Pressure‐Tuneable Visible‐Range Band Gap in the Ionic Spinel Tin Nitride

Abstract The application of pressure allows systematic tuning of the charge density of a material cleanly, that is, without changes to the chemical composition via dopants, and exploratory high‐pressure experiments can inform the design of bulk syntheses of materials that benefit from their properties under compression. The electronic and structural response of semiconducting tin nitride Sn3N4 under compression is now reported. A continuous opening of the optical band gap was observed from 1.3 eV to 3.0 eV over a range of 100 GPa, a 540 nm blue‐shift spanning the entire visible spectrum. The pressure‐mediated band gap opening is general to this material across numerous high‐density polymorphs, implicating the predominant ionic bonding in the material as the cause. The rate of decompression to ambient conditions permits access to recoverable metastable states with varying band gaps energies, opening the possibility of pressure‐tuneable electronic properties for future applications.


Computational methods
Searches on the enthalpy landscape were conducted with AIRSS [7,8] for cells of different formula units of Sn 3 N 4 and for different pressures up to 200 GPa. Energy, atomic forces, and stresses were evaluated at the hybrid-DFT level using the PBE0 functional. [9] A plane-wave basis set with a cut-off of 950 eV and 4×4×4 Γ-centered mesh were used in the projector augmented wave (PAW) method as implemented in the Vienna Ab Initio Simulation Package (VASP). [10] Geometry relaxations were halted as soon as forces and stresses reached the thresholds of 2 meVÅ −3 and 0.1 meVÅ −3 , respectively. Obtained structures were used to calculate the quasi-particle band gaps employing the G0W0 approach. These many-body calculations were carried out employing the linearized augmented plane-wave + local orbitals (LAPW+lo) basis set as implemented in the all-electron full-potential code "exciting". [11,12,13] The quasi-particle correction was applied to Kohn-Sham energies obtained within the local-density approximation using the LAPW cut-off R MT |G + k| max = 9 and 8 × 8 × 8 Brillouin zone sampling. The dielectric function was computed on a 2 × 2 × 2 Γ-centered k-grid using 600 empty states and 32 frequencies. These settings ensure that the quasi-particle band gaps are converged to 0.1 eV or better.
2 Ambient Sn 3 N 4 Sn 3 N 4 was prepared under solvothermal conditions in an inconel autoclave (Parr 4740CH) with a silica liner. Under N 2 0.6 g SnCl 4 and 30 cm 3 benzene were placed in the liner, then 0.211 g LiNH 2 was added to the solution and stirred. The autoclave was sealed and heated to 610 K for 12 hours. Typically 50 Atm pressure developed during heating. After cooling to room temperature, the solid was washed with deionised water (100 ml) and MeOH (50 ml) to remove the LiCl by-product. The powder was further washed with 3 M HCl (50 ml) to remove a tin metal contaminant due to thermal decomposition of the nitride. Combustion (CHN) analysis was outsourced to Medac Ltd with samples decomposed with a WO 3 combustion aid to maximise nitrogen recovery. The sample contained 11.5% nitrogen (13.58% calcd. for Sn 3 N 4 ), as well as 5.6% carbon and 1.5% hydrogen, may be attributed to the decomposition of benzene. (left) P 2 1 /c following annealing at 578 K at 58 GPa (right) R3c following annealing at 800 K at 125 GPa.

Recovered metastable states
Figure S 3: Recovered spinel Sn 3 N 4 at ambient pressure, inside a DAC, following rapid compression to 80 GPa and subsequent rapid decompression. The sample maintains a band gap which is greater than its ambient 1.3 eV, and within the red region of visible spectrum (∼ 1.8 eV). Scale bar 100 µm. Figure 4 summarizes the calculated Γ-Γ (optical) band gap for different polymorph of Sn 3 N 4 as a function of pressure. Dashed lines shows the hybrid-DFT (PBE0) calculations and solid lines are G 0 W 0 values. Obtained structures were used to calculate the quasi-particle band gaps employing the G 0 W 0 approach. These many-body calculations were carried out employing the linearized augmented plane-wave + local orbitals (LAPW+lo) basis set as implemented in the all-electron full-potential code exciting [11,12,13]. The quasi-particle correction was applied to Kohn-Sham energies obtained within the local-density approximation using the LAPW cutoff R MT |G + k| max = 9 and the 8 × 8 × 8 Brillouin zone sampling. The dielectric function was computed on the 2 × 2 × 2 Γ-centered k-grid using 600 empty states and 32 frequencies. These settings ensure that the quasi-particle band gaps are converged up to 0.1 eV or better.

