In the manufacture of semiconducting thin films, a thin film of solid arsenic laid down on the surface of a silicon water by the diffusion-limited chemical vapor deposition of arsine, AsH 3 . The gas...

In the manufacture of semiconducting thin films, a thin film of solid arsenic laid down on the surface of a silicon water by the diffusion-limited chemical vapor deposition of arsine, AsH₃.

The gas head space, 5 cm above the surface of the wafer, is stagnant. Arsenic atoms deposited on the surface then diffuse into the solid silicon to ‘‘dope’’ the wafer and impart semiconducting properties to the silicon, as shown in the figure below.- Well mixed feed gas (constant composition).

The process temperature is 1050C. The diffusion coefficient of aresenic in silicon is 5
 cm/s at this temperature and the maximum solubility of aresenic in silicon is 2
 10²¹
atoms/cm³. The density of solid silicon is 5
 10²²
atoms/cm³. As the diffusion coefficient is so small, the aresenic atoms do not ‘‘penetrate’’ very far into the silicon solid, usually less than a few microns. Consequently, a relatively thin silicon water can be considered as a ‘‘semi-infinite’’ medium for diffusion.

a. State at least five reasonable assumptions for the mass transfer of aresenic in this doping process.

b. What is the simplified form of the general differential equation for the mass transfer of the aresenic concentration within the silicon? Purpose reasonable boundary and initial conditions.