Effect of the Annealing on the Low-Temperature Charge Transport Properties of Heavily Boron-Doped Nanocrystalline Silicon Films for Thermoelectric Applications

1 Introduction

The need and the opportunity of converting low enthalpy heat into electricity using thermoelectric generators has motivated over the last decade an impressive surge of material research worldwide. On one side, macroharvesting, i. e. the recover of waste heat from industrial plants, homes, or car mufflers may help reduce the use of non–renewable primary energy sources, still today mostly of fossil origin, while favorably impacting on greenhouse gas emissions. On the other side, microharvesting is believed to be one of the most interesting power sources to enable wireless sensor networks, replacing batteries.

To this aim, however, novel thermoelectric materials are needed, since the current standards, based upon tellurium, could never cover the anticipated market requests in both macro and microharvesting due to raw material scarcity. In this respect, silicon and silicon–based thermoelectric materials would be game-changers, not only because of silicon geo-abundance but also because of the ease of integrating thermoelectric silicon with microelectronic components and circuits.

Rather unfortunately, single-crystalline silicon is a quite poor thermoelectric material, with a low thermoelectric figure of merit (≈0.01). Actually, while its power factor σα2 (where σ is the electrical conductivity and α is the Seebeck coefficient) may be relatively large, its thermal conductivity κ is >100 W/mK. Strategies to decrease κ in single crystals by selective scattering of phonons in one–dimensional nanostructures have demonstrated very effective (Hochbaum et al. 2008; Boukai et al. 2008), leading to figures of merit ZT=σα2T/κ≈0.8 at temperature T around 300 K. This is however not the only possible approach, as comparable ZT have been shown to be achievable in nanocrystalline silicon, where κ is reduced by phonon scattering at grain boundaries. It could be shown (Narducci et al. 2012, 2014) that proper annealing of the material may fully compensate for the reduction of electrical conductivity due to polycrystallinity through hole energy filtering (Narducci, Frabboni, and Zianni 2015).

While the physics of energy filtering itself is fairly well understood (Bahk, Bian, and Shakouri 2013; Neophytou et al. 2013; Zianni and Narducci 2015), the details of the chemical process leading to the formation of potential barriers at grain boundaries is still to be elucidated. Thus, a research endeavor has been undertaken to correlate annealing cycles, boron distribution, and transport properties in nanocrystalline silicon thin films. This paper focuses on understanding the correlation between thermal treatments and the electronic structure of nanosilicon films, using material transport properties as a probe. By comparing untreated and thermally treated films it will be shown that any prolonged thermal process at >900 °C leads to one, possibly unexpected, effect – that of converting degenerate nanosilicon back into a non–degenerate semiconductor.

2 Experimental Procedure

Nanocrystalline Si films were grown by chemical vapor deposition (CVD) at 610 °C onto oxidized (100) silicon wafers. Film thickness was measured to be 228±5 nm. Silicon was boron–doped by ion implantation (26 keV, 6×1015 cm−2+47 keV, 6×1015 cm−2) followed by rapid thermal processing (1,050 °C, 20 s) to a total nominal boron density of 4.4×1020 cm−3. Samples were cut from the wafer and then eventually submitted to additional thermal treatments in argon (Table 1). Prior to annealing them, samples were submitted to Piranha etch (H2SO4 96 % vol.:H2O2 30 % vol.=2:1, 95 °C, 30 min) to remove organic surface contaminants, then rinsed in ultrapure deionized water, and dried under nitrogen flux. Oxide was removed by DHF (HF 40 % vol.:H2O=1:10) up to obtaining a fully hydrophobic surface, then the specimen was rinsed in ultrapure deionized water, and finally dried under nitrogen flux. For double thermal treatments, an additional DHF etching was carried out between the two annealing steps to remove oxidized layers that might have formed.

Electrical resistivity, Hall resistance, and Seebeck coefficient were measured. Aluminum contact evaporation was carried out after removing eventual oxide layers by DHF. Contact characteristics were verified to be always linear.

Seebeck coefficients were measured at 300 K using the integral method. Each measurement was carried out in triplicate to assess its reproducibility. Hall resistivity RH was measured between 20 and 300 K with a maximum magnetic field of 0.5 T. Electrical conductivity was obtained as a function of temperature between 20 and 300 K extracting it from four–probe current–voltage characteristics. Further details on the experimental procedure were reported elsewhere (Zulian, Segrado, and Narducci 2017).

