Tania
Claudio
ab,
Niklas
Stein
c,
Daniel G.
Stroppa
d,
Benedikt
Klobes
a,
Michael Marek
Koza
e,
Petra
Kudejova
f,
Nils
Petermann
c,
Hartmut
Wiggers
c,
Gabi
Schierning
c and
Raphaël P.
Hermann
*ab
aJülich Centre for Neutron Science JCNS and Peter Grünberg Institut PGI, JARA-FIT, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany. E-mail: r.hermann@fz-juelich.de; Fax: +49 (0) 2461 61 2610; Tel: +49 (0) 2461 61 4786
bFaculté des Sciences, Université de Liège, B-4000 Liège, Belgium
cFaculty of Engineering and Center for Nano-integration Duisburg-Essen (CENIDE), University of Duisburg-Essen, D-47057, Duisburg, Germany
dPeter Grünberg Institut PGI-5, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
eInstitut Laue Langevin, 6 rue Jules Horowitz B.P. 156, F-38042 Grenoble, France
fTechnische Universitt München, Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM II), Lichtenbergstr. 1, D-85747 Garching, Germany
First published on 21st May 2014
Silicon has several advantages when compared to other thermoelectric materials, but until recently it was not used for thermoelectric applications due to its high thermal conductivity, 156 W K−1 m−1 at room temperature. Nanostructuration as means to decrease thermal transport through enhanced phonon scattering has been a subject of many studies. In this work we have evaluated the effects of nanostructuration on the lattice dynamics of bulk nanocrystalline doped silicon. The samples were prepared by gas phase synthesis, followed by current and pressure assisted sintering. The heat capacity, density of phonons states, and elastic constants were measured, which all reveal a significant, ≈25%, reduction in the speed of sound. The samples present a significantly decreased lattice thermal conductivity, ≈25 W K−1 m−1, which, combined with a very high carrier mobility, results in a dimensionless figure of merit with a competitive value that peaks at ZT ≈ 0.57 at 973 °C. Due to its easily scalable and extremely low-cost production process, nanocrystalline Si prepared by gas phase synthesis followed by sintering could become the material of choice for high temperature thermoelectric generators.
Single-crystalline and undoped silicon has a very high thermal conductivity, 156 W K−1 m−1 at room temperature,2 related to its low density and high Young's modulus. In heavily doped silicon, the thermal conductivity is significantly reduced, though still very high, close to 80 W K−1 m−1, at room temperature.3 As a direct result of its lattice structure with stiff tetrahedral covalent bonds connecting the atoms, it is a hard but brittle material.
Nanostructuration as means to improve the thermoelectric properties of a material has been intensively studied,4 since such processing decreases the lattice thermal conductivity by creating additional scattering centers for phonons at grain boundaries. By influencing mostly the lattice contribution to the thermal conductivity without also decreasing the electronic contribution, which is directly related to the electrical conductivity, an improvement in the dimensionless thermoelectric figure of merit (ZT) – and ultimately the efficiency of a thermoelectric generator – can be achieved, since ZT = S2σT/κ, where S is the Seebeck coefficient, σ the electrical conductivity, κ the thermal conductivity and T the temperature. Such approach is viable because phonons have usually a mean free path significantly larger than electrons, and the transport of the former can be disrupted without dramatically hindering the latter.
The effects of nanostructuration on the lattice dynamics were investigated by means of theoretical calculations5–12 and experimentally observed by methods such as inelastic neutron scattering,13–18 Raman spectroscopy,19,20 nuclear inelastic scattering (NIS)17,21 and measurements of the specific heat.22,23 Overall, these calculations and experiments reveal that an enhancement in the density of phonon states (DPS) at low energies and a broadening of the bands on the DPS is expected for nanocrystalline materials. These modifications in the vibrational modes are attributed to the vibrations of atoms located at the grain boundaries where the atomic structure is more open than within the crystalline grains, and result in a modified force field and a softening of the force constants.
Here we present a detailed experimental study on the effects of nanostructuration on the lattice dynamics and thermoelectric properties of nanocrystalline silicon which, except for the intentional doping, is virtually free of other impurities.
The nanopowder was compacted into 2 cm diameter dense pellets with a spark plasma sintering furnace from FCT Systeme GmbH in a 1 mbar Ar atmosphere. For the first batch (14 nm), sintering was carried out during 3 min (sample A). The second batch (52 nm) was divided into two parts. One part was sintered for 3 min (sample B) and the other for 30 min (sample C). Heating and cooling rates for all samples were fixed to 100 K min−1. The sintering temperature was 1150 °C and a 35 MPa pressure was applied during sintering.
