Lattice instability and elastic response of metastable Mo${}_{1-x}$Si${}_x$ thin films

We present a detailed experimental study on Mo${}_{1-x}$Si${}_x$ thin films, an archetypal alloy system combining metallic and semiconductor materials. The correlations between structure and elastic response are comprehensively investigated. We focus on assessing trends for understanding the evolution of elastic properties upon Si alloying in relation to the structural state (crystalline vs amorphous), bonding character (metallic vs covalent), and local atomic environment. By combining picosecond ultrasonics and Brillouin light scattering techniques, a complete set of effective elastic constants and mechanical moduli ($B$, $G$, $E$) is provided in the whole compositional range, covering bcc solid solutions ($x$ < 0.20) and the amorphous phase (0.20 < $x$ < 1.0). A softening of the shear and Young moduli and a concomitant decrease of the Debye temperature is revealed for crystalline alloys, with a significant drop being observed at $x$ ∼ 0.2 corresponding to the limit of crystal lattice stability. Amorphous alloys exhibit a more complex elastic response, related to variations in coordination number, atomic volume, and bonding state, depending on Si content. Finally, distinct evolutions of the G/B ratio as a function of Cauchy pressure are reported for crystalline and amorphous alloys, enabling us to identify signatures of ductility vs brittleness in the features of the local atomic environment. This work paves the way to design materials with improved mechanical properties by appropriate chemical substitution or impurity incorporation during thin-film growth.

Figure 1

XRD patterns for (a) representative crystalline Mo${}_{1-x}$Si${}_x$ films (total film thickness ∼150 nm) in the angular range covering the 110 and 220 reflections of the bcc structure (note that intensities for 220 peak are magnified ×50) and (b) for amorphous Mo${}_{1-x}$Si${}_x$ alloy films (total film thickness ∼550 nm). The data are plotted against the scattering vector magnitude |$q$| $=$ (4π sinθ)/λ. Standard reference diffraction lines for pure bcc-Mo are shown as dotted vertical lines. The inset in (a) displays representative ω scans of the 110 reflexion of Mo${}_{1-x}$Si${}_x$ solid solutions performed at a fixed angular position (2${\theta }_B$) corresponding to the Bragg (110) reflexion and inset in (b) shows the evolution of the reciprocal peak position, $Q_1^{-1}$ vs the Si concentration $x$ of amorphous alloys.

Figure 2

Representative XRR scans of Mo${}_{1-x}$Si${}_x$ thin films (100–150 nm thick) deposited on (001)Si substrates, except for the amorphous Si film deposited on (11$\overline{2}$0) Al${}_2$O${}_3$ substrate. Solid lines correspond to the best-fit simulations to experimental data (symbols), taking into account a MoSiO${}_x$ interfacial layer (thickness ∼1.2 nm) and a topmost oxidized surface layer (thickness ∼1–3 nm). Vertical dashed lines indicate the position of the critical angle ${\theta }_c$.

Figure 3

Experimental data for Mo${}_{1-x}$Si${}_x$ thin films: (a) mass density ρ deduced from simulations of the XRR scans; (b) average atomic volume $V_a$ deduced from ρ using Eq. (1). Values $V_a^{\left(\mathrm{XRD}\right)}$ deduced from the determination of the stress-free lattice parameter $a_0$ are also reported for comparison. The dashed lines are linear extrapolation of the data obtained in the range $x$ < 0.20. The vertical dotted line indicates the critical composition for which a transition from a bcc crystalline solid solution to an amorphous phase is observed. Values of silicon atomic volumes in the equilibrium diamond structure (Si-I) and also in metallic high pressure phases (Si-II, Si-V, and Si-VI) reported in the literature (Refs. 34, 35, 36, 37, 38, 39, 40, 41) are indicated on the right scale.

Figure 4

Room-temperature electrical resistivity ${\rho }_e^{300\mathrm{K}}$ vs the Si content $x$ of crystalline and amorphous Mo${}_{1-x}$Si${}_x$ thin films, shown on a logarithmic scale (a); temperature dependence of the resistivity ratio ${\rho }_e$/${\rho }_e$${}^{300\mathrm{K}}$ plotted for some representative Mo${}_{1-x}$Si${}_x$ thin films (b). The composition ranges (I) to (III) indicated in (a) are related to distinct electron conductivity behaviors (cf. text for discussion). The inset in (b) displays the evolution of the conductivity σ vs the temperature $T$ for three amorphous alloys with composition $x$ > 0.50; the best fit to a power law [Eq. (2)] is shown (solid line); a fit of experimental data with the Mott variable range hopping model [cf. text, Eq. (3)] is also shown for the amorphous Mo${}_{0.20}$Si${}_{0.80}$ thin film (dotted line).

