Enhanced Thermoelectric Performance in Cu-Intercalated BiTeI by Compensation Weakening Induced Mobility Improvement

The low weighted carrier mobility has long been considered to be the key challenge for improvement of thermoelectric (TE) performance in BiTeI. The Rashba-effect-induced two-dimensional density of states in this bulk semiconductor is beneficial for thermopower enhancement, which makes it a prospective compound for TE applications. In this report, we show that intercalation of minor Cu-dopants can substantially alter the equilibria of defect reactions, selectively mediate the donor-acceptor compensation, and tune the defect concentration in the carrier conductive network. Consequently, the potential fluctuations responsible for electron scattering are reduced and the carrier mobility in BiTeI can be enhanced by a factor of two to three between 10 K and 300 K. The carrier concentration can also be optimized by tuning the Te/I composition ratio, leading to higher thermopower in this Rashba system. Cu-intercalation in BiTeI gives rise to higher power factor, slightly lower lattice thermal conductivity, and consequently improved figure of merit. Compared with pristine BiTe0.98I1.02, the TE performance in Cu0.05BiTeI reveals a 150% and 20% enhancement at 300 and 520 K, respectively. These results demonstrate that defect equilibria mediated by selective doping in complex TE and energy materials could be an effective approach to carrier mobility and performance optimization.

Scientific RepoRts | 5:14319 | DOi: 10.1038/srep14319 TE technology is one potential candidate which can facilitate direct thermal-to-electrical energy conversion 9 . TE materials, combinations of fine electrical and poor thermal conductors, are the keys to improving the efficiency of this green technology. The performance of a TE material is determined by its dimensionless figure of merit ρκ μ κ = / = ( )⋅( / )⋅ ZT S T S n eT H 2 2 , where S is the thermopower, T the absolute temperature, ρ the electrical resistivity, κ the thermal conductivity, n the carrier concentration, and e the electron charge 10,11 . Doping strategies and defect related approaches have been successfully used to optimize TE properties in several classes of high efficiency TE material systems, such as CoSb 3 [12][13][14] , Mg 2 (Si, Sn) 15 , Bi 2 Te 3 16 , and Pb(Se, Te) 17,18 . Narrow gap semiconductors with low iconicity generally should have high carrier mobility 19 . However, methods to optimize the TE performance, such as doping to tune the carrier concentration and alloying to engineer the band structure or reduce lattice thermal conductivity, would inevitably introduced disorders and randomness to the materials, Thus, the carrier mobility μ H can be deteriorated to unexpectedly low values 6 .
In intrinsic semiconductors, the predominant carrier scattering source is the acoustic phonons, as shown in most conventional TE materials 20 . The mobility is coupled with carrier concentration (the Fermi level) by the deformation potential 21 . This situation leaves little room for mobility tuning. On the other hand, many complex TE compounds, including ternary and multinary materials, belong to the family of compensated semiconductors in the extrinsic regime, where all impurities are ionized, the transport carriers are generated by but at the same time strongly scattered by these ionized impurities including both acceptors and donors 22 . These localized scattering centers break the lattice periodicity and create electrostatic potential fluctuations. In real crystal lattices, the defects and imperfections in carrier conductive network can cause the undesirable potential fluctuations and strongly scatter the carriers. Carrier mobility is closely related to the concentration of ionized impurities N I , N I = N A + N D , where N A , N D are the concentration of negative-charged acceptors and positive-charged donors, respectively. Taking an n-type extrinsic semiconductor as an example, the electron concentration n can be expressed as n = N D − N A 23 . Then at a given electron concentration n (the optimal n is 10 19 -10 20 cm −3 for most TE materials), the impurity concentration is primarily determined by the compensation ratio K = N A /N D .
A Monte Carlo study clearly shows that compared with the situation in single-type-charged impurity (K = 0), impurities of two different charges (0 < K < 1) can lead to more severe potential fluctuations around the mean potential value 24 . Larger compensation ratio K will result in stronger potential fluctuations, which can strongly scatter transport carriers and thus lower the carrier mobility 24,25 . This study also implies that reducing K may become an unusual avenue to increase the carrier mobility and enhance the TE performance in systems with high compensation.
