# Light emission from ion-implanted SiGe quantum dots grown on Si substrates

L. Spindlberger, J. Aberl, L. Vukušić, T. Fromherz, J.-M. Hartmann, F.

Fournel, S. Prucnal, F. Murphy-Armando, M. Brehm

► To cite this version:

L. Spindlberger, J. Aberl, L. Vukušić, T. Fromherz, J.-M. Hartmann, et al., Light emission from ion-implanted SiGe quantum dots grown on Si substrates. Materials Science in Semiconductor Processing, 2024, 181, pp.108616. 10.1016/j.mssp.2024.108616. cea-04771112

HAL Id: cea-04771112

https://cea.hal.science/cea-04771112v1

Submitted on 7 Nov 2024

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# Light emission from ion-implanted SiGe quantum dots grown on Si substrates

L. Spindlberger<sup>a</sup>, J. Aberl<sup>a</sup>, L. Vukušić<sup>a</sup>, T. Fromherz<sup>a</sup>, J.-M. Hartmann<sup>b</sup>, F. Fournel<sup>b</sup>, S. Prucnal<sup>c</sup>, F. Murphy-Armando<sup>d</sup>, M. Brehm<sup>a,*</sup>

<figure><img src="image_3.png" /></figure>

## ABSTRACT

We report on electroluminescence spectroscopy experiments demonstrating room-temperature light emission from heavily alloyed SiGe quantum dots, for which the light emission properties are enhanced by incorporated split-[110] self-interstitials. The quantum dots are formed during molecular beam epitaxy deposition of Si<sub>0.6</sub>Ge<sub>0.4</sub> alloys on n-doped silicon-on-insulator substrates. To create the split-[110] self-interstitials the quantum dots were co-implanted in-situ using Si and Ge ions. The hybrid emitters were further embedded into the intrinsic region of a p-i-n diode structure to enable electrical pumping. Similar to previous theoretical results on unstrained Ge-based quantum dots containing these defects, radiative direct transitions are possible for these SiGe light emitters. However, in SiGe dots these transitions are not at the Brillouin zone center. Instead, first-principles calculations indicate that the presence of the split-[110] self-interstitial defect in strained and unstrained SiGe can lead to optically direct transitions in momentum space in the X-direction of the Brillouin zone.

## 1. Introduction

Photonics can bring a lot of versatility to our digital world, for example, by combining Si-based electronics with photonics, where applications related to short and medium-range data transfer and sensing on chips are envisioned. Integrated digital technology is dominated by Si, which is an excellent optical material due to its high refractive index and high-quality Si/SiO<sub>2</sub> interface. However, the integration of appropriate light sources for interlacing on-chip electronics and optics is challenging. On the one hand, different materials such as III-Vs have to be integrated on an industrial Si platform, yet achieving an efficient coupling of the respective light sources to other Si photonics components such as waveguides. On the other hand, Si-based telecom light emitters suffer inherently from the indirect band gap of Si and, thus, long carrier lifetimes and inefficient light emission. Integrating Ge, another group-IV material, can help to add versatility to the Si photonics platform [1]. While the band gap of compressively strained Ge on Si remains indirect, applying tensile strain to Ge can turn it into a direct one [2,3]. However, tensile biaxial strain in Ge further increases the lattice mismatch between strained Ge and Si, making the direct integration of tensile strained Ge on Si and the coupling to Si photonics waveguides more difficult.

Thus, without parting from the vast benefits of an integrated Si photonics platform, there is definitely a demand for room-temperature light emitters that can be homogeneously integrated with crystalline Si or silicon-on-insulator (SOI) substrates. Nanostructures, particularly quantum dots (QDs), could offer a pathway to soften the indirect-band-gap-induced recombination limitations due to the quantum confinement of charge carriers. Such SiGe QDs can be epitaxially fabricated with high crystalline quality through the deposition of (Si)Ge films on Si(001) substrates, as studied extensively in the past [4,5]. However, since their formation is strain-driven and the lattice mismatch between Ge and Si is only about 4.2%, the QDs are typically too large for significant quantum mechanical confinement effects.

Additionally, the extensive research on Ge and SiGe QDs over the past decades has shown that due to indirect band gap and type-II bandstructure alignment, the light emission from these nanostructures remains restricted to cryogenic temperatures [6–13].

