Effect of Chamber Pressure on Scattering of Sputtered Atoms and on the Growth Rate
A magnetron sputtering system performance is mainly defined by parameters like magnetic field strength, plasma discharge power, depth of target erosion zone, working gas pressure, and other structural and technological parameters. Working gas pressure during the magnetron sputtering deposition not only affects purity and quality of the layer, but plays an important role in transport of sputtered atoms to the substrate.
It is evident that the growth rate is directly related to the number of atoms reaching the substrate. Based on the elastic collision model it can be deduced that in deposition of silicon by magnetron sputtering, a silicon atom knocked out of the target surface loses around 97% of its energy during collision with an Ar atom, unable to reach the substrate through cathodesubstrate distance.
So unscattered silicon atoms mainly contribute to the layer growth. Hence, it is sensible to compare layer growth rate with ratio of unscattered sputtered atoms by working gas species. Here, the dependence of growth rate on the scattering of target particles, and so on working pressure, is calculated. To estimate the number of sputtered target particles per second, N_{s}, one can write equation (1):
N_{s}=N_{e} K(E_{0}) (1)
Where N_{p} is the number of primary ions per second and K(E_{0}) is the sputtering coefficient, which is related to the energy of chamber gas ions. K(E_{0}) is numerically equal to the ratio of number of primary ions bombarding the cathode to atoms leaving the target, demonstrating the sputtering efficiency. For ion energies lower than 1000 eV, sputtering coefficient is proportional to their energies.
The energy of chamber gas ions depends on the magnetron discharge voltage, hence on the chamber pressure. So, the sputtering coefficient and sputtering rate is also related to the chamber working pressure. N_{p} is determined by the fact that only ions in the nearcathode magnetron discharge region participate in current transport process. As well, N_{p} is proportional to magnetron discharge current:
N_{p}=I/e (2)
In equation (2), I is magnetron discharge current and e is the electron charge. The sputtered atoms mean free path distribution and their scattering by working gas atoms should be considered to describe their transport thoroughly. Moreover, a rough estimate shows if masses of target and working gas atoms are comparable, the sputtered atoms lose most of their energy during collision. So, uncollided atoms contribute to the energy transfer to the substrate and are studied here.
The probability of colliding a sputtered atom with working gas atom, C(L), in which the free path of an atom does not go beyond the cathodesubstrate distance is defined as:
C(L)= 1exp(L/λ) (3)
Where L is the than cathodesubstrate distance and λ is the mean free path calculated in a certain pressure, given by equation (4):
λ= (k_{B} T)/(√2 P_{g} σ) (4)
where P_{g} is the overall pressure produced by sputtered and working gas atoms, k_{B} is the Boltzmann constant, T is the temperature and σ is scattering cross section of total interactions, including momentum transfer between the colliding particles, ionization process and atomic excitations. Figure 1 shows the dependence of fraction of scattered sputtered atoms transporting in cathodesubstrate distance on the working gas pressure.
So, number of colliding sputtered atoms N_{f} in pressure P_{g} equals:
N_{f} = I K(E_{0})/e exp((√2 P_{g} σL)/(k_{B} T)) (5)
As an example, if the chamber pressure increases from 1.5 to 8.5 Torr, the number of unscattered sputtered atoms in cathodesubstrate distance reduces by 90%, following a 25% decrease in the layer growth rate (Figure 2).
For example, in magnetron sputtering of silver, the growth rate is different in various working pressures and applied powers. The effects of working pressure and cathode current on the growth rate are studied separately by DST1 magnetron sputtering system and the results are demonstrated in Figure 3.
As shown, decreasing the chamber working gas pressure has a greater effect on increasing the growth rate than raising the cathode current. Since higher cathode currents results in the substrate heating effects, it is preferable to reduce working pressure in order to achieve higher growth rate for temperaturesensitive depositions. Lower pressures for higher layer growth rates are accessible by utilizing turbomolecular vacuum pumps.
TurboPumped Coating Systems
Vaccoat Ltd. produces various turbopumped coating systems including desk sputter coater (DST1), triple target sputter coater (DST3) with thermal evaporator (DST3T), and carbon coaters like DCT and DSCT. For more information, you can visit the website or refer to the article below.
References

D.M. Mitin, A.A. Serdobintsev, Effect of Scattering of Sputtered Atoms on the Growth Rate of Films Fabricated by Magnetron Sputtering, Technical Physics Letters, 2017, Vol. 43, No. 9, pp. 814–816.