Until recently, non-centrosymmetric Rashba spin-split bismuth tellurohalides BiTeX (X = I, Br, Cl) have been reported as promising TE materials [26][27][28][29][30] . The electrical performance of BiTeI is superior than those in spin-degenerate materials, while the lattice thermal conductivity of undoped polycrystalline BiTeI is as low as ~1 W m −1 K −1 at room temperature 29 . However, the overall TE performance of BiTeI is still unassuming because of its low weighted mobility 6 . Antisite defects occur in BiTeI crystals owing to the similarity between Te and I atoms. Thus the dominant defects can be expressed as ′ Te I and • I Te . High concentrations of ionized impurities, including acceptors and donors, exist in this layered material 31 . Consequently, the electrons are scattered by both the ionized impurities and the acoustic phonons 31,32 . This material can be an ideal testbed for tuning carrier mobility by altering the impurity compensation.
Low temperature TE characterizations of BiTeI single crystals were performed in the 1970s 32 . A recent resurgence of interests in the TE properties of BiTeI included band structure calculations and galvanomagnetic characterizations 27 . It was found that thermopower of BiTeI can be enhanced with small amounts of CuI additions, while both thermal conductivity and electrical conductivity decrease in polycrystalline samples 26,33 . The TE figure of merit nevertheless deteriorates as compared with the undoped single crystals. It was also speculated that the Bi 3+ cations were substituted by the Cu + cations, thus reducing the carrier concentration. More recently, magneto-transport measurements have been performed on BiTeI single crystals with much higher Cu contents, where copper ions were argued to distribute randomly within the van der Waals gaps 34 . Cu-doping was shown to reduce the carrier concentration and increase the mobility. The occupancy of Cu in BiTeI and its influence on the transport properties are important for both spintronics and thermoelectrics.
Here we present that the intercalation of minor Cu dopants in BiTeI polycrystals can clearly change the equilibria of defect reactions, selectively mediate the compensation between donors and acceptors, and limit the defect concentration in the carrier conductive network. The intercalated • Cu i donors alter the compensation ratio between the donors ( • Cu i and • I Te ) and the acceptors ( ′ Te I ). Strikingly, the electron mobility is enhanced by three and two times at 10 K and 300 K, respectively. The significantly enhanced carrier mobility is driven by the weakened impurity compensation and reduced potential fluctuations. The carrier concentration of BiTeI is also optimized by Cu-intercalation and tuning the Te/I composition ratio, beneficial to power factor (PF = S 2 /ρ) enlargement. Cu intercalation induced ZT improvement for BiTeI is 150% and 20% at 300 K and 520 K, respectively, which mainly originates from the mobility enhancement and the carrier concentration optimization.  Compared to the calculated diffraction peaks of BiTeI, these samples show a preferred orientation of (0 0 1). Lattice parameter ratios (c/a) of the samples ( Fig. 1(b)) are calculated from cell refinements using the space group P3m1 and experimental lattice parameters a = b = 4.3392 Å and c = 6.8540 Å 35 . The pseudo-binary phase diagram between Bi 2 Te 3 and BiI 3 shows that stoichiometric BiTeI does not exist 36 . We also find that the Bi 2 Te 3 secondary phase is always present in the stoichiometric BiTeI, while the non-stoichiometric BiTe 0.98 I 1.02 is phase pure. However, single phase Cu 0.05 BiTeI can be formed without any impurities according to the XRD pattern.