Recently, it was shown that the QD's light emission can be enhanced by interlacing them with point defects introduced through in-situ low-energy ion implantation [14–16]. Thereby, the split-[110] self-interstitial, i.e., a pair of atoms aligned in [110]-direction at one lattice site, has been found to have a particularly low formation energy, both in Si [17] and Ge [18,19]. This defect leads to the presence of N+1 atoms in

<footnote><sup>a</sup> Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenberger Strasse 69, A-4040, Linz, Austria</footnote>

<footnote><sup>b</sup> University Grenoble Alpes, CEA, LETI, Grenoble, France</footnote>

<footnote><sup>c</sup> Institute of Ion Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, Dresden, 01328, Germany</footnote>

<footnote><sup>d</sup> Tyndall National Institute, University College Cork, Cork, T12R5CP, Ireland</footnote>

<footnote>* Corresponding author.
E-mail address: moritz.brehm@jku.at (M. Brehm).</footnote>
a volume where N atoms would make a perfect crystal. For these reasons, the split interstitial is a likely candidate to be formed when a group-IV layer is exposed to ion implantation. Theoretical works have revealed that the presence of point defects of the split-[110] self-interstitial type (SSI) in the QDs can open direct recombination paths in unstrained Ge at the Γ-point, at which electrons can recombine with holes located in the QD potential defined by the band offsets between Si and Ge [14,20,21]. Efficient electron-hole overlap can, however, only be obtained by interlacing the defects and the QDs, as in structures with higher dimensionality like quantum wells, holes can migrate away from the strained defect site, lowering the emission intensity [22].

Experimentally, such defect-enhanced quantum dots (DEQDs) show pronounced electro- and photoluminescence at telecom wavelengths even above room temperature (RT), in contrast to unimplanted QDs [15, 21]. The latter typically exhibit activation energies for thermal quenching of about 60 meV, while for DEQDs high activation energies of ~300 meV were found [15]. Also, signs of optically pumped lasing were obtained with such DEQDs being incorporated into optical resonators [15]. The split-interstitial present in the QDs does not lead to sharp emission features, as evidenced by theory and experiment [14,15,20], but it can explain the laser level scheme [14] and its emission energies by the combined effects of band offsets of the QDs and the band structure induced changes of the defects [14,15]. Furthermore, the thermal quenching of the optical emission well above room temperature is associated with the defect properties [14,22].

In previous works, Ge-rich QDs of hut-cluster shape were chosen as hosts for the SSI defects [14]. In the theoretically investigated case of unstrained pure Ge (i.e., the absence of significant amounts of Si) in the QDs, Γ- and L-point states of the lowest Ge conduction band (CB) would be mixed in the presence of an SSI-defect, resulting in an electron state with significant Γ-character, nearly degenerate with the L-character electron ground state of the DEQD. Due to its Γ-character, enhanced radiative electron-hole recombination could occur via this state [20].

However, QDs formed via the Stranski-Krastanow growth exhibit extensive SiGe intermixing, especially at elevated growth temperatures ($T_G$) [23–26]. While both, bulk Ge and Si are indirect bandgap semiconductors, their band structure is vastly different. For Ge, the CB minimum is at the L-points, 0.66 eV above the valence band (VB) maximum located at the Γ-point. Meanwhile, the energy separation at the local CB Γ-point minimum, ~0.80 eV, is only slightly larger in Ge. For Si, the CB minimum is at the Δ-points, separated by 1.12 eV from the valence band maximum at the Γ-point, while the respective separation of the local Γ-point minimum is relatively large (3.4 eV). Thus, adding substantial amounts of Si to a DEQD should strongly reduce the SSI-induced coupling of Γ- and L-like QD states that was shown to be beneficial for the radiative recombination efficiency in unstrained model Ge DEQDs [20]. Therefore, it is a priori not clear if the concept of an interlaced QD plus SSI defect light emitter, i.e., a DEQD, can be expanded to SiGe intermixed nanostructures, leading to pronounced light emission at RT.

Here, we used dense arrays of SiGe QDs that formed during molecular beam epitaxy (MBE) deposition of $Si_{0.6}Ge_{0.4}$ alloys with in-situ co-implementation of Si and Ge ions. We traced the morphological evolution of the QDs via atomic force microscopy (AFM) and the optical properties through electroluminescence (EL) measurements. We performed first-principles calculations to determine the band structure and the emission properties from SiGe alloys containing SSI defects, indicating that optically direct transitions in the SiGe DEQDs can occur. However, we find these transitions are not at Γ but in the X-direction of the Brillouin zone.

