Sb2Te3 and Its Superlattices: Optimization by Statistical Design - ACS

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SbTe and its superlattices: optimisation by statistical design Jitendra K. Behera, Xilin Zhou, Alok Ranjan, and Robert E. Simpson ACS Appl. Mater. Interfaces, Just Accepted Manuscript • Publication Date (Web): 13 Apr 2018 Downloaded from http://pubs.acs.org on April 13, 2018

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ACS Applied Materials & Interfaces

Sb2Te3 and its superlattices: optimisation by statistical design Jitendra K. Behera,∗,† Xilin Zhou,† Alok Ranjan,‡ and Robert E. Simpson∗,† †ACTA Lab, Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore ‡Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore E-mail: jitendra [email protected]; robert [email protected]

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Abstract

The objective of this work is to demonstrate the usefulness of fractional factorial design for optimising the crystal quality of chalcogenide van der Waals (vdW) crystals. We statistically analyse the growth parameters of highly c-axis oriented Sb2 Te3 crystals and Sb2 Te3 -GeTe phase change vdW heterostructure superlattices. The statistical significance of the growth parameters of temperature, pressure, power, buffer materials, and buffer layer thickness was found by fractional factorial design and response surface analysis. Temperature, pressure, power, and their second order interactions are the major factors that significantly influence the quality of the crystals. Additionally, using tungsten rather than molybdenum as a buffer layer, significantly enhances the crystal quality. Fractional factorial design minimises the number of experiments that are necessary to find the optimal growth conditions, resulting an order of magnitude improvement in the crystal quality. We highlight that statistical design of experiment methods, which is more commonly used in product design, should be considered more broadly by those designing and optimising materials. 2


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Keywords phase change material, superlattice, van der Waals epitaxy, design of experiments, crystal texture, fractional factorial design, Box-Behnken design

INTRODUCTION Chalcogenide Phase change materials (PCMs) have been studied extensively for the optical and electrical memory storage applications due to their excellent switching ability. 1–5 PCMs switch repeatedly and reversibly between the amorphous and crystalline states when a heat pulse is applied. The two different structural phases have significant contrast in their physical properties such as optical reflectivity and electrical conductivity. 6 These differences in physical properties combined with the nanosecond/picosecond time scale switching repeatability, 7 make PCMs suitable for non-volatile data storage, optical modulators, photonic switches, and neuromorphic-computing. 8–16 Two-dimensional vdW bonded layered chalcogenides materials, such as Sb2 Te3 , Bi2 Se3 , and Bi2 Te3 , are topological insulators and have recently gained attention for their applications in photonics, plasmonics, and electronic memory devices. 17,18 The growth processes of these two-dimensional layered materials impacts their structural and electrical properties, consequently effecting the performance of the devices. In particular, by growing Sb2 Te3 GeTe vdW superlattice structures reduces both switching time and switching energy of a memory device compared to the alloys by confining atomic diffusion to the interfaces. 19 These superlattice structures are composed of ultra thin chalcogenide crystal layers of GeTe and Sb2 Te3 . The Sb2 Te3 quintuple layers are arranged in a two-dimensional hexagonal lattice structure, whilst the GeTe crystal layer is in a rhombohedral structure. The hexagonal Sb2 Te3 unit cell consists of three quintuple layers each with the atomic layers sequence Te-Sb-Te-Sb-Te-. The quintuple layers are linked with weakly bonded vdW forces, whilst within the quintuple layers the atoms are covalently bonded. Preparing the alternating lay3



ered structure of GeTe and Sb2 Te3 , a biaxially strain the GeTe layers due to the in-plane lattice mismatch. The interfaces are switched between order and disorder to modulate the materials properties. 20 We recently showed that the activation energy for the first Ge atom to switch into the vdW interface defines an energy threshold for an avalanche switching effect. 21 This threshold depends on the stress in the GeTe layer. 22 Consequently, the Sb2 Te3 -GeTe interface substantially impacts the performance of switching devices. Therefore, growing high quality single crystals or highly oriented superlattice structures is expected to enhance the overall performance of these superlattices. Many of the exciting properties of chalcogenides such as thermoelectric, interfacial phase change memory, topological insulator require highly oriented crystalline thin films. 23 These material properties have nonlinear dependence on their composition and crystal structure, which are largely influenced by the growth process. 24,25 Sputtering, chemical vapour deposition, molecular beam epitaxy (MBE), co-evaporations, atomic layer deposition, and pulse laser deposition (PLD) have all been used to prepare chaclogenide films. 26–31 The growth procedure involves a large number of deposition parameters which significantly alter the materials properties. Therefore, growing single crystals or highly oriented films is challenging. Often trial and error methods were used to optimise two-dimensional chalcogenides. 32,33 Hence, the optimisation process is time consuming and labour intensive. Therefore, a more efficient optimisation approach is needed. Design of experiment (DoE) is a systematic and statistical optimisation approach that is more typically used in product design. 34 The DoE experiments and analysis allows one to infer the most important information by performing a minimum number of measurements. 35,36 Although DoE has been used to optimise the growth of carbon nanotubes, graphene, aerogel materials, microstructures, and in biological science, 37–44 it has not been used to optimise the growth of chalcogenide superlattices. In traditional growth design methods, the effect of one experimental variable is appraised by changing its value and keeping the other experimental variable values constant, hence known as one-factor-at-a-time (OFAT) optimisation method.