In order to verify the average crystallite size of the nanocrystalline pellets, X-Ray diffraction (XRD) was performed using synchrotron radiation at the high energy station 6-ID-D of the Advanced Photon Source (APS) at Argonne National Laboratory. The sample was 1 mm thick and the experiment was performed in transmission geometry in order to probe the bulk of the pellets. The X-ray wavelength was 0.124659 Å and a General Electric amorphous silicon detector was positioned at a distance of 1849 mm from the sample, a distance determined by a NIST640c Si standard. The data were reduced to diffraction patterns with the program FIT2D26 and no preferential orientation was observed. Rietveld refinements were carried out using the program FULLPROF,27 taking into consideration the Debye–Scherrer broadening of the diffraction peaks.
The average crystallite size was also investigated by Small Angle Neutron Scattering (SANS) measurements carried out using the instrument KWS1 operated by the Jülich Centre for Neutron Science (JCNS) at the FRM II (Garching, Germany).28 In the present work, only the essential results concerning characteristic crystallite sizes will be presented, while further analysis based on Gaussian random fields29 will be published elsewhere.
The elemental analysis was performed at the Prompt Gamma Ray Activation Analysis (PGAA) instrument positioned at the neutron guide NL4b of the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRM II – Garching, Germany).30 The cold neutron flux used for the measurement was 6.1 × 1010 n cm−2 s−1. A high-purity germanium (HPGe) detector was used to detect the gamma rays produced in the sample by neutron capture reactions. The emitted gamma rays have a characteristic energy which depends on the element or isotope which absorbs the neutrons. The peak-area is proportional to the concentration of the element in the sample. This method is therefore a non-invasive way to chemically characterize the sample, which gives precise information about the impurities and its amount in percentages, and it is a method of choice which can give nondestructively information about elements such as hydrogen and boron.
The Density of Phonon States (DPS) of all samples was obtained by inelastic neutron scattering measurements performed on the Time of Flight (TOF) spectrometer IN6 at the cold source of the Institute Laue-Langevin (Grenoble, France). The incident wavelength was 5.12 Å with an elastic energy resolution of 0.13 meV, as determined by the elastic neutron scattering on a vanadium sample.
The specific heat, Cp, was obtained in a commercial Physical Property Measurement System (PPMS) from Quantum Design for all sintered pellets between 4 and 400 K. The specific heat of a polycrystalline Si sample was also measured for comparison.
![]() | ||
Fig. 2 Kratky plot of the SANS curves. Each curve exhibits a broad maximum, which yields the pseudo-Guinier radius Rpg. |
TEM | XRD | SANS | ||||
---|---|---|---|---|---|---|
D min (nm) | D max (nm) | D av (nm) | D (nm) | ε (%) | D (nm) | |
Sample A | 48 | 264 | 114 | 40(2) | 0.00138 | 42 |
Sample B | — | — | — | 42(2) | 0.00133 | 58 |
Sample C | 47 | 246 | 112 | 33(1) | 0.00150 | 34 |
Sample A had an average crystallite size of 40(2) nm from XRD and 42 nm from SANS whereas TEM reveals grains ranging between 48 and 264 nm with an average of 114 nm. Sample C had a slightly smaller crystallite size of 33(1) and 34 nm from XRD and SANS, respectively, and a grain size distribution obtained by TEM between 47 and 246 nm with an average of 112 nm, and also showed amorphous precipitates with average size of 29 nm. The differences seen between TEM, SANS and XRD analysis have their origin in sensitivity of the different methods. TEM is sensitive to the outer contour of grains, not taking into account possible twinning or intragranular effects. XRD is sensitive to the crystallite size, i.e. to limited correlation length, which is in general smaller than the grain size due to the existence of planar defects and intra grain boundaries. Furthermore, SANS curves strongly depend on the size distribution of the scattering entities and may also be affected by inter-particle effects in the present case, though it still represents a measure of characteristic length scales.33 Besides, XRD and SANS are methods averaging over a larger volume, whereas TEM only gives an impression of a very small sample volume, not necessarily fully representative for the complete pellet. Correlating the different methods and known behavior of nanocrystalline silicon, the presence of significant amounts of an amorphous cover of silicon, in excess of one or two atomic layers, can be ruled out, in particular because of the large charge mobility, see below, and because a change in contrast would be noticeable at the grain boundaries next to regions in diffracting condition and would appear black in bright field TEM images.
