  Atomic-scale understanding of phosphorous donor wave functions underpins the
design and optimisation of silicon based quantum devices. The accuracy of
large-scale theoretical methods to compute donor wave functions is dependent on
descriptions of central-cell-corrections, which are empirically fitted to match
experimental binding energies, or other quantities associated with the global
properties of the wave function. Direct approaches to understanding such
effects in donor wave functions are of great interest. Here, we apply a
comprehensive atomistic theoretical framework to compute scanning tunnelling
microscopy (STM) images of subsurface donor wave functions with two
central-cell-correction formalisms previously employed in the literature. The
comparison between central-cell models based on real-space image features and
the Fourier transform profiles indicate that the central-cell effects are
visible in the simulated STM images up to ten monolayers below the silicon
surface. Our study motivates a future experimental investigation of the
central-cell effects via STM imaging technique with potential of fine tuning
theoretical models, which could play a vital role in the design of donor-based
quantum systems in scalable quantum computer architectures.
