Metallization and Electrical Transport Behaviors of GaSb under High-Pressure

The high-pressure metallization and electrical transport behaviors of GaSb were systematically investigated using in situ temperature-dependent electrical resistivity measurements, Hall effect measurements, transmission electron microscopy analysis, and first-principles calculations. The temperature-dependent resistivity measurements revealed pressure-induced metallization of GaSb at approximately 7.0 GPa, which corresponds to a structural phase transition from F-43m to Imma. In addition, the activation energies for the conductivity and Hall effect measurements indicated that GaSb undergoes a carrier-type inversion (p-type to n-type) at approximately 4.5 GPa before metallization. The first-principles calculations also revealed that GaSb undergoes a phase transition from F-43m to Imma at 7.0 GPa and explained the carrier-type inversion at approximately 4.5 GPa. Finally, transmission electron microscopy analysis revealed the effect of the interface on the electrical transport behavior of a small-resistance GaSb sample and explained the discontinuous change of resistivity after metallization. Under high pressure, GaSb undergoes grain refinement, the number of interfaces increases, and carrier transport becomes more difficult, increasing the electrical resistivity.

high-pressure XRD and resistance measurements; however, as GaSb undergoes a phase transition from F-43m to Imma at 7.0 GPa under non-hydrostatic conditions, it remains unknown if the Imma phase is a metallic state. Furthermore, XRD measurements cannot effectively reflect the electronic structure phase transition of the material, which demonstrates the need to conduct electrical property studies under pressure.
The electrical conductivity of materials under pressure is strongly affected by interfaces 18,19 . Therefore, it is necessary to study both the electrical properties and the effect of interfaces on these properties in samples under high pressure. Zhang et al. proposed a method to analyze the effect of interfaces on the electrical properties of Zn 2 SnO 4 by combining AC impedance and transmission electron microscopy (TEM) analyses in 2015 20 . However, the AC impedance analyzer used (1296/1260, Solartron Analytical) could not detect electrical properties in the low-frequency region for a low-resistance sample. To date, no effective method has been proposed for analyzing the electrical properties and interface effect of a low-resistance sample under pressure.
In this study, the metallization of GaSb was systemically investigated using in situ ρ measurements, Hall effect measurements, and first-principles calculations under high pressure. The results provide sufficient evidence for the metallization of the material at 7.0 GPa. Before metallization, GaSb underwent a carrier-type inversion at approximately 4.5 GPa, which was caused by band gap changes with pressure, inducing a change in the impurity level from the acceptor to the donor level. We explain the electronic property change of the sample after metallization through examining the crystal interface of sample powders by high-resolution TEM (HRTEM) after pressure relief.

