Open Access Article
Su Hyun Park,
Gyeong Min Seo,
Jeong Wook Kim,
Yun Ho Lee,
Gyubin Lee
,
Hong Jae Lee and
Byoung Don Kong
*
Department of Electrical Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea. E-mail: bdkong@postech.ac.kr
First published on 4th December 2025
We report a scalable, thermodynamically guided method for synthesizing germanium quantum dots embedded in a silicon oxide matrix with nanometer-scale precision. By engineering the oxidation and annealing conditions of silicon–germanium alloy layers, we achieved spatially confined, crystalline germanium quantum dots as small as 9.2 nanometers with tunneling oxide thicknesses down to 3.2 nanometers—suitable for room-temperature quantum confinement. Molecular dynamics simulations across a range of germanium compositions predict the agglomeration behaviour and size evolution of the quantum dots, while an analytical model enables predictive tuning of quantum dot dimensions and oxide thickness based on their initial alloy composition. Experimental validation using scanning transmission electron microscopy, X-ray diffraction, and photoluminescence spectroscopy confirms crystallinity and size-dependent optical emission in the visible range. In contrast to earlier nanocrystal memory systems that relied on randomly distributed germanium precipitates embedded deep in thick oxides, our method enables precise formation of shallow, single-layer quantum dots with controlled geometry. These findings establish a robust platform for room-temperature quantum dot electronics, combining tunable confinement and compatibility with integrated circuit architectures.
In solid-state systems, Ge nanocrystals spontaneously form in oxide matrices such as SiGeO during thermal processing. This phenomenon was originally discovered not in the pursuit of quantum control, but in the context of CMOS device fabrication, where Ge aggregation during SiGe oxidation complicated the formation of uniform gate dielectrics.9,10 Later, researchers repurposed this self-assembly behaviour for nonvolatile memory,11–14 emphasizing charge retention over control of size, position, or interface proximity. These early systems featured randomly distributed Ge precipitates, often embedded deep within thick oxide layers, and lacked the confinement precision required for fast, low-voltage quantum operations.15–18
The formation of Ge nanostructures through oxidation of SiGe alloys has been previously reported.19–21 In these earlier studies, polycrystalline SiGe layers embedded between oxides were oxidized, and Ge nanocrystals were formed within the oxide matrix during annealing steps. In contrast, our approach is designed to generate a single, spatially uniform layer of Ge QDs from a single SiGe layer directly on the Si substrate. The low temperature oxidation step is first used to convert the SiGe film into a homogeneous SiGeO layer while preserving a high-quality interface between SiGe and the oxide. Subsequent high temperature annealing then drives the self-limited condensation of Ge atoms into uniformly sized QDs. While both Si and Ge are oxidized at low temperatures, elevated annealing temperatures promote dissociation of Ge–O bonds, which are considerably less thermodynamically stable than Si–O bonds, thereby facilitating the precipitation of elemental Ge.16,22,23
Here, we advance this concept by demonstrating a deterministic, self-assembly-based strategy for producing spatially confined, crystalline Ge QDs within a SiOx matrix, positioned within 3.2 nm of the semiconductor interface. By carefully engineering the oxidation and double-step annealing of SiGe alloy layers, sub-10 nm Ge QDs are synthesized in a single plane, enabling tunable quantum confinement. The synthesis pathway is guided by molecular dynamics (MD) simulations and analytical modelling, allowing predictive design of QD size and tunnelling oxide thickness from the initial composition. Structural and photoluminescence characterization confirm quantum confinement effects at room temperature. The proposed synthesis method offers a practical and scalable approach for synthesizing Ge nanocrystal quantum dots (NCQDs) compatible with conventional Si-based technology. This work not only advances the understanding of selective oxidation and self-assembly mechanisms in the Si–Ge–O system but also provides a versatile platform for the fabrication of next-generation QD devices with broad applications in optoelectronics, memory, and sensing technologies.