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This method is unsuitable when there is a large number of experimental variables. For example, if we have “k” variables and each variable has “n” levels, then nk experiments are required to measure the effect of all the variables. The total number of experiments increases substantially with the number of experimental variables, which is a problem for the more common, Edison-like traditional optimisation methods. In contrast, DoE can minimise the number of measurements by half, quarter, and one eighth by exploiting fractional factorial design (FFD) and Box-Behnken design (BBD) methods. Both FFD and BBD methods are the subset of the DoE, where FFD is used to screen statistically significant variables and BBD is used to find the optimum condition. 45 DoE also measures the effect of interactions between the variables and provides the second order and higher order nonlinear dependence of the variables on the effect. This procedure used to optimise vdW epitaxy grown layered chalcogenides has not previously been discussed. We suspect most research groups use an inefficient OFAT optimisation method. Statistical design methods significantly accelerate materials design by substantially reducing redundant information during optimisation. This makes material optimisation less expensive, less labour intensive, and generally more efficient than traditional OFAT methods. We believe, therefore, that the substantial resources can be saved by adopting the FFD method, which was used herein. It would also be very interesting to compare the significance of growth factors for sputtering with MBE and PLD techniques. This paper demonstrates that DoE is an efficient method to grow highly (0 0 l ) textured vdW heterostructure superlattices. In particular, FFD extracts the key deposition variables and the BBD finds the optimum growth conditions. Herein, we employ these two methods to optimise the growth conditions of Sb2 Te3 film and grow highly (0 0 l ) oriented superlattices. This work establishes systematic methodology to grow highly textured superlattice of two-dimensional chalcogenides over a large scale by sputtering, which is necessary for mass production.

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EXPERIMENTAL DETAILS (0 0 l ) Texture Crystal Films Growth and Characterisation Highly (0 0 l ) oriented Sb2 Te3 thin films were grown on Si (1 0 0) substrates by RF sputtering under different temperatures. The vacuum chamber base pressure was better than 2.5 × 10−5 Pa. The silicon native oxide was removed by argon plasma etching for an hour at the deposition temperature. Others have shown that a tungsten buffer layered helps to seed strong (0 0 l ) textured Sb2 Te3 films. 46 We hypothesised that others metals that bond with tellurium (Te) to produce three atomic layers two-dimensional crystals could also be used to seed layered growth of Sb2 Te3 . For this reason we compare tungsten (W) and molybdenum (Mo). According to the classical theory of crystallisation, the temperature, pressure, deposition rate, and substrate surface condition alters the entropy, enthalpy during the crystal growth process, which in turn influences the crystal quality. 47,48 Therefore, we chose to investigate whether temperature, pressure, RF power, buffer layer thickness, and the buffer material significantly influence the (0 0 l ) growth. After growth, the films were naturally cooled to room temperature in the vacuum chamber to prevent oxidation. These optimised W buffered Sb2 Te3 structures were then used to grow Sb2 Te3 -GeTe vdW superlattices. The superlattice structures were prepared by alternately depositing thin layers of Sb2 Te3 and GeTe. The thickness of Sb2 Te3 layer was varied (1 nm, 4 nm) and the thickness of GeTe layer was fixed at 1 nm. The total thickness of the superlattice films were 100 nm and the thicknesses were calibrated by x-ray reflectivity. It is important to note that the condition of the sputter chamber plays an important role to grow (0 0 l ) texture films. A sacrificial deposition of Sb2 Te3 is needed to coat the inside chamber during the first deposition of new sample in order to prevent contamination and to get repeatable Sb2 Te3 quality crystals films. X-ray diffraction (XRD) patterns of the Sb2 Te3 crystals and the superlattice structures ˚ radiawere measured using a Bruker D8 Discover diffractometer with Cu K-α (λ = 1.54 A)