Experimental Results and Discussion
GaSb (99.9%) was purchased from Alpha Company (USA), and the required powders were obtained by mechanical grinding. We conducted XRD measurements of the mechanically ground sample powders and compared the results with those of JCPDS No. 7-215, as shown in Fig. 1. The approximate particle size of the sample by was calculated by the Scherrer equation 21,22 : where D is the mean particle size of the sample powders; K is a dimensionless shape factor, which is defined as 0.89 here; γ is the X-ray wavelength of 0.154056 nm; B is the line broadening at half the maximum intensity; and θ is the Bragg angle. The calculated result was 35.6 nm.
In Situ High-pressure Electrical Resistivity Measurements. As observed in Fig. 2(a), ρ decreased with increasing pressure below 10.0 GPa, with a sharp decline in the range of 7.0-10.0 GPa. Above 10.0 GPa, ρ slowly increased until 13.0 GPa and finally plateaued. Three regions with varying reduction rates for lnρ were observed below 10.0 GPa: from ambient pressure to 4.5, 4.5 to 7.0 GPa, and 7.0 to 10.0 GPa, the reduction rates were 0.62, 0.26, and 2.22 Ω·cm/GPa, respectively. Therefore, we suspected that metallization of GaSb occurred between 7.0 and 10.0 GPa. After pressure relief, ρ returned to its original order of magnitude, indicating that the change of the sample was reversible under high pressure, which is consistent with previous research 16 .
To verify whether GaSb undergoes pressure-induced metallization, we conducted high-pressure variable-temperature ρ measurements. The experimental results could be fitted using an Arrhenius equation, as shown in Fig. 2(b). Below 7.0 GPa, ρ decreased with increasing temperature, and the material exhibited semiconductor conductivity characteristics; above 7 GPa, ρ increased with increasing temperature, and the material exhibited clear metal conductivity. These results demonstrate that GaSb underwent a typical phase transition from semiconductor to metal near 7.0 GPa. Above 10.0 GPa, ρ remained almost constant with increasing pressure (Fig. 2(c)).
To further explore the evolution process and intrinsic conductivity mechanism of GaSb metallization, the change in the activation energy of GaSb with increasing pressure was studied. The activation energy for carrier conductivity of GaSb was determined based on the change of ρ with temperature: where ρ 0 is a constant determined by both the carrier mobility μ and the effective mass of the carrier, E I is the activation energy for conductivity, k B is the Boltzmann constant, and T is the temperature. The activation energy is generally temperature independent; however, we observed that the changes in ρ differed with increasing temperature when determining the activation energy of GaSb through fitting. Under different pressures, ln ρ vs. 1000/T could be linearly fitted in two sections: the changes in ρ with increasing temperature from 95 to 185 K were gentler than those above 185 K. In other words, the activation energy in the high-temperature range from 185 K to room temperature was greater than that in the low-temperature range from 95 to 185 K under the same pressure. This result was observed because dislocations appeared at the interface of the GaSb sample powder after mechanical grinding 23 , resulting in impurity energy levels in the band gap. The carriers participating in the conductivity could be excited to the low-impurity energy level in the low-temperature range from 95 to 185 K. The activation energy in the low-temperature range of 95 to 185 K was relatively low. With increasing temperature, the excited carriers became saturated and were not easily further excited to a higher impurity level. Figure 2(d) clearly shows that the activation energies in the two temperature ranges were both reduced with increasing pressure. This finding reflects the effect of pressure on the charge-transfer energy barrier. At 7.0 GPa, E I was close to 0; the typical semiconductor behavior of GaSb and accompanying energy barrier disappeared. This result indicates that there were no barriers to overcome in the carrier migration process. In other words, at this time, GaSb exhibited electronic conductivity, which is characteristic of metal conduction behavior. In addition, the negative slope indicates that the transport of carriers became easier with increasing pressure, and that the change in the activation energy for the conductivity of GaSb in different temperature ranges above and below 4.5 GPa showed two different trends. The reduction rates of the activation energy in the two temperature ranges below 4.5 GPa were smaller than those above 4.5 GPa, which corresponds to the inflection point of the high-pressure in situ ρ measurements at 4.5 GPa. However, no structural transformation was observed before metallization in previous XRD studies; therefore, we suspect that GaSb underwent an electronic structural phase transition from a p-type to an n-type semiconductor. In Situ Hall Effect Measurements Under High Pressure. Figure 3 presents the Hall effect measurements of GaSb for a magnetic field of 1.0 T. Under ambient pressure, the Hall coefficient R H , carrier concentration n, and μ were 22.47 cm 3 C −1 , 1.00 × 10 17 cm −3 , and 30.81 cm 2 V −1 s −1 , respectively. Before metallization, R H changed from positive to negative at approximately 4.5 GPa, which indicates that the sample underwent carrier-type inversion, changing from a p-type to an n-type semiconductor. Below 4.5 GPa, n decreased and μ increased with increasing pressure as observed in Fig. 3; therefore, the reduction of μ caused the reduction of ln ρ, and the reduction rate of ln ρ changed from 0.62 to 0.26 Ω·cm/GPa. At 4.5 GPa, the numbers of electrons and holes added were equal. Above 4.5 GPa, the number of electrons increased with increasing pressure, and the number of holes remained constant; however, the creation rate of electrons was less than the annihilation rate of electrons and holes. Therefore, n decreased with increasing pressure from 4.5 to 7.0 GPa. In the metallization process, the creation rate of electrons was greater than the annihilation rate of electrons and holes above 7.0 GPa; in addition, n and μ increased with increasing pressure and ln ρ decreased sharply at a rate of 2.22 Ω·cm/GPa. After metallization, R H was unchanged and close to 0, and n remained approximately 4.83 cm −3 and showed no change with increasing pressure. At this time, the excited carriers approached saturation; however, μ decreased with increasing pressure 4 . It could be assumed that the increasing ρ of the sample was caused by the reduction of μ. Above 13 GPa, μ remained as 3.74 cm 2 V −1 s −1 and showed no change with increasing pressure, and ρ showed no change. HRTEM Analysis after Decompression. The high-pressure in situ ρ measurements indicated that ρ of GaSb remained unchanged after a slight increase above 10.0 GPa. The high-pressure in situ Hall effect measurements also did not reveal an electronic phase transition; however, μ decreased with increasing pressure. No structural phase transition was observed in GaSb near this pressure in previous XRD experiments. The reduction of μ was thought to be associated with crystal refinement or breaking. Crystal breaking or refinement generally implies the generation of a new interface, which will result in physical property changes. To analyze this effect, HRTEM characterization was performed on the GaSb powders after relieving pressures of 5.0, 10.0, and 25.0 GPa.
The characterization results are presented in Fig. 4. Comparison of Fig. 4(a-c) reveals that the sample maintained the long-range order characteristic of a single crystal over a large area after relief of 5.0 GPa. However, after relief of 10.0 GPa, the sample was partially crushed, and the lattice direction was disordered. After relief of 25.0 GPa, the sample was similar to that after relief of 10.0 GPa without further refinement. Therefore, the same refinement produced many new interfaces, and it was difficult for the carriers to move in the crystal. Thus, above 10.0 GPa, μ decreased and ρ increased slightly. This finding may be caused by non-hydrostatic pressures in the DAC.