The initial oxidation process differs from conventional thermal oxidation of silicon wafers; it employs a very low oxygen flow to form a precisely controlled nanometer-scale SiGeO alloy. As illustrated in Fig. 1, the process begins with the deposition of a SixGe1−x film by molecular beam epitaxy (MBE) or ultra-high vacuum chemical vapor deposition (UHV-CVD), ensuring compatibility with standard silicon processing. Thermal oxidation was performed at 550–600 °C in a tube furnace under near-atmospheric pressure (770 Torr) with pure O2 gas supplied at 20 sccm. In this low temperature regime, the diffusivities of Si and Ge decrease more sharply than the oxidation rate, allowing both elements to oxidize and form a homogeneous amorphous SiGeO alloy layer. By adjusting the oxidation duration, the thickness and composition of this intermediate layer can be precisely controlled.
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| Fig. 1 (a–d) Schematic overview of the Ge QD synthesis process. This process was followed in the experiments. | ||
To suppress further oxygen ingress during subsequent annealing, which may increase the thickness, a SiN capping layer was deposited by plasma-enhanced chemical vapor deposition (PECVD). Actually, any dense material that can block the oxygen passage would serve for this, and indeed, for certain samples prepared for X-ray diffraction (XRD), a TiN layer was first deposited via atomic layer deposition (ALD), followed by the same SiN capping process.
Post-oxidation, Ge NCQDs were formed through rapid thermal annealing (RTA) in nitrogen. Before annealing, the chamber was evacuated to ∼1 × 10−3 Torr and then backfilled with N2 to ∼1 × 10−1 Torr. Two RTA strategies were employed: (1) single-step annealing at 800 °C and (2) double-step annealing consisting of an initial high-temperature pulse at 1000 °C followed by a lower-temperature step at 700–800 °C. According to the previous studies,15 the reduction of GeOx is more promoted at higher temperature annealing, enabling the initial formation of Ge nanoparticles. As GeOx defects are reduced during the first annealing at 1000 °C, the subsequent growth of Ge QDs occurs with improved size uniformity and spatial distribution within the oxide matrix. Furthermore, the vacuum conditions and pure N2 ambient conditions prevented reoxidation of Ge, facilitating phase-pure NCQD growth.
A critical feature of this method is the ability to control the vertical position of the Ge QDs and the surrounding oxide thickness by adjusting the thickness and composition of the SiGeO alloy. In our process, the SiGe layer is directly oxidized at low temperature, deliberately forming a homogeneous SiGeO alloy. After depositing a SiN capping layer, high temperature annealing drives Ge extraction from the SiGeO alloy. Importantly, this approach obviates the need for a separate tunnelling oxide growth step; an ultrathin tunnelling oxide forms spontaneously as the remaining SiGeO is converted to SiO2 during the annealing process.
Controlling the oxidation time and the initial SiGe composition enables deterministic control over the final QD size and oxide thickness, as it dictates the absolute amount of available germanium for aggregation. Moreover, compared to ion implantation methods, which typically introduce germanium at concentrations below 1019 cm−3, this SiGe oxidation strategy offers much higher atomic densities (up to 1022 cm−3) and superior control over depth and spatial confinement. Achieving nanometer-scale vertical accuracy using ion implantation remains highly challenging, while our method enables intrinsic alignment near the channel region with sub-5 nm oxide encapsulation.
