In Situ Monitoring and Model Simulation of BaTiO 3 Pulsed Laser Thin Film Deposition
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simulation of plume expansion. Post-expansion (far-field) MS-determined velocity distributions and temperatures were used to assign gasdynamic model parameters, from which the near-field nature of the plume was simulated. MODEL SIMULATION Our model simulation approach has been discussed earlier 1 ,2 and is based 5primarily on the 3 4
work of Dawson, et a1 , Singh and Narayan , and Predtechensky and Mayorov . In the present three-dimensional simulations, we continue to utilize the isothermal expansion approximation to model the plume region during the laser pulse 4. Following the ending time (t='r)of the laser pulse, the plume is considered to expand adiabatically (see Eq. 1). To model this expansion process with a background gas present, we adopted Predtechensky's approach 5 , converting his radial formulation to Cartesian coordinates assuming equivalent equations of motion in each direction (see Eq. 2). The adapted model correctly reduces to the Dawson model 3 when the
background gas density po - 0. Each individual species was considered independently of other species of differing mass. Thus, an effective combined pressure at the species-specific plume "front", Pi(t) for a species i at any time t > T, was treated using:
45 Mat. Res. Soc. Symp. Proc. Vol. 388 01995 Materials Research Society
Pi(t)
Z
P + P.1
(xrz
)v
0i 0
(1)
P,,i is the maximum partial pressure of species i at the target surface, Po is the static background pressure; the coordinates Xj(t), Yi(t), and Zi(t) are the Cartesian extents of the plume "front," an ellipsoidal "boundary" where the species vapor density has fallen to 60.65 percent of its maximum at t; X Y and Zo are the plume extent coordinates at the end of the isothermal expansion stage 4 ; y is the gasdynamic factor (the effective plume heat capacity ratio). The
equation of motion for the plume front location of species i in the z-direction (perpendicular to the target surface) is: (dZ
a 2Z.
XO(t)Y 1(OPOt-
__
dt 2
(W
'~2
X1(t)Y,(t)po I d I k dt) [+X)(t
(2)
) Zi(t)] pA)
Mi is the total vaporized mass (in gm) of species i; po is the mass density of the background gas,
determined from Po and the calculated volume at the end of the laser pulse. The time evolution of the plume extent was simulated using a step-wise Runge-Kutta method to obtain timedependent solutions of the model equations of motion. The model for the centerline (z-axis) 4 number density (n) of the plume during adiabatic expansion (t >,r) at distance z is given by :
n(z,t) =
20° 5x 'X(t) Y(t)Z(t)
x
e
i
2Z(02
(3)
where NT is the total population of all species produced during the isothermal stage.
The required model input parameters included: the initial plume coordinates that we obtained from direct measurements of the laser footprint at the target; the pressure and temperature of the vapor at the target, taken from estimates based on MS data and deposition rates6 ; the
measured pressure of any added background gas (usually, P.
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