Electronic Structure of CaSnN$_2$: a sustainable alternative for blue LEDs

TL;DR

This paper investigates CaSnN$_2$ in the $Pna2_1$ structure as a sustainable blue-light-emitting semiconductor. Using the QS$GW^{ ext{BSE}}$ method, it predicts a direct band gap at $oldsymbol{ extGamma}$ of $E_g = 2.680$ eV, corresponding to $ ext{λ} \, ext{≈}\,463$ nm, with the valence band maximum of $a_1$ symmetry enabling $E \\parallel c$ transitions to the conduction band minimum. The study also characterizes the anisotropic valence-band structure, computes effective masses, and provides a comprehensive exciton analysis, including several dark excitons, with a bare binding energy around $0.135$ eV (reduced to $ ext{≈ }3.66 imes 10^{-2}$ eV after dielectric corrections). Additionally, it reports the dielectric response and showcases how lattice polarization effects would influence exciton binding. Overall, CaSnN$_2$ emerges as a viable Ga/In-free blue LED candidate, contingent on experimental growth of high-quality thin films and feasible p/n-type doping strategies.

Abstract

The electronic band structure of CaSnN2 in the wurtzite-based Pna21 structure is calculated using the Quasiparticle Self-consistent (QS)GW$^{BSE}$ method, including ladder diagrams in the screened Coulomb interaction W$^{BSE}$ and is found to have a direct gap of 2.680 eV at Γ, which corresponds to blue light wavelength of 463 nm and makes it an attractive candidate for sustainable blue light-emitting diodes (LEDs), avoiding Ga and In. The valence band maximum has a1 symmetry and gives allowed transitions to the conduction band minimum for light polarized along the c-direction. The valence band splitting is analyzed in terms of symmetry labeling, and the effective mass tensor is calculated for several bands at Γ. The optical dielectric function, including electron-hole interaction effects is also reported, and the excitons are analyzed, including several dark excitons.

Figures (7)

• Figure 1: Crystal structure of CaSnN$_2$ with nearest neighbor CaN$_4$ tetrahedra in blue and nearest neighbor SnN$_4$ tetrahedra in gray shown from (a) side view and (b) top view. The image is generated using the VESTA3 software Vesta.
• Figure 2: Band structure of CaSnN$_2$ obtained in the QS$GW^{\mathrm{BSE}}$ method, the irreducible Brillouin zone is a rectangular box with corners $\Gamma=(0,0,0)$, $X=(\pi/a,0,0)$, $Y=(0,\pi/b,0)$, $S=(\pi/a,\pi/b,0)$, $Z=(0,0,\pi/c)$, $U=(\pi/a,0,\pi/c)$, $T=(0,\pi/b,\pi/c)$, $R=(\pi/a,\pi/b,\pi/c)$.
• Figure 3: Total and partial densities of states in $Pna2_1$ CaSnN$_2$. The partial contributions include the sum over all equivalent atoms, but refer to partial wave contributions inside the muffin-tin spheres only, excluding those from the interstitial region and only showing the major contributions. Here N$_1$ are the Nitrogen labeled as $\rm N_{Ca}$, and N$_2$ are $\rm N_{Sn}$ in Fig. \ref{['structure']}.
• Figure 4: Imaginary part of the optical dielectric function, $\varepsilon_2^{i}(\omega)$ shown in full line, obtained using the BSE with the broadening parameter of $\eta=0.005$ Ry (as in Eq. \ref{['epsmac']}), including top 15 valence bands and bottom 13 conduction bands. Independent particle approximation results using a finer $20\times20\times20$$\bf k$-point mesh, without any broadening factor (as in Eq. \ref{['eps2']}) is shown in dotted line. The three components of the macroscopic dielectric function parallel to $\mathbf{a}$,$\mathbf{b}$,$\mathbf{c}$ axes are shown in (a),(b),(c) respectively.
• Figure 5: Exciton wave function weights, $W_{v(c)\bf k}^{\lambda}$, for $\lambda=1\dots7$ contributed by CBM of $a_1$ symmetry and top six valence bands of $a_1$, $b_1$, $a_2$, $b_1$, $b_2$, and $a_1$ symmetries. The size of the colored circles are scaled with respect to the exciton weights, and the use of different colors serves to distinguish different bands. The $\lambda=3,6,8$ excitons are dark excitons, whereas the others are bright or semi-bright with respect to their oscillator strengths reported in Table \ref{['tab-exciton']}.