Optical band gap and the Burstein–Moss effect in iodine doped PbTe using diffuse reflectance infrared Fourier transform spectroscopy

Optical absorption edge measurements are performed on I doped PbTe using diffuse reflectance infrared Fourier transform spectroscopy. The Burstein–Moss shift, an increase in the absorption edge (optical band gap) with increasing doping level, is explored. The optical gap increases on the order of 0.1 eV for doping levels ranging from 3 × 10^(18) to 2 × 10^(20) cm^(−3), relevant doping levels for good thermoelectric materials. Chemical potential is estimated from transport measurements—specifically, Hall effect and Seebeck coefficient—using a single band Kane model. In heavily doped semiconductors, it is well-known that the band gap shrinks with increasing doping level. This effect, known as band gap renormalization, is fit here using an n^(1/3) scaling law which reflects an electron–electron exchange interaction. The renormalization effect in these samples is shown to be more than 0.1 eV, on the same order of magnitude as the band gap itself. Existing models do not explain such large relative changes in band gap and are not entirely self-consistent. An improved theory for the renormalization in narrow gap semiconductors is required

Resolving the true band gap of ZrNiSn half-Heusler thermoelectric materials

N-type XNiSn (X = Ti, Zr, Hf) half-Heusler (HH) compounds possess excellent thermoelectric properties, which are believed to be attributed to their relatively high mobility. However, p-type XNiSn HH compounds have poor figures of merit, zT, compared to XCoSb compounds. This can be traced to the suppression of the magnitude of the thermopower at high temperatures. E_g = 2eS_(max)T_(max) relates the band gap to the thermopower peak. However, from this formula, one would conclude that the band gap of p-type XNiSn solid solutions is only one-third that of n-type XNiSn, which effectively prevents p-type XNiSn HHs from being useful thermoelectric materials. The study of p-type HH Zr_(1−x)Sc_xNiSn solid solutions show that the large mobility difference between electrons and holes in XNiSn results in a significant correction to the Goldsmid–Sharp formula. This finding explains the difference in the thermopower band gap between n-type and p-type HH. The high electron-to-hole weighted mobility ratio leads to an effective suppression of the bipolar effect in the thermoelectric transport properties which is essential for high zT values in n-type XNiSn (X = Ti, Zr, Hf) HH compounds

Band gap estimation from temperature dependent Seebeck measurement — Deviations from the 2e|S|_(max)T_(max) relation

In characterizing thermoelectric materials, electrical and thermal transport measurements are often used to estimate electronic band structure properties such as the effective mass and band gap. The Goldsmid-Sharp band gap, Eg  = 2e|S|_(max)T_(max), is a tool widely employed to estimate the band gap from temperature dependent Seebeck coefficient measurements. However, significant deviations of more than a factor of two are now known to occur. We find that this is when either the majority-to-minority weighted mobility ratio (A) becomes very different from 1.0 or as the band gap (Eg) becomes significantly smaller than 10 kBT. For narrow gaps (Eg  ≲ 6 kBT), the Maxwell-Boltzmann statistics applied by Goldsmid-Sharp break down and Fermi-Dirac statistics are required. We generate a chart that can be used to quickly estimate the expected correction to the Goldsmid-Sharp band gap depending on A and S_(max); however, additional errors can occur for S < 150 μV/K due to degenerate behavior

Characterization of Lorenz number with Seebeck coefficient measurement

In analyzing zT improvements due to lattice thermal conductivity (κ_L ) reduction, electrical conductivity (σ) and total thermal conductivity (κ_(Total)) are often used to estimate the electronic component of the thermal conductivity (κ_E) and in turn κ_L from κ_L = ∼ κ_(Total) − LσT. The Wiedemann-Franz law, κ_E = LσT, where L is Lorenz number, is widely used to estimate κ_E from σ measurements. It is a common practice to treat L as a universal factor with 2.44 × 10^(−8) WΩK^(−2) (degenerate limit). However, significant deviations from the degenerate limit (approximately 40% or more for Kane bands) are known to occur for non-degenerate semiconductors where L converges to 1.5 × 10^(−8) WΩK^(−2) for acoustic phonon scattering. The decrease in L is correlated with an increase in thermopower (absolute value of Seebeck coefficient (S)). Thus, a first order correction to the degenerate limit of L can be based on the measured thermopower, |S|, independent of temperature or doping. We propose the equation: L=1.5+exp[−_(|S|)_(116)] (where L is in 10^(−8) WΩK^(−2) and S in μV/K) as a satisfactory approximation for L. This equation is accurate within 5% for single parabolic band/acoustic phonon scattering assumption and within 20% for PbSe, PbS, PbTe, Si_(0.8) Ge _(0.2) where more complexity is introduced, such as non-parabolic Kane bands, multiple bands, and/or alternate scattering mechanisms. The use of this equation for L rather than a constant value (when detailed band structure and scattering mechanism is not known) will significantly improve the estimation of lattice thermal conductivity

Tuning Nanocrystal Surface Depletion by Controlling Dopant Distribution as a Route Toward Enhanced Film Conductivity