Results and Discussion
In general, the lattice site occupancies of dopants have a significant impact on physical properties. There are two potential sites for Cu dopants in the layered BiTeI, i.e. substitution on the Bi site and intercalation into the van der Waals gap 26,34 . The c/a ratio increases with increasing Cu content x, as shown in Fig. 1(b), which suggests that intercalation is more likely. Formation energy calculations were performed to further determine the preferential site for Cu atoms 37 The formation energy for Cu-substitution on the Bi site and Cu-intercalation is calculated to be 2.24 eV and 1.17 eV, respectively. The intercalation requires lower energy than the substitution by 1.07 eV, further corroborating Cu-intercalation in BiTeI. The intercalated Cu atoms are located in the tetrahedrons formed by three I atoms and one Te atom, as shown in the inset of Fig. 1(b). The length of Cu-I and Cu-Te bond is calculated to be 2.561 Å and 2.502 Å, respectively. The electron energy loss spectrum (EELS) was used to measure the oxidation state of Cu in Cu 0.05 BiTeI by analyzing its L3 and L2 fine structures, as shown in Fig. 2. The acquired spectrum was compared to those from standard Cu 2 O and CuO 39 . The spectra are aligned to the L3 peak intensity maxima in order to have a clear comparison of the fine structures and peak intensity ratio. The fine structures of L3, L2 edges and the L3-to-L2 ratio on the EELS, can be used as fingerprints of the oxidation states for transition metal elements 40,41 . The spectrum for the Cu-intercalated BiTeI sample has the L3 and L2 sharp edges and intense peaks, which excludes the zero-valence state of Cu 42 . The spectrum in this work sits between those from Cu 2 O and CuO in terms of the fine structures. For example, the L2 peak intensity from Cu 0.05 BiTeI is lower than that of Cu 2 O but higher than that of CuO. The fine structures between L3 and L2, which are labeled as peak "A" and "B", resemble those of CuO, while the extended fine structure shows an intense peak (labeled as peak "C"), which is similar to that of Cu 2 O. Furthermore, the L3-to-L2 ratio of Cu 0.05 BiTeI is also between those in standard Cu 2 O and CuO. These evidences indicate that the Cu oxidation state in Cu-intercalated BiTeI is between 1+ and 2+ . The Cu ionization has a significant influence on the transport properties of these samples. Figure 3(a) shows that all Cu x BiTe 1-y I 1+y samples have negative Hall coefficients R H , suggesting n-type electron-dominant conduction. The carrier concentration n is nearly temperature independent ( Fig. 3(b)), which indicates that these samples are in the extrinsic region where all donors and accepters Most strikingly, the Hall mobility μ H is significantly enhanced by Cu intercalation, as shown in Fig. 3(c). The Hall mobility of the undoped sample is 92.3 cm 2 V −1 s −1 at 100 K and 86.0 cm 2 V −1 s −1 at 300 K, while the Cu 0.05 BiTe 0.98 I 1.02 sample has a mobility as high as 273.6 and 171.6 cm 2 V −1 s −1 at the respective temperatures. The mobility of some BiTeI single crystals exhibits a T −3/2 dependence, which suggests that carriers are predominantly scattered by the acoustic phonons 36 . Meanwhile, the mobility in other BiTeI single crystals displays a weaker temperature dependence 31,32 . The temperature dependence of mobility for these BiTeI single crystals has been discussed which includes ionized impurity and acoustic phonon scatterings 31,32 . Our mobility data for polycrystals are consistent with the mixed scattering model in the range of 4-300 K, which have the temperature dependence weaker than the T −1 relationship. If carriers are scattered by grain barriers, such as grain boundary phases or oxidized phases, the mobility would increase with increasing temperature 43 . Our mobility data for polycrystalline BiTeI show no such temperature dependence, which excludes such extrinsic scattering factors.
Therefore, the Hall mobility μ H can be analyzed by combining the scattering processes using the Matthiessen's law 44 where μ I and μ L represent the mobility component related to the ionized impurity and the acoustic phonon scattering, respectively. The acoustic phonon limited mobility μ L can be described by the equation 21 where c ii and E def represent the average elastic constant (in the centimeter-gram-second unit of Ba) and the deformation potential (in the unit of eV), respectively. The other constants include the electron mass m e , the reduced Planck constant π = / ħ h 2 , and the Boltzmann constant k. The effective mass m* of BiTeI is about 0.19 m e determined by the Shubnikov-de Haas oscillations 45 . The average elastic constant c ii of BiTeI is estimated to be 1.36 × 10 11 Ba by using the relation θ π , where D is the density, θ the Debye temperature, and V the unit cell volume 46 . The Debye temperature θ is calculated to be 87 K by taking the equation θ ν = / ħ k, where ν is the maximum frequency of acoustic branches (61 cm −1 ) given by the calculated phonon dispersion (shown below).
The mobility component μ I associated with the ionized impurity scattering can be expressed by the Brooks-Herring (BH) formula in the limit of electron degeneracy 47,48 In the BH formula, ε is the dielectric constant and equals to 14.5 for BiTeI 49 . The parameters N I and Z refer to the concentration of ionized impurity and charge of impurity (Z = 1).
