Effective mass approximation for spatial structures of two different single acceptors imaged by STM: bismuth in silicon and manganese in indium antimonide*

Impurities are known for introducing discrete energies in the band gap of their semiconductor hosts caused by localized states. Interestingly, those states could be qubits platforms controlled by external electric fields [1]. Comprehending spatial structures of these acceptors, such as energy exchange and density of states (DOS), is crucial for manipulating them [2]. With STM results [3], this work characterizes a single Bi acceptor state in Si in the effective mass approximation. Using ref.[4] we solve analytically the spherical Luttinger-Kohn Hamiltonian in the zero-range potential. Following that, a cubic symmetric wave-function is constructed which at different (001) planes shows a square-like shape for the DOS due to a bigger contribution of d-like states. The results are similar to the STM images, giving support for their acceptor nature. Furthermore, we extend these calculations to describe a magnetic Mn acceptor in InSb, and the results are compared with STM images from [5].

[1] A. M. Stoneham, et al., Journal of Phys. Cond. Matter 15,  27 (2003)

[2] D. Kitchen, A. Richardella, J.-M. Tang, et al., Nature 442, 436 (2006)

[3] M. Siegl, Ph.D. thesis, University College London (2018)

[4] A. M. Yakunin, A. Y. Silov, P. M. Koenraad, et al., Phys. Rev. Lett. 92, 216806 (2004)

[5] S. J. C. Mauger, J. Bocquel, P. M. Koenraad, et al., Appl. Phys. Lett. 107, 222102 (2015)