Impingement rate

The deposition rate increases upon increasing the pressure. This is explained by noting that the impingement rate per unit area, r,, of molecules on the filament is linearly dependent on the pressure as r, = pj 2nksT, with the gas temperature. However, as the pressure becomes higher, the collisional mean free path of the silane becomes smaller, and the silane supply to the filaments becomes restricted. Moreover, the transport of deposition precursors to the substrate is restricted as well. The mean free path of silane was estimated to be 2.5 cm at a pressure of 0.02 mbar [531]. i.e.. the mean free path about equals the distance between filament and substrate. Indeed, a maximum in deposition rate is observed at this pressure. This corresponds to a value of pdk of 0.06 (cf. [530]). The microstructure parameter plotted as a function of pd has a minimum around Ms = 0.06 0.02 [530]. 

A technique frequently used to characterize the pressure state in the high vacuum regime is the calculation of the time required to form a monomolecular or monoatomic layer on a gas-free surface, on the assumption that every molecule will stick to fhe surface. This monolayer formation time is closely related with fhe so-called impingement rate z. With a gas at rest the impingement rate will indicate the number of molecules which collide with the surfece inside the vacuum vessel per unit of time and surface area ... 

Consider now the vicinal surface where the impingement rate is the same as above. Adsorbed atoms will now either evaporate or diffuse to a ledge and become incorporated into the growing crystal. 

Gas molecules are transported to the interface. Long (1994) notes that the gas impingement rate is 1022 molecules/(cm2s) at the normal temperatures and pressures of hydrate formation. Kvamme (1996) indicates this step is transport of molecules through a stagnant boundary. 

Thus, XPS and TPRS investigations of Pd(lll) clearly show that at elevated pressures methanol decomposition to give CO and H2 occurs only to a small extent. There is a rapid self-poisoning by adsorbed CO and CH at 300 K, whereas at 400 K a rapid formation of CHX layers prevents a significant conversion. These results indicate that Pd(lll) is in fact able to break the C-O bond in methanol, but its observation may require a sufficient methanol impingement rate at temperatures greater than approximately 250 K. To produce CO and H2 from methanol on palladium catalysts, the CHX formation must be suppressed or CHX must be selectively removed from the surface. 

A molecule for adsorption is chosen to be A with the probability p and B2 with the probability 1 —p, where p < 1 is the parameter characterizing the relative impingement rates of A and B2. To realize adsorption of B2, a configuration for B2 is selected at random. An adsorption trial is considered to be successful provided that all the sites of the selected configuration are vacant and belong to the catalyst. Adsorption of the chosen molecule A is realized with the unit probability. 

If the deposition process is a first-order reaction having Arrhenius temperature dependence, the surface reaction rate, S, can be expressed as the product of the surface impingement rate and a reaction probability, ( ). In terms of the gas molar density and reactant mole fraction this is... 

It should be noted that the aforementioned nucleation models and mechanisms are applicable to the formation of single-crystal, polycrystaUine, and amorphons deposits, and of inorganic, organic, and hybrid deposits. Whether the deposit is single crystalline, polycrystalline, or amorphous depends on the growth conditions and the substrate. Deposition temperature and the impinging rate of growth species are the two most important factors and are briefly summarized below ... 

The attachment frequency is simply proportional to the impingement rate of atoms, i.e., proportional to the partial pressure of the atoms of the gas phase. It has roughly the same value for all surface sites. 

The interpretation of the nucleation rate equation in terms of its overpotential dependence is rather difficult to perceive as represented in the form of eq. (4.42). It has been shown already that the products in the denominator of this equation contain the formation energy AG(iV) of clusters of class N (cf. eq. (4.47)), and that, at a given overpotential, AG has a maximum determining the critically sized cluster, N=Ncnt-The n terms in the sum of the denominator of eq. (4.42) show a maximum for the critically sized cluster. All terms other than that for this cluster can be neglected including the unity in the denominator [4.13, 4.14). Note that/is always much smaller than the impingement rate ti att.o times the adsorption sites Z<, and hence the denominator is much larger than unity. Then ... 

Normalized rate of the A + B2 reaction as a function of the ratio of the impingement rates of A and B2 for the cases when A diffusion limitations inside the pore are negligible (thick lines) and significant (thin lines). The model parameters employed are typical for CO oxidation on noble metals at Pco + T o2 = 0.01 bar and r=500K. (Redrawn from Ref. [30].)... 

Fig. 4. Net rate of adsorption as a function of impingement rate. Xe at Tq = 300° K on tungsten 80° K. Slope = sticking coefficient intercept = evaporation rate = F-pfA. From ref. 88.

The key step in the derivation by Reuter et al. of their lattice model is the use of detailed balance to determine the sticking coefficients for each species on each type of site.31 The total adsorption rate at a particular site can be expressed as Tad = SI(p, T), where S is the local sticking coefficient and I(p,T) is the impingement rate of the species of interest from a gas phase with partial pressure p and temperature T. At steady state, the total adsorption and desorption rates must satisfy the detailed balance condition TdesjTad = exp[(Fb—/j,(T, p))/kT, where Fb is the free energy of the adsorbed species and fi(T, p) is the chemical potential of the gas phase species. The adsorption free energy is well approximated by the adsorption enthalpy, which is simply the adsorption energy calculated by a DFT calculation. This approach provides a direct link between the adsorption and desorption rates and the pressure and temperature of the bulk gas phase. 

Their results can be expressed as In = In tq + SWJkT where AH(desorp-tion) is 11.9 kcal mol and tq is 1 x 10 ° s. These values indicate mean lifetimes of a few hundredths of a second at room temperature. For a molecular impingement rate on to the surface of 1 x 10 molecules cm s this gives an equilibrium concentration on the surface of 10 molecules cm , or about 10 monolayer. The authors go on to express the view that the firmly-held chemisorbed species could not contribute to further chemical reaction and that the species involved in catalysis is probably the loosely-bound phase. 

It is clear that whether we deposit a film or not depends on the impingement rate and substrate temperature for a given combination of materials. We can, in fact, map out the conditions for film deposition, usually on a plot of log (impingement rate) versus reciprocal temperature as shown in Figure 1. At high temperatures and low rates of impingement, there is no deposit aside from the equilibrium adpopulation while for low temperatures (when binding to the substrate is influential) and rapid deposition rates, we observe film formation. 

Figure 1. Schematic plot of impingement rate vs. reciprocal absolute temperature showing conditions for film growth in conventional physical vapor deposition.

Fig. 4. Dependence of N0+ and PtO+ intensities on reaction time, tp.N0 pressure 1.3x10 Pa T = 543 K, = 28 V/nm T = mean lifetime of molecular adsorbed NO impingement rate 0.19 molecules/s into the monitored area.

Similarly, the dissociation probabilities,w, can be calculated by comparing the PtO intensities with the impingement rate. Within the measured time range, w is small. At a time tp =1 s, w is of the order of a few percent only. The dissociation probability of NO on stepped Ru(001) is higher and amounts to a constant value of more than 5 % (see Fig. 3). Note that the surface oxide coverage on both substrates, Ru as well as Pt, is far below a monolayer. Thus, the w values refer to the low coverage limit. 

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