Band-gap and strain engineering in GeSn alloys using post-growth pulsed laser melting

Ge_1−x Sn_x layers with a Sn concentration of 11% were epitaxially grown on (100) oriented 4 inch p-type Si substrates with a sheet resistance of ρ = 10–20 Ω cm by MBE at the Institute of Semiconductor Engineering, University of Stuttgart. The MBE process starts with a thermal desorption step at a substrate temperature of T_S = 900 °C to remove the native SiO₂ and therefore to prepare the substrate surface for the consecutive epitaxy. First, a 50 nm thick Si buffer layer was grown at a substrate temperature of T_S = 600 °C. Next, the substrate temperature was reduced to T_S = 330 °C and a 100 nm thick Ge layer was grown. Afterwards, a thermal annealing step at T_S = 830 °C for a duration of t = 5 min allows threading dislocations to annihilate and is used to form a virtual Ge substrate (Ge-VS). An additional 300 nm thick Ge buffer layer was grown on top and annealed at T_S = 750 °C for t = 5 min. Finally, a 290 nm thick Ge_1−x Sn_x layer was grown on top of the Ge buffer layer at T_S = 120 °C.

The band gap and strain engineering of the epitaxial Ge_1−x Sn_x layers was performed by PLM for 28 ns using a XeCl excimer laser with 308 nm wavelength. The energy density of the laser pulse varied from 0.2 to 0.6 J cm⁻². The homogeneously irradiated area was 5 × 5 mm². The annealing was done at atmospheric condition.

The influence of the PLM process on the microstructural, electrical, and optical properties of the Ge_1−x Sn_x alloys was studied using micro-Raman spectroscopy, high-resolution x-ray diffraction (HRXRD), Rutherford backscattering spectrometry in random (RBS/R) and channelling (RBS/C) directions, transmission electron microscopy (TEM) and low-temperature photoreflectance (LT-PR) spectroscopy.

Micro-Raman spectroscopy was performed on a Horiba LabRam n°1/24 h system equipped with Nd:YAG laser with a wavelength of 532 nm and a liquid-nitrogen-cooled charge-coupled device (CCD) camera. All measurements were performed in backscattering geometry with the laser power of 1 mW focused on a circular area with 1 µm diameter. The phonon spectra were recorded in the wavenumber range of 50–550 cm⁻¹.

HRXRD was performed with a Rigaku SmartLab x-ray diffractometer system. Three different types of measurements were carried out on each of the samples: polycrystal analysis, rocking curve (RC) measurements and reciprocal space map (RSM) measurements. The polycrystal analysis is a one-dimensional 2 theta scan with a fixed incident angle ω = 3°, which is fixed near the critical angle. The RC measurement is a one-dimensional scan and measures diffraction intensity distributions along a reciprocal lattice vector. With this measuring method (2 theta/omega scan), the symmetrical (004) reflection for the Ge_1−x Sn_x layers on a Si (100) substrate was investigated. The RSM measures diffraction intensity distributions by scanning both the diffraction angle and sample rotation. The asymmetrical (−2–24) reflections of the samples were measured using the RSM method. The lateral and vertical lattice constants can be determined from the RC and RSM results.

RBS/R and RBS/C experiments were performed at the Ion Beam Center of the Helmholtz-Zentrum Dresden-Rossendorf using its 2 MV van de Graaf accelerator. The He⁺ beam had an energy of 1.7 MeV with a diameter of about 1 mm. The RBS measurements were used to determine the thickness and composition of the grown Ge and Ge_1−x Sn_x layers. The obtained RBS spectra were fitted with the Software SIMNRA [19].

TEM investigations of the as-grown and pulsed-laser-molten samples were done in cross-sectional geometry using a Titan 80–300 microscope (FEI) operated at an accelerating voltage of 300 kV. High-angle annular dark-field scanning TEM imaging and spectrum imaging analysis based on energy-dispersive x-ray spectroscopy (EDXS) were performed at 200 kV with a Talos F200X microscope equipped with a Super-X EDX detector system (FEI). Prior to TEM analysis, the specimen mounted in a high-visibility low-background holder was placed for 10 s into a Model 1020 Plasma Cleaner (Fischione) to remove potential contamination.

The direct optical transitions in as-grown and annealed films were determined by LT-PR measurements at 30 K in a 'bright configuration' experimental setup. Samples were excited by continuous-wave 405 nm laser of 100 mW power chopped with the frequency of 280 Hz. A phase sensitive detection of the LT-PR signal is accomplished using a lock-in amplifier. This measurement was performed at Wroclaw University of Science and Technology.