Using Equations 3, 5 and 6, we can fit the experimental Hall mobility data with two variables, i.e. deformation potential E def and concentration of ionized impurity N I . The solid lines in Fig. 3(c) present the fits to mobility data and Table 1 Table 1. Donor and acceptor concentrations both decrease drastically upon Cu-intercalation. The compensation ratios become smaller in Cu-intercalated samples, as compared with that in the undoped BiTe 0.98 I 1.02 (K = 76.9%). The strong compensation in BiTeI is closely related to the similarity between Te and I atoms, including the ionic radii and atomic charges 50 . The two atoms can exchange their positions randomly in the crystal structure 31  The coefficients in Equation 7 have the condition of u > w, which is the origin of the n-type conduction in BiTeI. Figure 4 sheds light on the compensation-related physical parameters and their interrelations to the Hall mobility μ H . The Cu content x dependent n/N I and K are shown in Fig. 4(a,b). The term n/N I describes the "efficiency" of ionized impurities for providing the conducting carriers. As x increses from 0.00 to 0.05 (y = 0.02), the efficiency n/N I increases from 13.1% to 44   close to that of the x = 0.03, y = 0.02 sample. Therefore, the ionizations are more efficient with weaker compensation and less impurities in the Cu-intercalated samples. Figure 4(c,d) present the compensation ratio K dependent Hall mobility μ H at 10 K and 300 K. At 10 K, μ H increases almost linearly with the decreasing K, consistent with the picture that the mobility is mainly determined by the ionized impurity scattering at lower temperatures (below 100 K). Although acoustic phonon scattering emerges at higher temperatures, the Hall mobility is still strongly influenced by the impurity scattering in the compensated BiTeI. As shown in Fig. 4(d), the Hall mobility μ H at 300 K also varies inversely with the compensation ratio K. has no compensation effect, as intercalated Cu only act as donors. The overall compensation ratio K is then suppressed by the ionization of intercalated Cu. The compensation ratio K in particular captures the electrostatic potential fluctuations in semiconductors. If there are only negatively charged acceptors or positively charged donors in materials, K equals to zero. The potential fluctuations with respect to their mean potential value become larger with increasing compensation ratio K. Larger potential fluctuations cause stronger scattering for the electrons, thus reducing the carrier mobility 24 . In BiTeI, Cu-intercalation reduces the compensation ratio, i.e. the potential fluctuations, and weakens the electron scattering by ionized impurities, as shown in Fig. 5(b). Hence the mobility can be significantly enhanced in Cu-intercalated BiTeI. Actually, the enhanced mobility here can also be described as increased weighted mobility, as the effective mass should not altered by minor Cu dopants. The mobility enhancement has also been found in Cu-intercalated layered Bi 2 Te 3 52,53 , which may have the same underlying mechanism. In general, dopants in semiconductors, that occupy lattice sites with minimal influence on the charge-conducting band 54 or carrier-conduction network 55 , could lead to higher carrier mobility. The intercalated Cu atoms reduce the perturbation in the carrier-conducting Bi-Te network. Herein we only considered the long-range interaction in ionized impurity scattering, due to the relatively low dielectric constant (14.5) in BiTeI. However, short-range interactions may be dominant in compounds with large dielectric constant, which can also be tuned for higher mobility 54 . Figure 6(a,b) show the electrical resistivity ρ and thermopower S of Cu x BiTe 1−y I 1+y as a function of temperature (300-520 K). These samples exhibit a metallic behavior in resistivity, which is typical for degenerate semiconductors. The non-systematic resistivity variation with copper doping has been revealed in the carrier concentration and mobility. Compared to the doped samples, the resistivity of pure BiTe 0.98 I 1.02 (x = 0.00, y = 0.02) demonstrates a weaker temperature dependence, which is compatible with its temperature-dependent Hall mobility. For Cu 0.01 BiTe 0.98 I 1.02 (x = 0.01, y = 0.02) and Cu 0.05 BiTeI (x = 0.05, y = 0.00), the resistivity starts decreasing as holes are excited at higher temperatures.  and (b) after Cu-intercalation. In pristine BiTeI, highly compensated antisite defects can generate large potential fluctuations, which strongly scatter electrons and lead to low carrier mobility. Upon Cuintercalation, the intrinsic defect equilibrium is altered and the compensation ratio is reduced. Electron scattering from the compensated defects is weakened. Consequently, higher carrier mobility can be achieved in Cu-intercalated BiTeI.