Methodology for EXAFS analysis
All data handling was carried out using the Demeter software package developed by Bruce Ravel. Athena was used for data processing, calibration, and file merging. A tin foil standard was used for calibrating the tin K-edge position of 29200 eV. For data analysis, the Artemis package was used as the front end for ab initio calculations of scattering amplitudes using muffin tin potentials via Feff, as well as fitting via the Feffit fitting code.

105 GPa data set
For data analysis, the Artemis package was used as the front end for Feff calculations and Feffit fitting. Using ab initio calculations, the ground state structure of Sn 3 N 4 at 105 GPa has been predicted to be either the trigonal structure with the R3c space group, or the cubic structure in the I43d space group. Crystallographically, the two structure types show very similar diffraction patterns, making it very difficult to solve the structure. One major difference between the two structure types is the local coordination of the tin atoms. The R3c structure has 7 nitrogen atoms in the local environment of the tin, whereas the I43d phase structure has 8 nitrogen atoms. Due to its sensitivity to the local coordination of the absorbing atom, EXAFS is a useful tool for verifying the structure type. Each structure type was tested against the 105 GPa data set. Feff input files were generated from the crystallographic information files created from the predicted structures. For fitting, the following fitting model was used for both structures: 1. The Correlated Debye model can be used to describe the disorder of the tin atoms.
2. The Einstein model can be used describe the disorder of the nitrogen atoms.
4. Shell displacements for the Nitrogen and tin atoms are independent.
5. The Fermi energy correction of the first shell is independent of the rest of the shells.
Fitting results for the R3c structure type: Using the Nyquist criterion for the total number of independent points in a packed signal, there were 36.33 independent points in this data set. Of those points, 22 variables were required to adequately fit to the EXAFS spectrum. The following table lists the guess parameters used: The parameter for ∆ R of each nitrogen shell and each tin shell was given an independent variable. As stated earlier, the disorder of the tin atoms was described using the Debye model, and the Debye temperature for this structure is given by the parameter thetad, this can be correlated to the Debye-Waller terms for each of the tin atoms, and these values are given in table S 10. As in the ambient data, do to the large mass of tin, the core-hole broadening effects was considered, in order to properly account for this, the electron self energy term, Ei, was included for the tin sites. This was given by the parameter EiSn, which was evaluated to 8.41 +/-1.48 eV. The Einstein model was used to describe the nitrogen disorder, and the Einstein temperature was given the parameter thetaeN, using this, it was determined that the Debye-Waller term for the nitrogen atoms was 0.001Å 2 . Two Fermi energy corrections were used, one for the first coordination shell (Enot1), and one for the rest (Enot). This compensates for incomplete core-hole shielding between the nitrogen and the tin in the first coordination shell. The McMaster correction given from the Feff calculation was added to all disorder terms through the set parameter mmc. The following correlations between fit parameters were above 80%:  Fit results with residuals to the magnitude of the fourier transform of the EXAFS spectrum and the real part of the fourier transform of the EXAFS spectrum weighted by k. There is a large distortion to the first shell, which in contrast to the previous structures, is a result of the local static disorder of the first coordination shell. In the R3c structure, the 7 coordinated nitrogen atoms have 4 unique distances from the absorbing tin atom, creating a large level of static distortion. This fact can also be seen in the high third and fourth cumulants. All spectra are phase corrected using the phase amplitude of the first nitrogen shell.
Fitting results for I43d structure: Using the Nyquist criterion for the total number of independent points in a packed signal, there were 36.33 independent points in this data set. Of those points, 21 variables were required to properly fit to the EXAFS spectrum. The following tables list the results of the fit: The R-factor by k-weight for this fit is = 1 ⇒ 0.08931, 2 ⇒ 0.06826, 3 ⇒ 0.10772 When comparing the fits of the R3c structure and the I43d structure, it can clearly be seen that the R3c structure is the more likely structure.  Left Top: Fit results to the magnitude of the fourier transform of the EXAFS spectrum weighted by k, k 2 , and k 3 . Right Top: Fit results to the EXAFS spectrum weighted by k, k 2 , and k 3 . bottom: Fit results with residuals to the magnitude of the fourier transform of the EXAFS spectrum and the real part of the fourier transform of the EXAFS spectrum weighted by k. In the R3c structure, the 7 coordinated nitrogen atoms have 4 unique distances from the absorbing tin atom, whereas the I43d structure has 8 coordinated nitrogen atoms with only 2 unique distances from the absorbing tin atom. Though there is one extra nitrogen atom in the I43d structure, they are far more ordered than in the R3c structure. Using the more ordered I43d structure type can not properly describe the asymmetry and extra features in the first peak of the EXAFS spectrum. All spectra are phase corrected using the phase amplitude of the first nitrogen shell.  (7)