The samples which were processed with the same sintering parameters, but with initially different nanoparticles sizes (14 and 52 nm for samples A and C, respectively), present only a small different average nanocrystallite sizes after sintering. Sample A presented strong grain growth during sintering. Sample C presented a large amount of defects such as twins and a certain amount, ∼6%, of amorphous precipitates, which energy-dispersive X-ray spectroscopy indicated to be essentially Si, both visible in Fig. 1(b), resulting in an increased strain as obtained from XRD refinement. A grain boundary between two nanocrystals in sample A with different relative orientation without any amorphous layer is shown in Fig. 1(c) and a high resolution image of an amorphous precipitate on sample C in Fig. 1(d). Those precipitates are rather spherical and are found on all images acquired on this sample, indicated by blue arrows in Fig. 1(b).
Overall, although the three different measurements yielded different values of nanocrystallite sizes, the same trend in sizes is observed, ranging from the smallest being sample C and the largest being sample B.
Samples B and C were investigated exemplarily by PGAA. The spectra reveal that the samples were 99.0(1)% Si with 1.0(7)% of P dopant as expected. A small amount of H (0.20(1)%) was detected on the sample with smaller initial nanocrystallite size (sample C). Furthermore, in both samples, a very small ppm contribution of boron was detected. This impurity could originate from a contamination of the precursor silane, which is prepared by fractional distillation, as it is not easy to completely separate silane from diborane.
The values obtained for the elastic constants C11 and C44 with RUS are summarized in Table 2. The speed of sound was then calculated: 3/vs3 = 1/vlong3 + 2/vtrans3, where and
for the polycrystals are the longitudinal and transversal speed of sound, respectively. The values of speed of sound for single-crystalline Si were calculated previously (ref. 25) using the Hershey–Kröner–Eshelby average.
The elastic constant C11 = 172(3) and 173(3) GPa for the samples with smaller and larger nanocrystallites sizes, respectively, corresponding to the bulk modulus (B) is ≈8% larger than in single crystalline Si. The shear modulus, G = C44 = 58.2(7) and 59.0(8) GPa, is ∼25% smaller than in single crystalline Si. Such a decrease in the resistance to shear deformation (G) combined with an increase of the resistance to dilation (B) shows that the mechanical properties of a material with as many grain boundaries and defects are significantly modified when compared with the single-crystalline material, leading to a softening of the material. This is also confirmed by the decrease of the speed of sound calculated from the elastic constants. Such a decrease relates to a decrease in thermal conductivity.
The DPS of two samples of nanocrystalline Si obtained from inelastic neutron scattering are shown in Fig. 3 and compared with polycrystalline Si.25 Note that the area under the DPS curve of all samples was normalized to 1 between 0 and 70 meV.
In the incoherent scattering approximation, and because the sample essentially contains only one chemical element, the speed of sound can be obtained from the low energy limit of g(E)/E2 with 1/vs3 = 2π2NV/ℏ3g(E)/E2 where NV is the number of atoms per unit volume.17 In the case of the nanocrystalline Si samples an increase on the Debye level, , in the reduced DPS is observed. Note that the incoherent scattering approximation is not perfectly suitable for silicon, which is a strong coherent scatterer. Therefore, the speed of sound is obtained by a second approach using RUS measurements, and the data is compared. An extrapolation using the asymptotic limit from RUS, considering the speed of sound summarized in Table 2, shown as dotted lines in Fig. 3, reveals a fair agreement of both methods.
On one hand, the sample containing a small amount of grain boundaries (sample A) presented the same results of speed of sound calculated from the reduced DPS and obtained with RUS, with only a small part of the reduced DPS data being above the asymptotic limit from RUS. On the other hand, the reduced DPS of the sample with larger amount of grain boundaries, defects, and amorphous contribution (sample C) is significantly above the asymptotic limit from RUS and has a pronounced increase for E → 0. We therefore conclude that the excess states in the reduced DPS, which is probed only above 3 meV, are above the asymptotic limit and can be considered as contribution due to the larger amount of grain boundaries, defects and amorphous inclusions.