Scientific RepoRts | 5:14319 | DOi: 10.1038/srep14319 The negative thermopower S of all samples is consistent with the Hall coefficient R H , confirming the dominant n-type conduction. All samples show degenerate behaviors near room temperature. Unlike other samples, Cu 0.01 BiTe 0.98 I 1.02 and Cu 0.05 BiTeI have the bipolar effect at higher temperatures as holes are excited. The variation of room temperature thermopower S can be related to the carrier concentration n, as shown in Fig. 6(c). The absolute value of S increases with decreasing n, showing an S ∝ n −1 dependence. The spin-splitting bands have a two-dimensional-like constant density of states 56,57 , that can have a significant influence on the TE properties of the Rashba materials 58 , The spin-splitting bands of BiTeI have been revealed by an angle-resolved photo-emission spectroscopy (ARPES) experiment and first principles calculations 50,59 . We've demonstrated that the electrical term S 2 n can indeed be enhanced because of the unusual density of states in the Rashba bands 29,30 . Our work also showed that the lower Fermi level for a given optimal carrier concentration is the underlying mechanism for electrical property enhancement 29,30 . In conventional semiconductors with parabolic bands, the S-n plot typically follows an S ∝ n −2/3 relationship. We have previously developed a theoretical model to address the thermopower vs. the carrier concentration relationship in the bulk Rashba system 29 . Under a degenerate approximation, the thermopower in bulk materials with Rashba spin-splitting bands can be written as where E 0 is the Rashba energy and r the carrier scattering parameter. The band structure of BiTeI has been calculated (inset of Fig. 6(c)), showing the Rashba energy E 0 = 0.11 eV, which is comparable to the ARPES and previous calculation results 50,59 . The scattering parameter r is − 0.5 and 1.5 for the acoustic phonon and the ionized impurity scattering, respectively 20 . The dashed line in Fig. 6(c) corresponds to calculated results using Equation 9 with the scattering parameter r equal to −0.096, indicative of the mixed scatterings in BiTeI, which is consistent with our Hall mobility analysis. The temperature dependent power factor PF = S 2 /ρ is shown in Fig. 6(d). The significant PF enhancement in Cu-doped samples is attributed to the improvement of electrical term S 2 n and mobility μ H . The PF in the Cu 0.05 BiTeI (x = 0.05, y = 0.00) sample is 2.3 times higher than that of the undoped sample at room temperature. Figure 7(a) shows the calculated phonon dispersion of BiTeI along the high symmetry points in the reciprocal space. The maximum frequency is 157 cm −1 for all phonon branches and 61 cm −1 for the acoustic branches. Three heat-carrying acoustic phonon branches are related to the lattice vibrations of all atoms 60 . Figure 7(b) shows the temperature dependent thermal conductivity of the Cu x BiTe 1−y I 1+y samples with different values of x and y. The thermal conductivity of all samples decreases with increasing temperature, and is lower than 1 W m −1 K −1 at 520 K for most samples. The total thermal conductivity can be divided to two components by κ = κ e + κ L , where κ e and κ L represent the electronic and lattice thermal conductivity, respectively. κ L can be calculated by deducting κ e from κ using the Wiedemann-Franz law κ e = LT/ρ, where L is the Lorenz number and equals to 2.45 × 10 −8 V 2 K −2 . The choice of the Lorenz number here does not alter the overall conclusion we present. As the solid lines in Fig. 7(b) show, the derived κ L of Cu x BiTe 0.98 I 1.02 decreases as the copper content increases from x = 0.00 to x = 0.05. The Cu 0.05 BiTe 0.98 I 1.02 sample has κ L as low as 0.36 W m −1 K −1 at 520 K, which is close to the theoretical minimum κ L of 0.3 W m −1 K −1 61 . The lattice thermal conductivity can be calculated via the Debye-Callaway method 62 , as the dashed line shows in Fig. 7(b). The temperature dependence of theoretical values is reasonably consistent with the experimental results of undoped sample. Above room temperature, the κ L of all samples follows the T −1 relationship, proving that the phonon-phonon interaction is dominant in the temperature range. The lower κ L in Cu-intercalated samples is a result of the additional phonon scattering by point defects, especially the light Cu breaks the periodicity of the layered structure and introduces large mass fluctuations in BiTeI. Figure 8(a) shows the overall figure of merit ZT of all Cu x BiTe 1−y I 1+y samples. The ZT for Cu 0.05 BiTeI has a ~150% and 20% enhancement at 300 K and 520 K over the undoped sample, respectively. The ZT enhancement in Cu-intercalated BiTeI is a joint result of power factor improvement and thermal  conductivity reduction. In fact, the mobility enlargement and carrier concentration optimization are the main reasons for the enhanced ZT in Cu 0.05 BiTeI, as shown in Fig. 8(b). The high temperature TE property of these materials is, however, still limited by the bipolar effect in the best sample, whose thermopower is suppressed above 475 K. Through substituting iodine with bromine, the band gap of the solid solution may become larger than the pristine BiTeI to mitigate the bipolar conduction at high temperatures 63 .