Electron conduction through bare metal oxide nanocrystal (NC) films is hindered by surface depletion regions resulting from the presence of surface states. We control the radial dopant distribution in tin-doped indium oxide (ITO) NCs as a means to manipulate the NC depletion width. We find in films of ITO NCs of equal overall dopant concentration that those with dopant-enriched surfaces show decreased depletion width and increased conductivity. Variable temperature conductivity data shows electron localization length increases and associated depletion width decreases monotonically with increased density of dopants near the NC surface. We calculate band profiles for NCs of differing radial dopant distributions and, in agreement with variable temperature conductivity fits, find NCs with dopant-enriched surfaces have narrower depletion widths and longer localization lengths than those with dopant-enriched cores. Following amelioration of NC surface depletion by atomic layer deposition of alumina, all films of equal overall dopant concentration have similar conductivity. Variable temperature conductivity measurements on alumina-capped films indicate all films behave as granular metals. Herein, we conclude that dopant-enriched surfaces decrease the near-surface depletion region, which directly increases the electron localization length and conductivity of NC films

Thermopower enhancement in Pb_(1−x)Mn_xTe alloys and its effect on thermoelectric efficiency

The Seebeck coefficient of p-type PbTe can be enhanced at 300 K, either due to the addition of Tl-resonant states or by manipulation of the multiple valence bands by alloying with isovalent compounds, such as MgTe. PbTe alloyed with MnTe shows a similar thermopower enhancement that could be due to either mechanism. Here we investigate the characteristics that distinguish the resonant state mechanism from that due to multiple valence bands and their effect on the thermoelectric figure of merit, zT. Ultimately, we find that the transport properties of PbTe alloyed with MnTe can be explained by alloy scattering and multiple band model that result in a zT as high as 1.6 at 700 K, and additionally a ~30% enhancement of the average zT

Thermoelectric Enhancement in BaGa_2Sb_2 by Zn Doping

The Zintl phase BaGa_2Sb_2 has a unique crystal structure in which large tunnels formed by ethane-like dimeric [Sb_3Ga−GaSb_3] units are filled with Ba atoms. BaGa_2Sb_2 was obtained in high purity from ball-milling followed by hot pressing. It shows semiconducting behavior, in agreement with the valence precise Zintl counting and band structure calculations, with a band gap ∼0.4 eV. The thermal conductivity of BaGa_2Sb_2 is found to be relatively low (0.95 W/K m at 550 K), which is an inherent property of compounds with complex crystal structures. As BaGa_2Sb_2 has a low carrier concentration (∼2 × 10^18 h^+/cm^3) at room temperature, the charge carrier tuning was performed by substituting trivalent Ga with divalent Zn. Zn-doped samples display heavily doped p-type semiconducting behavior with carrier concentrations in the range (5−8) × 10^19 h^+/cm^3. Correspondingly, the zT values were increased by a factor of 6 by doping compared to the undoped sample, reaching a value of ∼0.6 at 800 K. Zn-doped BaGa_2Sb_2 can thus be considered as a promising new thermoelectric material for intermediate-temperature applications

Thermoelectric performance of co-doped SnTe with resonant levels

Some group III elements such as Indium are known to produce the resonant impurity states in IV-VI compounds. The discovery of these impurity states has opened up new ways for engineering the thermoelectric properties of IV-VI compounds. In this work, resonant states in SnTe were studied by co-doping with both resonant (In) and extrinsic (Ag, I) dopants. A characteristic nonlinear relationship was observed between the Hall carrier concentration (n_H) and extrinsic dopant concentration (N_I, N_(Ag)) in the stabilization region, where a linear increase of dopant concentration does not lead to linear response in the measured n_H. Upon substituting extrinsic dopants beyond a certain amount, the nH changed proportionally with additional dopants (Ag, I) (the doping region). The Seebeck coefficients are enhanced as the resonant impurity is introduced, whereas the use of extrinsic doping only induces minor changes. Modest zT enhancements are observed at lower temperatures, which lead to an increase in the average zT values over a broad range of temperatures (300–773 K). The improved average zT obtained through co-doping indicates the promise of fine carrier density control in maximizing the favorable effect of resonant levels for thermoelectric materials

Optimization of thermoelectric efficiency in SnTe: the case for the light band

p-Type PbTe is an outstanding high temperature thermoelectric material with zT of 2 at high temperatures due to its complex band structure which leads to high valley degeneracy. Lead-free SnTe has a similar electronic band structure, which suggests that it may also be a good thermoelectric material. However, stoichiometric SnTe is a strongly p-type semiconductor with a carrier concentration of about 1 × 10^(20) cm^(−3), which corresponds to a minimum Seebeck coefficient and zT. While in the case of p-PbTe (and n-type La3Te4) one would normally achieve higher zT by using high carrier density in order to populate the secondary band with higher valley degeneracy, SnTe behaves differently. It has a very light, upper valence band which is shown in this work to provide higher zT than doping towards the heavier second band. Therefore, decreasing the hole concentration to maximize the performance of the light band results in higher zT than doping into the high degeneracy heavy band. Here we tune the electrical transport properties of SnTe by decreasing the carrier concentration with iodine doping, and increasing the carrier concentration with Gd doping or by making the samples Te deficient. A peak zT value of 0.6 at 700 K was obtained for SnTe0.985I0.015 which optimizes the light, upper valence band, which is about 50% higher than the other peak zT value of 0.4 for Gd_zSn_(1−zT)e and SnTe_(1+y) which utilize the high valley degeneracy secondary valence band

Temperature dependent band gap in PbX (X=S, Se, Te)

PbTe is an important thermoelectric material for power generation applications due its high conversion efficiency and reliability. Its extraordinary thermoelectric performance is attributed to band convergence of the light L and heavy Σ bands. However, the temperature at which these bands converge is disputed. In this letter, we provide direct experimental evidence combined with ab initio calculations that confirm an increasing optical gap up to 673 K and predict a band convergence temperature of 700 K, much higher than previous measurements showing saturation and band convergence at 450 K