3 Results and Discussion

The temperature dependencies of σ and RH were preliminary analyzed in a previous publication (Zulian, Segrado, and Narducci 2017). Thus, they will be only summarized hereafter.

Inspection of experimental data immediately shows the remarkable qualitative difference between the untreated (non annealed) film on one side; and all the heat–treated films on the other side. Actually, the untreated sample displays a monotonic increase of σ as T decreases, with the carrier density being almost constant from 20 K up to 300 K (Figure 1, top). Instead, in all annealed samples σ reaches a maximum, then decreases getting to an asymptotic value in the zero-temperature limit (Figure 1, bottom).

For the untreated sample it is quite immediate to conclude that the large boron doping brings silicon beyond the degeneracy threshold. The impurity band due to acceptor interactions overlaps with the valence band. Continuity of electronic states leads to a quasi–metallic electronic structure (weak degeneracy) (Blackemore 2002) so that the carrier density remains constant when raising the temperature while the conductivity slowly drops with it due to electron–phonon scattering.

Figure 1:

Comparative trend of the electrical conductivity and of the carrier density vs. the reciprocal temperature in untreated (top) and heat–treated (bottom) samples. While the former shows a typical metal–like behavior, heat treatments leads to non-monotonic p(T) and σ(T) curves. Freeze–out temperature Tout marks the maximum of σ and a saddle point of p while the freeze–in temperature Tin is displayed as a minimum for the carrier density.

This standard picture does not apply instead to the heat–treated samples. The trend that is observed may however be explained as follows (Hung and Gliessman 1954). In the low temperature limit acceptors contribute to charge transport only by hopping. As temperature raises an increasingly large number of centers gets ionized, leading to an increasing carrier density for band transport up to a temperature at which all centers are ionized. This causes an increase of σ. For higher temperature no additional carriers can be made available, save for those generated by interband transitions. Therefore conductivity is dominated by the mobility decrease due to the augmented phonon–electron scattering rate. Two critical temperatures may be then defined, namely

1. a freeze–out temperature Tout at which all acceptors are ionized, so that the conductivity gets to a maximum;

2. a freeze–in temperature Tin, at which acceptor ionization is virtually zero.

A signature of the two temperatures is expected to be displayed by both σ(T) and p(T). The clearest mark of Tout is obviously set by the maximum of σ. However, also p(T) reports it. Actually, since at Tout all acceptors are ionized, at such temperature the carrier density p should display a plateau, eventually followed by a new increase at higher temperatures, where intrinsic carriers begin contributing to hole density. This is actually the case in lightly doped semiconductors (Luryi, Shklovskii, and Efros 2013). Instead, in heavily doped silicon the plateau reduces to a saddle point. As of Tin, since competition between delocalized (band) and hopping carriers occurs when all acceptors are frozen in their neutral state, Tin is the temperature at which carrier density p(T) gets to its minimum. Figure 1 displays both critical temperatures with reference to a typical annealed sample.

This analysis is corroborated by the comparison of the electrical conductivity in the low and high temperature limits. In general, both hopping and band conduction contribute to σ as (Hung 1950)

where the subscripts label hopping (h) and band (b) terms. Likewise, the Hall resistance reads

where r is a constant of the order of unity. Thus, in the low-temperature limit pb≅0 and then ph≅p so that RH≅r/(eph)≅r/(ep). Instead in the high temperature limit ph≅0 and pb≅p so that RH≅r/(epb)≅r/(ep). Thus, the two limiting Hall resistivities are predicted to be equal to each other. This was actually shown to be the case in all annealed samples (Chroboczek, Pollak, and Staunton 1984; Zulian, Segrado, and Narducci 2017).

Carrier freeze–out provides additional information concerning the density of states (DOS) in the samples. Interactions among acceptor states in heavily doped nanocrystalline semiconductors lead to the formation of an impurity band that may eventually overlap with the valence band. In a simplistic view, boron levels open up to form an impurity band centered at the isolated acceptor energy EA (measured from the top of the valence band) with a width (Schubert 2015)

where ε is the semiconductor permittivity. Thus, overlap starts occurring for a critical acceptor density

In silicon this sets pc≅9×1019 cm−3, namely about a fifth of the nominal boron concentration of the present samples. Whenever a significant band overlap occurs, however, no freeze–out should be observed since the Fermi level would sweep a continuum of states. Actually, carrier density in all samples is lower than pc at room temperature (Table 1), being obviously even lower at lower temperatures – confirming that a relevant part of boron impurities cluster and precipitate within silicon (Narducci et al. 2012, 2014).

