Thermal stability, atomic vibrational dynamics, and superheating of confined interfacial Sn layers in $\mathrm{Sn}∕\mathrm{Si}$ multilayers

Multilayers composed of materials with low (Sn) and high (Si) bulk melting points were grown at room temperature by ultrahigh vacuum deposition. ${}^{119}\mathrm{Sn}$ Mössbauer spectroscopy has been used to investigate the temperature dependence of the Debye-Waller factor $f$, the mean-square displacement, and the mean-square velocity of ${}^{119}\mathrm{Sn}$ nuclei in ultrathin ($10\mathrm{\AA }$ thick) $\alpha$-like Sn layers embedded between $50\mathrm{\AA }$ thick Si layers. The $f$ factor was found to be nonzero with a value of $0.036\pm 0.009$ even at $450°\mathrm{C}$. This provides unequivocal proof of the solid state of the confined $\alpha$-like Sn layers at least up to $450°\mathrm{C}$. Melting can only be achieved by superheating to $T>450°\mathrm{C}$. This temperature is significantly higher than the melting temperature of bulk $\beta \text{−}\mathrm{Sn}$ $(231.9°\mathrm{C})$ and of a nonconfined epitaxial $\alpha \text{−}\mathrm{Sn}$ single layer grown on InSb(111) $(170°\mathrm{C})$ previously reported in the literature [T. Osaka et al., Phys. Rev. B 50, 7567 (1994)]. Our molecular dynamics calculations show that melting of bulk-like $\alpha \text{−}\mathrm{Sn}$ starts at $\sim 380°\mathrm{C}$ and is complete at $\sim 530°\mathrm{C}$ according to the Lindemann criterion. Since we still observe the solid state at $450°\mathrm{C}$ for the confined $\alpha$-like Sn films, considerable superheating is observed for this system. The stability of the ultrathin confined $\alpha$-like Sn layers arises from electronic interactions with the surrounding Si layers, as evidenced by the Mössbauer chemical shift.

Figure 1

(Color online) Transmission ${}^{119}\mathrm{Sn}$ Mössbauer spectra of the ${[{}^{119}\mathrm{Sn}\left(10\mathrm{\AA }\right)∕\mathrm{Si}\left(50\mathrm{\AA }\right)]}_{50}$ multilayer on polyimid (kapton) foil (sample 1) measured in situ at the indicated temperatures. The measurements were performed by increasing the temperature stepwise from RT to $450°\mathrm{C}$. Least-squares fitting (full line) was performed with a single Lorentzian line located close to the velocity position for $\alpha \text{−}\mathrm{Sn}$. [The vertical full (dashed) line indicates the velocity position (center line shift) of bulk $\alpha \text{−}\mathrm{Sn}$ (bulk $\beta \text{−}\mathrm{Sn}$) at RT.]

Figure 2

(Color online) (a) Measured $T$ dependence of the center-line shift $\delta$ (full circles) obtained from Fig. 1. The straight line in (a) indicates the (classical) high-$T$ limit, $T⪢{\theta }_D$ (${\theta }_D=\text{Debye}$ temperature) for the second-order Doppler shift (SOD) according to Eq. (13). Full triangles: high-$T$ data points corrected for the decrease in the chemical shift $\Delta {\delta }_{\mathit{chem}}=\Delta \delta$ measured at RT before and after annealing to $350°\mathrm{C}$ and $450°\mathrm{C}$, respectively, according to Table . (b) Measured $T$ dependence of $-\ln A$ obtained from Fig. 1. ($A$ being the relative spectral area of the $\alpha \text{−}\mathrm{Sn}$ line normalized with the nonresonant intensity.) The straight line is a least-squares fit to the data points, according to Eqs. (6, 8), resulting in ${\theta }_D=209\mathrm{K}$.

Figure 3

(Color online) ${}^{119}\mathrm{Sn}$ CEM spectra of ${[\mathrm{Sn}\left(10\mathrm{\AA }\right)∕\mathrm{Si}\left(50\mathrm{\AA }\right)]}_{50}$ multilayer on MgO(110) (sample 2) measured ex situ at RT after isochronal annealing $\left(1\mathrm{h}\right)$ at the indicated temperatures. The sample was annealed stepwise from RT to $500°\mathrm{C}$. The full line through the data points is a least-squares fit with one Lorentzian line for $\alpha \text{−}\mathrm{Sn}$ (RT to $355°\mathrm{C}$) or with two Lorentzian lines for $\alpha \text{−}\mathrm{Sn}$ and $\beta \text{−}\mathrm{Sn}$, respectively $(400°\mathrm{C}\text{to}500°\mathrm{C})$. The vertical full (dashed) line indicates the velocity position (center-line shift) of bulk $\alpha \text{−}\mathrm{Sn}$ (bulk $\beta \text{−}\mathrm{Sn}$) at RT.

