The use of thin films for developing new crystalline materials is an attractive approach because the crystal growth process is fast, the volume of required material is small, and a relatively large number of samples with varying composition or structure can be rapidly synthesized. However, the physical properties of thin films are very sensitive to small changes in the various process parameters that control the film growth. Besides the usual thermodynamic parameters, such as pressures or temperatures, thin film growth is also affected by kinetic effects, such the growth rate. For this reason, the process space, in addition to the composition space, can be very multi-dimensional. Exhaustive mapping of materials properties over the whole available temperature, pressure, growth rate, etc. ranges is therefore very time consuming and in practice, a human operator would struggle in determining the optimum combination of parameter combinations to test to complete a materials exploration or optimization task with the smallest number of experiments. In this regard, help may be available from the various machine learning methods that have been developed in recent years. In particular, the dimensionality problem of the process parameter space can be handled by Bayesian optimization, as illustrated in Fig. 1.

The thin film synthesis system illustrated in Fig. 1 was recently developed by Dr. Ohkubo at NIMS [1]. Nitride thin films are grown by metal-organic molecular beam epitaxy (MO-MBE) from an organic precursor in the presence of activated nitrogen plasma. In this work, the growth of TiN was attempted as a demonstration of the MO-MBE process using tetrakis(dimethylamido)titanium (TDMAT) as a Ti source. The TiN films were characterized by x-ray diffraction (XRD) and transport analysis. In particular, the superconducting transition temperature of TiN was used as a more sensitive measure of the crystalline quality of the films than is possible by XRD analysis. A small set of initial samples was synthesized by manually selecting the primary process parameters: the film growth temperature, the TDMAT source foreline pressure, the nitrogen flow rate, and the excitation power of the nitrogen plasma source. These four parameters effectively determine the growth mode (temperature), rate (TDMAT flow rate), and the nitrogen activity.

Fig. 1. Closed-loop optimization of epitaxial thin film growth conditions using a Bayesian approach. Nitride thin films were grown by metal-organic molecular beam epitaxy (b) and characterized by x-ray diffraction (c). The film peak intensity was used as the feedback for the Bayesian optimizer (a).

After the initial set of samples were synthesized and characterized by XRD, further combinations of the four main parameters were selected by a Bayesian optimization process using the normalized TiN peak intensity in the XRD pattern as the objective function. The growth temperature range was limited to 550 to 900 °C, the TDMAT pressure was between 0.5 and 10.5 Torr, the N₂ flow rate was limited to 0.5 to 5 sccm, and the plasma source power limits were 270 to 500 W, forming a search grid of 7 × 100 × 45 × 23 points. After every film growth experiment, the XRD pattern was analyzed and a new process point was determined by the Bayesian process. The cycle was repeated for 20 times. No further improvement of the XRD peak intensity was obtained after 10 cycles.

The low-temperature superconducting transition temperature measurements were done at ISSP. The gradual improvement of the critical temperature in the Bayesian optimization process is shown in Fig. 2. It can be seen that the maximum Tc of 5.2 K was obtained on the tenth cycle, after which no further increase was obtained.

Fig. 2. Gradual improvement of the superconducting transition temperature of TiN thin films as a function of the synthesis-characterization-selection cycle index. No further improvement was obtained after just 10 synthesis experiments.

This experiment was the first demonstration of closed-loop thin film synthesis controlled by a machine learning algorithm for reducing the number of film growth experiments required to reach the optimal physical properties. In this work, XRD was used as the source of the feedback signal for the Bayesian process. This means that the cycle time (Fig. 1) was limited by the diffraction analysis, not by synthesis. In addition to the XRD and transport data, in situ electron diffraction data was also collected. In the future, it may be possible to greatly increase the rate of materials development by using real-time in situ characterization tools for providing the feedback signal for a Bayesian process optimizer.

References

• [1] I. Ohkubo, Z. Hou, J. N. Lee, T. Aizawa, M. Lippmaa, T. Chikyow, K. Tsuda, and T. Mori, Mater. Today Phys. 16, 100296 (2021).

Authors

• I. Ohkubo^a, Z. Hou^a, J. N. Lee, T. Aizawa^a, M. Lippmaa, T. Chikyow^a, K. Tsuda^a, and T. Mori^a
• ^aNIMS