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Proxy - a New Approach for Proximity Correction in Electron Beam Lithography
Microelectronic Engineering 17 (1992) pp. 413-416


V V Aristov, A I Erko, B N Gaifullin, A A Svintsov, S I Zaitsev,
R R Jede+, H Raith+

Institute of Microelectronics Technology, Academy of Sciences,
Chernogolovka, Moscow district, 142432, Russia
+Raith GmbH, Emil-Figger Str.76, D-4600 Dortmund 50, Germany

A procedure for electron beam proximity correction is discussed which accounts for forward and backscatter-ing effects as well as resist development resulting in high structural accuracy even for low contrast positive resists on heavy substrates.


The established correction method after PARIKH /1/ uses the "Two Gaussian Model" describing electron scattering in order to calculate the required dose distribution for achieving an even absorbed dose throughout the structure. There is no doubt that this method provides very good results for infinitely small substructures, but these cannot be realized. In all practical cases it is necessary to minimize the substructuring for getting a computation in a limited time. Therefore the main question is now how to achieve the minimum substructuring for getting the required correction considering backscat-tering, forward scattering and possibly also the effects of resist development.


The backscattering effect depends mainly on the substrate and is described by the parameters and . Its correction can be done separately from the effect of forward scattering by treating the first Gaussian as a delta function. The method of "simple compensation", introduced by ARISTOV et al /2/, does such a correction. It divides the structure into physical meaningful zones, separated by isolines, each representing a different required dose level. These zones can be automatically divided into rectangles for which a self consistent dose distribution can be calculated.

The software package "PROXY" does such a correction on a PC. The given example in Fig. 1 shows a structure with critical dimensions of 0.5 m (lines, gaps, squares in different proximity) . The calculation was done for PMMA on GaAs exposed with 25 keV. The used parameters were =1.21 um and =3.24, measured by RISHTON and KERN /3/.

A structure with critical dimensions of 0.5 um. Design and results of correction.
Fig. 1

The white areas in Fig.1a have been exposed by electrons. Considering a strong backscattering effect makes it evident that areas around the hole and near the gaps must get much lower primary doses than the isolated lines and the isolated gap. The calculated isolines in fig.1b show the required dose levels in even steps between 100% (clearing dose) and approx. 400%.

The zones separated by isolines were automatically divided into many rectangles (fig.1c). The calculation of a stable, self consistent dose distribution can be done either by iterations with steps of "simple compensation" (PROXY) leading to maximum required dose values for individual rectangles or by the conventional PARIKH method leading to average values.

Fig.1 Proximity correction for a critical stucture to be exposed on GaAs with 25keV
a) basic structure with 0.5 um lines and gaps in different proximity
b) calculated isolines showing increasing required dose in equal steps
c) automatic division into rectangles for calculating a self consistent dose distribution

Up to now only the backscattering effect has been considered, but not the forward scattering and not the development process. While the backscattering does almost not depend on resist parameters, the forward scattering and the resist development do not depend on the substrate. Therefore the forward scattering can be treated separately, too, assuming there is no backscattering effect (=0). In this case the correction can be done by a superimposed frame along the structure boundaries of width and with constant dose.

Ignoring for proximity correction by considering just a perfectly corrected dose distribution for backscattered electrons will lead to a lower absorbed dose at the boundaries. This draws the boundaries inside the structure similar to the case when no backscattering effect exists (=0 - e.g. for thin foils). This dose deficit can be corrected by a superimposed frame with a dose of approx. 100% (equal to the clearing dose). But now the development speed of positive resist is strongly increased inside the overexposed frame, which leads to a resist development from the side, pushing the boundaries outwards. But this effect can be calculated for positive resist by the model of local isotropic etching and therefore it is possible to balance both effects by a specially calculated frame dose.

The diagrams in Fig.2 show the required frame doses as a function of resist type, thickness and contrast, calculated by PROXY.

 Calculated required  frame doses as a function of resist type, thickness and contrast
Fig. 2

For low contrast positive resist it is very important to consider the development process. On the other hand it can be seen that high contrast negative resist requires high frame doses leading to similar results compared to the conventional PARIKH method.

Fig.2 Calculated dose for a superimposed frame of width , assuming a perfect correction for and has been done before (full squares for positive resist open squares for negative resist)
a) Dose dependance of resist thickness and type assuming that is 0.05 m and the resist contrast is 2
b) Dose dependance on resist contrast, assuming a is 0.05 m and the resist thickness is 0.5 m


Experimental results are presented as light optical photographs, because these allow the study of underexposed areas better than by using "lift off", which is generally difficult to realize for underexposed patterns.

The test pattern has been exposed on GaAs covered by 0.3 m PMMA using 25 keV beam energy in an SEM combined with the lithography attachment "ELPHY" (Fig.3). The test pattern consists of four horizontal rows. The upper two rows show uncorrected pattern with different, but constant exposure doses between 140% and 420% in equal steps of 40%. No exposure in these two rows is acceptable, because either the isolated lines are not fully exposed or the gaps are closed. The third row shows fully corrected patterns at different dose levels, where the calculated dose distribution has been scaled by 0.9, 0.95, 1, and 1.05 from left to the right in order to find the

best exposure. The bottom row contains just large areas exposed at 90%, 95%, 100% and 105% for recognizing where the clearing dose is reached, which should correspond to the optimum corrected pattern in the row above.

Image of exposed test pattern on GaAs
Fig. 3

The best exposed structure is the third one in the third row just above the large area, where the center has reached the clearing dose. Considering that this clearing dose is 100% while the doses inside the corrected structure varies between 100% and 400% proves that the correction has been done well. It shows also that the parameters used, measured by RISHTON and KERN /3/ are appropriate to our model.

Fig.3 Test pattern exposed on GaAs with 0.3 um PMMA using electrons with 25 keV


A new method for proximity correction has been described which is realized in the software package PROXY. It allows to correct for the effects of backscattering, forward scattering and resist development. Additionally, the result after the development process can be simulated (modelling), showing whether the calculated correction using a certain substructur-ing was good enough. This simulation feature can also be used for "measuring" the parameters for backscattered electrons just by comparing experimental results with simulated patterns using different parameters. The described method allows ultimate corrections and general studies of proximity effects in experimental structures. For production purposes fast software packages like CAPROX /4/ can be combined with PROXY routines at least for finding the optimum substructuring in critical areas.


/1/ M. Parikh, J. Appl. Phys., 50 (1979) 4371-4391
/2/ V.V. Aristov, A.A. Svintsov, S.I. Zaitsev, Microelectronic Engineering 11 (1990) 641-644
/3/ S.A. Rishton, D.A. Kern, J. Vac. Sci. Technol. B5 (1987) 135
/4/ E. Knapek, C.K. Kalus, M. Madore, M. Hintermeier, U. Hofmann, H. Scherer-Winner, R. Schlager, Microelectronic Engineering 13 (1991) 181-184

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