The specific heat, represented as Cp/T3vs. T, of the nanocrystalline silicon samples measured between 4 and 400 K compared to bulk Si is shown in Fig. 4. The nanocrystalline samples have the same Cp at high temperatures as bulk Si. Below 30 K an increased lattice contribution, related to the increased Debye level and decreased speed of sound, is observed. Further, an electronic contribution, linear in temperature, and thus ∝1/T2 in Cp/T3, is observed at the lowest temperatures, because with such high carrier concentrations, in the % range, there is no freeze-out of the charge carriers as would be expected in semiconductors.
![]() | ||
Fig. 4 Specific heat divided by T3 for both nanocrystalline Si compared with polycrystalline Si. Inset: specific heat (error bars are smaller than the symbol size). |
At the lowest temperatures, a simple model of the heat capacity can be designed by considering an electronic contribution (γT) and a lattice contribution that can be described using the Debye model and an Einstein term to describe the excess Cp at approximately 45 K:25
Cp(T) = γT + dCD(T) + eCE(T) | (1) |
γ (mJ mol−1 K−2) | e (J mol−1 K−1) | Θ E | d (J mol−1 K−1) | Θ HTD | |||
---|---|---|---|---|---|---|---|
(K) | (meV) | (K) | (meV) | ||||
Bulk | — | 3.8(3) | 188(2) | 16.2(2) | 11.4(3) | 501(17) | 43(2) |
Sample A | 0.114(5) | 2.76(7) | 186(1) | 16.0(1) | 9.8(1) | 410(5) | 35.3(5) |
Sample C | 0.12(2) | 2.02(3) | 184(1) | 15.9(1) | 11.2(9) | 402(11) | 34.6(9) |
The Si sample with smaller nanocrystallite sizes presents a lower electrical conductivity between room temperature and 750 °C when compared with the two other samples. The sample which was sintered for a longer period of time has lower σ than the sample with large nanocrystallites sintered for a short time. Both samples which were sintered for a short period of time presented similar values of the Seebeck coefficient (Fig. 5(b)), i.e., likely a very similar charge carrier concentration. The sample with smaller nanocrystallites presented a lower σ than the sample with larger crystallites, due to a large amount of grain boundaries, defects and amorphous contribution leading to a more pronounced scattering of electrons. This results in a better power factor for the sample with large nanocrystallites, but sintered for a short period of time (Fig. 5(c)).
Although the sample which was sintered for a longer period of time (sample B) had a slightly higher density when compared with the other samples (only 1.1% higher, see in Table 4), its electronic properties were not better. During the long sintering period (30 minutes) at high temperatures (1150 °C), diffusion processes occur. Those do not only lead to a healing of defects, which rather improve the crystalline quality of the sample as seen by higher values of thermal conductivity (Fig. 5(d)) and by the higher density, but also to diffusion of the impurities (dopants). The latter have a tendency to aggregate on grain boundaries. This agglomeration of dopants can be seen in the weak increase in σ for T > 750 °C. Overall, the power factor of this sample is lower than for the two samples sintered within only 3 minutes (samples A and C), see Fig. 5(c).
Single-cryst.32 | Nanocryst.32 | Nanocryst.25 | Sample A | Sample B | Sample C | |
---|---|---|---|---|---|---|
Nanoparticles production | — | Ball-milling | Gas phase synthesis | Gas phase synthesis | ||
SPS temperature (°C) | — | — | 1050 | 1150 | 1150 | 1150 |
SPS hold time (min) | — | — | 3 | 3 | 30 | 3 |
Additives/impurities | — | (From ball-mill) | P, SiO2, H | P | P | P |
Av. nanocryst. size (nm) | — | 50–100 | 30 | 42 | 58 | 33 |
Density (g cm−3) | 2.329 | — | 2.189 | 2.259 | 2.284 | 2.257 |
S (μV K−1) | −86 | −70 | −81.2 | −94.3 | −116 | −114 |
ρ (μΩ m) | 3.3 | 9.1 | 23.7 | 9.3 | 11.0 | 13.2 |
n Mott (×1026 m−3) | — | — | — | 1.3 | 1.6 | 1.3 |
μ Mott (×10−4 m2 V−1 s−1) | — | — | — | 52 | 36 | 38 |
n Hall (×1026 m−3) | 4.5 | 4.6 | — | 1.1 | 2.3 | 1.0 |
μ Hall (×10−4 m2 V−1 s−1) | 42.8 | 15.1 | — | 61 | 25 | 47 |
κ Total (W K−1 m−1) | 89.3 | 7.0 | 14.8 | 25.0 | 27.2 | 21.9 |
κ Lattice (W K−1 m−1) | 87.3 | 6.3 | 14.5 | 24.3 | 26.6 | 21.4 |
S 2 σ (mW K−2 m−1) | 0.3 | 0.5 | 0.2 | 1.4 | 0.8 | 1.0 |
ZT at RT | 0.008 | 0.023 | 0.0055 | 0.017 | 0.009 | 0.014 |
ZT max at 980 °C | — | 0.68 | — | 0.57 | 0.43 | 0.52 |
The charge carrier concentration (n) can be estimated from the slope of the Seebeck coefficient (for T < 750 °C):38
![]() | (2) |
