  In order to fabricate precise atomic-scale devices in silicon using a
combination of scanning tunnelling microscopy (STM) and molecular beam epitaxy
it is necessary to minimize the segregation/diffusion of dopant atoms during
silicon encapsulation. We characterize the surface segregation/diffusion of
phosphorus atoms from a $\delta$-doped layer in silicon after encapsulation at
250$^{\circ}$C and room temperature using secondary ion mass spectrometry
(SIMS), Auger electron spectroscopy (AES), and STM. We show that the surface
phosphorus density can be reduced to a few percent of the initial
$\delta$-doped density if the phosphorus atoms are encapsulated with 5 or 10
monolayers of epitaxial silicon at room temperature. We highlight the
limitations of SIMS and AES to determine phosphorus segregation at the
atomic-scale and the advantage of using STM directly.
