# Innovative developpement of silicon germanium alloy enhanced with nanoprecipitates by additive manufacturing

Maxime Baudry, Guillaume Savelli, Guilhem Roux

## ► To cite this version:

Maxime Baudry, Guillaume Savelli, Guilhem Roux. Innovative developpement of silicon germanium alloy enhanced with nanoprecipitates by additive manufacturing. 2024 IEEE 14th International Conference Nanomaterials: Applications & Properties (NAP), Sep 2024, Riga, France. pp.1-7, 10.1109/NAP62956.2024.10739715. [hal-05444484](https://hal.science/hal-05444484v1)

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Submitted on 6 Jan 2026

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Innovative development of silicon germanium
alloy enhanced with nanoprecipitates by additive
manufacturing

Maxime Baudry
French Alternative Energies and
Atomic Energy Commission Laboratory
for Innovation in New Energies
Technologies and Nanotechnology
Grenoble, France
maxime.baudry@cea.fr

Guillaume Savelli
French Alternative Energies and
Atomic Energy Commission Laboratory
for Innovation in New Energies
Technologies and Nanotechnology
Grenoble, France
guillaume.savelli@cea.fr

Guilhem Roux
French Alternative Energies and
Atomic Energy Commission Laboratory
for Innovation in New Energies
Technologies and Nanotechnology
Grenoble, France
guilhem.roux@cea.fr

Thermoelectric (TE) devices is presented as an environmentally-friendly technology useful for several niche applications in electricity generation and cooling systems. Recent advances in additive manufacturing (AM) techniques, such as Laser Powder Bed Fusion (L-PBF), allow manufacturing of a wide range of materials, including TE materials. AM of TE materials open new possibilities in TE devices' shapes that can facilitate their integration and improve their performance.

This work presents the development of silicon germanium (SiGe) alloys by L-PBF process. The first attempt at producing this material resulted in a dense material with promising Seebeck coefficient and thermal conductivity, but its other properties were hindered by mechanical cracking occurring during L-PBF processing. To address this issue, a new approach was studied: nanoprecipitates formation during cooling. Nanoprecipitates can simultaneously enhance TE properties by scattering phonons, and enhance mechanical properties by acting as nucleating agents for silicon germanium matrix, and reduce grain size. It is the first time that such approach is studied in AM of TE materials.

A specific study has been performed to define the best nanoprecipitates candidates. Three systems of nanoprecipitates were retained: SiC, WSi2 and MoSi2. This work will present how these nanoprecipitates were chosen, then their impacts on SiGe structural and TE properties.

Keywords: Silicon-germanium; Thermoelectricity; Laser powder bed fusion; Nanocomposites; Additive manufacturing; Eco-friendly

I. INTRODUCTION

Faced with current environmental issues, the need for
fossil fuels-free ways of producing electricity is growing.
Thermoelectric (TE) effects encompass reversible
phenomena observed in both conductor and semi-conductor
materials that allow conversion of thermal energy into
electrical energy and vice-versa [1].

Thanks to the Seebeck effect, TE systems can act as voltage
generators while under temperature differences. Reliable
sources of temperature differences can be found in many
human facilities, where waste heat could be converted into
electricity with TE Generators (TEG). TEG involves only
motionless solid-state materials, and therefore require low
maintenance and are highly durable. Nowadays, the main

setback for TEG is their efficiency [2]. TEG efficiency
depends of three factors: TE figure of merit (ZT) of active
materials, defined by (1), device optimisation, and its
integration.

$$
ZT = \frac{\sigma S^2}{\kappa} T \quad (1)
$$

TE material's figure of merit at a temperature T depends of
its electrical conductivity σ, Seebeck coefficient S, and its
thermal conductivity κ. Device optimisation is achieved by
choosing the number of TE legs in the generator, or by
reducing electrical contact resistances between TE
components and metallic tracks. Device integration is
achieved by adjusting TEG to its environment to obtain the
highest thermal gradient between each TEG's ends.