The formation of Ge NCQDs and their crystallinity were confirmed through structural and optical characterization. Cross-sectional scanning transmission electron microscopy (STEM) and X-ray diffraction (XRD) measurements were performed. The STEM imaging of single-step annealed samples (800 °C, 30 minutes) revealed Ge NCQDs with a rather broad spatial distribution. The average diameter turned out to be 3.7 nm, and the total oxide thickness was ∼12.0 nm (Fig. 3(b)). XRD results (Fig. 2) confirmed crystallinity with Bragg peaks corresponding to Ge(220) planes. The Ge(220) peak exhibited a full width at half maximum (FWHM) of 0.279°, further validating nanocrystal formation. Weak peaks at Ge(200) and (211) were also observed, which can be attributed to truncation effects and structural disorders arising from the nanoscale QD size.26,27
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| Fig. 3 Bright field STEM images of Ge NCQDs embedded in the oxide after (a and b) single-step annealing and (c and d) double-step annealing. | ||
The double-step annealing process appears to be more suitable to achieve improved spatial confinement for the controlled formation of QD arrays. For the double-step annealing process, the samples were first annealed at 1000 °C for 5 minutes, followed by a second step at 700 °C for 1 minute. This strategy leverages the enhanced mobility and reduction of GeOx at high temperature to seed NCQD formation, while the second step stabilizes the growth and improves uniformity. As shown in Fig. 3(d), this method yielded a single row of Ge NCQDs embedded in a 17.8 nm-thick oxide layer, with QD diameters of ∼9.2 nm and tunnelling oxide thickness as low as 3.2 nm. From the energy-dispersive spectroscopy (EDS) mapping in Fig. 4, a nicely formed single layer of QDs with an even spatial distribution can be clearly identified. The QDs are distinctly represented by the red colour, with the corresponding vacancies observed in the elemental maps of other atoms.
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| Fig. 4 EDS maps of the sample after double-step annealing. (a) Dark field STEM image. (b–d) Elemental distribution maps of Si, Ge and O corresponding to the STEM image. | ||
Temperature control, for example during the low temperature Si–Ge–O matrix formation and successive annealing, appeared to be critical. The temperature-dependent oxidation behaviour of SiGe/Si layers was experimentally investigated at two different temperatures (600 °C and 850 °C) under near-atmospheric conditions, as detailed in the SI. At 850 °C, preferential oxidation of Si leads to Ge accumulation and the formation of a Ge-rich layer (GRL) near the SiO2/SiGe interface (SI Fig. S3). In contrast, at 600 °C both Si and Ge oxidize, supporting SiGeO alloy formation. These observations align with prior thermodynamic studies and confirm the dual role of low temperature oxidation and high temperature annealing in producing confined crystalline Ge NCQDs. Consequently, the temperature-dependent behaviour of the Si–Ge–O system directly contributed to the formation of a single row of Ge NCQDs through the double-step annealing process.
| Sample A3 | Sample B3 | Sample C3 | ||||
|---|---|---|---|---|---|---|
| Peak (eV) | FWHM (eV) | Peak (eV) | FWHM (eV) | Peak (eV) | FWHM (eV) | |
| a | 2.283 ± 0.0015 | 0.271 | 2.281 ± 0.0008 | 0.226 | 2.255 ± 0.0011 | 0.216 |
| b | 2.604 ± 0.0015 | 0.227 | 2.588 ± 0.0007 | 0.212 | 2.568 ± 0.0014 | 0.234 |
| c | 2.885 ± 0.0016 | 0.251 | 2.877 ± 0.0009 | 0.224 | 2.824 ± 0.0015 | 0.207 |
| d | 3.167 ± 0.0045 | 0.207 | 3.149 ± 0.0025 | 0.179 | 3.138 ± 0.0027 | 0.304 |
| e | 3.466 ± 0.0137 | 0.361 | 3.412 ± 0.0038 | 0.222 | 3.400 ± 0.0021 | 0.059 |
It is worth noting that even QDs of the same nominal size may differ structurally. For example, small aggregates of Au or Pt atoms can exhibit confinement-like effects without crystallinity. However, such non-crystalline clusters would not behave as semiconductor QDs: their discretized levels would be much smaller, requiring much smaller sizes to account for the observed PL range. In contrast, the agreement of our PL spectra with the Brus formula, which assumes semiconductor effective masses derived from a periodic lattice, indicates that the Ge QDs here are at least partially crystalline. With respect to defects, only states within the band gap can contribute to PL, while states inside the bands are filled and inactive. The discrete energy levels we observed were much larger than typical defect-related energies, and no sub-gap peaks were detected, making it unlikely that intrinsic defect states are involved. One might also consider defect states in the Si or SiGe substrates; however, since both are indirect band gap materials and the observed PL emission is above 2 eV, it is unlikely that substrate-related defects contribute to the measured spectra.
