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Abstract
A Ge/GeSn/Ge single quantum well with 5% Sn content was grown by chemical vapor deposition on a Si substrate using Ge2H6 and SnCl4 precursors. External biaxial tensile strain was mechanically applied to the Ge/Ge0.95Sn0.05/Ge quantum well for the photoluminescence measurement. Note that the Ge0.95Sn0.05 layer is still under compressive strain due to the large internal compressive strain of the GeSn, although the external bending produces the tensile strain. The direct emission of tensily strained Ge buffer shifts toward lower energy, while the direct emission of pseudomorphic Ge0.95Sn0.05 quantum well does not have significant shift. The strain-induced energy changes of heavy holes and light holes in the Γ valley are extracted by fitting the photoluminescence spectra. Based on the nonlocal empirical pseudopotential method and the model-solid theory, a type-I band alignment is used for the fitting of photoluminescence spectra. The experimentally extracted band edge shifts from the photoluminescence measurement have good agreement with theoretical calculation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
GeSn has drawn a lot of attention due to the indirect-to-direct transition of Sn content of 7-11% [1–4] and larger absorption coefficient than Ge [5]. GeSn quantum wells (QW) grown on Ge buffer layers can be used for electronic [6,7] and photonic devices [8–12]. GeSn-based high efficiency multiple-quantum-well waveguide photodetectors [13] and large bandwidth normal incidence photodetectors [14] were demonstrated. Although Sn incorporation can shrink the bandgaps at the Γ (EgΓ) [8] and L (EgL) [15] valleys, the biaxial compressive strain due to misfit between GeSn and Ge is not favorable to achieve the indirect-to-direct transition. Photoluminescence (PL) spectra of strained Ge1-xSnx (s-GeSn)/Ge were used to characterize the transition energies for various Sn content, and EgΓ was shown to decrease faster than EgL with increasing Sn content [3,15]. Biaxial tensile strain can be introduced by mechanical bending [15], microbridge structure [17], Si3N4 stressor [18], laser annealing [19], and epitaxial growth [20]. It has been reported that mechanical biaxial tensile strain can enhance direct transitions in the PL spectra of Ge wafers [16] and tensile strain GeSn microdisk structure can achieve lasing at low temperature by optical pumping [3]. In this work, the PL spectra under mechanical biaxial tensile strain of Ge/s-GeSn/Ge QW was investigated. Currently, this technology is not compatible for the CMOS processing but it can understand the strain response of the new material. The effects of alloying Sn into Ge and external biaxial tensile strains on the energy shifts of heavy hole (HH), light hole (LH), electron Γ valley, and electron L valleys are extracted by using PL spectra at room temperature (RT). The type-I band alignment calculated by the empirical pseudopotential method (EPM) and the model-solid theory (MST) is used to fit the PL spectra.
2. Experiment
Figure 1 shows schematically energy changes in the conduction (ΔEcΓ and ΔEcL) and valence (ΔELH and ΔEHH) band edges with respect to the valence band edge of relaxed Ge under biaxial tensile strain (Fig. 1(a)) and compressive strain (Fig. 1(b)). The relative energy positions are determined using the EPM and the MST [21,22]. The two kinds of biaxial strain have energy shifts in the opposite direction. The Γ valley and LH have higher sensitivities to the biaxial strain than L valleys and HH.
Fig. 1 Schematic band structures along <111> and <001> directions of Ge using the EPM calculation. The tensile (a) and compressive (b) biaxial strains on (001) plane yield opposite shifts in energy for ΔEcΓ, ΔEcL ΔELH, and ΔEHH with respect to the relaxed Ge valence band edge.
A 1.1μm Ge buffer layer was grown before the GeSn QW as a virtual substrate by chemical vapor deposition (CVD) on a Si (001) substrate. The 11nm pseudomorphic Ge0.95Sn0.05 was sandwiched by Ge as described in Ref. 9. Ge2H6 and SnCl4 were used as Ge and Sn precursors, respectively [9]. In order to have strong PL spectra, a Ge capped layer was grown after the GeSn growth. High resolution (004) x-ray diffraction was used to extract Sn content using the linearly interpolated lattice constant. By fitting the curve of the XRD spectra (Fig. 2), the GeSn layer is fully compressively strained to Ge, indicating the GeSn layer has ~0.6% compressive strain. Due to the small external tensile strain (0.18%), the GeSn layer still under compressive strain based on superposition (−0.6% + 0.18% = −0.42%). The Ge buffer layer has 0.15% tensile strain due to the thermal expansion coefficient mismatch between the Ge buffer layer and the Si substrate during the cooling process [23]. The inset of Fig. 2 shows the schematic cross-sectional view of the Ge/s-Ge0.95Sn0.05/Ge QW sample.