Traditional manufacturing methods such as hot pressing, zone melting, or Spark Plasma Sintering (SPS) have enabled the production of cuboid-shaped TEGs. However, the limitations in shapes diversity restrict integration and yield potential of this technology. Consequently, there is a growing focus on leveraging Additive Manufacturing (AM) techniques for TE materials, aiming to overcome these constraints [3,4]. AM techniques enable also eco-friendly manufacturing compared to standard techniques thanks to a reduction of material losses during manufacturing. Among the various AM methods, Laser Powder Bed Fusion (L-PBF) stands out as a prominent approach for printing complex metal parts in small to medium series. L-PBF process uses powder as base material. To build part, powder is spread into a thin layer (typically 30µm thick) on a build plate, and then fused locally with a laser (Fig. 1). This process is then repeated layer by layer until reaching the full height of the object.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Illustration of laser powder bed fusion (L-PBF) process [5].</figcaption></figure>
Recent advances in L-PBF processing have paved the way for the fabrication of novel materials, including TE materials such as bismuth telluride [6-8] and Half-Heusler [9]. Our work presents the development of silicon germanium (SiGe) alloys TE material, tailored for applications at high temperatures. It is the first time that this material has been manufactured by L-PBF process. The first developments for this material manufacturing resulted in dense samples with promising Seebeck coefficient and thermal conductivity but low electrical conductivity. This low values were attributed to the high density of cracks present in all samples. These cracks were then identified as mechanical cracking occurring during L-PBF processing due to material induced stresses [10].

Grain refining can be achieved in L-PBF by introducing other elements into the powder [11], that can form precipitates that presents interfaces which promotes SiGe nucleation. More nucleation leads to the formation of smaller grains, that can withstand better mechanical stress during processing.

Moreover, if nucleating agents precipitates are sufficiently small (<100nm) they could also enhance TE properties by scattering phonons. Several works on SiGe manufactured with current processing methods show a reduction of thermal conductivity thanks to phonon scattering on nanoinclusions [12-17].

Research works on the role of inclusions in SiGe matrix focus mainly on silicides (SiₓMᵧ, with M being a transition metal) [18], as they are chemically stable with SiGe. However, currently there is no study discussing the use of these crystalline phases as nucleating agents for SiGe.

Bathula et al. [19] showed record ZT=1.7 at 900°C and mechanical properties enhancement in N-doped SiGe with SiC nanoinclusions produced by SPS. Mackey et al. [12] presents also an improvement of ZT with the addition of WSi₂ nanoinclusions in SiGe N-doped and P-doped samples obtained by SPS.

This work presents a study of SiGe grain refining with selected precipitates. It is the first time that grain refining is studied in L-PBF processed of TE materials. As there is currently no data on the use of nucleating agents with SiGe, a specific study was performed to define the best candidates for SiGe grain refining. Three systems of precipitates were retained, based on SiC, WSi₂ and MoSi₂ precipitates. This work will present how these precipitates were chosen, and then, their impacts on SiGe structural and TE properties will be discussed.

## II. MATERIALS & METHODS

### A. Precipitates selection

Two criteria are essential to achieve grain refining with nucleating agents in L-PBF:

- 1) Nucleant phase must exist within the melt before matrix solidification.

- 2) Nucleant phase must present interfaces with the liquid that promotes matrix nucleation.

To meet criterion 1) in L-PBF processing, either nucleant phase is introduced directly in the powder and stays stable during all processing, or either nucleant phase forms during processing by precipitation before matrix solidification.

In the second case, this means that nucleant phase must form before matrix starting solidification. Therefore, nucleant phase solidification temperature must be higher than matrix. In this study, SiGe Si-rich phase matrix liquidus temperature is 1408°C. In L-PBF process, it is difficult to predict which phase forms preferentially, as high solidification speeds can promote unstable phases formation, high undercooling, and high melt pool temperature.

Mechanisms underlying grain refinement were extensively studied in the case of Al alloys grain refining [20-22], discussing the influence of several factors: contact angle between nucleant and liquid, interactions between nucleant particles and alloy chemistry, settling of nucleant particles, nucleant particles geometry, etc. Nucleant particles size, number and crystallographic matching between matrix and nucleant were found to be the most critical parameters in controlling the efficiency of grain refinement in Al alloys. As no data is available for silicon germanium alloys, this study uses only crystallographic matching between matrix and nucleant as selection criterion.

Zur and McGill designed an algorithm (Fig 2a) that compares two 2D lattices with different atomic arrangement, and determine if there is a geometrical "lattice match" between them [23]. On a delimited area within each 2D lattices, the algorithm tries to form two superlattices cells with the closest vector length and angles. If area ratios, vector lengths differences and angle differences between superlattices are smaller than a tolerance chosen by the user, the algorithm consider the two lattices as a geometrical "lattice match". This algorithm proved useful to investigate crystallographic compatibility between two crystalline planes in epitaxial growth studies [24-26]. Although the presence of a lattice match between two surfaces is known as neither sufficient nor necessary for heteroepitaxial growth, as other phenomenon such as interfacial chemistry play a significant role, this algorithm was used to verify poor match between undesired orientations and the substrate.