Figure 4

X-ray diffractometry scans $\left(\Theta \text{−}2\Theta \right)$ of a ${[{}^{119}\mathrm{Sn}\left(10\mathrm{\AA }\right)∕\mathrm{Si}\left(50\mathrm{\AA }\right)]}_{43}$ multilayer deposited on MgO(110) (sample 3). The XRD scans were recorded ex situ at RT after stepwise isochronal annealing $\left(1\mathrm{h}\right)$ from RT to $500°\mathrm{C}$. The observed Bragg peaks of Si and $\beta \text{−}\mathrm{Sn}$ are indicated $({\lambda }_{K_{\alpha }}=1.54178\mathrm{\AA })$.

Figure 5

(Color online) Temperature dependence of (a) the ${}^{119}\mathrm{Sn}$ Debye-Waller factor ($f$ factor) of confined $\alpha$-like Sn obtained from the Mössbauer data in Fig. 2b (full circles), from NRIXS at $300\mathrm{K}$ for epitaxial $\alpha \text{−}\mathrm{Sn}∕\mathrm{In}\mathrm{Sb}$ (Ref. 24) (cross) and $\beta \text{−}\mathrm{Sn}$ (Ref. 49) (full triangle), and from the present theory (open squares). The Mössbauer data were normalized to $f=0.21$ at $300\mathrm{K}$ obtained by NRIXS (Ref. 24) on a ${[{}^{119}\mathrm{Sn}\left(10\mathrm{\AA }\right)∕\mathrm{Si}\left(50\mathrm{\AA }\right)]}_{50}$ multilayer on Si(111). (b) Mean square displacement $⟨x^2⟩$ of the ${}^{119}\mathrm{Sn}$ Mössbauer atom obtained from the experimental $f$ factor [(a)] (full circles), from NRIXS at $300\mathrm{K}$ for epitaxial $\alpha \text{−}\mathrm{Sn}∕\mathrm{In}\mathrm{Sb}$ (Ref. 24) (cross), for $\beta \text{−}\mathrm{Sn}$ (Ref. 49) (full triangle), and from the present theory (open squares). The upper straight line (dotted) is a least-squares-fit of our theoretical results for temperatures below $650\mathrm{K}$. The middle straight line indicates the classical behavior $(T⪢{\theta }_D)$ for epitaxial $\alpha \text{−}\mathrm{Sn}∕\mathrm{In}\mathrm{Sb}$ $({\theta }_D=165.1\mathrm{K})$, while the lower straight line is a least-squares fit to the present Mössbauer data (full circles), indicating classical behavior. The horizontal dashed line indicates $⟨x^2⟩$ according to the Lindemann theorem, where melting occurs. (c) Mean-square velocity $⟨v^2⟩$ of the ${}^{119}\mathrm{Sn}$ atom obtained from the Mössbauer data in Fig. 2a (full circles). Full triangles: corrected $⟨v^2⟩$ values at high $T$, obtained from the corresponding corrected data points in Fig. 2a (full triangles). The straight line indicates the classical high-$T$ limit for the second-order Doppler shift $\left({\delta }_{\mathit{SOD}}\right)$ according to Eq. (13). Data obtained from NRIXS at $300\mathrm{K}$ for epitaxial $\alpha \text{−}\mathrm{Sn}∕\mathrm{In}\mathrm{Sb}$ (Ref. 24) (cross) and amorphous $\alpha$-like Sn (Ref. 24) (open circle), and from the present theory (open squares), are also plotted. $T_m$ $\left(\beta \text{−}\mathrm{Sn}\right)$ is the experimental melting temperature of bulk $\beta \text{−}\mathrm{Sn}$, while $T_m{}^{\mathit{th}}\left(\alpha \text{−}\mathrm{Sn}\right)$ is the theoretical melting temperature of bulk $\alpha \text{−}\mathrm{Sn}$ according to the present theory and the Lindemann theorem.

Figure 6

Energy versus temperature plot for $\alpha \text{−}\mathrm{Sn}$ as obtained from ab initio molecular dynamics simulations using VASP. The simulation at each temperature was done for 4000 steps with a time step of $1\mathrm{fs}$. The last 2000 steps were used for calculation of average quantities. The rather sudden increase of the caloric curve is a hint of melting.