Microelectronic devices are fabricated by forming many layers of thin films onto a silicon wafer….

Microelectronic devices are fabricated by
forming many layers of thin films onto a silicon wafer. For example, thin films
of arsenic as a common dopant for silicon are commonly deposited onto silicon
by chemical vapor deposition, or CVD, of arsine (AsH3) vapor onto
the surface of the wafer. The chemical reaction for this CVD process is

It is proposed to allow this process to
take place at a pressure of 303.9 Pa and a temperature of 600C. In many CVD
reactors, the gas phase over the thin film is not mixed. Furthermore, at high
temperatures, the surface reaction is very rapid. Consequently,
»

Microelectronic devices are fabricated by
forming many layers of thin films onto a silicon wafer. For example, thin films
of arsenic as a common dopant for silicon are commonly deposited onto silicon
by chemical vapor deposition, or CVD, of arsine (AsH3) vapor onto
the surface of the wafer. The chemical reaction for this CVD process is

It is proposed to allow this process to
take place at a pressure of 303.9 Pa and a temperature of 600C. In many CVD
reactors, the gas phase over the thin film is not mixed. Furthermore, at high
temperatures, the surface reaction is very rapid. Consequently, the molecular
diffusion of AsH3 vapor to the surface often controls the rate of
As(s) formation. Consider the very simplified CVD reactor illustrated in
Chapter 25, Problem 25.11.

A mixture of arsine and hydrogen gas
continuously flows into the reactor. The mixture contains 20 mol% arsine. A
diffuser provides a quiescent gas space over the growing As film. The distance
from the diffuser to the film surface is 6.0 cm. The gas mixture may be assumed
to behave as an ideal gas. The molecular weight of arsenic, As, is 75 g/g mol.
The Lennard– Jones parameters for SiH4 are

a. What is the molecular diffusion
coefficient of arsine vapor in hydrogen gas at 600C and 303.9 Pa?

b. Develop a model to predict the diffusion-limited
flux of arsine to the surface of the wafer. State at least three assumptions
relevant to this process.

c. The diameter of the wafer is 15 cm.
Estimate the initial deposition rate of arsenic onto the surface of the wafer,
in units of grams of As per minute.

Problem 25.11

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.

»

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