The microstructure and element composition of the as-grown and PLM-treated samples were investigated using cross-sectional TEM-based analysis. Figure 1(a) depicts a representative bright-field TEM image of the Ge_0.89Sn_0.11 layer grown on a Ge virtual substrate. To record this bright-field TEM image, the TEM specimen was oriented in Si $\left[ {1\bar 10} \right]$ zone axis geometry relative to the electron beam. While the Ge virtual substrate is characterised by a uniform contrast (besides the presence of some dislocations close to the Si substrate), the Ge_0.89Sn_0.11 layer shows a columnar signature, particularly in the upper three quarters of the film. Comparing with the EDXS-based element analysis in figure 1(b), this columnar contrast seems to arise from a slightly varying Sn distribution in the as-grown Ge_0.89Sn_0.11 layer. Regarding the microstructure, the Ge–Sn film grows epitaxially on the Ge virtual substrate, as derived from the fast Fourier transform (FFT, depicting a $\left[ {1\bar 10} \right]$ zone axis pattern) of the representative high-resolution (HRTEM) image in figure 1(c). At the border regions between the columns, there are no defects visible.

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After PLM with an energy density of 0.5 J cm⁻², the columnar signature changed and the sample surface morphology is restructured (figure 1(d)). Comparing the superimposed Sn and Ge element maps in figures 1(b) and (e), it can be concluded that PLM leads to a slight Sn redistribution. In particular figure 1(e) shows the separation of the original Ge_0.89Sn_0.11 layer into three regions: from top to bottom (a) the Ge_0.89Sn_0.11 film molten during PLM, (b) an almost pure Ge layer as interface between molten and non-molten region, and (c) the residual Ge_0.89Sn_0.11 film not molten during PLM. Besides Sn-rich cluster formation, the molten region shows Sn-rich filaments, reaching up to the sample surface. Both features may be the combined effect of a slightly varying Sn distribution already in the as-grown sample and an enhanced Sn diffusion during PLM. It should be mentioned that a wall-like structure, having its plane normal perpendicular to the normal of the TEM lamella plane, may also appear as filament in a two-dimensional TEM-based projection image. Similar filament structures have been observed after laser annealing of Ge_1−x Sn_x [20]. Their origin is still under discussion [20]. Beside small Sn segregation, the molten layer has a comparable composition (Ge_0.90Sn_0.10) and similar structural properties as the as-grown sample, i.e. it is of single-crystalline nature. In particular, the FFT analysis of the HRTEM image in figure 1(f) leads to a $\left[ {1\bar 10} \right]$ zone axis pattern comparable to the one given in the inset of figure 1(c). However, there may be some defect structures at the Sn-enriched locations, as exemplarily shown in the enlarged part of the HRTEM image depicted in the upper right inset of figure 1(f).

By varying the energy density of the pulse laser, we can control the thickness of the molten layer, as shown in figure 2. Taking into account the mass density in Ge_1−x Sn_x , the atomic thicknesses of the molten layer were determined from RBS/R data (see supplementary materials S1). Melting of Ge_0.89Sn_0.11 was observed already at an energy density of 0.25 J cm⁻², and the thickness of the molten layer increases with increasing the energy density of the laser pulses. The estimated temperature during PLM with 0.25 J cm⁻² is in the range of 900 °C. This temperature corresponds to the melting point of Ge_1−x Sn_x with about 10% of Sn [21]. There is an almost linear dependence between the thickness of the molten layer and the energy density (see red regression line in figure 2). The conversion from the extracted melting depth in atoms cm⁻² by SIMNRA into melting depth in nm leads to about 13% thinner Ge_1−x Sn_x layers. This error was determined by comparing the RBS/R (supplementary materials S1(a)) and TEM (figure 1) results of the as grown state. The error comes from the not well determined mass density of the Ge_1−x Sn_x alloy grown by MBE and the mass approximation by Vegard's law. After PLM, the mass density is getting inconstant due to the atoms and strain redistributions

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In more details the microstructural properties of the Ge and Ge_1−x Sn_x layers, i.e. the crystallographic orientation and strain, were studied by HRXRD, µ-Raman spectroscopy and PR measurements. Figure 3(a) shows the high-resolution RC obtained from the samples in as-grown state and after PLM with energy densities of 0.4, 0.5 and 0.6 J cm⁻². The as grown state shows three XRD peaks located at about 64.18°, 66.07° and 69.13° corresponding to Ge_0.89Sn_0.11, the Ge-virtual substrate and the Si substrate, respectively. After PLM the GeSn peak is divided in two peaks located at 64.22° and 65.24° for 0.5 J cm⁻² (see figure 3(a)) because of the relaxation of the top layer. In figure 3(b) the polycrystal analysis is depicted. The 2θ scan exhibits one sharp peak at about 38.08° in the as-grown state and 38.18° after PLM with 0.5 J cm⁻², which can be due to some Sn segregation visualised in the cross-sectional TEM image taken from the as-grown sample (see figure 1(a)) or some inclusions of small nanocrystals. The absence of other well distinguishable peaks confirms the epitaxial growth of Ge_1−x Sn_x alloy on the Ge-virtual substrate. Additionally, it can be concluded that PLM does not change the crystal quality because the polycrystal analyses before and after annealing are very similar.