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tion in a symmetric Bragg-Brentano geometry. XRD data were collected at room temperature in the 2θ range of 7◦ to 60◦ at a step of 0.02◦ . The full width half maximum (FWHM) and the relative peak intensity of all the diffraction peaks were analysed by Gaussian fitting. The resulted FWHM and the relative intensity values were further used to evaluate the degree of orientation of the textured films. The morphology and structure of the c-axis oriented films were investigated using scanning electron microscopy (SEM, JOEL-7600F), operated at 15 kV. The crystal orientation of the textured films were analysed using electron backscatter diffraction (EBSD). The EBSD data is represented by the pole figures. Additionally, the surface morphology and roughness of the films were measured by atomic force microscopy (AFM, Asylum Research-MFP-3D) in tapping mode under ambient conditions. Three-dimensional AFM images of the crystals were used to visualise the columnar hexagonal shape crystals growing along the c-axis.

Statistical Analysis Using DoE DoE was used to statistically analyse the effect of the deposition parameters and their interactions on the crystallographic texture of the film. The degree of c-axis orientation, quality of the film was calculated from the measured XRD patterns by equation 1: 49

Qn(00l)

N I00l 1 X = N FWHM00l

(1)

i=1

Where, I00l is the intensity of the (0 0 l ) peak, FWHM00l is the full width half maximum of the corresponding peak, and N is the total number of (0 0 l ) oriented peaks observed in the XRD pattern. In order to get highly (0 0 l ) textured films, equation 1 needs to be maximised, i.e., large Qn values indicated strong (0 0 l ) texture. For the five sputter deposition variables considered for the DoE, see Table 1, each variable has two different levels, where the highest level is coded as +1 and the lowest level coded is -1. The central point between these two levels was calculated by taking the mean and coded

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Table 1: Independent deposition variables and the corresponding levels. Factors

Symbols

Temperature (◦ C) Power (W) Pressure (mTorr) Buffer layer thickness (nm) Buffer type

X1 X2 X3 X4 X5

Level -1 0 150 200 6 13 2.7 3.7 5 12.5 Mo

+1 250 20 4.7 20 W

as 0. The DoE optimisation was conducted by first screening using a FFD method to find the most significant deposition variable. A deposition variable is significant if a small change in the deposition parameter significantly changes Qn . With five deposition variables and two levels of each variable, there are 25−1 =16 experiments with deposition conditions for which the significant factors need to be identified. These 16 experiments produce different crystal qualities and are assigned names from F-1 to F-16 as listed in Table 2. The second stage of DoE was the optimisation process, in which the BBD method was used to examine the non-linear correlation between the deposition parameters. Three variables, each at three levels, coded as -1, 0, and +1, with an additional 15 experiments to FFD were tested. Samples were prepared with different experimental settings and were named as R-1 to R-15. To test the experimental reproducibility, three experiments were performed at the central point. The Qn values are calculated from the XRD patterns by measuring the peak intensity and FWHM values. A matrix of different experimental settings and the resultant normalised Qn values for these 15 measurements are listed in Table 3. A response surface analysis (RSA) model was used to evaluate the coefficient of the significant factors and their corresponding interactions. The experimental data were fitted with a second order polynomial using nonlinear regression methods, which is defined by equation 2: 50

Y = K0 +

n X i=1

K i Xi +

n X

Kij Xij +

i,j=1 i6=j

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n X i=1

Kii Xii2

(2)

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Table 2: Experimental matrix for deposition variables for FFD methods. Experiment Temperature Power Pressure name (◦ C) (W) (mTorr) X1 X2 X3 F-1 150 (-1) 6 (-1) 2.7 (-1) F-2 250 (+1) 6 (-1) 2.7 (-1) F-3 150 (-1) 20 (+1) 2.7 (-1) F-4 250 (+1) 20 (+1) 2.7 (-1) F-5 150 (-1) 6 (-1) 4.7 (+1) F-6 250 (+1) 6 (-1) 4.7 (+1) F-7 150 (-1) 20 (+1) 4.7 (+1) F-8 250 (+1) 20 (+1) 4.7 (+1) F-9 150 (-1) 6 (-1) 2.7 (-1) F-10 250 (+1) 6 (-1) 2.7 (-1) F-11 150 (-1) 20 (+1) 2.7 (-1) F-12 250 (+1) 20 (+1) 2.7 (-1) F-13 150 (-1) 6 (-1) 4.7 (+1) F-14 250 (+1) 6 (-1) 4.7 (+1) F-15 150 (-1) 20 (+1) 4.7 (+1) F-16 250 (+1) 20 (+1) 4.7 (+1)