The algorithm used in this work consider all crystal lattices that can be built with {0; 1; -1} miller indices values planes in nucleant and SiGe crystal structures. Then, for each possible pair of nucleant and SiGe planes, Zurr and McGill's algorithm is checked and the number of lattice matches obtained between the two crystal structures is calculated. Nucleant phases with high number of lattices matches with SiGe are likely to present orientation relationship that successfully promotes matrix nucleation. Therefore the number of lattice matches is used as an indicator for criterion 2). Nucleant phases files from materials' project database (Table 1) were tested with the algorithm for lattice matches with a SiGe diamond phase with lattice parameter a=5.44Å.

<table><caption>TABLE I. ALGORITHM PARAMETERS AND CRYSTAL STRUCTURES SOURCE FILES</caption><thead><tr><th colspan="5">Zur & Mc Gill algorithm parameters</th></tr><tr><th>max area</th><th>area ratio tolerance</th><th>Δ length tolerance</th><th>Δ angle tolerance</th><th></th></tr></thead><tbody><tr><td>400Å</td><td>0.09</td><td>0.03Å</td><td>0.01°</td><td></td></tr><tr><th colspan="5">Database files</th></tr><tr><th>NiSi<sub>2</sub></th><th>SiC</th><th>MoSi<sub>2</sub></th><th>WSi<sub>2</sub></th><th>CrSi<sub>2</sub></th></tr><tr><td>mp-2291</td><td>mp-8062</td><td>mp-2592</td><td>mp-1620</td><td>mp-1222</td></tr><tr><th>Mg<sub>2</sub>Si</th><th>MnSi</th><th>V<sub>2</sub>Si<sub>3</sub></th><th>W</th><th>Mo</th></tr><tr><td>mp-1367</td><td>mp-1431</td><td>mp-570483</td><td>mp-91</td><td>mp-129</td></tr></tbody></table>
<figure><img src="image_3.png" /><figcaption>Fig. 2. Illustration of Zur & McGill's algorithm</figcaption></figure>

Table 2 shows nucleant performances with criteria 1) and 2). The three phases that meet criterion 1) requirements and have the highest number of lattice matches are SiC, MoSi₂, and WSi₂. These three precipitates were already studied in literature as inclusions in SiGe matrix [12,13], [19], [27-30], showing phonon scattering behaviours. In the case that Mo and W elements stays in their metallic form during L-PBF processing, their high number of lattice matches with SiGe suggest that they could also act as good nucleants.

## B. Powder preparation

To add respectively C, W and Mo elements to the SiGe base powder, nanoparticles of SiC, W and Mo were mixed with the base powder with a T2C© tumbler mixer.

<table><caption>TABLE II. NUCLEANT PERFORMANCES WITH CRITERIA 1 AND 2</caption><thead><tr><th rowspan="2">Nucleant</th><th colspan="2">Performances</th></tr><tr><th>Criterion 1</th><th>Criterion 2</th></tr></thead><tbody><tr><td>NiSi<sub>2</sub></td><td>Not met ; T<sub>sol</sub> SiGe &gt; T<sub>sol</sub> NiSi<sub>2</sub></td><td>673 lattice matches</td></tr><tr><td>SiC</td><td>Met, SiC lowest formation enthalpy of Si-Ge-C system</td><td>520 lattice matches</td></tr><tr><td>MoSi<sub>2</sub></td><td>Met, MoSi<sub>2</sub> lowest formation enthalpy of Si-Ge-Mo system</td><td>303 lattice matches</td></tr><tr><td>WSi<sub>2</sub></td><td>Met, WSi<sub>2</sub> lowest formation enthalpy of Si-Ge-W system</td><td>278 lattice matches</td></tr><tr><td>CrSi<sub>2</sub></td><td>Met, CrSi<sub>2</sub> lowest formation enthalpy of Si-Ge-Mg system</td><td>277 lattice matches</td></tr><tr><td>Mg<sub>2</sub>Si</td><td>Met, Mg<sub>2</sub>Si lowest formation enthalpy of Si-Ge-Mg system</td><td>264 lattice matches</td></tr><tr><td>MnSi</td><td>Met, MnSi lowest formation enthalpy of Si-Ge-Mn system</td><td>108 lattice matches</td></tr><tr><td>V<sub>5</sub>Si<sub>3</sub></td><td>Met, V<sub>5</sub>Si<sub>3</sub> lowest formation enthalpy of Si-Ge-V system</td><td>23 lattice matches</td></tr><tr><td>Mo</td><td>Met if no formation of complex between Si Ge and Mo</td><td>615 lattice matches</td></tr><tr><td>W</td><td>Met if no formation of complex between Si Ge and W</td><td>617 lattice matches</td></tr></tbody></table>

Nanoparticles can be coated on coarser SiGe particles thanks to static gripping, which allows to mix evenly elements to the base powder while retaining some properties of the base powder, like particles morphology.