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Figure 4 shows the space mapping results of as-grown (a) and PLM 0.4 J cm⁻² (b), PLM 0.5 J cm⁻² (c) and PLM 0.6 J cm⁻² (d) samples. For a better visualisation, the reciprocal coordinates were transformed in coordinates of the real space. Using the real space, both the in-plane a_|| and out-of-plane a_⊥ lattice parameters can be determined. Details about the calculation of a₀, a_|| and a_⊥ can be found elsewhere [22]. By comparing the lattice parameter for relaxed Ge_1−x Sn_x alloy a₀ for known Sn content with our experimental results, the in-plane strain _{|| XRD} can be calculated by equation (1)

$$\begin{equation}{\varepsilon _{\parallel {\text{XRD}}}} = ({a_\parallel } - {a_0})/{a_0}.\end{equation} \tag{ 1 }$$

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The obtained values are summarised in table 1. The a_|| and a_⊥ for the as-grown Ge-virtual substrate are 5.6647 and 5.6503 Å, respectively, while the tabulated value for relaxed Ge is 5.6575 Å [23]. This means that the virtual substrate is slightly strained by _{|| XRD} = 0.009. In the as-grown sample, the GeSn peak is shifted to a larger a_|| value compared to the Ge-virtual substrate peak. The in-plane lattice parameter of GeSn is a_|| = 5.6928 Å, but the calculated value of a₀ for relaxed Ge_0.9Sn_0.1 is 5.7502 Å. Hence, our Ge_0.9Sn_0.1 layer in as-grown state is under compressive strain _{|| XRD} = −0.010 because of pseudomorphic growth of Ge_0.9Sn_0.1 on Ge-virtual substrate. The a_⊥ for as-grown Ge_0.9Sn_0.1 is 5.7944 Å due to the out-of-plane tensile strain. After PLM with 0.5 J cm⁻² the new a_|| and a_⊥ from the top layer are 5.7478 and 5.7190 Å, respectively, while the lattice parameters from the non-molten layer remain almost unchanged. The in-plane strain is changed from compressive _{|| XRD} = −0.0100 in the as-grown sample to tensile _{|| XRD} = 0.0028 after PLM with an energy density of 0.5 J cm⁻² and to _{|| XRD} = 0.0038 after PLM at 0.6 J cm⁻². The Ge_0.904Sn_0.096 layer after PLM with 0.4 J cm⁻² is still in plane compressive strained with _{|| XRD} = −0.0003, but strain is reduced compared to the as grown state. The a₀ for top Ge_1−x Sn_x layer is a bit different due to Sn redistribution after PLM (see figure 1(d)).

Table 1. HRXRD in-plane a_|| and out-of-plane a_⊥ lattice parameters and _||XRD strain calculated for as-grown and PLM-treated samples with their composition dependant relaxed lattice parameter a₀. Ge_as-grown and GeSn_as-grown belong to the material in the as grown state. The results of GeSn pertain to the not effected material by PLM (see figure 1(e)). GeSn_PLM-0.4, GeSn_PLM-0.5 and GeSn_PLM-0.6 are samples annealed with 0.4, 0.5 and 0.6 J cm⁻², respectively. The accuracy of the out of plane lattice parameter a_⊥ is ±0.0001 Å and in plane a_|| ±0.001 Å.

	Sn (at.%)	a|| (Å)	a⊥ (Å)	a0 (Å)	|| XRD
Geas-grown	—	5.665	5.6503	5.6575	0.0009
GeSnas-grown	11.1 ± 0.5	5.693	5.7944	5.7502	−0.0100
GeSn	10.2 ± 0.5	5.681	5.7907	5.7430	−0.0108
GeSnPLM-0.4	9.6 ± 0.5	5.736	5.7394	5.7380	−0.0003
GeSnPLM-0.5	8.9 ± 0.5	5.748	5.7190	5.7316	0.0028
GeSnPLM-0.6	8.9 ± 0.5	5.754	5.7149	5.7318	0.0038

Table 2. Strain calculation by using the LO-Ge–Ge phonon mode. ω_{GeSn-measurment} is the obtained peak position of the samples after Lorentz fitting and Δω_{GeSn-alloy relaxed} is the expected peak shift due to alloying Ge with Sn according to equation (3). The Sn concentration x_Sn is obtained by XRD. As a comparative value the in plane strain _{|| XRD} was obtained from table 1. The accuracy of the measured LO-Ge–Ge phonon mode is 0.1 cm^−1.

