 $\mathrm{In}$ islands (gray) on a ${\mathrm{Si}\mathrm{N}}_x$ thin membrane (green).