Physical Model
Manufacturing of GMR Thin Films
Physical Model
The integrated physical model consists of the following individual modules which simulate the various physical phenomena occurring during thin film deposition in a RF sputtering chamber.
Fluid Flow Model
SC Solutions has developed a detailed three-dimensional finite element fluid flow model for an RF sputter chamber using the commercial FEM software package ADINAâ. The figure on the right shows the generated finite element mesh. The FEM model yields spatial distributions of gas velocities, and pressure differentials across the chamber.
RF Plasma & Sputter Models
The RF plasma model developed by SC Solutions uses inputs such as the RF power, electrode spacing, and carrier gas temperature and pressure, and produces outputs such as ion energies and flux (or current), and sheath voltages. The sputter model calculates the sputtered flux from the target as a function of the incoming ion flux and ion energy.
DSMC Model
The Direct Simulation Monte Carlo (DSMC) model uses kinetic theory to track the paths of a statistically significant number of sputtered atoms as they traverse the distance between the target and the substrate. Since these calculations are computationally intensive, the integrated model uses bilinear interpolation of the detailed results for rapid calculations. The DSMC calculations yield radial flux distribution and energy distribution of the sputtered atoms incident to the substrate.
Integrated Model
The reduced-order integrated model simulates a deposition process on a PC as a Windows NT application. It predicts sputter deposition rate and uniformity. The model has been calibrated and validated using experimental data (see the figure on the left). Since each simulation run takes less than a second, an engineer can run several simulations rapidly to investigate the process variable space. The figure below shows the graphical user interface (GUI).
The integrated model provides valuable information about the sensitivity of deposition rate and film thickness uniformity to process parameters such as RF power, carrier gas pressure and temperature, and electrode spacing. Hence, the operating tolerance needed to meet the tight deposition thickness specifications can be determined as shown below.
Sensitivity to Operating Conditions (Control Tolerances)
Deposition specifications for the copper layer (16 ± 0.25Å),:
At deposition rate of 200 Å/min, process time: 4.8 ± 0.1 s.
Exceeding the following tolerances for any one component will contribute a deposition error of 0.25Å over 4.8 seconds:
Power: 175 ± 5.9 W (3.4 %)
Pressure: 20 ± 0.24 mTorr (1.2%)
Temperature: 400 ± 7.0 K (1.8 %)
Electrode Spacing: 3.81 ± 0.090 cm (2.4%)
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Relatively small changes in the key process variables such as RF power or temperature can cause the product to go out of specification.
Thermal Model of Chamber
SC Solutions has developed a heat transfer model for the sputter chamber. The axisymmetric finite-volume model has structured grids as shown in the figure to the right. A steady-state solution to the heat conduction equation was obtained for both solid and gaseous media. Convection is negligible at these low pressures of 5-50 mTorrs.
The contour plot to the left shows the temperature distribution in the plasma. Because there is significant volumetric heat generation in the plasma (over 100 W), the temperatures are the highest close to the centerline. There is a significant temperature gradient in the vertical direction as seen in the graph below. However, the difference between the wafer center temperature and the wafer edge temperature is much smaller, about 2-3°C
The heat transfer model shows that the plasma temperature is sensitive to the temperatures of the bounding solids such as the target, substrate, and the dark-space shield. Any drift in the temperatures of these solids would affect the plasma temperature and hence the deposition rate, leading to possible thickness variability from run to run.