Microelectronic Engineering 5 (1986) pp. 329-334
ARISTOV V.V., BORSENKO T.B., KUDRYASHOV V.A., SVINTSOV A.A., ZAITSEV S.I.
Institute of Microelectronics Technology and Superpure Materials,
The effect of different experimental conditions on the profiles of the structures formed in negative resists, is discussed. A new approach to the mathematical simulation of structure profile formation in negative resists is suggested. The results of computer simulation for various exposure and development parameters are reported. It is also theoretically and experimentally shown that undercut profiles can be easily achieved for negative resists.
It is known, that the sensitivity of negative resists to X-ray radiation is generally 10-100 times higher than that of conventional positive ones . Our previous work presented a potentially high resolution 0.1 um of negative resists at photoelectron exposure. Yet, at conventional resist exposure through the mask this resolution can hardly be achieved because the formation process of structure profiles is still insufficiently understood .
The work by Yoshiki Suzuki  gave the first results of the experimental and theoretical studies of width and height of the lines, formed in negative resists, as a function of exposure parameters. Both the width and height of the structures, formed in the resist, were shown to decrease with decreasing exposure. However, more detailed investigation into the dependences of element structure width on the value of latent image penumbral blurring is essential. Furthermore, the effect of different experimental conditions on the profiles of the structures formed in negative resists, is of great importance but still remains obscure.
The simple mathematical model (given in ) and the method for calculating structure profiles in negative resists provide results which are in good agreement with the experimental data only in most simple cases, when exposure is constant along the resist depth. But, it is well known , that in the case of positive resists the resist depth exposure nonuniformity and, particularly, the resist exposure with photoelectrons from the substrate and mask are the main factors determining the distinctive features of the structure profile. Hence, the role of these factors in structure profile formation in negative resists must be considered.
2. MATHEMATICAL SIMULATION OF PROFILE STRUCTURE FORMATION IN NEGATIVE RESISTS
The behavior of negative resist upon development (simulated in this work) can be briefly described in the following way. When developing the negative resist, whose latent image is formed on X-ray exposure, the polymer gel-fraction remains intact. Its initial spatial density distribution is determined by the exposure at each point D(x1,x2, x3) and by the dose-thickness curve V/V0 = (D) of the resist, while the sol-fraction which makes up [1- (D)] of the resist is washed out by the solvent. On drying the solvent is removed from the polymer net and the residual resist fragments decrease in volume so that the resist density becomes equal to the initial one. The lower layer of the resist qel-net adjacent to the substrate remains fixed. He suppose the contribution of surface tension to the processes of profile formation to be small and neglect this contribution in the first approximation.
Thus, as a result of the development, a point (x1,x2,x3) of the initial resist is transferred to a point (x'1,x'2,x'3) and this "one-to-one" correspondence can be defined by the function
To find a final structure form in the resist it is necessary to determine the type of the function fi (x1 ,x2,x3) . For this purpose the actual process of development is substituted by the following procedure. We mentally cut the exposed resist into cubes so small, that the exposure within each of them can be considered homogeneous. Define, how the cubic cells will transform after washing out the sol-fraction and drying. After drying the cells are likely to regain their shape though smaller in size, their volume being 1/ times less. Then, deform the cells without changing their volumes so that they could be glued together without disturbing their continuity. This procedure defines some transformation fi , hut the second stage (deformation and gluing) can be fulfilled by numerous ways. This ambiguity is eliminated if one assumes that the originating structure is thermodynamically equilibrium. Thus, it is essential that the only transformation should be found which transform the resist to the state with a minimum free energy.
As known , the free energy density Fdef at the polymer deformation is described by the affine transformation and expressed by the approximation formula
where ai is the tension factor along the corresponding axes; kT is the temperature in energy units; Nc is the number of polymeric chains it volume unit, in fact, it is the number of pinning points. It includes bonds caused by radiation and, perhaps, crossings of macromolecules. Free energy the whole resist in the final state, F, equals the sum of energies of all elementary cells and is the transformation functional of
The generation of (2) for arbitrary transformation gives
If the main contribution is obtained from crossbonds then it should be assumed that Nc (x1,x2,x3) ~ D. But if the number of bonds is small, then Nc (x1,x2,x3) ~ .
Variation of (3) should be made at constant density det(fi/xk) = (x1,x2,x3) using the method of indefinite Lagrangian multipliers (x1,x2,x3). As result we obtain
where Ai is an algebraic adjunct of the elements of the matrix (fi/xk ). The boundary conditions on the free surface S with normal (n1,n2,n3) are the following :
The condition of complete fixing fi (x1,x2,x3) = xi is given for the resist adjacent to the substrate, .
Numerical solution was used to define the transformation fi(x1,x2,x3). which transformed the initial rectangular cell net of resist division into a nonrectangular one, satisfying the conditions indicated above. In our calculations the cases Nc~D and Nc ~ resulted in practically identical resist profiles.