Although this picture properly describes the band conduction, a more accurate description of the impurity band is needed to explain the low temperature carrier transport. Should one simply take the acceptor levels to provide a single impurity band, a hopping activation energy εh comparable to EA would be expected, in blatant contrast with observations. Actually, in heavily doped silicon the electrostatic interactions lead to the formation of three sub-bands, A⁽⁰⁾, A^(–), and A⁽⁺⁾ (this being formally a donor sub-band), depending on the charge state of the impurity itself. Computations (Poklonskii and Syaglo 1999) predict a band split EA(+)−EA(0) of ≈5 meV at an acceptor density NA≈1017−1018 cm−3. Since the separation between the A⁽⁰⁾ and the A⁽⁺⁾ sub-bands is also the activation energy for the hopping transport, we may estimate that at carrier densities in the order of 1020 cm−3 the sub–band split reduces to fractions of meV (Table 1). Thus, considering that, using eq. [3], the sub–band width may be estimated to be ≈ 38 meV, the convoluted impurity band can be predicted to display a non–monotonic dependency on the energy due to the sub-band overlap.

Further insights in the electronic structure of the material come from the analysis of the Seebeck coefficient. Figure 2 displays the dependence of α upon 1/Tout. It is to be noted that Tout increases with the doping level (Figure 3), as at larger impurity contents a higher temperature is needed for all dopant levels to be ionized. Stated differently, silicon must be set to a higher temperature for the overall carrier density (as resulting from both extrinsic and intrinsic contributions) to equal the dopant density. One may actually verify that lnNA∝1/Tout. Thus, also the Seebeck coefficient should decrease with Tout, as actually observed. As however α is approximately proportional to 1/Tout, one may also conclude that Mott’s formula for metals and semi-metals,

Figure 2:

Relationship between the Seebeck coefficient at 300 K and the experimental freeze–out temperature. Confidence bands are at 95 %.

Figure 3:

Ratio between the total carrier density and the impurity concentration in boron–doped silicon as a function of the reciprocal temperature at various doping levels.

(where kB, h, and m∗ are the Boltzmann constant, the Planck constant, and the effective mass of the majority carrier) although often invoked in the analysis of the Seebeck coefficient for heavily doped semiconductors (Ioffe 1957), is of no use in this case. Instead, Pisarenko equation

is apparently more consistent with the experiment, in spite of the high doping level.

On the basis of temperature dependencies of the carrier density and of the electrical conductivity, and of the just mentioned consistency of the experimental α(p) with the Pisarenko equation one may safely conclude that heat treatments succeed at removing the (weak) degeneracy of nanosilicon films observed in the untreated sample. It is sensible that such an effect is related to the precipitation of boron-enriched second phases at grain boundaries, that has been widely proved to be a necessary condition for ZT enhancement in nanosilicon (Narducci et al. 2012). The consequent reduction of the dissolved boron density, along with the relatively low solubility of boron into silicon (compared, e. g., to phosphorus), justifies the formation of a gap between the impurity (acceptor) band and the valence band, leading in turn to carrier freeze–out at temperatures around 100 K. Consistently, hopping conduction is observed at low temperatures.

4 Summary and Conclusions

In this paper we have analyzed the differences between the electronic transport properties of untreated and heat–treated heavily boron–doped nanosilicon films. It has been shown that untreated samples are degenerate, reporting a quasi–metallic behavior. Instead, any long-term thermal treatment at >900 °C converts the degenerate nanosilicon back into a non–degenerate semiconductor. Full consistency of p(T), σ(T), and α(p) curves with this model has been discussed. Removal of degeneracy is also consistent with the experimentally assessed evidence that high-temperature annealing promote the diffusion–limited precipitation of boron at grain boundaries, enabling energy filtering of majority carriers and a favorable microscopic distribution of the temperature gradient within the material.

The availability of a model for the evolution of nanosilicon electronic structure enables a more detailed analysis of the quantitative differences among nanosilicon films experiencing single or repeated thermal processing. Such a comparative study will be the subject of a forthcoming publication.