SUPPLEMENTARY MATERIAL FOR
“PREVENTING THE KINETIC ROUGHENING IN PHYSICAL
VAPOR-PHASE DEPOSITED FILMS”
E. Vasco, C. Polop and J.L. Sacedón
Abstract: Detailed information on the physical meaning of the simulation
parameters describing the interaction of energetic species evaporated from a
hyperthermal source with the growing film by physical vapor-phase deposition.
Contents.
1. Cluster break-up power of an energetic flux
p. 1
2. References
p. 3
1) Cluster break-up power of an energetic flux
The cluster break-up power ( X n ) describes the interaction of energetic
species in a flux emitted from a hyperthermal source (e.g., a laser ablation spot
where T~104 K >> vaporization temperature) with the surface of a growing film
by physical vapor-phase deposition. For a flux containing a non-negligible
fraction of energetic species   
E kin 
E kin  Ethvac
Xn  
F ( E )E  >0, X n can be estimated as:
E kin 
E kin  Ethvac
F ( E )  n ( E )E 
(S1),
where F ( E kin ) is the Maxwell-Boltzmann-type kinetic-energy distribution of the
species in the vapor expanding adiabatically at supersonic velocity (typicallys1
v =104 m/s, which implies E kin ~46.5 eV for Zr/Y atoms) in vacuum. F ( E kin )
curve
used
for
the
simulations
in
Fig.
1,
is
shown
in
Fig.
S1.
 n ( E kin )   n E tr ( E kin ) –termed surface adatom-vacancy pair generation yield–
1
estimates the break-up probability of an n-sized cluster through the removal of
any of its


n perimeter atoms.  n  6 ln 1  E ndiss E 0  2 E ndiss (Ref. s2), where
E ndiss and E0 =25 eV are the cluster dissociation energy and displacement
energy to remove a Zr atom from its lattice position, respectively; whereas
E tr ( E kin ) corresponds to the transferred energy by nuclear stopping during the
incident species–surface collision. Ethvac denotes the threshold energy to
activate the cluster break-up phenomenon.
Fig. S1 Dependences of surface adatom-vacancy pair generation (  n , □—left axis)
and sputtering (  s , ■—right axis) average yields on the kinetic energy of
the incident species for a 3-ML thick YSZ surfaces3/InP (Ref. s4). The solid
black curve F ( E kin ) corresponds to the normalized Maxwell-Boltzmann
energy distribution of the incident species emitted from a hyperthermal
source. Inset: E kin dependence of the transferred energy E tr to the YSZ film
by nuclear stopping powers5 during the impact of energetic species.
2
 n ( E kin ) averaged over the populations of different-sized clusters at t=30s
(the longest simulation time) and added by ML up (assuming the stopping
power of 1 ML to be negligible) was calculated from the E tr ( E kin ) dependence
(Fig. S1 inset) computed for a 3-ML thick YSZ surfaces3/InP (Ref. s4) by MonteCarlo simulation.s5 E kin dependence of thus-calculated  n is plotted in Fig. S1
together with the sputtering yield  s –this latter computed directly by TRIMs5–
of the minority chemical species in the flux. These species are assumed to be
atomic Zr and Y considering the deposition gas atmosphere as an infinite
reservoir of oxygen. The linear interpolations of the  n
& s
-versus- E kin
dependences (according to the linear collision-cascade theory)s2 as well as the
estimated threshold energies ( Ethvac =24 and Ethspt =52 eV) to activate the
considered processes (cluster break-up and sputtering, respectively) are
specified in the figure. These values are in good agreement with the threshold
energies attained by kinetic Monte Carlo–molecular dynamics simulations
considering the local structure of the surface at potential sites of impacts.s6
REFERENCES:
S1. D.B. Chrisey and G.K. Hubler, Pulsed Laser Deposition of Thin Films (John Wiley
& Sons., New York, 1994) Chapter 5
S2. P. Sigmund, Appl. Phys. Lett. 14, 114 (1969) and Phys. Rev. 184, 383 (1969)
S3. For the calculation, the =3-ML thick YSZ film was considered to have a reduced
ysz
(surface-like) density  bulk



 k  that corresponds to a no closed film.
k 1
S4. E. Vasco and C. Zaldo, J. Phys:-Condens. Mat. 16, 8201 (2004)
S5. J.F. Ziegler, J.P. Biersack, and U. Littmark, The Stopping and Range of Ions in
Solids (Pergamon Press, New York, 1985)
S6. J.M. Pomeroy, J. Jacobsen, C.C. Hill, et al., Phys. Rev. B 66, 235412 (2002)
3