First-principles calculations of hyperfine interaction, binding energy, and quadrupole coupling for shallow donors in silicon

Abstract

Spin qubits based on shallow donors in silicon are a promising quantum information technology with enormous potential scalability due to the existence of robust silicon-processing infrastructure. However, the most accurate theories of donor electronic structure lack predictive power because of their reliance on empirical fitting parameters, while predictive ab initio methods have so far been lacking in accuracy due to size of the donor wavefunction compared to typical simulation cells. We show that density functional theory with hybrid and traditional functionals working in tandem can bridge this gap. Our first-principles approach allows remarkable accuracy in binding energies (67 meV for bismuth and 54 meV for arsenic) without the use of empirical fitting. We also obtain reasonable hyperfine parameters (1263 MHz for Bi and 133 MHz for As) and superhyperfine parameters. We demonstrate the importance of a predictive model by showing that hydrostatic strain has much larger effect on the hyperfine structure than predicted by effective mass theory, and by elucidating the underlying mechanisms through symmetry analysis of the shallow donor charge density.

Effective Donor Dopants for Lead Halide Perovskites

“…As is shown in Figure 3, Y and Sc remain shallow donors in all three LHPs, consistent with their atomic orbitals sitting above those of the Pb 6p states. An estimated ionization energy of 0.1 eV is used for these donors in each compound (determining shallow-donor ionization energies to higher accuracy are very challenging 53 and outside the scope of this work). Since CsPbCl 3 has among the highest-lying CBM in LHPs (and FAPbI 3 among the lowest), this behavior is likely to be consistent in all LHPs.…”

Frenkel Excitons in Vacancy-Ordered Titanium Halide Perovskites (Cs2TiX6)

“…As discussed in Section S3, quasiparticle band gaps and thus exciton binding energies from GW (+BSE) remain overestimated for these vacancy-ordered compounds, consistent with recent studies that attribute this behavior to underscreening errors within the random phase approximation (RPA) employed within GW . ,− As such, to avoid this issue and obtain a reasonable estimate of the exciton binding energies in these systems, we also employed a constrained-supercell approach in which an exciton state is generated by controlling spin initialization and band occupation. Here we calculate the exciton binding energy using hybrid DFT for multiple supercell sizes of ≤972 atoms and then extrapolate to the dilute limit using the relevant scaling relationship to avoid supercell-size effects. , With this approach, we obtain localized Frenkel exciton states as expected for each Cs 2 TiX 6 (Figure S13, TOC), with extrapolated binding energies of 0.44, 0.52, and 0.72 eV for X = I, Br, and Cl, respectively (Figure S14), which when subtracted from the HSE06+SOC direct-allowed transition energies in Table brings the hybrid DFT optical transition energy into agreement with the experimental values in each case. For Cs 2 SnX 6 , the electron and hole remain delocalized across the supercell with this approach [under a maximum cell length of 23.1 Å (Figure S13)], yielding extrapolated binding energies close to zero (Figure S15).…”

Frenkel Excitons in Vacancy-ordered Titanium Halide Perovskites (Cs₂TiX₆)

“…Here we calculate the exciton binding energy using hybrid DFT for multiple supercell sizes up to 972 atoms, then extrapolate to the dilute limit using the relevant scaling relationship to avoid supercell-size effects. 65,66 With this approach, we obtain localised Frenkel exciton states as expected for each Cs 2 TiX 6 (Fig. S13, TOC), with extrapolated binding energies of 0.44 eV, 0.52 eV and 0.72 eV for X = I, Br, Cl (Fig.…”