Buffer layer thickness (nm) X4 5 (-1) 5 (-1) 5 (-1) 5(-1) 5 (-1) 5 (-1) 5 (-1) 5 (-1) 20 (+1) 20 (+1) 20 (+1) 20 (+1) 20 (+1) 20 (+1) 20 (+1) 20 (+1)

Buffer type X5 W (+1) Mo (-1) Mo (-1) W (+1) Mo (-1) W (+1) W (+1) Mo (-1) Mo (-1) W (+1) W (+1) Mo (-1) W (+1) Mo (-1) W (+1) Mo (-1)

Results Qn(hkl) 1021.87 390.513 10.9391 168.236 285.14 2066.29 150.458 156.91 36.2637 1473.33 26.6066 38.9689 925.927 681.213 5.08018 2298.29

Table 3: Experimental matrix for deposition variables for BBD methods. Experiment Temperature name (◦ C) X1 R-1 200 (0) R-2 200 (0) R-3 200 (0) R-4 200 (0) R-5 200 (0) R-6 200 (0) R-7 200 (0) R-8 200 (0) R-9 200 (0) R-10 200 (0) R-11 200 (0) R-12 200 (0) R-13 200 (0) R-14 200 (0) R-15 200 (0)

Power Pressure (W) (mTorr) X2 X3 13 (0) 3.7 (0) 6 (-1) 3.7 (0) 20 (+1) 2.7 (-1) 13 (0) 4.7 (+1) 13 (0) 4.7 (+1) 13 (0) 3.7 (0) 6 (-1) 2.7 (-1) 6 (-1) 3.7 (0) 13 (0) 3.7 (0) 20 (+1) 3.7 (0) 6 (-1) 4.7 (+1) 20 (+1) 4.7 (+1) 13 (0) 2.7 (-1) 20 (+1) 3.7(0) 13 (0) 2.7 (-1)

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Buffer layer thickness (nm) X4 12.5 (0) 20 (+1) 12.5 (0) 20 (+1) 5 (-1) 12.5 (0) 12.5 (0) 5 (-1) 12.5 (0) 20 (+1) 12.5 (0) 12.5 (0) 5 (-1) 5 (-1) 20 (+1)


Buffer type X5 W (+1) W (+1) W (+1) W (+1) W (+1) W (+1) W (+1) W(+1) W (+1) W (+1) W (+1) W (+1) W (+1) W(+1) W (+1)

Results Norm. Qn(hkl) 0.264062 0.568001 0.0263102 0.39927 0.23494 0.199582 0.323184 0.24461 0.246771 0.0686239 1.00 0.221048 0.0263788 0.0496524 0.0324446


Where, Y is the predicted response (Qn ), K0 is the model constant, and Xi is the deposition variable. The corresponding coefficient for the main deposition variables, Ki , and the coefficient for their interaction, Ki Kj , were obtained from the RSA model fitting. The third or higher order interactions are insignificant, therefore not considered in the model fitting. The value of “n” is equal to the number of independent variables considered for the optimisation. The optimum growth conditions were estimated from the RSA model by maximising the predicted response values and the model was validated using the MINITAB. 51 The FFD method gives a linear dependence on the factors, whilst the RSA method provides linear, quadratic and cubic interaction terms, which are useful for fine optimisation of the growth parameters. Therefore, we used the FFD method to identify the most significant factors, and then used a response surface model for the optimisation.