Base SiGe powder was produced by gas-atomisation, and has been P-doped with boron. Table 3 shows SiGe base powder's characteristics and Fig. 3 shows SiGe base powder Scanning Electron Microscope (SEM) image. As germanium is costly, this base powder is slightly less rich in germanium than the more common Si<sub>80</sub>Ge<sub>20</sub> composition. Even if this powder displays poor flowability, it is still usable with L-PBF device equipped with a roller recoating system.

The objective with this study is to incorporate as much added element with nanoparticles, to identify more easily precipitates' nature and their effects. Then, nanoparticles to base powder ratios were calculated to saturate SiGe particle's surface with nanoparticles. Table 4 summarises powder to SiGe ratios. Mixing times were respectively 1h for the SiGe+SiC mix and 3h for SiGe+W and SiGe+Mo. Fig. 4 shows SEM images of SiGe particles coated with nanoparticles, which confirms static gripping was successful for the three types of nanoparticles.

## C. Material densification

Powder mixes and base powder were processed by L-PBF with a ProX200 device from 3D Systems©. Printing parameters developed for SiGe processing in previous works [10], [31] (Table 5) were used to print samples on four different plates with the four powder mixes.

<table><caption>TABLE III. SiGe BASE POWDER MEASURED PROPERTIES</caption><thead><tr><th colspan="4">Chemical Composition</th></tr><tr><th>%at Si</th><th>%at Ge</th><th>%at B</th><th>%at O</th></tr></thead><tbody><tr><td>83</td><td>16</td><td>1,1</td><td>0,09</td></tr><tr><th colspan="4">Granulometry</th></tr><tr><th>d10</th><th>d50</th><th>d90</th><th>Span</th></tr><tr><td>11µm</td><td>22µm</td><td>55µm</td><td>2,0</td></tr><tr><th colspan="4">Morphology</th></tr><tr><th>10%</th><th>50%</th><th>90%</th><th></th></tr><tr><td>0,70</td><td>0,90</td><td>0,97</td><td></td></tr><tr><th colspan="4">Density</th></tr><tr><td>Pycnometer density (g.cm<sup>-1</sup>)</td><td colspan="3">2,76</td></tr><tr><td>Apparent density (g.cm<sup>-1</sup>)</td><td colspan="3">1,39</td></tr><tr><td>Tapped density (g.cm<sup>-1</sup>)</td><td colspan="3">1,90</td></tr><tr><th colspan="4">Flowability</th></tr><tr><td>Carr index</td><td colspan="3">27,2</td></tr><tr><td>Avalanche angle</td><td colspan="3">53,3°</td></tr><tr><td>Flowability qualification</td><td colspan="3">Poor flowability</td></tr><tr><th colspan="4">Laser absorption</th></tr><tr><td colspan="4">93% at λ = 1064nm</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 3. SEM image of SiGe base powder</figcaption></figure>
### D. Characterisation techniques

Chemical composition of samples and powder was characterized by Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). Powder granulometry and morphology were measured respectively with a Master sizer 2000 granulometer and a mopho-granulometer G3 from Malvern instruments©. Pycnometer powder density was measured with an Accupyc1340 from Micrometric instruments. Powder apparent and tapped densities were measured according to standard 3923-2. Avalanche angle was measured with a revolution mercury scientific rotating drum. Finally, laser absorption was measured with the Lambda 950 UV-Vis-NIR spectrometer from Perkin Elmer©. Samples microstructures were investigated with X-ray diffraction (XRD) with D8 advance diffractometer from Bruker and SEM LEO 1530 from SEMtechsolutions©. Samples density was measured with Archimedes method. Electrical conductivity and Seebeck coefficient were measured with ZEM3 from Ulvac©.

## III. RESULTS AND DISCUSSION

### A. Phase identification

Fig. 5 shows XRD spectra from samples processed with base powder and powder mixes. All samples display peaks corresponding to two SiGe phases with different stoichiometry. A Si-rich phase with a lattice parameter a=5,44Å, and a Ge-rich phase with a lattice parameter a=5,51Å.

