Thermal Stability

The diamond-like cubic alpha-Sn phase is only stable up to a temperature of 13 °C; at higher temperatures the tin crystal structure will change phase to β-Sn, which has a non-cubic lattice and a metallic nature. However, the epitaxially grown α-Sn onto low lattice mismatched substrates increased the temperature limit to ~70 °C [64]. The melting temperature of Sn is relatively low, 505 K, compared to those of Ge and Si shown in Table 1. The Sn bulk melting temperature is close to the typical Ge1-xSnx

CVD growth temperature which is typically 520 K and above. This may be expected to have implications for the interdiffusion of Sn atoms between the Ge1-xSnx epilayer

readily diffusing across the Ge1-xSnx/Ge interface, leading to a less abrupt interface.

However, this is not reported in the literature, where even high Sn fraction Ge1-xSnx

layers grown on a Ge buffer have been demonstrated which do not exhibit interdiffusion when annealed at 300 °C [65].

The maximum equilibrium solid solubility Sn fraction is ~1 at. %, the alloy phase diagram is shown in Figure 2-5, with two distinct phases being thermodynamically favourable at higher Sn fractions. Thus, growth of single phase alloys with a higher Sn fraction requires out-of-equilibrium conditions; with the need for conditions to be increasing far from equilibrium as the target Sn fraction increases.

Due to the equilibrium state being phase separation, once grown single crystalline epitaxial layers of Ge1-xSnx alloys are metastable; any post-growth treatments at

sufficiently high temperatures will induce alloy segregation into Sn-rich and Ge-rich regions and is no longer monocrystalline. The thermal stability of alloy layers is dependent on multiple factors, including the Sn fraction [66,67].

Thermal treatments are used for annealing epilayers to improve crystal quality [30]. As grown material will typically have atoms not just in substitutional sites, but there will also be atoms in interstitial sites and the crystal will have vacancies where a lattice atom should be located. Treatment of the sample at high temperatures provides the thermal energy necessary for atoms to move, allowing interstitial defects and vacancies to move and annihilate, thus improving the crystal quality. The increased thermal energy can also allow small crystal imperfections to re-orientate to the match the rest of the crystal. Thermal cycling has been used to reduce the density of threading dislocations in Ge epilayers [68]. These processes improve the crystal quality, but excessive thermal treatments can cause alloy segregation [69].

In addition to improving material quality, thermal treatments are also necessary for Ohmic contact formation; the increased thermal energy facilitates atoms from the metal contact to diffuse into the Ge1-xSnx epilayer, forming a high quality contact.

Again this must be done without significantly degrading the crystal quality of the whole layer [70].

The coefficient of thermal expansion is an important material parameter as it contributes to lattice strain after growth, for example it causes the over relaxation of Ge buffers grown on Si substrates. This effect of different expansion coefficient of heteroepitaxial layers has been used to induce strain in Si-Ge epilayers with multiple thermal cycles [32]. The α-Sn linear thermal expansion coefficient, given in Table 1, is intermediate between Ge and Si, but how the coefficient changes with alloy composition has yet to be investigated.

Metastable high Sn fraction crystalline Ge1-xSnx alloys heated to high temperatures

Figure 2-5 The phase diagram of Ge-rich Ge1-xSnx alloys. Note the

maximum Sn fraction that can be incorporated into the Ge matrix is ~1 at. %. At the opposite range, essentially no Ge fraction can be incorporated into the Sn matrix. Image obtained from Kasper et al. [6].

exhibit Sn segregation, with Sn features appearing on the sample surface. As the Sn fraction of the alloy increases the temperature at which this segregation takes place decreases, as the original alloy is further from equilibrium [19]. It has been suggested that there exists a critical temperature, where a Ge1-xSnx alloy layer is relatively

stable below this temperature but the crystallinity severely degraded with Sn segregation above this temperature [69]. Understanding the nature of the Ge1-xSnx

response to thermal treatments, whether the critical temperature does exist and if so what material parameters influence it, is vital for optimal material processing without causing critical damage to the crystal quality. However, a sufficient level of understanding has yet to be reached. Currently, the critical temperature has only been suggested, but not confirmed, and additionally there are conflicting published results of whether strain relaxation can be achieved with thermal treatments before the onset of material degradation [67].

The melting temperatures of Si, Ge and α-Sn are given in Table 1. All temperatures used for Ge1-xSnx alloy growth and thermal treatments are significantly below the

melting points of Si and Ge, thus it can be safely assumed that the Ge buffer and Si substrate layers will be stable. The melting temperature for Sn is above the temperature at which Sn undergoes a phase change to β-Sn. As mentioned previously, the Sn melting temperature is close to that of typical growth temperatures and below the thermal treatment temperatures used in this work. It is anticipated therefore that the response of Ge1-xSnx alloys to high temperatures will vary from the

Silicon (Si) Germanium (Ge) Alpha-Tin (α-Sn) Lattice parameter (Ǻ) [5] 5.431 5.658 6.493 Elastic constants (GPa) [5] C11 165.8 128.8 66 C12 63.9 48.3 34 C44 79.6 66.8 29 Poisson Ratio ((100) Orientation)[59] 0.28 0.26 0.263 Melting point (K)[71] 1687 1211 505 Linear thermal expansion coefficient (K-1) [71] 2.92×10-6 (293 K) 5.90×10-6 (293 K) 4.7×10-6 (293 K) Atomic Covalent Radius (pm) [71] 117 122 140 Energy band gap (eV) [71] 1.1242 (at 300 K) 0.664 (at 291 K) -0.4 Table 1- Several of the material properties of bulk Si, Ge and α-Sn