Figure 5

Standard time-resolved picosecond acoustics reflectivity measurements obtained for (a) crystalline Mo${}_{0.92}$Si${}_{0.08}$ ($h_f$ = 308.3 nm; ρ = 10.05 g.cm${}^{-3}$) and (b) amorphous Mo${}_{0.60}$Si${}_{0.40}$ ($h_f$ = 140.4 nm; ρ = 7.82 g.cm${}^{-3}$) thin films using a Michelson interferometer (imaginary part of the reflectivity changes). Low-frequency acoustic waves reflected at the film-substrate interface emerge periodically at the film surface (echoes). Moreover, one can notice that the photothermal background signature exhibits a faster damping rate in the crystalline phase due to a better thermal diffusion.

Figure 6

Longitudinal (respectively, transversal) sound velocity deduced from the analysis of PU reflectivity measurements (respectively, BLS spectra) on Mo${}_{1-x}$Si${}_x$ thin films vs the Si content $x$. Distinct symbols, squares, and triangles, refer to films deposited onto thin $a$-Si and $c$-Mo sublayers, respectively. Dashed lines are only guides for the eyes.

Figure 7

Effective elastic constants (a) $C_{33}$ deduced from PU reflectivity measurements and (b) $C_{44}$ deduced from BLS spectra vs the Si content $x$. Distinct symbols triangles (up or down) refer to films deposited onto thin $a$-Si and $c-$Mo sublayers, respectively. Theoretical values of the effective elastic constants calculated in the Hill approximation for a $\{$110$\}$ fiber-textured Mo thin film using the known crystallographic constants (Ref. 45) are indicated. Dashed lines are only guides for the eyes.

Figure 8

Typical experimental BLS spectrum compared to the calculated one for a Mo${}_{0.75}$Si${}_{0.25}$ thin film (thickness $=$ 501 nm, density = 8.87 g.cm${}^{-3}$) performed at an incidence angle θ = 65°. R denotes the Rayleigh surface mode, and $S_i$, the so-called Sezawa modes, observed at higher frequencies.

Figure 9

Acoustic Debye temperature ${\theta }_D$ vs the Si content $x$ of crystalline and amorphous Mo${}_{1-x}$Si${}_x$ thin films. Reference values for bulk (bcc) Mo and diamond Si ($d$-Si) are indicated. Dashed lines are only guides for the eyes.

Figure 10

Evolution of (a) Young modulus $E$ (squares) and indentation modulus $E_{IT}$ (circles) and (b) bulk modulus $B$ (circles) and Poisson ratio ν (diamonds) vs the Si content $x$ of crystalline and amorphous Mo${}_{1-x}$Si${}_x$ thin films.

Figure 11

Indentation modulus $E_{IT}$ for several Mo${}_{1-x}$Si${}_x$ alloy thin films on MgO(100) substrates as a function of $h_c$/h${}_f$, where $h_{\mathrm{c}}$ is the contact penetration depth and $h_f$ is the film thickness ($h_f$ ∼ 500–600 nm, depending of the sample). Five samples are shown ranging from pure Mo ($x$ = 0 to pure Si ($x$ = 1) compositions. The brown shaded region indicates the values of $E_{IT}$ that were selected for the plot of Fig. 10.

Figure 12

Evolution of (a) the shear modulus to bulk modulus ratio (G/B) vs the Si content $x$ of crystalline and amorphous Mo${}_{1-x}$Si${}_x$ thin films and (b) map of shear modulus to bulk modulus ratio (G/B) vs the Cauchy pressure ($C_{12}-$C${}_{44}$) showing the different ductility and brittleness trends as estimated from this work. In both figures, horizontal G/B lines refer to distinct thresholds for ductile to brittle transition in bcc metals and in metallic glasses, rectangular shaded regions to the ductile character of the crystalline (brown shaded region), or amorphous (grey shaded region) alloys. Data points corresponding to crystalline samples are shown as red full circles, whereas amorphous samples correspond to black full circles.