<table><caption>TABLE IV. NANOPARTICLES TO BASE POWDER RATIOS</caption><thead><tr><th colspan="3">Nanoparticles to base powder weight ratios</th></tr><tr><th>L-PBF Sample 2</th><th>L-PBF Sample 3</th><th>L-PBF Sample 4</th></tr><tr><th>SiC wt%</th><th>W wt%</th><th>Mo wt%</th></tr></thead><tbody><tr><td>2,0</td><td>10,1</td><td>5,8</td></tr></tbody><thead><tr><th colspan="3">Nanoparticles to base powder volume ratios</th></tr><tr><th>L-PBF Sample 2</th><th>L-PBF Sample 3</th><th>L-PBF Sample 4</th></tr><tr><th>SiC vol%</th><th>W vol%</th><th>Mo vol%</th></tr></thead><tbody><tr><td>0,9</td><td>0,8</td><td>0,8</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 4. SEM images of a. base powder, b. base powder mixed with W nanoparticles, c. base powder mixed with Mo nanoparticles, and d. base powder mixed with SiC nanoparticles.</figcaption></figure>

SiGe lattice parameter a can be expressed as a function of Ge content thanks to (2) [32]:

$$a = 5,431 + 0,20x + 0,027x^2 \quad (2)$$

With x corresponding to Ge at%. From this equation, Si and Ge content can be deduced for these two phases. The Si-rich and Ge-rich phases calculated stoichiometry are $Si_{96}Ge_{04}$ and $Si_{63}Ge_{37}$ respectively.

All L-PBF processed samples display [220] and [440] peaks more pronounced than other SiGe peaks, which reflect strong anisotropy within these samples.

Peaks corresponding to desired precipitate phase (SiC, WSi₂ and MoSi₂) are observed in their respective samples, which confirms success of their formation.

Table 6 shows chemical composition of L-PBF processed samples. All samples chemical compositions correspond to aimed values, with no signs of strong vaporisations for Ge,C, W and Mo elements.

### B. Microstructure

Fig 6 shows SEM images from samples microstructure. SiGe samples processed by L-PBF exhibits columnar solidification structures with Si-rich phase at the centre and Ge-rich phase at the edge, which appear brighter (Fig. 6a).

<table><caption>TABLE V. PRINTING PARAMETERS</caption><thead><tr><th>Printing parameters</th><th>Set 1</th><th>Set 2</th><th>Set 3</th><th>Set 4</th><th>Set 5</th></tr></thead><tbody><tr><td>Laser power (W)</td><td>117</td><td>125</td><td>125</td><td>125</td><td>131</td></tr><tr><td>Scan speed (mm.s<sup>-1</sup>)</td><td>350</td><td>300</td><td>350</td><td>400</td><td>350</td></tr><tr><td>Hatch (μm)</td><td>45</td><td>45</td><td>45</td><td>45</td><td>45</td></tr><tr><td>Layer thickness (μm)</td><td>30</td><td>30</td><td>30</td><td>30</td><td>30</td></tr><tr><td>Volumic energy density (J.mm<sup>-3</sup>)</td><td>248</td><td>309</td><td>265</td><td>231</td><td>277</td></tr></tbody></table>

<table><caption>TABLE VI. L-PBF SAMPLES CHEMICAL COMPOSITION</caption><thead><tr><th></th><th>L-PBF<br>Sample 1</th><th>L-PBF<br>Sample 2</th><th>L-PBF<br>Sample 3</th><th>L-PBF<br>Sample 4</th></tr></thead><tbody><tr><td>Si %at</td><td>84</td><td>82</td><td>83</td><td>82</td></tr><tr><td>Ge %at</td><td>15</td><td>15</td><td>15</td><td>14</td></tr><tr><td>B %at</td><td>1.0</td><td>1.0</td><td>1.1</td><td>1.1</td></tr><tr><td>C %at</td><td>/</td><td>1.9</td><td>/</td><td>/</td></tr><tr><td>W %at</td><td>/</td><td>/</td><td>1.3</td><td>/</td></tr><tr><td>Mo %at</td><td>/</td><td>/</td><td>/</td><td>2.0</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Fig. 5. XRD measurements on L-PBF samples and SiGe base powder.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 6. SEM images of L-PBF samples as built.</figcaption></figure>

Inclusions in SiGe are visible in Fig. 6b to 6d and are likely to be precipitates of SiC, WSi₂, and MoSi₂ respectively. EDS maps of the elements C, W and Mo corroborates this hypothesis. Visible precipitates size varies from less than 1µm to 2µm in samples 2 and 4, up to 6µm in sample 3. In samples 3 and 4, some precipitates are located at the center of Si-rich solidification structures. Further observations at smaller scale would be interesting, as grain refining is generally induced by smaller precipitates. In these two samples, a slight reduction of solidification structures size can still be observed, which supports the hypothesis of WSi₂, and MoSi₂ precipitates acting as nucleating agents for SiGe.