A clear redshift in PL emission was observed with increasing Ge content—from Si0.8Ge0.2 to Si0.5Ge0.5—consistent with quantum confinement behaviour (Fig. 5(d)). As the Ge supply in the Si–Ge–O matrices increases, the QD size increases, and the effective bandgap narrows, leading to lower-energy emission.31 Based on the PL peak positions presented in Table 1, the estimated QD diameters ranged from ∼4 nm to ∼6 nm across all sample sets. The emission wavelengths, spanning 358–550 nm, demonstrate tunability within the visible spectrum through control of Ge content and annealing time.
These results underscore the role of annealing in achieving size-controlled QD formation. While 30 minutes of annealing was sufficient to produce crystalline Ge QDs, extending to 40 minutes yielded narrower and more reproducible PL peaks, indicating better size distribution and thermal stabilization. Collectively, the structural and optical data confirm that the Ge NCQDs exhibit pronounced quantum confinement effects and tunable optical properties at room temperature, positioning them as promising building blocks for integrated optoelectronic and quantum devices.
The samples were thermally annealed at 3000 K using an isothermal–isobaric (NPT) ensemble, a temperature below the melting point of Ge.33 Although this temperature exceeds realistic processing conditions, such elevated values are commonly used in MD simulations to accelerate atomic diffusion within computationally tractable timescales. Temperature and pressure were controlled via a Nosé–Hoover thermostat and barostat with damping constants of 100 and 1000, respectively, and a 1 fs timestep was used throughout.
After 100 ns of simulated annealing, the formation of nearly spherical Ge clusters in samples was observed with up to 30% Ge content (Fig. 6(f–h)). In the 30% Ge sample, a single Ge NCQD was clearly resolved. For samples with 40% and 50% Ge (Fig. 6(i and j)), partial agglomeration occurred, but additional annealing would be required to achieve full spherical confinement. As shown in Fig. 6(k–o), partial radial distribution functions (PRDFs) were calculated to assess the atomic structure. First-neighbour Ge–Ge correlation peaks were found at 2.53 Å (10% Ge), 2.63 Å (20%, 30%), 2.48 Å (40%), and 2.53 Å (50%), with a lack of well-defined second or third peaks, suggesting that the Ge NCQDs were predominantly amorphous under the simulated conditions. This is consistent with the limited timescales of MD simulations, which constrain the development of long-range crystalline order. The average radii of Ge NCQDs were estimated as 0.68 nm, 0.89 nm, and 1.83 nm for the 10%, 20%, and 30% Ge models, respectively. These results indicate a direct scaling relationship between Ge content and NCQD size, providing a predictive framework for tuning QD dimensions via compositional control of the starting Si1−xGexO2 alloy.
The MD simulations successfully predict general trends in QD formation behaviour, which were corroborated by experimental STEM and XRD analyses. For the quantitative QD formation modelling, an analytical model was derived to predict the radius of Ge NCQDs and the surrounding oxide thickness as functions of the Ge content in Si1−xGexO2 alloys. This model captures the redistribution of mass and volume during high-temperature annealing and provides a scalable framework for composition-driven NCQD design.
Assuming that the annealing time is enough so that most of the Ge atoms agglomerate, the mass and density relationships before and after annealing can be found. Besides, this assumption seems effective in most of the cases since we observed that 80–90% of the agglomeration was completed within 5–15 minutes of RTA. When the final NCQD radius is R and the tunnelling oxide thickness is d, which is equally distributed at the top and bottom of the NCQD, the initial volume of the SiGeO layer, Vinitial, and the final volume, Vfinal, of Ge QD and the surrounding SiO2 can be expressed in the following equations:
![]() | (1) |
![]() | (2) |
![]() | (3) |
![]() | (4) |
Here, t and t′ represent the cube lengths of the oxide before and after annealing, which are derived from the density difference between the GeOx and Ge QDs. N is the total number of Si and Ge atoms, while x is the Ge content of Si1−xGexO2 alloys. m and ρ are the atomic masses and material densities, respectively. Consequently, the tunnelling oxide thickness, d, can be determined using the final volume and the QD radius from eqn (2) and (3), and expressed in eqn (4).