Fig. 2 Measured and simulated (004) HRXRD curves of the Ge/GeSn/Ge single quantum well with [Sn] = 5% grown on a Si (100) substrate. The Ge virtual substrate has 0.15% tensile strain. The fringes reflect the abruptness between GeSn/Ge interfaces. The inset shows the schematic cross-section.
The laser wavelength of 671nm and the power density of 35W/cm2 are used for the PL measurement. InGaAs photodetector is used to cover the spectral range from 1.2 to 2.2μm. Figure 3 shows normalized PL spectra at RT of Ge/s-Ge0.95Sn0.05/Ge under external biaxial tensile strains of 0.09% and 0.18% by mechanical bending as well as the as grown samples. The value of the strain is simulated by ANSYS finite element solver using vertical displacement of the four point screws on each side (The inset of Fig. 3) and is calibrated by the Raman spectroscopy measurements [24–26]. For the external tensile strain larger than 0.18%, the sample is easily shattered. The peak energy around 670meV and 780meV are attributed to the direct transition of the s-Ge0.95Sn0.05 QW and Ge buffer, respectively [9]. The inset of the Fig. 3 shows the bending mechanism.
Fig. 3 The normalized PL spectra at RT of Ge/s- Ge0.95Sn0.05 /Ge QW on a Si substrate under 0.09%, 0.18% external tensile strain as well as the as-grown samples. The inset shows the bending mechanism. As the tensile strain is introduced to the sample, the direct emission of the Ge buffer shifts toward lower energy significantly, while the Ge0.95Sn0.05 QW direct emission shifts weakly.
With applying external tensile strain, redshifts in PL spectra of Ge buffer transition are observed. However, the direct transition of the s-Ge0.95Sn0.05 QW in PL spectra has weak shifts. Although the tensile strain is introduced by bending mechanism, the Ge0.95Sn0.05 layer is still under compressive strain due to the large compressive strain of the GeSn QW.
In order to know the origin of the shift, the PL spectra of the unbended QW sample and the mechanically biaxialy tensiled QW are fitted by the electron-hole plasma recombination model [27] and the direct band gap recombination model [28]. The two optical phonons, longitudinal acoustic phonons (LA = 27meV) and transverse optical phonons (TO = 37meV), are considered in the fitting models. The transitions from Γ valley conduction band edge to light hole band (cΓ–LH) and the Γ valley conduction band edge to heavy hole band (cΓ–HH) of Ge contribute the Ge direct emission (Fig. 4(a)). The Γ valley conduction band edge to HH (cΓ1–HH1) dominates the transition in the strained GeSn QW (Fig. 4(a)). cΓ1-HH2 transition is forbidden according to the envelope-function selection rule [29]. HH1 and HH2 are the ground state and the first excited state in the GeSn QW, respectively. 3D [16,28] and 2D [30] phenomenological line-shape models are used to fit the PL spectra of the transitions in Ge buffer and the s-Ge0.95Sn0.05 QW, respectively. Since the energy difference between the ground state of Γ valley of GeSn well and the Lvalleys of Ge buffer is 94meV (cΓ1 (GeSn)-cL(Ge)) (Fig. 4 (d)). The GeSn Γ valley has a small density of electrons and leads to weaker PL intensity than the Lvalleys of Ge buffer.
Fig. 4 The PL spectra of the Ge/s-Ge0.95Sn0.05/Ge without external tensile strain (a) and with 0.18% external tensile strain (b) fitted by the phenomenological line-shape models. Transitions from cΓ-LH, cΓ-HH in Ge buffer and cΓ1-HH1, cL1-HH1 in Ge0.95Sn0.05 QW are included in the model. (c) The PL spectra fitting curve of the Ge/s-Ge0.95Sn0.05/Ge without external tensile strain and with 0.18% external tensile strain. The PL spectrum peak of the Ge buffer has larger shift than that of Ge0.95Sn0.05 QW (d)The calculated type-I band edge profiles including HH, LH, cL, and cΓ without external tensile strain (black lines) and 0.18% external tensile strain (red lines). The energy level of heavy hole of s-GeSn is the energy reference.
