Ab initio Green's function calculation of hyperfine interactions for shallow defects in semiconductors

Abstract

The structural identification of shallow defects and the control of their concentration is one of the key ingredients in semiconductor technology. Electron paramagnetic resonance (EPR) is the most sensitive experimental technique to address this problem, but requires comparative theoretical simulation of the microscopic structures. Whereas the standard supercell approach provides an accurate first principles analysis of localized deep defects, the wave function of shallow dopants often extends over several thousands of atoms and has to be treated in an empirical one-particle approach, the effective mass approximation (EMA). We report that modelling the shallow defects via a Green's functions approach allows an ab inito description of the so-called central-cell correction to EMA that accounts for the specific local part of the potential. The spatial distribution of the donor wave functions comes out within an accuracy that allows a prediction of hyperfine interactions including the Kohn-Luttinger oscillations within the ligand hyperfine structure -an effect that in quantum computing plays a key role in the control of the exchange coupling of qubits in semiconductors. For phosphorus in silicon, we show that in strained material these Kohn-Luttinger oscillations are partially suppressed. Our results indicate that in contrast to the prediction of the EMA, there exists no high-stress limit for the reduction of the central P-related hf splitting. The application of the approach onto donors in SiC confirms an incorporation of the P atoms onto both, the silicon as well as the carbon sublattice, if the donors are incorporated far away from thermal equilibrium.

Electronic structure of the nitrogen donors in 6H SiC as studied by pulsed ENDOR and TRIPLE ENDOR spectroscopy

“…Therefore, ab initio approaches are requested for the analysis of such detailed properties of the shfi parameters of the shallow donors, where rehybridization and spin polarization effects are hidden in real values of the product | u k ( r )| 2 ( S P ) 2 /| r l − r | 5 . This conclusion is supported by ab initio calculations of the hf and shf interactions for group‐V donors in Si which has been recently performed within Green's functions approach 28 and can be successfully applied for the description of the shfi constants of shallow N donors in SiC.…”

Which electronic structure method for the study of defects: A commentary

“…A remarkable feat of such methods is that they are able to describe the correct defect wave functions well outside the region in which the potential (and possibly the structure) is perturbed. This is emphasized in the contribution by Gerstmann [15] in this issue. It is evidenced by the degree of accuracy with which it can describe hyperfine and super-hyperfine interactions.…”

“…I have also tried to draw some attention to some of the ''forgotten'' problems and approaches, which were not very much represented during the workshop. In particular, the problem of EMT of shallow defects may see some revival and the paper included here on the Green's function approach [15] will hopefully remind some people of the promise held by this method.…”

“…The scissor shift is easily incorporated in Green's function methods [4,8,15]. In that case, one could even relatively easily include different shifts at different k-points instead of a uniform shift.…”

“…But nowadays, only a few practitioners of that approach remain. One at least is represented in this compilation [15]. Development of methodologies for dealing with ever larger systems, has of course continued, in particular, the development of order-N methods.…”