Model predictions were validated against MD simulations and the experimental results. The analytical model yielded results closely matching the MD data (Table 2). The slight discrepancy in QD radius (∼0.25 nm) is attributed to the overestimation of Ge density in the MD simulation, likely due to the limited relaxation time following high-temperature annealing.
| x | Methods | α (t′/t) | R (nm) | d (nm) |
|---|---|---|---|---|
| 0.10 | Equation | 0.976 | 1.04 | 1.19 |
| Simulation | 0.947 | 0.68 | 0.49 | |
| 0.17 | Equation | 0.960 | 1.56 | 1.23 |
| Simulation | 0.938 | 1.33 | 1.39 | |
| 0.20 | Equation | 0.951 | 1.17 | 0.79 |
| Simulation | 0.888 | 0.88 | 0.95 | |
| 0.25 | Equation | 0.940 | 1.79 | 0.96 |
| Simulation | 0.889 | 1.60 | 1.00 | |
| 0.30 | Equation | 0.928 | 1.88 | 0.82 |
| Simulation | 0.887 | 1.75 | 0.83 | |
| 0.35 | Equation | 0.916 | 2.01 | 0.70 |
| Simulation | 0.870 | 1.70 | 0.88 |
The oxide length ratio α, defined as t′/t, depends only on the Ge content, x, and remains independent of system size. This parameter captures the volumetric shrinkage resulting from the densification and crystallization of Ge within the oxide. As x increases, the difference in oxide lengths becomes more pronounced. In Fig. 7, the MD data yielded results closely matching the analytical model with the slight underestimation in α, indicating that model predictions were validated against MD simulations for a 10–35% Ge alloy. For x = 0.3 in Fig. 6(h), the theoretical value of α was calculated to be 0.928, while the MD simulation yielded a slightly lower value of 0.887 due to the relatively small QD radius. When x = 0.2, the calculated ratio was 0.952 from the equations.
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| Fig. 7 Comparison of the oxide length ratios (α) obtained from simulations and experiments compared with the calculations from eqn (2)–(4). x represents the Ge content relative to Si in the SiGeO alloy. For the experimental results, the error bar denotes the standard deviation (±0.1). | ||
In experimental measurement in Fig. 7, the samples prepared by double-step annealing were closely fitted with the analytical model prediction. During oxidation, the Si0.5Ge0.5 substrate forms a SiGeO alloy containing ∼20% of Ge content. The Ge NCQD sample in Fig. 6 exhibits a slight overestimation of α (∼0.045) and an underestimation of R (∼0.13) as the Ge QDs were not fully crystallized and contained regions with GeOx boundaries. Consequently, the ratio increased to 0.997. Nevertheless, the enhanced Ge agglomeration achieved by double-step annealing ensures that the overall trend in both oxide length ratio and QD radius was consistent with the model's predictions.
The combination of MD simulations and experimental validation demonstrates that Ge NCQDs can be reliably synthesized within a SiOx matrix from our method. The MD simulations provide valuable insights into the agglomeration dynamics of Ge atoms, predicting the QDs’ sizes with different Ge contents. Experimental results corroborate these findings, showing that Ge NCQDs through the self-assembly method exhibit crystalline properties under optimized annealing conditions. Furthermore, the analytical model provides a reliable first-order tool for predicting both the QD size and surrounding oxide thickness as functions of initial alloy composition and processing. This modelling approach enables rational design of Ge QD-based structures with tailored geometry for quantum confinement and efficient charge transfer. It serves as a valuable foundation for implementing predictive control in quantum nanomaterial synthesis and device integration.
The double-step annealing process enabled the formation of spatially confined, single-row Ge NCQDs with a size of 9.2 nm, separated from the SiGe channel by oxide barriers as thin as 3.2 nm. Moreover, PL measurements confirmed size-dependent emission in the visible range, highlighting quantum confinement effects at room temperature. This work lays the foundation for materials-driven control of QD geometries, enabling a reproducible route toward next-generation QD technologies.
Supplementary information is available. See DOI: https://doi.org/10.1039/d5nr04252f.
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