The QW PL spectra could be composed by overlap spectra from multiple transitions between confined states. A fitting broadening parameter of 11meV is adopted in the 2D line-shape model for GeSn spectra [30]. Note that the broadening parameter for 3D Ge is 9meV. Indirect transitions in the Ge buffers were ignored because of the weak PL intensity [9,31]. The confined energies calculated by the EPM and the MST are used to fit the PL spectra [21,22]. The GeSn bandgap energies, EgΓ and EgL, are calculated at 0K by using the EPM and adjusted to the RT value with the assumption of 98 meV and 83meV reduction, respectively, the same as Ge due to the low Sn content [32]. Note that the results have good agreement with the reported experimental data of relaxed GeSn at RT [33,34]. For GeSn transitions, the calculated confined energies of 22meV (cΓ1–cΓ) and 9meV (HH1–HH) in the quantum well are used to obtain an EgΓ of 652meV for s-Ge0.95Sn0.05. Noted that the holes subband energies is derived from the one-electron Schrödinger equation by 6x6 kp method using the barrier height of 22meV (LH(Ge)-LH(GeSn)), while the electrons subband energies is derived by parabolic band method using the barrier height of 35meV(cΓ(Ge)-cΓ1(GeSn)). The bandgap energy of 652meV at Γ valley corresponds to the compressive strain of ~−0.61% which is consistent with the (004) HRXRD (Fig. 2). Due to the low PL intensity from GeSn Γ valley, the noise smears out the shift of 13meV. However, the fitting curve which removes the noise has a clear shift of −13meV (Fig. 4(c)). Figure 4(d) shows the calculated type-I band alignments for the unbened QW and the 0.18% tensily strained QW, including the HH1, LH, cL, and cΓ1 levels of the Ge/s-Ge0.95Sn0.05/Ge. For the unbended sample, the band offset of Γ valley, LH and HH at GeSn/Ge interface is 35meV (cΓ(Ge)-cΓ1(GeSn)), 22meV (LH(Ge) –LH (GeSn)), and 68meV (HH(Ge) –HH1(GeSn)), respectively. The split of LH and HH band (Fig. 4(d)) in Ge buffer is due to ~0.15% residual tensile strain.
The band edge shifts caused by the 0.18% biaxial tensile strain for the Γ valley, L valleys, HH, and LH of Ge and GeSn in Fig. 4 are shown numerically in Table. 1. The energy shift is defined as ΔE = E0.18% external tensile strain – Eno external strain and ΔE>0 indicates upward shifts. Under 0.18% external tensile strain, a large redshift in PL spectra is observed for the Γ valley conduction band edge to LH of the tensily strained Ge buffer (Fig. 3), because of the large upshift of LH and the large downshift of Γ valley conduction band edge (Table 1). On the other hand, the Γ valley conduction band edge to HH of compressively strained Ge0.95Sn0.05 quantum well does not have significant shift (Fig. 3) due to small shifts of downward HH and downshift of Γ valley conduction band edge (Table 1). The extracted energy levels of Ge buffer and s-Ge0.95Sn0.05 QW (EcΓ, ELH, and EHH) are shown in Fig. 5. The extracted experimental data together with others Ge data [35] agree well with our EPM calculation. The calculated change rates versus biaxial strain of EcΓ (Ge), ELH (Ge), EcΓ (GeSn), and EHH (GeSn) are −85, 80, −85 and −11, meV/%, respectively. The strain induced upward ELH of Ge and downward EcΓ of Ge is responsible for the redshift of Ge peaks.
Table 1. strain induced energy shifts for 0.18% external tensile strain (meV)
Fig. 5 Calculated energy changes in LH, HH, and cΓ of Ge and Ge0.95Sn0.05 with respect to the relaxed valence bands using the EPM and the MST. The calculated change rates versus biaxial strain of EcΓ (Ge), ELH (Ge), EcΓ (GeSn), and EHH (GeSn) are −85, 80, −85 and −11, meV/%, respectively. The extracted cΓ-LH and cΓ-HH of Ge buffer, and cΓ-HH of s-Ge0.95Sn0.05 from PL spectra under external tensile strain are shown (solid squares) as well as the reported Ge data [35] (orange diamond).
3. Summary
In summary, the extracted energy levels in Ge and GeSn band structures are obtained by PL spectra and have good agreement with EPM and MST calculation. Our data can be used to design further Ge/GeSn photonic and electronic devices. In order to obtain the clear PL spectra and enhance the performance of photonics devices, SiGeSn barriers can be grown on the GeSn QW to increase valance band and conduction band offset [36,37]. Moreover, increasing the Sn content and tensile strain can enable GeSn to reach the indirect-to-direct point which is favorable for the photonics and electronic devices [38].
Funding
Ministry of Science and Technology, Taiwan, R.O.C (106-2622-8-002-001, 107-2218-E-002-044 -, 107-3113-E-492-001-CC2).
Acknowledgment
This work was supported by Ministry of Science and Technology, Taiwan, R.O.C. The initial epi growth by Applied Materials is also highly acknowledged.
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