Sample	ωGeSn-measurement (cm−1)	ΔωGeSn-alloy relaxed (cm−1)	Δωstrain (cm−1)	xSn (at.%)	|| Raman	|| XRD
As grown	296.2	−9.2	5.0	11.1 ± 0.5	−0.0132	−0.0100
PLM-0.4 J cm−2	291.2	−8.0	−1.3	9.6 ± 0.5	0.0035	−0.0003
PLM-0.5 J cm−2	290.6	−8.5	−1.4	10.2 ± 0.5	0.0038	0.0028
PLM-0.6 J cm−2	290.7	−7.4	−2.4	8.9 ± 0.5	0.0064	0.0038

In order to validate the HRXRD results and investigate the in-plane strain distribution of the as-grown and the annealed states, µ-Raman measurements are performed. Figure 5 shows the µ-Raman spectra obtained from the Ge_0.89Sn_0.11 samples before and after PLM with energy densities between 0.2 and 0.6 J cm⁻².

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The Ge–Ge longitudinal optical (LO) phonon mode in relaxed Ge ω_Ge is at 300.5 ± 0.1 cm⁻¹, as also seen in the figure 5 [24]. Due to the pseudomorphic growth of Ge_0.89Sn_0.11 epitaxial on a Ge-virtual substrate with a smaller lattice parameter, the Ge_0.89Sn_0.11 layer is compressively strained. Hence, the Ge–Ge phonon mode in as-grown Ge_0.89Sn_0.11 is located at 296.6 cm⁻¹ instead of 291.3 cm⁻¹. The PLM process leads to strain relaxation and a slight Sn redistribution within the annealed Ge_1−x Sn_x layer. This strain relaxation is visible as the shift of the Ge–Ge phonon mode after PLM towards lower wavenumber. The sample annealed with 0.20 J cm⁻² has only a slight red shift because the laser energy is close to the melting threshold. This can be confirmed by the RBS/R spectra revealing the same Sn distribution like in the as-grown sample (see supplementary materials S1(a)). All other samples annealed with the pulsed laser energy densities of 0.25 J cm⁻² and higher show the main Ge–Ge phonon mode at about 290 ± 1 cm⁻¹. The penetration depth of the green laser in Ge, used for sample excitation in the micro-Raman spectroscopy, is approximately 20 nm from the surface [25]. Due to alloying with Sn, the penetration depth of the green laser in Ge_1−x Sn_x layer can be even smaller. Hence, the detected micro-Raman spectra can be used to determine the strain distribution in the top layer of about 15 nm thick only. The measured phonon peak position is influenced by the composition of the Ge_1−x Sn_x alloy Δω_alloy and the strain Δω_strain. This can be expressed by equation (2). Δω_alloy is influenced by (a) the different mass Δω_mass of the Ge and Sn atoms in the alloy and (b) the change of bond length Δω_bond between Ge atoms due to alloying with Sn. Since the strain, mass difference and bond length depend linearly on the concentration of Sn, the value for Δω_alloy can be calculated with equation (3). By using the disorder parameter b, which is reported as b = −83.11 [26], the Raman shift in a fully relaxed Ge_1−x Sn_x with a low concentration of Sn can be calculated. The shift due to the in-plane strain _{|| Raman} can be calculated using equation (4). The strain coefficient c = −374.53 [26] was used

$$\begin{equation}\Delta \omega = \Delta {\omega _{{\text{GeSn}}}} - {\omega _{{\text{Ge}}}} = \Delta {\omega _{{\text{alloy}}}} + \Delta {\omega _{{\text{strain}}}}\end{equation} \tag{ 2 }$$

$$\begin{equation}\Delta {\omega _{{\text{alloy}}}} = \Delta {\omega _{{\text{mass}}}} + \Delta {\omega _{{\text{bond}}}} = b \times {x_{{\text{Sn}}}}\end{equation} \tag{ 3 }$$

$$\begin{equation}\Delta {\omega _{{\text{strain}}}} = c \times {\varepsilon _{\parallel {\text{Raman}}}}.\end{equation} \tag{ 4 }$$

Since there is no contribution of the Sn rich filaments to the Raman spectra, the in-plane strain _{|| Raman} can be calculated by using equation (4). The results for the as grown state and the PLM samples with 0.4, 0.5 and 0.6 J cm⁻² are shown in table 2.

