A typical artificial neural network is shown schematically in the figure:
The input neuron layer comprises the independent variables such as feed gas mole fractions, power, gas pressure, and gas flow rate. The output layer of neurons represents the dependent variables or observables such as electron and ion densities and etch rate.
The topology of the response surface is essentially stored as the matrix of weights connecting the neurons in the network.
The neural network can be "trained" to model the multi-dimensional response surface that relates the dependent variables to the independent variables. An example of this can be seen in the next figure. This shows the response surface of the measured etch rate as a function of the power and C2F6 pressure in an inductively coupled reactor.
If we are interested in finding "flat" regions on the response hypersurface we can look for local minima with respect to the gradients on the surface, as can be seen in the next figure:
We can look at responses to more than two variables at a time by assigning other independent variables, such as bias power, to the arrow keys on the keyboard and displaying the dynamic surface plot via Open GL graphics Some graphics frames for three values of bias power based on data from the GEC/ ICP reactor using C4F8 are shown in the next figure:
A similar plot showing etch rate as a function of bias power and inductive power and parametric in pressure (5 Torr and 25 Torr) is shown in the next figure:
Finally, we can perform an optimization calculation where we locate regions of the response hyper-surface that satisfy certain criteria. In the next figure we see plotted the points on the response surface where a 10% change in bias, pressure, or power result in a 5% or smaller change in the etch rate for etch rates greater than 50 nm/ min.
