Stability and molecular pathways to the formation of spin defects in silicon carbide

Abstract

Spin defects in wide-bandgap semiconductors provide a promising platform to create qubits for quantum technologies. Their synthesis, however, presents considerable challenges, and the mechanisms responsible for their generation or annihilation are poorly understood. Here, we elucidate spin defect formation processes in a binary crystal for a key qubit candidate-the divacancy complex (VV) in silicon carbide (SiC). Using atomistic models, enhanced sampling simulations, and density functional theory calculations, we find that VV formation is a thermally activated process that competes with the conversion of silicon (V_Si) to carbon monovacancies (V_C), and that VV reorientation can occur without dissociation. We also find that increasing the concentration of V_Si relative to V_C favors the formation of divacancies. Moreover, we identify pathways to create spin defects consisting of antisite-double vacancy complexes and determine their electronic properties. The detailed view of the mechanisms that underpin the formation and dynamics of spin defects presented here may facilitate the realization of qubits in an industrially relevant material.

Fig. 1. Ball-and-stick representation of defects in cubic SiC (3C-SiC).

A divacancy-defect complex (VV) consists of a carbon vacancy (V_C) paired with a silicon vacancy (V_Si). Carbon and silicon atoms are shown as gray and blue spheres, respectively, whereas vacancies are depicted as white solid circles.

Fig. 2. Dynamics of vacancy formation and migration from classical molecular dynamics (MD) simulations.

A series of snapshots from classical MD simulations at temperatures above 1000 K show the mechanisms for a–d, the divacancy formation, e–h, divacancy reorientation, and i–l, conversion from a V_Si to a V_C before the V_Si encounters an existing V_C. Three-dimensional vacancy volumes colored in teal blue show the location, size, and shape of void volumes at the defect site. a A carbon atom in-between the V_C and V_Si sites displaces the V_C and forms a VV, following the path marked by a red arrow. b, c During intermediate steps, the mobile carbon atom interacts with neighboring atoms as the local coordination changes from five- and threefold. d The divacancy consists of a carbon vacancy adjacent to a silicon vacancy. e The orientation of VV changes as a carbon atom adjacent to V_Si migrates to the V_C site. f, g C–C bonds are formed and broken during intermediate steps. h The V_Si–V_C axis in the final VV configuration is rotated compared to that in the initial configuration, within the laboratory frame. i, j V_Si converts into C_SiV_C as a nearest-neighbor carbon atom displaces it. Red circle indicates the C_Si site. k, l C_SiV_C dissociates into V_C and C_Si as V_C exchanges position with a nearest carbon atom.

Fig. 3. Free-energy landscapes of vacancy conversion processes for VV and V_Si.

Potentials of mean force (PMFs) were computed using enhanced sampling simulations with FPMD. Two-dimensional order parameters, ${\xi }_i=\left({\xi }_{i,x},{\xi }_{i,y}\right)$, are used to describe the position of a carbon atom migrating toward a vacancy site, which is the primary mechanism for VV formation (a, d), VV reorientation (b, e), and V_Si to C_SiV_C conversion processes (c, f). a–c 2D-PMFs show free energy surfaces of vacancy-conversion processes at 1500 K, whose minimum free-energy pathways are marked by white dotted lines. d–f Free-energy profiles reveal intermediate (state M_i) and transition states (state T_i) along the reaction coordinates. The gray shaded regions denote the error in the PMF determined by block averaging. All three mechanisms are thermally activated processes with relatively high-energy barriers (>1.3 eV).

Fig. 4. Effects of temperature on the divacancy formation and destabilization.

a Fraction of divacancies computed from classical MD simulations up to 10 ns, starting with only VVs. The black circles are experimental data, showing normalized EPR intensity of VV measured after annealing a nonirradiated 4H-SiC sample for 30 min. The dotted black line is a fit to experimental data (see descriptions in the text). Both the simulations and the experiment indicate that divacancies begin to dissociate at ~1700 K. b Population of defects after VV dissociation. Solid and dotted lines indicate classical MD (10-ns long) and kinetic Monte Carlo (KMC) (${10}^{15}{k_0}^{-1}$-long) simulations, respectively. Both sets of data demonstrate that V_C’s are the dominant defect species at high temperatures. At each temperature, the number of defects created from VV-dissociation process (V_C, V_Si, and C_SiV_C) is normalized by the initial number of VVs. c Photoluminescence (PL) intensity of VV versus annealing temperature based on data from recent experimental studies using irradiated or ion-implanted samples of 4H-SiC^,. The PL intensity in each data set is normalized by the maximum signal measured. The type of implantation ion and the dose are shown in the legend. The dotted line is the fitted curve using a Gaussian process model, which predicts an optimum annealing temperature of ~1193 K. The temperature regime for optimal VV formation from MD simulations is between ~1000 K and ~1500 K (blue shaded region).

Fig. 5. Dependence of VV-conversion efficiency on the initial composition of monovacancies.

a (top panel) KMC simulations showing changes in the long-time limit of VV population starting with varying concentrations of V_Si, i.e., the number of V_Si over the total number of vacancies, at two different temperatures T (black line at T_KMC = 1500 K, red line at T_KMC = 2000 K). (bottom panel) Classical MD simulations showing the time evolution of mono- to divacancy conversion up to 100 ns at T_MD=1500 K, starting with different fractions of V_Si, i.e., the number of V_Si over the total number of V_Si and V_C. The VV formation favors higher concentrations of V_Si, agreeing with the high-temperature behavior of the KMC model. b–c Schematics for controlling divacancy formation by tuning the V_Si-to-V_C ratio during thermal annealing at high temperature based on the results from panel a. b Samples having a greater number of V_Si than V_C prior to annealing (left) producing more VV after annealing (right). c Samples having a fewer number of V_Si than V_C prior to annealing (left), producing fewer VV after annealing (right).

Fig. 6. Electronic structures of VV⁰ and antisite-vacancy complexes identified from MD simulations of VV dissociation.

Defect structures (top) and defect energy-level diagrams (bottom) are shown for neutral a, VV, b, V_CC_SiV_C, and c, [C_SiV_C + V_C]_n=3. For the [C_SiV_C + V_C] defect shown here, the two carbon vacancies are separated by at least n = 3 atoms. For each defect, the lowest electronic configuration is a triplet state. Shaded gray areas indicate energy levels below the valence band (VB) and above the conduction band (CB). The spin-majority (spin-minority) channel is denoted by upward- (downward-) pointing arrows.