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3d Design in e-Beam Lithography. Proximity Correction for 3D Structures
Microelectronic Engineering 27 (1995) 195-198

Proximity Correction for 3D Structures

S.V. Dubonos, B.N. Gaifullin, H.F. Raith*, A.A. Svintsov, S.I. Zaitsev
Institute of Microelectronics Technology, Academy of Sciences, Chernogolovka, Russia
*Raith GmbH, Hauert 18, D-44227 Dortmund, Germany

The generation of small 3-dimensional resist structures requires a special method for proximity correction. In the following, a new method is introduced and described in detail. First results are presented.


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 [1] 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.


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 JSM 6400.

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 [5], 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 Two-Gaussian-function.

A mathematical treatment for solving this problem in a perfect way, was given by KERN [6]. 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 dose distribution.


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 , and for the case T1(x,y) = D(x,y). This leads to a new dose distribution D1(x,y).

After that an improved exposure distribution will be created by:

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 for = 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.


[1] V.V. Aristov, A.A. Svintsov, S.I. Zaitsev, Microelectronic Engineering 11 (1990) 641-644

[2] V.V. Aristov, B.N. Gaifullin, A.A. Svintsov, S.I. Zaitsev, R.R. Jede, H.F. Raith, ME 17 (1992) 413

[3] 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

[4] S.V. Dubonos, B.N. Gaifullin, H.F. Raith, A.A. Svintsov, S.I. Zaitsev, ME 21 (1993) 293

[5] G. Owen, P. Rissmann, J.Appl.Phys.54 (1983) 3575

[6]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

Half zone lens (total view)
Fig. 1a: Half zone lens (total view)
Half zone lens (enlarged view)
Fig. 1b: Half zone lens (enlarged view)
Calculated half zone lens pattern
Fig. 2: Calculated half zone lens pattern
Cross-sections of linear blazed gratings
Fig. 3: "Cross-sections" of linear
blazed gratings
Wanted resist structure on Si
Fig. 4a
Wanted resist structure on Si (sectional view)
H = actual thickness
H0 = original thickness

Fig. 4b
Dose requirement (D) by considering =2 for PMMA (without proximity correction)
D0=T0=clearing dose=1

Fig. 4c
Exposure dose (T/T0) aftwer 3D proximity correction for Si and 20 keV
= 0.1 um
= 2.2 um
= 0.75

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