Comparing the samples produced from different nanoparticle batches (14 nm vs. 52 nm), but sintered for the same short period of time (3 minutes), no significant decrease of the thermal conductivity was observed, since sample A showed a more pronounced grain coarsening during sintering. The sample with initially smaller nanocrystallite size has a thermal conductivity κ which is 12% lower at room temperature than the sample with initially larger nanocrystallite size, but at high temperatures the thermal conductivity data of both samples converges. The lattice contribution to the thermal conductivity accounts for up to 97% of the total thermal conductivity at room temperature and decreases to around 77% at the highest measured temperature. In single crystalline silicon, 90% of the heat is transported by phonons with mean free path larger than 100 nm.44 Therefore, an average grain size around 100 nm or slightly smaller is already effective in lowering the lattice thermal conductivity as can be seen from the investigated samples.
The thermal conductivity of the pure nanocrystalline samples studied in this paper is still large when compared with previously reported results on nanocrystalline Si,25,32,42 but in those samples, several impurities were present either from exposing the nanopowder to air before sintering25,42 or due to additives used for nanopowder preparation with ball-milling.32 These impurities may significantly affect the mobility of charge carriers, μ, leading to a smaller power factor for the samples in earlier reports than for the samples discussed herein, see Table 4. Next to impurities, a second possible cause for both the higher mobility and thermal conductivity for the samples investigated here, is the fabrication method. Where the bottom up gas phase synthesis followed by sintering is expected to lead to well crystallized particles, the top down approach using ball-milling32 is more prone to lead to a strained lattice, and thus, smaller mobility but also smaller thermal conductivity.
Overall, despite the large thermal conductivity, the dimensionless figure of merit of the silicon nanocomposites investigated herein still reaches competitive values due to a very high carrier mobility resulting in comparatively high power factors. With a ZT of 0.57 at 973 °C, the sample produced with 52 nm nanoparticles and sintered for 3 minutes can compete with other results published so far,32 with the advantage of a more easily scalable production process.
The sample with small initial nanoparticle size showed a significant grain growth during sintering as analyzed by XRD refinement and TEM, and also a larger amount of defects and a certain amount of amorphous precipitates, leading to a further decrease on the speed of sound and to an excess of vibration modes at low energies. It also presented slightly worse electronic properties, which compensates the lower thermal conductivity and leads to a similar dimensionless figure of merit as the sample prepared with larger nanoparticles and same sintering parameters.
A systematic trend in the decrease of the speed of sound obtained from the density of phonon states, resonant ultrasound spectroscopy, and specific heat, combined with the large amount of grain boundaries in nanostructured Si materials, resulted in a thermal conductivity four times lower than for a single-crystal.
When compared with previously reported results on nanocrystalline Si, the samples still present a somewhat large thermal conductivity, which is compensated by a very high power factor and results in competitive values of the dimensionless figure of merit with a peak ZT of 0.57 at 973 °C. When compared to other materials which are used in this temperature range such as nanocrystalline SiGe, Si has a ZT which is approximately half of the results reported so far (1.3 at 900 °C45), with the advantage of being approximately 14 times cheaper than SiGe.
Since the thermal conductivity of the nanocrystalline Si samples presented in this work is still large when compared to other thermoelectric materials, further optimization of the parameters leading to the reduction of the thermal conductivity could lead to an even better ZT value.
Furthermore, studies have shown that the energy cost of Si nanopowder production through gas phase synthesis is drastically reduced with increasing production amount.46 Therefore, when compared with other methods such as ball-milling, gas phase synthesis has the great advantage of being a continuous and a more easily scalable method.
Footnote |
† BET (Brunauer, Emmett, Teller): surface area analysis. |
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