Theoretical Calculation Results
The theoretical calculation results are presented in Fig. 5. The enthalpy of the F-43m and Imma phases intersect at 7.1 GPa, which indicates that the Imma phase of GaSb is more stable than F-43m above 7.1 GPa. The band structure calculation results indicate that the F-43m structure of GaSb is a direct-band-gap semiconductor. For the Imma phase, the band gap across the Fermi level indicates that the Imma phase is metallic. These theoretical calculation results agree with our experimental data, confirming the metallization of GaSb near 7.0 GPa.
Before metallization, the band gaps of GaSb were 0.586, 0.375, and 0.538 eV at 2.0, 4.0, and 6.0 GPa, respectively. Thus, the band gap first decreased and then increased with increasing pressure, corresponding to the carrier-type inversion before metallization. A low concentration of impurities and defects is present in commercially obtained GaSb; therefore, impurity levels are present in the band gap. At ambient pressure, the impurity level is close to the valence band, and electrons can move more easily from the valence band to the impurity levels. Therefore, the impurity level acts as an acceptor level, and the conductivity depends mostly on holes; thus, GaSb is a strong p-type semiconductor. With increasing pressure, the conduction band approaches the impurity levels, and the number of electrons increases in the conduction band; therefore, GaSb gradually becomes a weak p-type semiconductor. When the pressure is increased further, the valence band moves away from the impurity levels and electrons more easily move from the impurity levels to the conduction band. Therefore, the impurity level acts as a donor level, the conductivity mostly relies on electrons, and GaSb becomes an n-type semiconductor, as observed in Fig. 5(c).

Conclusion
Using high-pressure in situ ρ measurements, we confirmed that the metallization process of GaSb starts at 7.0 GPa and observed two anomalous changes of ρ at 4.5 and 10.0 GPa before and after metallization, respectively. High-pressure Hall measurements revealed that GaSb undergoes a carrier-type inversion from a p-type to an n-type semiconductor as a pre-process for metallization at 4.5 GPa. These effects were explained by theoretical calculations, which revealed that the changes of the band structure with increasing pressure transform the impurity levels from acceptor to donor levels. In addition, TEM analysis and Hall effect measurements elucidated the effect of the interface on the electrical transport behavior of small-resistance GaSb samples under high pressure and explained the discontinuous change of ρ after metallization. GaSb undergoes grain refinement under high pressure; thus, the number of interfaces increases, making carrier transport more difficult and decreasing μ and increasing ρ.

Methods
The high-pressure device was a Mao-Bell 24 DAC, with an anvil face of 300 μm. The laser drilling technique was used to drill a hole with a diameter of 100 μm in a non-magnetic Re gasket with a thickness of 50 μm as the sample cavity. The hole was filled with a mixture of alumina powder and epoxy resin as the insulator. Because of the possibility of anvil deformation, the thickness of the sample under high pressure was measured with a micrometer with an accuracy of up to 0.5 μm, and the pressure was standardized by using the ruby fluorescence spectra method 25,26 . To avoid the introduction of impurities during the measurements and to ensure good electrical contact for the electronic parameter measurements, a pressure transmission medium was not used in the experiments. The high-pressure ρ and Hall effect measurements were performed in the DAC integrated microcircuit using the van der Pauw method 27, 28 . In the ρ and Hall effect measurements, source meters (2400 and 2700, Keithley) were used to provide the current and measure the voltage, respectively. All the instruments were connected to the computer using an interface adapter (KUSB-488, Keithley) and a GPIB cable, and the entire testing process was run automatically with a computer-controlled program. The reverse current method was used in the Hall effect measurements to avoid the thermoelectric offset current. A 9060-type electromagnet provided the magnetic field, and a gauss meter (420, Lakeshore) was used to calibrate the magnetic field. The strength of the magnetic field was 1.0 T. For the temperature-dependent ρ measurements, liquid nitrogen was used to obtain low temperatures of 95 to 275 K. The temperature was measured by connecting a standard K-type thermocouple to the voltage meter, with a 0 °C ice-water mixture used as the cold end. As diamond exhibits good thermal conductivity, the thermocouple was connected to the bare diamond in the DAC to ensure accurate measurements.
The first-principles calculations were performed using density functional theory and the pseudopotential method, and CASTEP code was used for calculating the electric structure. The exchange and correlation terms were described using a generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBZ) scheme. Structural optimizations were performed using the Broyden-Fletcher-Goldfarb-Shanno minimization algorithm provided in this code. Integration in the Brillouin zone was performed using special k points generated by 7 × 7 × 7 and 10 × 7 × 3 mesh parameter grids for the F-43m and Imma phases, respectively. The one-electron valence state was expanded on the basis of a plane wave with the cutoff energies of 528 eV and 580 eV, respectively. The structure parameters obtained from previous study after optimized 16,29 .