The results of these calculations are plotted in Fig.1 (a,b,c).
Mathematical simulation of the structure profile in the negative resist: a) distribution of exposure D throughout the resist volume; b) distribution of relative volume variation in the exposure area; c) structure profile formed in the resist.
Figs.1 (a,b) show the distribution of the exposure D(x,z) along the resist depth and that of the value V/V0 = throughout the resist volume, respectively. Fiq.1 (c) shows the resist structure profile calculated for the following development and exposure parameters: mask contrast 10, resist contrast 1, mass absorption coefficient 4000 cm-1, resist initial thickness 0.5 um, the element width on the mask 0.4 um penumbral blurring 0.2 um the exposure provides equal to 0.7.
3. EXPERIMENTAL INVESTIGATION OF STRUCTURE PROFILES IN NEGATIVE RESISTS
Resist exposure was realized by an X-ray tube with water-cooled anodes enabling radiation over the range of 0.417-4.47 nm to be used and providing exposure up to 103 cm3 . Test polymer X-ray masks with masking gold coating 0.4-1.1 um thick and negative resists with a contrast range from 0.8 to 2, and besides, a PMMA-based positive resist was also used.
1. Computer simulation of structure profiles in negative resists shows t the width of resist structures decrease with decreasing resist exposure. This process is more easily controlled enabling the element width to be corrected over a wide range in respect to the initial width of transparent areas of mask. Fiq.2 (a,b) presents the structure profiles formed in negative resist at different exposure values and other conditions being constant.
Structures in the negative resist at different values of exposure: a) profiles calculated for the data mentioned above and exposure values =1, 0.7, 0.5 and 0.3; b) photographs of the test structures formed under identical conditions but at different values of exposure.
In this case the structure width varies more than by a factor of two.
2. It is also particularly interesting to study the effect of the value of penumbral blurring of latent image boundary on structure profiles in negative resists. With this in view, the value of boundary penumbral blurring varies within 0.4 and 0.005 um, other conditions being identical. Fig.3 (a) gives profiles calculated for the conditions indicated above. Fig.3 (b) shows photograph of the structures obtained at blurring values of 0.2 um. A marked decrease (from 0.4 to 0.05 um) in boundary blurring is unlikely to improve the profile equivalently. As for a certain increase in accuracy when reproducing the structure sizes it is obtainable by simple ways, for instance, by exposure correction as shown above.
3. It is essential to investigate the structure profile for resist exposure inhomogeneous along the depth. In this case not only vertical but overhanging structure profiles can be formed in negative resists. To do this, the exposure of the upper resist layer should be a bit larger than that of the lower one It occurs in two cases: 1) on strong absorption of radiation by the resist; 2) at additional exposure of the upper resist layer with photoelectrons from the mask or a metal layer deposited on the resist . We observed the overhanging effect in both cases. Fiqs.4 (a) and (b) show a photograph of the structure and profile calculated for an additional exposure of the upper resist layer with photoelectrons from a metal film.
4. Among other things, we have made an experiment to form inclined structures in negative resists. Structures with a large height-to-width aspect ratio are
Test structure profiles in the negative resist at different values of boundary shadow blurring : a) calculated for blurring = 50, 100, 200 and 400 nm; b) test structures 0.8 um wide obtained at = 0.2 um.
known to be easily formed in positive resists. For example, test structures (Fig.5,a) 0.8 um wide were produced in PMMA 4 um thick. When the exposed sample is not perpendicular to radiation but at a certain angle to the
Structures in the negative resist at photoelectron exposure of the upper layer: a) calculated profile; b) experimentally obtained profile.
latter, the structures (Fig.5,b) formed in the positive resists are inclined at the same angle to the substrate. The question arises what the neqative resist behavior under these conditions is. The experiment on negative resist exposure by radiation showed that the inclined structures are formed when the incident radiation is not perpendicular to the surface. This structure is shown in Fin.5,c. The result proves that the contribution of surface tension to the mechanism of structure profile formation is small. If it were a deciding factor, the structure lateral surfaces would take vertical position upon development.
A mathematical model has been developed and used to calculate structure profiles in negative resists for different exposure distribution over the resist value. The effect of exposure, the value of penumbral blurring and
Structures in the positive (a and b) and negative (c) resist at vertical (a) and off-normal X-ray incidence (b and c).
resist exposure inhomogeneous along the depth on the form of profiles and structure width in negative resists has been experimentally investigated. Structures with inclined lateral surfaces have been first experimentally obtained in negative resists. Our experimental results correlate with the mathematically simulated ones proving the assumptions suggested and the validity of the model.
 Spiller, E. and Feder, R., Topics in Appl.Phys. 22 (1977) 35-92.
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