RESULTS AND DISCUSSION Fractional Factorial Design: Structural Characterisation The Sb2 Te3 films were prepared with the experimental settings, which were calculated using the Yates algorithm. 52 The actual combinations of growth parameters for temperature, pressure, power, buffer layer thickness, and buffer type are given in Table 2. The corresponding Qn values were calculated from the resultant XRD patterns. The diffraction patterns are arranged by the increasing order of the Qn in Fig. 1. The peak intensity varies and FWHM is highly sensitive to the growth conditions, which implies that the degree of c-axis orientation is influenced by the deposition parameters and can be significantly improved by optimising the growth conditions. Only the (0 0 l ) peaks are observed, suggesting a c-axis oriented growth of the Sb2 Te3 crystal. Under the growth conditions of F-16 and F-6, the Sb2 Te3 films have higher Qn and therefore a higher degree of (0 0 l ) texture, whilst conditions F-3 and F-15 result in a lower (0 0 l ) crystal quality. A randomly oriented powder diffraction peak (1 0 10) of Sb2 Te3 is only observed for the F-3 experimental condition. The main reason for 10


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Figure 1: XRD patterns of highly (0 0 l ) textured Sb2 Te3 films deposited at different growth conditions using FFD method. The films were prepared by varying the deposition temperature, pressure, RF power, and buffer layer thickness. W or Mo was used as the buffer layer. The colour code represents the degree of c-axis orientation, which is quantitatively characterised by Qn . The XRD patterns are arranged in the increasing order.

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most samples showing (0 0 l ) orientation is the relatively local region of the design parameter space studied.

Figure 2: SEM images of the Sb2 Te3 films deposited at different growth condition using FFD methods. (a-p) For samples F-1 to F-16, listed in Table 2.

Figure 2 shows the SEM images of the Sb2 Te3 film structure grown with the conditions F-1 to F-16, which we listed in Table 2. Different crystal shapes and sizes of Sb2 Te3 crystals were observed, when samples were grown with different growth conditions. All samples exhibited facets associate with hexagonal Sb2 Te3 crystallites of sub-µm length scale and with edge lengths of 50-300 nm. The F-6 sample shows complete hexagonal Sb2 Te3 crystallites, whereas the samples prepared with other growth conditions tend to exhibit fragmented hexagonal crystallites. The hexagonal Sb2 Te3 crystals grow out of the substrate plane with (0 0 l ) facets parallel to the substrate. In contrast, the incomplete hexagonal crystals exhibit the (0 0 l ) facets that tend to be tilted with a small inclination with respect to the substrate plane. It is evident that the deposition parameters effect the growth process and consequently change

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the quality of the Sb2 Te3 crystal. We now assess the growth parameters that have the most significant influence on the Sb2 Te3 crystal quality. The effect of the deposition parameters and their interactions were measured using analysis of variance (ANOVA) and the results are given in Fig. 3. Figure 3a is a Pareto chart that shows the standardised effect of individual growth parameters and their second order interaction based on the Student t-values. The length of each bar in the Pareto chart represents the absolute value of the standardised effect of the deposition parameter on the Qn values. The standardised effect values were calculated using the Student t-statistic. Growth parameters with standardised t-values larger than standardised threshold, 13.33, were considered statistically significant. The standardised threshold is shown as a pink dashed line in Fig. 3a. We found that temperature, power, pressure, buffer type, and their corresponding second order interactions are statistically significant, whereas the buffer thickness and the third order interactions have a smaller effect on the degree of orientation of the Sb2 Te3 crystal. The significant parameters are shown by the blue colour bar whilst the insignificant parameters are shown by green colour bars, see Fig. 3a. Figure 3b shows the main effect for all five independent deposition variables. The main effect of a deposition variable represents the difference of average Qn values between factors grown at two levels, high (+1) and low (-1). We observed that when the temperature and pressure were increased from a low level (-1) to a high level (+1), the output response Qn increases, indicating a positive impact on the texture of the crystal. In contrast, the RF power has a negative impact and significantly decrease the Qn , when increased from 6 W to 20 W. Additionally, we found that the buffer thickness has a less positive impact, and growing Sb2 Te3 films on W buffer layer rather than Mo, increases Qn by a factor of five. The statistical significance effects of interaction between any two deposition parameters were statistically calculated using the FFD method. The effect of interaction is shown in Fig. 3c. Each block shown in Fig. 3c shows how two individual factors combine to affect the crystal quality, Qn . The first box from the lefthand side of Fig. 3c shows the interaction

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Figure 3: Fractional factorial design analysis of highly (0 0 l ) textured Sb2 Te3 films. (a) Pareto chart shows the significant deposition parameters. Parameters in green are insignificant whilst the blue are significant, (b) main effect plots, and (c) interaction plots, nonparallel lines are indicative of an interaction. The red and black lines in the interaction plot correspond to the maximum (+) and minimum (-) levels of the vertical parameters defined in Table 1 respectively. Temperature, pressure, RF power, buffer layer thickness, and buffer type were the deposition parameters under investigation.

