Common Cluster Beam Formation Techniques

Cluster ion beam is a deposition process where high quality films are formed through clusters of electrically charged ions. In IC manufacturing, cluster ion beam is used for film formation of dielectric and other wafer layers at low substrate temperature.

While there are different techniques to generate clusters, the criteria of identifying the appropriate type of technique typically depend on the requirement of the project (see Common Techniques Used to Form Cluster Ions). After considering several factors on generating cluster ions, the next phase is choosing the right method of extracting the clusters from the chamber and forming a high quality beam. This phase is critical to the efficiency of the whole cluster ion beam process, since using an improper method will disturb the flow of clusters and disperse the beam, hence, will cause some of the clusters to go astray.

The pressure gradient between the condensation chamber and the high vacuum region causes the cluster flow to accelerate as the clusters exit from the chamber. This acceleration is dependent on the pressure ratio:



P0 is the source pressure of the nozzle from the condensation chamber.

Pb is the pressure at the high vacuum region (background pressure).

Once this ratio exceeds the constant G, which is always less 2.1 for gases, the flow will be faster than the local speed of sound in the gas and the Mach number, M>1. This means the flow has become supersonic and shock waves may cause problems on the process. Shock waves are undesirable and, unfortunately, unavoidable in cluster beams. These shock waves causes beam scattering, which degrades the intensity of the beam. Shock waves manifest because there is a need for the cluster flow to adapt on the boundary conditions downstream. However, the propagation speed against the flow of the information on downstream conditions is the same as the local speed of sound, which means at M>1, it will be difficult to propagate the information upstream. Thus, when the cluster flow adapts with the boundary conditions, shock waves are formed in the cluster beam.

The following are four of the most common cluster beam formation techniques:

1.      Supersonic Jet Expansion

In a supersonic jet expansion system, the cluster flow accelerates in the nozzle at approximately M=1. As it moves away from the nozzle, the cluster will continue to accelerate and expand until it over expands. The over-expanded clusters are recompressed by a series of shocks generated in a barrel shock, which is located between the nozzle and the Mach disk. The Mach disk serves as the transition point of the flow from supersonic back to subsonic. It is situated perpendicular to the flow at a characteristic distance given by-

XM/d = 0.67(Pb/P0)1/2


XM/d is the correlation of the distance from the nozzle to the Mach disk in nozzle units

To steer clear of the scattering by the shocks, the extraction must occur before the beam reaches the Mach disk from the zone of silence. The zone of silence is the isolated region inside the barrel shock, which the information of the conditions outside cannot penetrate. A skimmer is used to pass the clusters through the center without any disturbance and to deflect the off axis molecules away from the axis.

2.      Campargue Source

This method operates at a relatively high background pressure of ≥10-2 mbar and uses Roots pumps to pump out the gas from the chamber to the beam. Moreover, its Mach disk is placed within the zone of silence, which turns the expansion as if it was in a perfect vacuum. The high background pressure has significantly lessened the required energy to pump the gas out of the chamber, which also equates to reduction of the system size. However, the scattering inside the skimmer has intensifies at high pressure since there are shock waves at the edge of the skimmer. This leads to a formation boundary layer at the skimmer opening, which also means reduction on the open channel through the skimmer. Thus, the design of the skimmer in Campargue source systems is very crucial. To meet the small external angle requirement of keeping away from the scattering outside the skimmer back in to the beam, and the large internal angle requirement of preventing the scattering inside the skimmer from the gas molecules, the skimmer opening must around 50°.

3.      Fenn Type Free Jet

Fenn type free jets also use high background pressure (Pb ≥10-4 mbar) but its Mach disk is located far from the nozzle or sometimes it is not present at all, which allows smooth transition from the expansion to the molecular flow. Unlike the Campargue source, the skimmer’s design is much less crucial. The typical optimum skimmer opening angle is around 30° and its location on the system depends on the beam’s angular divergence. 

4.      Mixed Beams, velocity slip

By introducing small concentrations of heavier gas molecules, the heavy molecules in mixed beams will be able to flow at the same acceleration as the lighter ones and most likely will gain kinetic energy of several electron volts. However, there is a possibility for velocity slip to occur, where the heavier molecules may not have enough acceleration when its weight becomes too much greater than the lighter molecules at low source pressure. This usually happens at regions with large pressure gradient like the subsonic region of the condensation chamber’s nozzle and the supersonic region of the high vacuum region. Velocity slip can bring in dependency of energy on mass, which means it is crucial when mass-selecting the beam.

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