Geometrically, the flux distribution
at an off-center position can be formulated by shifting the origin of the
analytical function
used to describe the
radially symmetric distribution of the incident particles for the center wafer
position. The position on the wafer is determined by the polar angle
,
pointing from the position towards the center of the wafer and the azimuthal
angle
, given as angle between the positive, vertical z-direction and
the direction to the center of the sputter target (cf. Fig. 6.4).
By shifting its origin, the distribution function is transformed to the local
coordinates and
.
gives the polar angle in
the plane normal to the direction pointing from the structure to the target
center and
the azimuthal angle with respect to this direction. The
distribution function at the off-center position is now radially symmetric with
respect to
and can be written as
Fig. 6.5 shows the three-dimensional representation of the exponential
distribution function from (6.4). The left hand side shows the
distribution for the center wafer position, which is radially symmetrical with
respect to the z-axis. In the figure on the right hand side the tilt
angle
for the distribution is 15
. For a target to wafer
distance of 20cm, the 15
tilt angle represents a position
shifted 55mm off the wafer center.
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The shift in the flux distribution represents the change in the configuration of the position on the wafer with respect to the racetrack groove of the sputter target. The result is that the flux predominantly attacks those sidewalls of the feature, which are directed towards the center of the sputter target and thus exposed to the predominant direction of particle incidence. This effect is of significant importance, when the geometry of the considered structures is not radially symmetric. In this case the polar orientation plays an important role for the evolving profiles.
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