Fig 7 shows EBSD maps of samples 1, 3 and 4, displaying grain orientations relative to building direction (BD) and grain boundaries. Along BD, grains with orientation close to [101] are predominant on all samples. This preferential orientation corroborates XRD measurements and was also observed in earlier works on SiGe processed by L-PBF [10]. EBSD maps confirms a slight grain size reduction observed with all samples with precipitates. Unfortunately, this reduction did not stop cracks formation, as cracks are still visible in all samples.

<figure><img src="image_8.png" /><figcaption>Fig. 7. EBSD maps of L-PBF samples 1, 3 and 4.</figcaption></figure>

### C. TE properties

Fig 8 shows Seebeck coefficient and electrical conductivity of L-PBF samples measured perpendicular to building direction. Contrary to what was observed in earlier works on L-PBF of N-type SiGe [10], Seebeck coefficient of as built L-PBF P-type samples is lower than zone melted P-type SiGe. Between zone melted and L-PBF samples, the amount of doping elements and their degree of activation in the matrix may not be same, which may explain this difference. Moreover, Si-rich and Ge-rich regions in L-PBF as built microstructures may less scatter low energy carriers than a more disordered homogenous SiGe phase of the same average composition. Finally SiC, WSi₂ and MoSi₂ precipitates seem to have little to no effect on Seebeck coefficient [33].

Electrical conductivity in L-PBF samples is one magnitude lower than zone melted reference samples. Low electrical conductivities are attributed to cracks, that are still present in all L-PBF samples. Electrical conductivities of L-PBF Si₈₅Ge₁₅ samples are slightly higher than L-PBF Si₈₀Ge₂₀ samples from previous works. Lower Ge content may explain this difference as carrier mobility is enhanced, but it is difficult to decouple that effect from others factors such as doping level, or variance of cracks density within samples. Sample 4 with MoSi₂ display slightly higher electrical conductivity than other L-PBF processed samples, but it may also be the result of cracks density variance within samples.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Seebeck coefficient and electrical conductivity measured on L-PBF as built samples in comparison to the first L-PBF samples, made with N-doped Si₈₀Ge₂₀ [10] and zone melted Si₈₅Ge₁₅ P-doped samples [32].</figcaption></figure>
Power factor PF, was calculated with Seebeck coefficient and electrical conductivity values thanks to equation (3):

$$PF = \sigma \times S^2 \quad (3)$$

Power factor of L-PBF samples are still lower than zone melted reference samples due to their low electrical conductivity. However, no significant variation was observed between L-PBF samples, which suggest that the effect of precipitates on power factor is negligible in comparison to the effect of cracks.

<figure><img src="image_10.png" /><figcaption>Fig. 9. Power factor of L-PBF as built samples in comparison to zone melted Si<sub>85</sub>Ge<sub>15</sub> P-doped samples [32].</figcaption></figure>

## CONCLUSION

This study constitutes the first attempt at achieving grain refining of a TE material in L-PBF processing. Nucleants for SiGe grain refining were selected through a method involving Zur & McGill algorithm, which can prove useful for nucleating agents prospection. Samples with SiC, WSi<sub>2</sub> and MoSi<sub>2</sub> nanoprecipitates were produced. Precipitates ranging from 2 to less than 1µm were visible on SEM images, with some MoSi<sub>2</sub> and WSi<sub>2</sub> at the center of SiGe solidification structures. Slight grain refining is observed on samples with precipitates, but it wasn't enough to reduce cracks formation, as a high number of cracks is still present on all samples. Finally, the impact of precipitates on power factor seem to be negligible in comparison to the effect of cracks. Further studies need to be done to investigate the effect of precipitates on SiGe samples thermal conductivity.

Overall, this work shows an occurrence of precipitates on TE matrix that does not reduce power factor. If thermal conductivity reduction is successfully achieved with these precipitates, this may result in ZT improvement. Similar approaches could then be studied on other TE materials such as Bi<sub>2</sub>Te<sub>3</sub> with the objective to improve ZT in L-PBF processed samples.

## ACKNOWLEDGMENT

The research leading to these results has been performed within the project FASTE and received funding from the French Research Agency program under Grant Agreement n° ANR-22-CE50-0021

## REFERENCES

[1] D. M. Rowe, Éd., CRC handbook of thermoelectrics. Boca Raton, FL: CRC Press, 1995.

[2] D. Champier, «Générateurs thermoélectriques: de la conception aux applications », Conversion de l'énergie électrique, mars 2018, doi: 10.51257/a-v1-d3241.

[3] Y. Du, J. Chen, Q. Meng, Y. Dou, J. Xu, et S. Z. Shen, «Thermoelectric materials and devices fabricated by additive manufacturing », Vacuum, vol. 178, p. 109384, août 2020, doi: 10.1016/j.vacuum.2020.109384.

