Baltic Electronics Conference /October 7-11, 1996/ pp.121-124, Tallinn, Estonia
V V Aristov, B N Gaifullin, A A Svintsov, S I Zaitsev,
Institute of Microelectronics Technology, Academy of Sciences,
The PROXY software package was designed in the Institute of Microelectronics Technology in cooperation with Raith GmbH stands for a special attachment which enables any scanning electron microscope (SEM) to perform electron lithography. PROXY provides rapid and easy to operate pattern generation and writing on any substrate surface. The PROXY software package works on the IBM PC, and any compatible computer. It may be connected to various hardware components and includes mark recognition and control system for combining with motorized stage. Now, calculation of proximity correction, simulation of the results after development, distortion correction are possible in very easy and convenient way. By this way a correction procedure implemented in PROXY provides effective and automatic correction of proximity effect related with backscattered electrons and improves significantly proximity effects dealt with beam size resulting to a guaranteed accuracy about 40% of an electron beam radii.
Large and sophisticated electron beam lithography instruments are a necessity in modern IC production - but besides this, there are many applications which need electron beam lithography at a much smaller scale. Some of these fields are: optimizing of electron resist, integrated optics experiments, X-ray optics with zone lenses, experiments with individually created IC components, window etching in ICs for failure analysis, epitaxial and galvanic experiments. Main phenomenon restricting a resolution of e-beam lithography is so called proximity effect when backscatered electrons expose places far from inlet point of e-beam. A proximity distance depending on electron energy and substrate material belongs to micron (several microns) range. First attempts to correct proximity effect were made more than fifteen years ago [1,4,6]. Proximity correction means to calculate a required primary exposure dose in each point of structure in order to obtain an even absorbed dose inside all structures considering the contribution of backscattered electrons, beam size and forward scattering. Many studies have been done in this field, suggesting different correction methods. But no method allows to calculate a guaranteed final accuracy especially by taking into account the process of resist development, except the method of "simple compensation" which was introduced by Aristov et al [6,8]. Another process in e-beam lithography influencing on structure shape is development. Using models considered in [2,3] a fast and effective algorithm for development simulation was suggested. This work describes models of exposure and development, method of proximity correction and its accuracy. All this is a base of software package PROXY which enables any scanning electron microscope (SEM) to perform electron lithography
1. FORMULATION OF THE PROBLEM OF PROXIMITY EFFECT CORRECTION
The general problem proximity correction can be defined as follows:
Given is a two-dimensional x,y structure consisting of non intersecting regions Qi , i=1,2,...,N, shown in Fig.1 by solid lines. Exposure doses are
After development during time t the resist projection onto the substrate surface (plane x,y) represents structure Qi* comprising the elements Qi shown in Fig.1 by dotted lines. We suggest that the error should be defined by the maximum distance between the boundaries of structures Qi and Qi*.
The problem of the correction is to find such distribution of exposure doses T(x,y) that after exposure and development the errors of the whole lithographic process would be less than a prescribed or desirable value.
2. EXPOSURE AND DEVELOPMENT MODELS
Absorbed dose distribution D(r), r=(x,y,z), in the resist depends linearly on exposure dose T(x,y). For correction it is generally assumed that D is independent on resist depth z  , which leads to
D0 and T0are absorption and exposure sensitivities of a resist respectively. The proximity function I(r), r=(x,y), is written as a sum of two Gaussians,
which are interpreted as contributions of primary beam, I1(), and backscattered electrons, I2(), Here I, I1 and I2 are normalized on unity. The primary beam is concentrated in the area of radius 1 and the backscattered one in the area of radius 2, with ????. Factor ? characterizes the contribution of backscattered electrons to the exposure in a large area. Hence, 1and 2 are the characteristic lengths of the exposure process.
We use Two Gaussian model due to several reasons. First, two contributions have clear physical meaning (primary electrons and backscattered ones). Second, experimental measurements and simulation of absorbed dose are described by Gaussian model very well . And third, an appearance of the third Gaussian is dealt in our opinion with an influence of a development which usually is not taken into account in measurements of proximity function. In  was shown that considering development the third Gaussian disappeared.