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between the buffer thickness and buffer type. The red curve shows the how Qn changes with thick (+1) and thin (-1) buffer layers, whilst the buffer type was set to W (+1). Similarly, the black curve represents shows how Qn changes for thick (+1) and thin (-1) buffer layers whilst the buffer type was set to Mo (-1). The two lines in each cell show the variation of the Qn at its high (+1) and low (-1) level. Parallel lines indicate no interaction between two deposition parameters, whilst the non-parallel lines indicate an interaction. The angle between the non parallel lines measures the degree of interaction, i.e., larger the angle will have a stronger interaction between the two deposition parameters. Here we see that temperature in combination with the pressure and buffer thickness has a strong interaction and significantly alters the Qn value. Similarly the RF power and deposition pressure in combination with buffer thickness affects the orientation of the Sb2 Te3 crystal. In contrast, temperature does not interact with RF power and buffer type as the lines are parallel and do not cross. Hence, these deposition parameters have no mutual effect on the Sb2 Te3 crystal texture.

Optimisation by Response Surface Analysis We conducted a response surface analysis (RSA) model to optimise the growth of highly c-axis oriented Sb2 Te3 films. In order to minimise the number of deposition variables in the optimisation process, we prepared all the samples at the middle point level (0), at a fixed temperature of 200 ◦ C. The FFD main effect result shows that W enhances the crystal quality therefore used as a buffer type for all the sample. The buffer type levels are discrete into two values W and Mo, therefore not considered for the RSA optimisation. The remaining deposition variable, power, pressure, and buffer thickness were considered for optimisation and a second order correlation between response and the variables are obtained by performing an additional 15 experiments using the BBD method. Samples were prepared using the experimental settings listed in Table 3 and the resultant normalised Qn values were calculated from the XRD patterns. The normalised Qn were fitted with the response surface 15



Figure 4: Response surface plots of the degree of orientation, crystal quality Qn , as a function of two independent deposition variables, while keeping the remaining variables fixed. (a) Pressure and buffer layer thickness, at RF power = 13 W, (b) power and buffer layer thickness, at pressure = 3.7 mTorr, and (c) pressure and power, at buffer layer thickness = 12.5 nm.

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model using equation (2). An empirical relationship between the deposition variables and the optimised response, Qn was found in the form of second order polynomial that is given by: Qn = − 0.23 − 0.007(RF Power) − 0.02(Pressure) + 0.06(Buffer layer thickness) − 0.02(RF Power) (Pressure) + 0.006(RF Power)(Buffer layer thickness) − 0.002(Pressure)(Buffer layer thickness) + 0.002(RF Power)2 + 0.05(Pressure)2 − 0.002(Buffer layer thickness)2 (3) The goodness of fit of the regression model was found with a coefficient of R2 value of 0.98. The fitted response surface plots of these 15 experiments using the BBD method are shown in Fig. 4. The correlation between two independent factors is examined by calculating Qn , while keeping the other factors fixed at its mean value. We observed that Qn increased by increasing both the buffer layer thickness and pressure, as shown in Fig. 4a. At low deposition pressure, Qn increases as the buffer layer thickness is increased to 13 nm and then gradually decreases. For a thicker buffer layer Qn significantly increases with increasing deposition pressure. Increasing the W buffer layer thickness decreases the stress on the surface by minimising lattice mismatch, and the concomitant interfacial surface energy. 53–55 The surface stress of the buffer layer changes the chemical reactivity of the W and promotes the self organised vdW epitaxial layer growth of Sb2 Te3 . 46 Figures 4b show that the Sb2 Te3 texture quality increases by increasing the buffer layer thickness and lowering the power at a constant deposition pressure. Increasing the pressure and decreasing the RF power would decrease the overall deposition rate. Therefore, giving the sputtered atoms ample time to rearrange on the surface to form a hexagonal crystal by minimising the total Gibbs free energy. 54 Moreover, the RSA results show that for a fixed buffer layer thickness the texture quality of the Sb2 Te3 films increases by decreasing the RF power and increasing the deposition pressure, see Fig. 4c. The covalent bonds within the quintuple layers of Sb2 Te3 crystals are significantly stronger than the vdW force between 17