[4] D. Zhang, W. Y. S. Lim, S. S. F. Duran, X. J. Loh, et A. Suwardi, «Additive Manufacturing of Thermoelectrics: Emerging Trends and Outlook », ACS Energy Lett., vol. 7, n° 2, p. 720-735, févr. 2022, doi: 10.1021/acsenergylett.1c02553.

[5] A. Wiberg, Towards Design Automation for Additive Manufacturing: A Multidisciplinary Optimization approach. 2019, doi: 10.3384/lic.diva-160888.

[6] R. Zhan et al., « Large-scale SHS based 3D printing of high-performance n-type BiTeSe: Comprehensive development from materials to modules », Materials Today Physics, vol. 24, p. 100670, mai 2022, doi: 10.1016/j.mtphys.2022.100670.

[7] J. Qiu et al., « 3D Printing of highly textured bulk thermoelectric materials: mechanically robust BiSbTe alloys with superior performance », Energy Environ. Sci., vol. 12, n° 10, p. 3106-3117, oct. 2019, doi: 10.1039/C9EE02044F.

[8] Q. Hu, D. Luo, J. Guo, et W. Qiu, « 3D Printing of Bi2Te3-Based Thermoelectric Materials with High Performance and Shape Controllability », ACS Appl. Mater. Interfaces, vol. 15, n° 32, p. 38623-38632, août 2023, doi: 10.1021/acsami.3c08116.

[9] Y. Yan et al., «Thermoelectric properties of n-type ZrNiSn prepared by rapid non-equilibrium laser processing », RSC Adv., vol. 8, n° 28, p. 15796-15803, avr. 2018, doi: 10.1039/C8RA00992A.

[10] M. Baudry, G. Savelli, et G. Roux, « 3D printing of bulk thermoelectric materials: Laser powder bed fusion of N-type silicon germanium », Materials Science and Engineering: B, vol. 298, p. 116897, déc. 2023, doi: 10.1016/j.mseb.2023.116897.

[11] S. Dépinoy, «Fabrication Additive - Métallurgie hors équilibre et traitements thermiques - Master Design des Matériaux et Structures », J. Mackey, F. Dynys, et A. Sehirlioglu, « Si/Ge-WSi2 composites: Processing and thermoelectric properties », Acta Materialia, vol. 98, p. 263-274, oct. 2015, doi: 10.1016/j.actamat.2015.07.025.

[12] K. Favier et al., «Influence of in situ formed MoSi2 inclusions on the thermoelectrical properties of an N-type silicon-geranium alloy », Acta Materialia, vol. 64, p. 429-442, févr. 2014, doi: 10.1016/j.actamat.2013.10.062.

[13] G. Bernard-Granger et al., «Thermoelectric properties of an N-type silicon-geranium alloy related to the presence of silica nodules dispersed in the microstructure », Scripta Materialia, vol. 93, p. 40-43, déc. 2014, doi: 10.1016/j.scriptamat.2014.08.026.

[14] S. Ahmad et al., « Boosting thermoelectric performance of p-type SiGe alloys through in-situ metallic YSi2 nanoinclusions », Nano Energy, vol. 27, p. 282-297, sept. 2016, doi: 10.1016/j.nanoen.2016.07.002.

[15] M. Omprakash et al., «Enhancement of the Thermoelectric Performance of Si-Ge Nanocomposites Containing a Small Amount of Au and Optimization of Boron Doping », J. Electron. Mater., vol. 49, n° 5, p. 2813-2824, mai 2020, doi: 10.1007/s11664-019-07857-5.

[16] M. Omprakash et al., «Au and B co-doped p-type Si-Ge nanocomposites possessing ZT = 1.63 synthesized by ball milling and low-temperature sintering », Jpn. J. Appl. Phys., vol. 58, n° 12, p. 125501, nov. 2019, doi: 10.7567/1347-4065/ab4fb9.

[17] M. Omprakash et al., «Au and B doped p-type Si-Ge nanocomposites possessing ZT = 1.63 synthesized by ball milling and low-temperature sintering », Jpn. J. Appl. Phys., vol. 58, n° 12, p. 125501, nov. 2019, doi: 10.7567/1347-4065/ab4fb9.

[18] N. Mingo, D. Hauser, N. P. Kobayashi, M. Plissonnier, et A. Shakouri, « “Nanoparticle-in-Alloy” Approach to Efficient Thermoelectrics: Silicides in SiGe », Nano Lett., vol. 9, n° 2, p. 711-715, févr. 2009, doi: 10.1021/nl8031982.