By comparing the results of the in-plane strain from HRXRD _{|| XRD} with the µ-Raman results in table 2, we can conclude that the Ge_1−x Sn_x layer is compressively strained before annealing and tensile strained after annealing. In fact, the strain obtained by XRD and Raman for the PLM samples are different, but this can be explained with the different penetration depths of the methods. With µ-Raman we get signals only from the top ca. 15 nm and with XRD one measures the whole layer. Additionally, the disorder parameter b and the strain coefficient c are determined for Ge_1−x Sn_x alloys with x = 0.025 and 0.077 [26]. In our case, the Sn concentration is significantly higher. Therefore, slight differences can be expected. Further, by converting the in-plane strain into in-plane lattice parameter and adding this value in figure 4 it is visible that some surface generated tail regions of the Ge_1−x Sn_x RSM matches the Raman results.

The change of the fundamental optical transition in Ge_1−x Sn_x alloys after PLM with 0.4 and 0.5 J cm⁻² is determined by PR spectroscopy. The results of the measurements are displayed in figures 6(a)–(c). The obtained low temperature PR signal is fitted with the low-field electromodulation Lorentzian line-shape function form known as the Aspnes formula equation (5) [27]

$$\begin{equation}\frac{{\Delta R}}{R}(E) = \operatorname{Re} \left[ {\sum\limits_{j = 1}^n {{C_j}{{\text{e}}^{{\text{i}}{\theta _j}}}{{\left( {\hbar \omega - {E_j} + {\text{i}}{\Gamma _j}} \right)}^{ - {m_j}}}} } \right],\end{equation} \tag{ 5 }$$

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where $\frac{{\Delta R}}{R}\left( E \right)$ is the energy dependence of PR signal, n is the number of PR resonances used to simulate PR signal, $\hbar \omega$ is the photon energy of the probe beam, E_j is the energy of optical transition, and Γ_j, C_j and θ_j are the broadening, amplitude and phase angle of PR resonance, respectively. At 30 K, the nature of optical transitions (PR resonances) in Ge_1−x Sn_x alloys is excitonic and therefore the exponent m_j is assumed to be 2. The fitting curves are plotted in figures 6(a)–(c) by colour lines together with the moduli of the individual PR resonances (colour lines with filling), which are obtained from the equation (5) with parameters derived from the fit according to the equation (6)

$$\begin{equation}\Delta {\rho _j}\left( E \right) = \frac{{\left| {{C_j}} \right|}}{{{{\left[ {{{\left( {\hbar \omega - {E_j}} \right)}^2} + {\Gamma _j}^2} \right]}^{\frac{{{m_j}}}{2}}}}}.\end{equation} \tag{ 6 }$$

So far, the Aspnes formula has been widely used to analyse electro-reflection spectra in a variety of semiconductor materials, including GeSn [28–30]. The dependence of the energies extracted from the spectra on the in-plane strain _{|| XRD}, given in table 1, is shown in figure 6(d). Resonances at around 0.86 and 1.14 eV are related to optical transitions in the Ge layer beneath the Ge_0.89Sn_0.11 layer. The resonance at 0.86 eV is associated with the direct band gap of Ge [31], while the resonance at 1.14 eV is separated from it by the value of spin–orbit split-off energy of Ge [27]. The energies assigned to resonances at around 0.55 eV for as-grown samples are in good agreement with the values calculated for Ge_0.89Sn_0.11 at 30 K when the lateral compressive strain of −1% is applied. Therefore, the PR resonance at 0.51 eV is attributed to the optical transition between the heavy-hole band and the conduction band, while the resonance at 0.58 eV is attributed to the optical transition between the light-hole band and the conduction band. The effect of strain on the band gap is also known from strain investigations on Ge [32]. It is worth noticing that these resonances may show a Franz–Keldysh oscillation [27], which complicates the analysis of PR spectra with two Aspnes resonances and the determination of the optical transition at higher energy (light-hole and heavy-hole transition, respectively, in the case of compressive and tensile strain). Therefore, clear interpretation of the optical transition energies for Ge_1−x Sn_x (around 0.55 eV) in the samples after PLM is difficult, due to both the more complex structure of the materials after the melting process and the possible Franz–Keldysh oscillations in the measured spectra. Nevertheless, these spectra are fitted with two resonances and the obtained values undoubtedly support simultaneous change of the average content of Sn in the alloy and the reduction of the in-plane compressive strain such that the tensile strain can be observed, see figure 6(d).