## 2. Materials and methods

### 2.1. Material growth and device fabrication

The epitaxial growth was carried out in a solid-source Riber SIVA-45

MBE system on silicon-on-insulator (SOI) and float zone (FZ) Si(001) sample pieces. On the latter, the QDs were grown for the AFM investigation. For the former, the buried oxide (BOX) was 2 µm thick. For the electrically-driven devices, the Si device layer of the SOI consisted of 100 nm intrinsic Si onto which a 400 nm thick highly n-doped (4•10¹⁹ cm⁻³) Si:P layer was grown by chemical vapor deposition. In all cases, after a standard substrate cleaning process, including a bath in a Piranha solution followed by a Radio Corporation of America (RCA) cleaning procedure [27], substrates were dipped for 30 s in diluted hydrofluoric acid (HF 1%) to remove the native oxide before their introduction into the load-lock vacuum chamber. Next, substrates were degassed at 650 °C for 30 min before the growth of a 138 nm thick crystalline Si buffer layer with a growth rate of 0.9 Å/s and a growth temperature ($T_G$) ramped from 475 up to 650 °C. Both, Si and Ge were deposited using solid sources and electron beam evaporators. After the Si buffer growth, 8 nm of $Si_{0.6}Ge_{0.4}$ were deposited at $T_G$ = 650 °C. From previous works, it is known [28] that a two-dimensional SiGe wetting layer forms during the first 1.8 nm of $Si_{0.6}Ge_{0.4}$ deposition. Then, Stranski-Krastanow QDs appear formed via the Asaro-Tiller-Grinfeld instability (see, e.g., Ref. [29]) and grow during the deposition of the remaining 6.2 nm (see Fig. 1(a)). The total amount of deposited SiGe material was chosen so that uniform and densely spaced SiGe QDs formed [28], as shown by the QD’s height distribution in Fig. 1(b). Parallel to the QD formation, i.e., during the growth of the final 6.2 nm SiGe, a bias potential of -2 kV was applied to the substrate to implant the evolving QDs with $Ge^+$ and $Si^+$ ions (dose: ~1•10⁵ µm⁻²) [14,15]. These ions are created as a fraction of the evaporated atoms passes through the electron beam that is used to melt the solid source materials. The single QD layer was then capped with 668 nm of intrinsic Si, deposited at $T_G$ = 600 °C. This ensured that the QDs were positioned at the calculated maximum of the fundamental radiative TE mode propagating perpendicularly to the sample surface in the final device.

The topmost ~400 nm of the Si cap were subsequently heavily p-type doped by implantation of boron ions (Si:B, 4•10¹⁹ cm⁻³) followed by dopant activation to obtain the full diode structure. For the AFM investigation, the deposition of the whole Si capping layer was omitted.

The final structure, comprising the epilayer stack atop the doped SOI substrate, the contact metallization, and the passivation/isolation layers, is shown as a cross-sectional scheme in Fig. 1(c). Fig. 1(d) and (e) show color-coded scanning electron microscopy (SEM) images of the diode after deposition of the bottom contact Fig. 1(d) and top contact (Fig. 1(e)). The SEM images were recorded for structures fabricated on bulk FZ-Si substrates without SiGe DEQDs, as the BOX of the SOI led to charging effects during SEM imaging. After conditioning the sample surface with hexamethyldisilazane (HDMS) to promote adhesion, a MICROPOSIT™ S1818 photoresist was spun on the sample. After the resist exposure with a microdisk pattern, the pattern was transferred by ICP-RIE dry etching. The etching process was stopped at a depth of 800 nm, i.e., just above the interface between the intrinsic and the highly n-doped device layer. A further thinning of the n-doped layer would limit the maximum current throughput of the device. After cleaning using acetone and IPA, a 400 nm thick layer of $SiO_x$ was deposited by plasma-enhanced chemical vapor deposition (PECVD). The advantage of PECVD, as opposed to, e.g., physical vapor deposition (PVD), is the conformal deposition of materials, with, thus, a covering of sidewalls, as seen in Fig. 1(d) and (e) SEM images. Hereafter, top- and bottom-contact openings were lithographically defined and etched through the SiOx by ICP-RIE. Next, a lithographic mask was used to fabricate the bottom contacts by a lift-off process. Directly before PVD metal deposition, an HF (1%) dip was applied for 60 s to remove the native $SiO_2$. About 500 nm of Aluminum, i.e., a thickness high enough to ensure electrical contact over the $SiO_2$-step profile, was used for bottom metallization. (Fig. 1(c)). After Al deposition, the sample was placed in acetone for the lift-off process. Subsequently, Al was driven in during a rapid thermal annealing step at 380 °C for 40 s in forming gas. The resulting structure is shown in Fig. 1(d). Finally, AlSi was used for top contact metallization.
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) AFM micrograph (4 × 4 µm²) of Si<sub>0.6</sub>Ge<sub>0.4</sub>-QDs (b) Height distribution of the SiGe DEQDs (c) Sample schematic of the diode on SOI containing a single layer of Si<sub>0.6</sub>Ge<sub>0.4</sub>-DEQDs after processing (d) Colored SEM image of the device before and (e) after deposition of the top contact layer.</figcaption></figure>