[19] S. Bathula, M. Jayasimhadri, B. Gahtori, A. Kumar, A. K. Srivastava, et A. Dhar, «Enhancement in thermoelectric performance of SiGe nanoalloys dispersed with SiC nanoparticles », Phys. Chem. Chem. Phys., vol. 19, n° 36, p. 25180-25185, sept. 2017, doi: 10.1039/C7CP04240J.

[20] A. L. Greer, A. M. Bunn, A. Tronche, P. V. Evans, et D. J. Bristow, «Modelling of inoculation of metallic melts: application to grain refinement of aluminium by Al-Ti-B », Acta Materialia, vol. 48, n° 11, p. 2823-2835, juin 2000, doi: 10.1016/S1359-6454(00)00094-X.

[21] M. Easton et D. StJohn, «Grain refinement of aluminum alloys: Part I. the nucleant and solute paradigms—a review of the literature», J. Mater. Sci. Mater. A, vol. 32, n° 10, p. 1171-1179, oct. 2013, doi: 10.1007/s11711-013-0119-9.
*Metall Mater Trans A*, vol. 30, n° 6, p. 1613-1623, juin 1999, doi: 10.1007/s11661-999-0098-5.

[22] F. Wang, D. Qiu, Z. Liu, J. Taylor, M. Easton, et M. Zhang, « Crystallographic study of grain refinement of Al by Nb addition », *Journal of Applied Crystallography*, vol. 47, avr. 2014, doi: 10.1107/S1600576714004476.

[23] A. Zur et T. C. McGill, « Lattice match: An application to heteroepitaxy », *Journal of Applied Physics*, vol. 55, n° 2, p. 378-386, janv. 1984, doi: 10.1063/1.333084.

[24] L. J. Chen et K. N. Tu, « Epitaxial growth of transition-metal silicides on silicon », *Materials Science Reports*, vol. 6, n° 2, p. 53-140, mars 1991, doi: 10.1016/0920-2307(91)90004-7.

[25] J. E. Mahan et al., « Epitaxial films of semiconducting FeSi2 on (001) silicon », *Applied Physics Letters*, vol. 56, n° 21, p. 2126-2128, mai 1990, doi: 10.1063/1.103235.

[26] W. T. Lin et L. J. Chen, « Localized epitaxial growth of WSi2 on silicon », *Journal of Applied Physics*, vol. 59, n° 10, p. 3481-3488, mai 1986, doi: 10.1063/1.336818.

[27] N. K. Upadhyay et al., « Facile synthesis of earth-abundant and non-toxic p-type Si96B4/SiCp nanocomposites with enhanced thermoelectric performance », *Materials Science in Semiconductor Processing*, vol. 75, p. 234-238, mars 2018, doi: 10.1016/j.mssp.2017.11.039.

[28] X.-Y. Yang, J.-H. Wu, D.-D. Ren, T.-S. Zhang, et L.-D. Chen, « Microstructure and thermoelectric properties of p-type Si80Ge20B0.6-SiC nanocomposite », *Wuji Cailiao Xuebao/Journal of Inorganic Materials*, vol. 31, n° 9, p. 997-1003, 2016, doi: 10.15541/jim20160060.

[29] J. Stoetzel et al., « Microstructure and thermoelectric properties of Si-WSi2 nanocomposites », *Acta Materialia*, vol. 125, p. 321-326, févr. 2017, doi: 10.1016/j.actamat.2016.11.069.

[30] F. W. Dynys, A. Sayir, J. Mackey, et A. Sehirlioglu, « Thermoelectric properties of WSi2-SixGe1-x composites », *Journal of Alloys and Compounds*, vol. 604, p. 196-203, août 2014, doi: 10.1016/j.jallcom.2014.03.133.

[31] M. Baudry, G. Savelli, et G. Roux, « Development Of Bulk Thermoelectric N-Type Sige Alloy By Laser Powder Bed Fusion », présenté à World PM 2022 Congress Proceedings, 2022.

[32] J. P. Dismukes, L. Ekstrom, E. F. Steigmeier, I. Kudman, et D. S. Beers, « Thermal and Electrical Properties of Heavily Doped Ge-Si Alloys up to 1300°K », *Journal of Applied Physics*, vol. 35, n° 10, p. 2899-2907, oct. 1964, doi: 10.1063/1.1713126.

[33] N. M. Ravindra, B. Jariwala, A. Bañobre, et A. Maske, « Thermoelectric Properties of Silicon-Germanium Alloys », in *Thermoelectrics: Fundamentals, Materials Selection, Properties, and Performance*, N. M. Ravindra, B. Jariwala, A. Bañobre, et A. Maske, Éd., in SpringerBriefs in Materials, Cham: Springer International Publishing, 2019, p. 49-67. doi: 10.1007/978-3-319-96341-9_4.