Quantitative Modelling of Residual Molecular Contamination in Low-Pressure Processing Environments
Authors: Mertens Paul W. 
Published: December 2024

During the fabrication, micro-chips circuits are very sensitive to all kinds of contamination present in the environments fluid in contact with the wafers.
A previous study [1] describes the issue of wafer molecular surface contamination as a result of exposure to clean room air. If needed clean room air can be purified to the desired level using appropriate chemical filters.
A lot of state-of-the-art processing steps occur in low pressure environments, or so called vacuum cluster tools comprising a wafer handler equipped with different chambers. All of these chambers have a finite residual base pressure (typically on the order of 1 Pa).
A major part of the residual gas may consist of rather harmless inert gas such as N2 or Ar. A fraction of the background ambient may consist of uncontrolled residual gas that could originate from different sources (e.g. desorption from reactor walls or wafer backside, back diffusion from vacuum pumps, )
Such uncontrolled molecules could adhere to the wafer surface and leave some surface contaminants that can negatively impact the subsequent process step (e.g.).
The current study quantitatively describes this issue.
In a gas ambient the ideal gas law provides eq.1
Where:

C

i
is the volume concentration of impurity i

h
i
: the fraction of the number of impurity molecules, i, over the total number of all molecules

p is the total pressure of all residual gas.

In the current study we assume the sticking coefficient to be 1. This is a safe worst-case scenario and also the scenario for the impurity molecules that stick the best and are thus most detrimental and of major concern.
The thermal contamination build-up on the surface, si, is determined by the mean thermal velocity. The surface concentration of contaminant i building up on the surface, normalized to its volume concentration in the gas phase, is given by the average thermal bombardment velocity on the surface (= arrival velocity) multiplied with the exposure time. The thermal velocity is roughly independent of pressure and is primarily determined by the temperature and the mass of the molecules: for room temperature air it is as high as 500 m/s. this implies that molecules travel very fast. The normalized concentration is then given by eq.2
This normalized concentration has the dimension of length (expressed in units of m).
One can compare this length to the characteristic space available in the vacuum chamber perpendicular to the wafer surface. For most systems this is expected to be on the order of 1 to 10 cm.
3 numerical examples are provided in Table I.
These examples show that significant amounts of contamination (1e11 to 1e13 at/cm2) can readily build-up on the surface.
As can be seen, on Figure 1 the normalized deposition reaches already 10 cm in as little 1 msec implying that all available contamination gas inside the reactor would have deposited on the wafer surface in only 1 msec.
In real cases there is typically a continuous supply of impurity molecules to the gas phase (from desorption from other surfaces etc..) with the surface with the highest sticking coefficient ultimately collecting the most contaminants.
Figure 1 shows the surface concentration of surface contamination normalized to the impurity volume concentration in the ambient as a function of time.
References

P.W. Mertens, ECSTransactions 92, p.237, (2019);

Figure 1