The properties of neutral acceptor states in zinc-blende semiconductors are re-examined in the frame of extended-basis $sp^3d^5s^*$ tight-binding model. The symmetry discrepancy between envelope function theory and atomistic calculations is explained in terms of over symmetric potential in current k$cdot$p approaches. Spherical harmonics decomposition of microscopic Local Density Of States (LDOS) allows for the direct analysis of the tight-binding results in terms of envelope function. Lifting of degeneracy by strain and electric field and their effect on LDOS is examined. The fine structure of magnetic impurity caused by exchange interaction of hole with impurity $d$-shell and its dependence on strain is studied. It is shown that exchange interaction by mixing heavy and light hole makes the ground state more isotropic. The results are important in the context of Scanning Tunneling Microscopy (STM) images of subsurface impurities.
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