using again PVD and a lift-off process, see Fig. 1(e).

## 2.2. Material characterization

For the uncapped samples grown on FZ Si(001) substrates, we investigated the sample surface morphology by AFM using a Veeco Dimension 3100 atomic force microscope. The nanostructures forming during the deposition of 8 nm of Si<sub>0.6</sub>Ge<sub>0.4</sub> on Si(001) are significantly larger than the only 2–3 nm high Ge hut cluster DEQDs described before [14,15], as the strain contrast of the SiGe QDs to the Si substrate is lower. Nevertheless, a homogeneous size distribution of the QDs can be achieved by carefully adjusting the amount of deposited SiGe alloy. The average height of the QDs is 33.7 ± 2.7 nm, see Fig. 1(b).

For the electroluminescence (EL) measurements, samples were mounted on a chip carrier by In-bonding, and individual devices were contacted by Al-wire bonding. Each sample was mounted on the cold finger of a liquid He cryostat, allowing for sample cooling to <10 K. We used a Keithley 236 source-measure unit for low direct-current (DC) operation during sample alignment and for recording current-voltage (I–V) curves. For duty cycle and pulse width control, a HP-8114A pulse generator with a maximum output current limited to 1 A was used. An oscilloscope measured the voltage drop across a 47 Ω series resistor. The current was recorded with the same oscilloscope via an inductive current probe. The EL emission was collected with a lens (focal length, f = 150 mm), and coupled (via a fiber-coupler) to a multi-mode fiber. The multi-mode fiber was connected to a grating spectrometer with 300 mm focal length and a numerical aperture of 0.25, equipped with 300 or 600 grooves/mm gratings blazed for wavelengths of 1 µm or 1.6 µm, respectively. We detected the dispersed signal with a liquid-N₂-cooled InGaAs line detector (cut-off at 1600 nm) containing 1024 pixels at 25 µm pitch and a liquid N₂-cooled wavelength extended InGaAs line detector with a cut-off wavelength of 2200 nm.

## 2.3. Materials theory and simulation

We used the first-principles density functional theory (DFT) in the local density approximation (LDA) methods as implemented in ABINIT [30] to calculate the electronic band structure of a Ge [110]-split self-interstitial in relaxed (i.e., unstrained) Si<sub>0.6</sub>Ge<sub>0.4</sub>. To simulate the SiGe alloy, we employ Si and Ge Hartwigesen-Goedecker-Hutter (HGH) norm-conserving pseudopotentials [31] to build an averaged SiGe atom,

called “alchemical mixing” in ABINIT. We simulated 4 × 4 × 4 face-centered cubic (fcc) primitive cells with a total of 129 atoms, with the [110] split self-interstitial Ge atom at the center, as seen in Fig. 3(b). The calculation was converged with a k mesh of 4 × 4 × 4 and a plane-wave energy cut-off of 680 eV. The calculation of the luminescence required the momentum matrix elements $P_{cv}$ between the electronic bands, obtained from the calculated wave functions as explained in Ref. [20]. The calculation of the luminescence from the electronic band structure of the interstitials throughout the Brillouin Zone was performed with a 2000-band k·p extrapolation based on the ab-initio wavefunctions, following the procedure described in Ref. [20]. The presence of strain due to growth of SiGe/Si requires the calculation of two different symmetry configurations of the interstitial, relative to the strain direction. We considered biaxial compressive strain parallel to the [110] interstitial, i.e. $\epsilon_x+\epsilon_y$ and relaxed $\epsilon_z$, and compressive biaxial strain $\epsilon_z+\epsilon_y$ and relaxed $\epsilon_x$.

