Directional Deposition and Etching: IonMilling and Nonconvex Sputter Laws
Physical Effects/Overview of Mechanism:

We now analyze a deposition/etching effect, including the effects of
visibility. Let Y(theta) be the
yield function, that is the effectiveness of the etching/deposition
process as a function of the angle theta between the normal to the
surface and the direction of the beam.
In the case of pure isotropic deposition, F(theta)=1 [in the case of
etching, F(theta)=1].
In the case of simple dependence on incoming angle, we would have that
F(theta) = cos theta, thus, no ionmilling takes place if the
beam is tangential to the surface, while the full effect takes place
if the beam is normal to the surface.
As is wellknown, there are other cases in which the ionmilling term is
most effective at an angle other than theta=0; that is, the yield is
largest at some intermediate angle located between normal to the surface
and tangential to the surface. These three typical yield curves as
shown in the figures below.



Isotropic Yield Curve

Cosine Yield Curve

IonMilling Yield Curve

As is wellknown, the last case produces faceting related to the
optimal angle.
The difficulty in traditional numerical methods lies in determining how
to advance the surface at places where the normal is not defined.
Level Set Methodology:

The level set methodology advances the surface by solving the
appropriate initial value partial differential equation, using the
correct viscous limit of the HamiltonJacobi equation. Thus, the normal
is correctly defined as the weak limit in places where differentiability
is lost. In the case of strong ionmilling effects, the resulting
equation becomes nonconvex; while nonconvex update schemes are
then required, this does not pose any particular difficulty.
Results and Sample Simulations:

We consider three different speed functions:
 F=1 (Isotropic)
 F=cos(theta1 (Cosine Yield Curve)
 F=[1+4 sin(theta)*sin(theta)] * cos(theta) (IonMilling)

2D Etching of Downward Block under Various Yield Laws:



Isotropic Yield Curve

Cosine Yield Curve

IonMilling Yield Curve

Movie: 1.2mb

Movie: .8mb

Movie: 1.3mb


3D Etching of Saddle Surface Under IonMilling Nonconvex Yield
Function:


Initial Saddle Shape

Intermediate Shape





Final Saddle Shape

Final Shape Rotated

Return to Overview Page