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adjacent quintuple layers. This limits the degree of freedom for the crystal to grow in any random direction, thereby promoting the growth along out-of-plane (0 0 l ) direction. 55 We found that depositing films at a low deposition rate, high deposition pressure with a thicker buffer layer, increases the Qn values, consequently improving the c-axis degree of orientation along the (0 0 l ) Sb2 Te3 . The optimum growth condition was calculated from the maximum point of the surface plots and occurs when the deposition rate is slow, X2 = 6 W, the deposition pressure is high, X3 = 4.7 mTorr, and the buffer layer thickness is, X4 = 18 nm. To analyse the robustness of the optimised RSA model, (0 0 l ) textured Sb2 Te3 crystal films were grown with four predicted growth conditions. The predicted growth conditions were obtained for different normalised Qn values using equation 3 and are listed in Table 4. Table 4: Predicted growth conditions for different Qn values. Predicted Qn Power (W) 0.2 0.4 0.6 0.8

15 10 8 6

Predicted growth conditions Pressure Buffer thick- Buffer type (mTorr) ness (nm) 4.0 13 W 4.2 15 W 4.7 12 W 4.2 20 W

Temperature (◦ C) 200 200 200 200

The corresponding XRD patterns were recorded and the results are shown in Fig. 5a. The normalised ratio of the XRD peak intensity to FWHM for all the samples were measured, and the experimental normalised Qn values were calculated. The experimental normalised Qn values are plotted against the predicted values, and show a one to one linear correlation, see Fig. 5b. The Pearson correlation factor is 0.97. These results demonstrate the predictive power of our response model and provide substantial confidence in our assertion that lower RF power, higher pressures, thicker buffer layers of W at 200 ◦ C provide the highest quality crystals. This knowledge may be useful for determining the thermodynamics of the growth process.

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Figure 5: (a) XRD patterns of the (0 0 l ) texture Sb2 Te3 crystal films grown at the different predicted condition with predicted normalised Qn values from 0.2 to 0.8. (b) The normalised Qn values obtained from the experiment as a function of the predicted values with the Pearson correlation factor of 0.97.

Validation of Statistical Model by Experiment. To validate the RSA model, Sb2 Te3 films were prepared with the optimal growth conditions. The XRD patterns for the optimised Sb2 Te3 films are shown in Fig. 6a. The patterns corresponds to hexagonal structure. Only the diffraction peaks along c-axis direction, such as (0 0 3), (0 0 6), (0 0 9), (0 0 12), (0 0 15), (0 0 18), and (0 0 21) were observed and no strong powder diffraction peaks for randomly oriented Sb2 Te3 crystals were identified. The normalised ratio of the XRD peak intensity to FWHM was calculated to be 0.98, thus the Sb2 Te3 crystals were highly (0 0 l ) textured with the basal plane parallel to the substrate. Figure 6b shows a SEM image of the optimised (0 0 l ) textured Sb2 Te3 film. Hexagonal Sb2 Te3 crystal surfaces are observed with closed-spaced morphology. The high-magnification image (Fig. 6c) shows that the crystallite domain size is of sub-µm length scales with lateral dimension of 300 ± 18 nm. This was also confirmed from the AFM images, which was shown in Figs. 6d and 6e. Additionally, Fig. 6e shows a three dimensional AFM image of a single Sb2 Te3 crystal, which reveals that the columnar pillar like hexagonal crystals of shapes are standing on the flat surface. The average roughness of the textured films was measured to

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Figure 6: Highly (0 0 l ) textured Sb2 Te3 films were grown at optimised growth conditions. (a) XRD patterns, (b) SEM image, (c) magnified SEM image, (d) AFM image, (e) three dimensional magnified AFM image, (f) magnified AFM image of a single Sb2 Te3 crystal, (g) line scan of a single hexagonal Sb2 Te3 crystal showing the crystal height to be 15 nm and edge width of 300 nm, and (h) EBSD measured pole figures for (1 0 0), (1 1 0), (0 0 1), and (1 1 1) crystallographic planes. The textured Sb2 Te3 crystals grow as a hexagonal structure with the basal plane parallel to the substrate surface.