## 3. Results and discussion

The I–V characteristics of a disk-shaped mesa device with a radius of 50 µm measured at room temperature is shown in Fig. 2(a). The inset in Fig. 2(a) depicts an SEM image of a smaller disk with a radius of 10 µm fabricated on a reference Si FZ wafer. Fig. 2(b) depicts the EL emission spectra from SiGe DEQDs on SOI for driving currents ($I_A$) in the 1.14 kAcm⁻² – 3.3 kAcm⁻² range. Spectra were recorded at a heat sink temperature of 7 K, a pulse width of 500 ns, and a repetition rate of 50 kHz. The colored spectra correspond to $I_A = 1.32$ kAcm⁻², $1.53$ kAcm⁻², $1.71$ kAcm⁻², $1.90$ kAcm⁻², $2.10$ kAcm⁻², $2.34$ kAcm⁻², $2.59$ kAcm⁻², $2.85$ kAcm⁻², $3.07$ kAcm⁻², and $3.30$ kAcm⁻². Weak EL emission from Si is visible in the 1100–1200 nm wavelength range. Spectra are dominated by peaks at 1410 nm and 1560 nm, respectively. We note that, especially at low excitation currents, the shape of the emission spectra of the Si<sub>0.6</sub>Ge<sub>0.4</sub>-DEQDs is affected by the detector cut-off of standard InGaAs detectors at around 1600 nm. To demonstrate that no additional luminescence features arise for wavelengths longer than 1600 nm, the inset of Fig. 2(b) shows the low-temperature EL spectrum of a disk mesa device with a radius of 100 µm and the signal detected by an extended-range InGaAs photodiode array. The red line represents the smoothed data using a Savitzky-Golay filter, which guides the eye. No additional spectral features are observed up to a detected wavelength of 2200 nm. The shaded area in the inset indicates the cut-off range of the
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** (a) Current versus voltage curve of a disk mesa device with 50 µm radius, measured at 300 K. (b) EL spectra for the disk with 50 µm radius, recorded at T<sub>EL</sub> = 7 K with a pulse width of 500 ns and a repetition rate of 50 kHz. I<sub>A</sub> increases from 1.14 kAcm<sup>-2</sup> up to 3.3 kAcm<sup>-2</sup>. Inset: EL spectrum from a disk with 100 µm radius recorded at I<sub>A</sub> = 318 Acm<sup>-2</sup> and T<sub>EL</sub> = 7 K using an extended range InGaAs detector. The cut-off region of the standard InGaAs detector is indicated by the shaded area. (c) Light output and voltage versus applied current at room temperature for the disk with 50 µm radius. A pulse with of 500 ns and a repetition rate of 10 kHz were used. The light output is directly proportional to the injected current. (d) Room-temperature EL spectra of a disk with 100 µm radius, measured for I<sub>A</sub> = 16 Acm<sup>-2</sup>, 31 Acm<sup>-2</sup>, 185 Acm<sup>-2</sup>, and 312 Acm<sup>-2</sup> with 100 % duty cycle. (e) Normalized EL spectra of a disk with 50 µm radius measured at RT. The emission is collected from different angles in respect to the sample's surface, indicating the role of Fabry-Pérot interferences in growth direction.</figcaption></figure>

standard high-sensitivity InGaAs detector used for all other
measurements.

Additionally, the integrated EL emission (I<sub>EL</sub>) at RT under pulsed excitation with a pulse width of 500 ns and a pulse repetition rate of 10 kHz is plotted in Fig. 2(c) for different amplitudes of the current pulses (I<sub>A</sub>). Data were fitted using a simple power law I<sub>EL</sub> ~ I<sub>A</sub><sup>m</sup>. We found that the DEQD emission was in a very good approximation (m = 0.96) directly proportional to the driving current. The second graph in Fig. 2 (c) depicts the corresponding I-V curve of the device. Typically, power exponents m of about 0.6 are observed for group-IV devices, pointing towards Auger recombination at higher I<sub>A</sub> [32]. The power exponent of m = 0.96 observed here indicates that Auger recombination is not a limiting factor in this SiGe DEQD device. Fig. 2(d) depicts the EL spectra of a disk with a 100 µm radius, recorded at room temperature and under 100 % duty cycle. The higher sample temperature leads to a broadening of the EL emission towards smaller wavelengths. We note that the high-temperature luminescence emission is atypical for conventional group-IV quantum dots in general and SiGe QDs in particular [6–13,32, 33]. This indicates the excellent quality of the present QDs. A further improvement of the SiGe DEQD emission properties might be possible using thermal annealing treatment or dangling bond passivation using hydrogen treatment, as successfully applied to Ge DEQD emitters [34, 35].

