All established methods for proximity correction aim to correct
for two-dimensional structures. Most of them just take care for an absorbed
dose of 100% inside the exposed structures and do not consider the dose distribution
outside, which is below the 100% level.
Today there is an increasing demand for producing real three-dimensional
structures, such as blazed gratings, Fresnel lenses, spherical lens arrays etc.,
where usual methods cannot be used.
In order to obtain such relief structures in resist, or in
the substrate after pattern transfer, each point of the total exposure area
has to be assigned first with a certain required remaining resist thickness
H(x,y). Considering the resist contrast (gamma value) this leads to a required
distribution for the absorbed dose D(x,y). Now proximity correction is needed
in order to calculate the distribution of the required exposure dose T(x,y),
which was not available in the past. Of course, in such cases the total area
has to be exposed with almost continuously variable dose distributions.
Starting with "Simple Compensation", introduced by ARISTOV
et al  a very powerful tool for correction and simulation of proximity effects
has been developed [2,3,4] which led to the widely used software package "PROXY".
Now it allows also 3D proximity correction.
2. FIRST RESULTS
Fig. la & 1b show the half of a blazed zone lens with 100
urn diameter and its magnified view. The SEM images (presented in TIFF format)
were taken from a tilted sample showing the boundary like a "cross-section"
- but it is not! This "cross-section" has been produced by exposure with a sophisticated
dose distribution (fig. 2), calculated by a 3-dimensional proximity correction.
The exposure has been done on 0.7 m PMMA on Si with 25 keV using the SEM type
Fig. 3 shows such artificial "cross-sections" of linear blazed grating as another example.
In order to achieve such results, many small areas
have to be exposed with different doses. The software package "PROXY" allows
such designs and does the 3D proximity correction including the division into
all sub-structures fully automatically.
"PROXY-WRITER" can expose all these irregular
shapes with continuously variable doses directly without any pattern transformation
and in connection with any SEM. Its alignment capabilities allow in addition
to collect the shown TIFF images.
This new method of 3-dimensional proximity correction can also
be used for producing real "2D-structures" with only two levels of absorbed
doses -the full clearing dose inside the structure and a low dose outside. This
leads, of course, to a reduced contrast, but it could be useful e.g. for uniform
pattern transfer via ion etching. Approaches in this direction were already
done by OWEN and KERN.
The "Ghost method", introduced by OWEN et al , avoids the
proximity correction by exposing the areas outside the structure in a second
step using a strongly defocused beam. But this method is only a rough approximation,
because it is not easily possible to generate a defocused beam according to a well defined
A mathematical treatment for solving this problem in a perfect
way, was given by KERN . But this method has also not been realised, because
the calculation method is quite complicated and time consuming - in addition
most e-beam machines are not able to expose structures with continuously variable
3. CALCULATION METHOD
We assume, that the finally wanted distribution of
the absorbed dose is D(x,y) - which is, of course, not equal to the
distribution of the needed exposure dose T(x,y). In a first step we
make a numerical simulation according to the Two-Gaussian-function with
the proximity parameters ,
for the case T1(x,y) = D(x,y). This leads to a new dose distribution
After that an improved exposure distribution will be created
T2(x,y) = T1(x,y) + (1 + )
* ( D(x,y) - D1(x,y) )
Again the simulation will be calculated with T2(x,y) leading
to D2(x,y), which allows to achieve an even better exposure distribution
T3(x,y) etc. Normally approx. 5-10 iterations are needed in order to
reach a self consistent exposure distribution leading to the wanted
distribution for the absorbed dose.
Fig. 4 shows as an example how to generate a periodic
staircase in resist. The upper curve describes the wanted steps in resist
thickness. Assuming we are not in a micron scale we would have just
to consider the resist contrast
in order to calculate the needed exposure dose using the formula:
H/H0= 1 - (D/D0)
h0 is the original resist thickness and H the remaining
one after development. D0 is the clearing dose leading to
full development and D is the needed absorbed dose. Only when proximity
correction is not applied, this absorbed dose D corresponds to the needed
exposure dose T. The middle curve shows this distribution calculated
= 2. Finally at the bottom the staircase is shown with the needed exposure
dose T in each step of 1 um width after 3D proximity correction.
The calculation was done for Silicon and 20 keV (
= 0.1 um,
= 2.2 um,
= 0.75). These curves represent only a central section of an infinite
blazed grating in order to keep it simple.
The software package "PROXY" allows now, in addition to many
other functions, a proximity correction for generation of a 3-dimensional resist
relief, which can also be checked by simulation. Any SEM can be made into an
experimental e-beam machine for writing such calculated structures with any
shapes and with continuously variable doses by using PROXY-WRITER.
 V.V. Aristov, A.A. Svintsov, S.I. Zaitsev, Microelectronic
Engineering 11 (1990) 641-644
 V.V. Aristov, B.N. Gaifullin, A.A. Svintsov, S.I. Zaitsev,
R.R. Jede, H.F. Raith, ME 17 (1992) 413
 V.V. Aristov, B.N. Gaifullin, A.A. Svintsov, S.I. Zaitsev,
H.F. Raith and R.R. Jede, J Vac. Sci. Technol. B 10(6), Nov/Dec 1992
 S.V. Dubonos, B.N. Gaifullin, H.F. Raith, A.A. Svintsov,
S.I. Zaitsev, ME 21 (1993) 293
 G. Owen, P. Rissmann, J.Appl.Phys.54 (1983) 3575
D.P. Kern, Proc. 9th International Conference on Electron
and Ion Beam Science and Technology, R. Bakish Ed., Electrochemical Society
PV 80-6 (1980) 491-507