An independence of proximity function I() on depth z is a good approximation due to the fact that the transport length of a resist for conventional in electron beam lithography energy normally is much more than resist thickness H . Therefore it is possible to neglect low-angle spreading of a primary beam. In any case below we assume the value of a beam size on interface of resist-substrate as upper estimation of ?.
Because ? is normally much smaller than ? and than the resist thickness H , it can be assumed (this is shown in ) that it causes an edge effect only, and therefore the correction can be done separately just inside a small structure frame in a secondary step.
Considering first the backscattering effect only (described by ? and ?), it is possible (according to the arguments of ) to substitute the first Gaussian by ?-function I. As a result if a structure Q is presented as a set of elements Qi (Q=Q1+Q2+Q3+ ...) and dose distribution D(x,y) is defined as D(x,y)=Do=100% inside structure Q and zero outside then the method of "simple compensation" for exposure T in point (x,y) may be written (in equivalent to [6,8] form)
Pay attention that only the second Gaussian, I2, corresponding to backscattered electrons is used. In the formular exposures T and D are measured in percents with T0 and D0 equal to 100%
3. 3D-SIMULATION OF THE DEVELOPMENT
Liquid development of positive resists is adequately described by the model of isotropic local etching [2-4] (ILE-model) which assumes that the velocity of resist boundary movement is independent of the boundary form (locality of etching) and the direction of the boundary (isotropy of etching), but defined only by development rate V at the point which the boundary passes through at a given moment. Development rate V, in turn, is defined by absorbed dose distribution D and the dose characteristic of the resist written as 
where is the contrast of positive resist. A numerical method for development simulation is especially fast and effective for 2D case [2,3].
The development simulation is a convenient tool for research and industrial applications. For known T(x,y), I , and dose characteristic (?,D0 ), it is principally possible to calculate the resist profile at any moment during development, but practically this 3D problem is very difficult. To provide the possibility of development simulation after proximity correction the 2D-method for the 3D-case (V=V(x,y)) was extended. For this we use a set of cross-sections of the resist. Each cross-section has to contain a vector of rate gradient. In case of step function the latter means that the cross-section is perpendicular to the level contour. And now it is possible to solve the development problem of reduced dimensionality in each cross-section separately using 2D-algorithm mentioned above.
4. REALIZATION AND EXAMPLES
The procedures of proximity correction and development simulation comprise a kernel of a software package PROXY. Besides this it contains an effective tool for design of structures and additional option allowing to control exposure by SEM via a special hardware called pattern generator.
In comparison to production beam lithography machines, the PROXY-SEM combination offers more flexibility in operation, more capabilities with respect to nanolitography, experimental electron beam lithography at a small fraction of the cost of currently available instrumentation. PROXY cannot be used as an IC production machine, however, PROXY offers much in fields of beam lithography research and development, especially since it is not limited to SEM's only, but to any other scanning system.
The first example is a structure which is not occasionally looks like a field transistor (Fig.2) where parts A and C simulate source and drain, B is a gate, parts D and E are wires situated partly far from and partly very close to large pads. The original structure was designed by PROXY graphical editor, the gate B and two slots between gate and parts A,B were designed as 200nm. Consider a situation when each point of the structure is exposed with exposure dose T equal to 150%. Development simulation (Fig.3) shows that due to proximity effect it is not possible to obtain the structure uniform exposure. Gate area is overexposed where as area D with single standing wire is underexposed. Fig.2b shows distribution of exposure time according to “simple compensation” generated by PROXY where as Fig.3b with simulation data predicts promising result. We carried out special experiments to check correction and simulation. We used JSM-840 as a lithograph under PROXY control for exposure the structures without correction and according to proximity corrected data. E-beam exposure and development of positive resist were followed by thin metal deposition and “lift off” operation so light image is Al layer. Comparison of simulated pictures with experimental ones show beautiful coincidence which confirms physical models of exposure and development, numerical algorithms and procedures implement in PROXY and correct operation of the system at whole.
Next example demonstrates ultimate possibilities of e-beam exposure and comprises a world map written in an area of micron size (Fig.4). A STEM with very fine beam was used for direct writing using layer of aluminum fluoride.
More practical structure is shown on Fig.5, the structure was created for experiments with single electron transport.
 M.Parikh IBM J. Res. Dev., 1980, v.24, N.4, p.438-451.
The previous general declarations will be illustrated in the report by set of examples. It includes:
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