In the EL-plots in Fig. 2(b) and (d), a pronounced peak and valley structure is observed, originating from Fabry-Pérot interference. We note that these spectral features are independent of the disk diameter for samples with the same thickness of the active layer, as can be seen in the supplementary material, Fig. S1, in the EL spectra of disks with different diameters containing QDs. Therefore, we stress that these Fabry-Pérot modes are not caused by interference of standing waves across the disk diameter and reflected by the disk-oxide sidewall interface. Indeed, the

periodicity caused by such reflections would be much narrower than the
ones observed (~1–3 nm at 1400 nm for disk radii of 100 µm and 50 µm,
respectively), due to the relatively large disk sizes employed. In turn, the
Fabry-Pérot originated from reflections at the Si/AlSi, the top Si/SiO<sub>2</sub>,
and the bottom SiO<sub>2</sub> interfaces of the SOI substrate. Previously, we
observed similar dips in photoluminescence (PL) spectra of hut-cluster
DEQDs grown on SOI substrates, while dips were absent for samples
grown on bulk Si substrates [35]. Here, we further confirmed the origin
of the dips by varying the sample inclination in the EL measurements.
Emission minima systematically shifted toward shorter wavelengths
when increasing the inclination of the sample surface with respect to the
optical axis, as expected for Fabry-Pérot interference fringes, see Fig. 2
(e). Notably, the spectral response collected in-plane is barely affected
by the Fabry-Pérot interference fringes, and thus does not show a pro-
nounced peak and valley structure, black curve in Fig. 2(e) and sup-
plementary material.

We note that the EL emission from the SiGe DEQDs is spectrally
broad despite the relatively narrow size distribution of QDs shown in
Fig. 1(a) and (b). On the one hand, this broad emission may be a result of
the ensemble measurement performed in this work. Since the QDs are
rather large (~35 nm in height) size confinement can be neglected.
However, significant quantum confinement can be induced by varia-
tions of the Ge composition within the QDs leading to inhomogeneous
linewidth broadening. It was found for conventional Stranski-Krastanow
islands that the intermixing of Si and Ge varies from nanostructure to
nanostructure [36-38]. To minimize the elastic energy, QDs tend to be
Si rich at the base and Ge-rich at the apex, leading to charge carrier
confinement at the apex of the nanostructure, even if the nanostructure
ifself would be too large for significant quantum confinement. The
fluctuations in the composition of the individual QDs leads to varying
potential wells in the QD ensemble that again reflects itself in an
increased linewidth in the ensemble luminescence response [39].

On the other hand, we are dealing here with DEQDs, nanostructures that underwent low-energy ion bombardment. Therefore, in the following, we have theoretically examined the influence of Ge-SSI within a Si<sub>0.6</sub>Ge<sub>0.4</sub> matrix environment on the band structure of the system and the resulting radiative transitions. Fig. 3(a) shows the electronic band structure of an additional Ge interstitial in a 128 atom supercell of unstrained SiGe. The most striking impacts of such an interstitial on the band structure are the appearance of a conduction band impurity state, and 3 raised interstitial valence bands at the ¼ X position of the Brillouin zone and localized at the interstitial site (see Fig. 3 (b)). The colored arrows show the defect-induced transitions with non-zero oscillator strengths that give rise to the luminescence spectra of Fig. 3(e).

To better compare the theoretical results to the experimental mea-
surements, we calculated the band structure and EL in a strained
configuration resulting from the growth of Si<sub>0.6</sub>Ge<sub>0.4</sub>/Si, as explained in
the methods section. This strain set-up has two possible inequivalent
interstitial configurations: parallel and perpendicular to the growth di-
rection. Fig. 3(c) and (d) show the calculated electronic band structures
of the two configurations, and Fig. 3(f) shows the corresponding oscil-
lator strength. The resulting EL from the combination of the two inter-
stitial configurations is shown in Fig. 3(g). Both peaks occur due to direct
transitions between the impurity states with a ¼ X band character.