Conclusions
In conclusion, we have demonstrated that mobility enhancement via compensation weakening is an effective method for improving the TE properties in BiTeI. Cu-intercalation changes the balance of defect equilibria and weakens the compensation between donors and acceptors. As a result, the potential fluctuations are reduced in the carrier conductive network and electron scattering are substantially suppressed, leading to enhanced electron mobility. The carrier concentration is also tuned by Cu-intercalation and higher thermopower is shown in this Rashba spin-splitting system. An enhanced power factor and lowered lattice thermal conductivity yield higher figure of merit ZT in Cu-intercalated BiTeI. It is further suggested that even better performance can be achieved in BiTeI. The beneficial effects of defect equilibria mediation and compensation weakening we demonstrated in BiTeI should be applicable to other complex TE and energy materials.

Methods
Polycrystalline Cu x BiTe 1−y I 1+y samples were synthesized by melting stoichiometric elements of Bi, Te, I 2 , and Cu (99.999%, Sigma-Aldrich) in sealed quartz tubes. The mixtures were first kept at 135 °C (above the melting point of iodine) for 2 h for pre-reaction, and then held at 720 °C for 24 h. Melts were subsequently slow-cooled to 510 °C and held for three days before cooled in furnace. The grown ingots were ground into fine powders, which could be filtered by a 75 μ m standard sieve. Powders (weighted around 10 g) were sintered to consolidated bulk samples at 370 °C in a Spark Plasma System (SPS) using a graphite die with a diameter of 12.7 mm under a pressure of 40 MPa.
Powder X-ray diffraction (XRD) was performed at room temperature on a Bruke Focus D8 equipped with Cu Kα radiation (wavelength λ = 1.5418 Å). EDS and elemental mapping was carried out on a Hitachi TM 3100. The EELS spectrum from Cu 0.05 BiTeI is acquired on a FEI-Titan 300/60S STEM/TEM at 300 kV using a Gatan GIF 865 spectrometer. The beam convergence angle and collection angle used in this experiment are 30 mrad and 45 mrad, respectively. The spectrum is averaged on 20 individual acquisitions. The thermopower (S) and electrical resistivity (ρ) from 300 K to 573 K were measured on an ULVAC ZEM-3 system using bar samples (2.5 × 2.5 × 10 mm 3 ), which were cut from sintered materials vertically to the direction of SPS pressure. Thermal conductivity was determined by thermal diffusivity (α), density (D) and heat capacity (C p ) using the equation κ = C p × D × α. Thermal diffusivity (α) was measured by a Netzsch LFA 457, vertically to the direction of SPS pressure on square samples with dimensions of ~10 × 10 × 1.5 mm 3 . Archimedes method was used for density of sintered samples while heat capacity was estimated by the Dulong-Petit law. Estimated uncertainties of the measured electric resistivity, Seebeck coefficient, and calculated thermal conductivity are ± 5%, ± 3%, and ± 10%, respectively 19,[64][65][66] . Hall measurements were realized on thin bar samples (2 × 9 × 0.6 mm 3 ) in a Janis cryostat equipped with an AC resistance bridge and a 9-T magnet (up to ± 4 T used in this work). The currents (± 2 mA) for all Hall measurements were applied perpendicular to direction of the SPS pressure while magnetic fields were in parallel. Hall coefficient (R H ) was calculated from slope of Hall voltage vs. magnetic field curves. Carrier concentration (n) and Hall mobility (μ H ) were calculated from measured Hall coefficients and resistivity using β = / n eR H andμ ρ = / R H H , respectively, where β approximately equals to one in the degenerate BiTeI.
Defect formation energies are calculated in a Bi 27 Te 27 I 27 supercell, with the Cu atom in the substitution site or the intercalation site. The change of Fermi energy (~0.026 eV) is small compared to the defect formation energy (2.24 eV and 1.17 eV). Thus the values of formation energy correspond to the proper electron chemical potentials. Band structure of BiTeI was calculated by the Density Functional Theory, where the modified Becke-Johnson (mBJ) exchange potential and the local density approximation (LDA) were used. The spin-orbit coupling was fully taken into account in the calculations. In theoretical lattice thermal conductivity calculation, the calculated phonon velocities are 1543, 1849, and 2316 m s −1 for three acoustic branches, while the average Grüneisen parameters are 2.42, 1.76, and 2.10, respectively.