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be 15 ± 3 nm. By performing a line scan over a single hexagonal Sb2 Te3 crystal, a step height of 12 nm and width of 300 nm was observed, as evident from the line profile given in Figs. 6f and 6g. The height difference of the surface hexagonal crystallites is probably caused by cluster diffusion, recrystallisation, and restructuring of Sb2 Te3 crystals. 25,54,56 As a result the grains enlarge and the grain boundaries migrate and then merge to form a homogeneous film. 25 We collected the orientation data of the Sb2 Te3 texture films using EBSD and the results are shown by the pole figures in Fig. 6h. The lower intensity patterns for the (1 0 0), (1 1 0), and (1 1 1) crystallographic planes show that the crystals are not randomly oriented. In contrast, the intense signal at the centre of the (0 0 1) crystallographic plane shows that the majority of Sb2 Te3 crystals are oriented with their crystallographic c-axis aligned perpendicular to the substrate surface. Therefore, it is evident from the above results that the optimal growth parameters produce a highly (0 0 l ) textured Sb2 Te3 crystal films. The highly (0 0 l ) oriented Sb2 Te3 -GeTe superlattices were grown under optimised growth parameters. Two types of superlattice structures, 4 nm-1 nm, and 1 nm-1 nm were prepared using a W buffered Sb2 Te3 template. We found that the superlattice structures grow along the out-of-plane direction of the Sb2 Te3 scaffold, as evident by the XRD patterns given in Fig. 7a. The XRD peaks of the superlattice structures similar to the optimised Sb2 Te3 template. The AFM and SEM images of the 4 nm-1 nm and 1 nm-1 nm superlattice structures are displayed in Fig. 7b-7e. Hexagonal crystals with average size of 300 ± 18 nm are observed. To demonstrate the potential of the DoE method, we compared the current work with (0 0 l ) textured Sb2 Te3 crystal and superlattices, which were optimised using OFAT method. 20 The Qn for OFAT-optimised and FFD-optimised samples were evaluated from the XRD patterns. The results are given in the XRD patterns shown in Fig. 7a. For the pure Sb2 Te3 crystal film, Qn increased by more than an order of magnitude from 152 to 1716 for Sb2 Te3 relative to the sample that was optimised by OFAT. The Sb2 Te3 -GeTe superlattice crystal quality increased by 6 times from from 75 to 495 when it was grown with

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Figure 7: (a) XRD patterns of the Sb2 Te3 template and superlattice structures. The thin line represents the previously designed sub-optimal structures and the thick line shows the present work, DoE-optimised structures. Three dimensional AFM images of (b) 1 nm-1 nm and (c) 4 nm-1 nm superlattices. Top view of SEM images of (d) 1 nm-1 nm and (e) 4 nm-1 nm superlattice structures.

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the Sb2 Te3 optimised growth conditions, thus confirming the applicability of DoE to van der Waals epitaxy. Moreover, the XRD profiles of the previously designed 1nm-1nm OFAToptimised superlattice shows the (0 1 5) diffraction peak at 2θ=28.2◦ for Sb2 Te3 , indicating a lower (0 0 l ) orientation. In contrast, only (0 0 l ) oriented peaks are seen in the DoEled optimised superlattices. Therefore confirming that the DoE method is well suited to optimising the growth conditions of vdW layered chalcogenides.

CONCLUSIONS In this paper, we exploited statistical design of experiment methodologies to optimise the growth of strong (0 0 l ) textured Sb2 Te3 crystal films and Sb2 Te3 -GeTe vdW superlattices. Temperature, pressure, RF power, buffer materials, and their second order interactions were the key factors that significantly affected the texture of the Sb2 Te3 crystal. We experimentally verified the applicability of DoE methods by growing the c-axis oriented (0 0 l ) superlattices under the optimal growth condition. Systematic statistical design and analysis methods, such as FFD-BBD, are convenient for optimising layered materials by vdW epitaxy and we should be considered for other deposition methods, beyond sputtering, which was used here. We strongly recommend FFD and BBD for optimising the growth of crystalline films and interfaces. We are of the impression that many statistical methods used in product design could be applied to the optimisation of films. The main problem of this approach is that it does not produce a physical model to describe growth. However, the statistical significance of the grow parameters can provide clues into the growth mechanism. The true power of statistical optimisation techniques is evident during simultaneous optimisation of multiple objectives. We believe the most powerful design approach will combine statistical design, reported here with crystal nucleation and growth models. The DoE-led materials growth optimisation method has potential to accelerate the development of large scale layered

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two-dimensional materials optimisation and facilitate the development of memory devices, topological insulators, thermoelectrics, and tuneable photonics devices.

ACKNOWLEDGMENTS The research was performed under auspices of the SUTD-MIT international design centre (IDC). The project was in part funded by the A-STAR Singapore-China joint research program (grant #142020046), and in part funded by the Ministry of Education (MOE) Teir 2 grant MOE2017-T2-1-161 “Electric field induced transition in chalcogenide monolayers and superlattices”. JKB is grateful for his PhD presidential graduate fellowship and acknowledges support from MOE, Singapore.

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