This transition has been previously observed in our calculation of Ge
interstitials in Ge [20]. The corresponding oscillator strength for this
transition is calculated to be 0.1, a similar value for the same transition
occurring in unstrained Ge containing such an SSI. However, there are
no direct transitions at the Γ-point in SiGe, at variance with pure Ge.
This is due to the much larger direct gap in SiGe compared to Ge,

effectively inhibiting the mixing of higher and lower CB states in SiGe
under the perturbation of an interstitial.

The behavior of the calculated luminescence with pump intensity is qualitatively similar to the experimentally observed electroluminescence spectra, see Fig. 3(h). Compared to our simulations performed for unstrained SiGe, we observe that including strain corresponding to SiGe/Si shifts the spectra to wavelengths corresponding to those of the experiment. This is because the localized interstitial state at the conduction band has a predominantly X character. Introducing compressive biaxial strain reduces the energy gap of the strain-split 4-fold degenerate X states, and raises the perpendicular 2-fold X-states.

4. Conclusion

In summary, we have presented EL experiments that demonstrate light emission from heavily alloyed SiGe quantum dots, for which the light emission properties are enhanced by the presence of split-[110] self-interstitials in the SiGe matrix. We note that the EL persists up to room temperature, atypical for SiGe light emitters [32]. Previous results on unstrained Ge-based DEQDs showed that optically direct transitions at the Brillouin zone center were possible and were based on mixed-L-Γ conduction bands. In strained Ge/Si DEQDs, recombination paths are similar [40]. However, for these alloyed light emitters, a different light emission path needs to be exploited as the direct conduction band shifts to higher energies in the presence of SiGe alloying. We found that the SSI defect in SiGe can lead to optically direct transitions in momentum space, however, not at the Γ-point, but in the X-direction of the Brillouin zone.

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** (a) Electronic band structure calculations of a 128 atom supercell of unstrained Si<sub>0.6</sub>Ge<sub>0.4</sub> containing a Ge [110] split self-interstitial. Charge carrier transition paths in the X-direction from the defect-induced conduction band to the three valence bands, raised in the presence of the defect, are indicated. (b) Electron and hole densities of the band edge states at the ¼ X_y k-point in the supercell Brillouin zone. These states are responsible for the luminescence due to a split intersitial. (c),(d) Electronic band structure for strained Si<sub>0.6</sub>Ge<sub>0.4</sub> containing an interstitial oriented in in-plane (x-direction) and in growth direction (z-direction) and (e) The respective influence of these transitions in unstrained Si<sub>0.6</sub>Ge<sub>0.4</sub> (see (a)) on the calculated photoluminescence spectra. We consider the inverted quasi-fermi distributions to be at room temperature. (f) Calculated oscillator strength for the two different interstitial configurations in the strained Si<sub>0.6</sub>Ge<sub>0.4</sub> lattice. The relevant oscillator strength in this configuration is that around the ¼ X_y point, with a value of ~0.12. (g) Calculated emission spectra for the two interstitial configurations in strained Si<sub>0.6</sub>Ge<sub>0.4</sub>. (h) EL spectra from Si<sub>0.6</sub>Ge<sub>0.4</sub> DEQDs for two different excitation currents, 1.14 kAcm<sup>-2</sup> and 2.1 kAcm<sup>-2</sup>.</figcaption></figure>
## Funding sources

This work was funded by the Austrian Science Fund (FWF) under grant no. Y1238–N36 and the Linz Institute of Technology (LIT) under grant no. LIT-2019-7-SEE-114. The modeling work at Tyndall National Institute was supported by Science Foundation Ireland under Grant No. 19/FFP/6953.

## CRediT authorship contribution statement

**L. Spindlberger:** Writing – review & editing, Visualization, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **J. Aberl:** Writing – review & editing, Methodology, Investigation, Data curation. **L. Vukušić:** Writing – review & editing, Methodology, Investigation. **T. Fromherz:** Writing – review & editing, Supervision, Methodology, Data curation, Conceptualization. **J.-M. Hartmann:** Writing – review & editing, Resources, Formal analysis. **F. Fournel:** Writing – review & editing, Resources, Formal analysis. **S. Prucnal:** Writing – review & editing, Resources, Formal analysis. **F. Murphy-Armando:** Writing – review & editing, Software, Formal analysis, Data curation. **M. Brehm:** Writing – original draft, Visualization, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

Data will be made available on request.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.mssp.2024.108616.

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