Bader charge analysis
Bader charge analysis allows for the evaluation of charge localization around specific ions in the system and can help in the identification of the ionization states of atoms. From Figure 8 we see that Sn-atoms are positively ionized, while N-atoms are negatively ionized in the spinel (F d3m) phase of Sn 3 N 4 , congruent with the ionic character of the bonding elucidated in the main body of the article. We observe that with increasing pressure the polarity of the bonding is also increasing, with charges becoming more localized around the respective ions.

Charge analysis
The conduction band and valence band charge density for the spinel unit cell is shown in Figure 9 for different pressures. A decrease in the interatomic spacing d from 2.08Å at ambient to 1.95Å at 50 GPa and 1.88Å at 100 GPa is accompanied by an increase in localization of conduction band charge density -most notably around the N atoms and in the interstitial between Sn sites. This increase in charge localization with pressure in turn produces deeper potentials and, as a result, sees the unoccupied levels in the CBM become harder to access energetically, notably this effect is less dramatic in valance charge (bottom panel). Figure 10 shows the changes in the conduction band charge as function of pressure from 40 to 100 GPa. Clearly visible for first neighbors Sn-N atoms (right part), localization increases with pressure. Figure 11 shows the changes in the conduction band charge as function of pressure from 80 to 120 GPa. Despite the electron differences become less pronounced at higher pressures, for the R3c phase substantially gain in ionization potential is seen for first neighbors N-Sn atoms.   11 Summary of experimental runs 12 Optical band gap measurements via in-house UV-vis Figure S 12: Circuit diagram for optical absorption measurements, using a Thorlabs FD05P InGaAs photodiode. The diode was attached to an op-amp to minimize any potential reverse bias current. Any signal output by the diode would cause a charge to build up on C2 proportional to the intensity of transmitted light incident on the diode. A voltmeter was then used to read the charge on C2, which was the intensity data point at a given wavelength selected by the monochromator.
Optical absorption measurements were undertaken at UNLV, using our home built design. a 300'W tungsten bulb was used as the source of polychromatic white light. Two means of data collection were implemented. The first method involved focusing white light through the sample chamber of a DAC and collecting the transmitted light with an Ocean Optics HR2000+ES spectrometer sensitive from 190-1100 nm -allowing for optical measurements from 1.20-3.25 eV. Alternatively, the source light was first sent through a Bauch & Lomb high-intensity monochromator with a transmission diffraction grating with a groove density of 337.5 g/mm. This allowed for the isolation of specific wavelengths in the visible and IR to be sent through a DAC and analysed by a Thorlabs FD05D InGaAs photodiode, with a maximum responsivity at 2300 nm. This allowed for absorption measurements of energies from 0.50-1.70 eV with high efficiency. An integrating circuit was used with the photodiode to allow for long collection times as the monochromator was scanned across a range of wavelengths from the visible into the IR. Fig. 12 is the circuit diagram for this system. The signal from the photodiode would charge a 1 µF capacitor, and a Triplett 1101-b multimeter was used to measure the voltage across the capacitor after a given exposure time. The voltage at each peak wavelength selected by the monochromator allowed for the compilation of a complete absorption spectrum through the sample across the visible and near IR. These measurements were normalised to I 0 by collecting thought the same, empty, DAC geometry.