Dong-Soo Sohn

Analysis of the relation between exposure parameters and critical dimension by response surface model

It is important to know the relationship between the soft bake conditions and the Dill exposure parameters in order to control the lithographic process well. It has been reported that exposure parameter A can be significantly affected by the soft bake conditions, while the exposure parameters B and C show no dependency on the soft bake conditions. The exposure parameters have been considered less important in 193 nm chemically amplified resist (CAR) simulation. Since the critical dimension variation depends on the exposure parameters, if we know the relationship between them it would be helpful in developing resist and resist process. In this paper the profiles of a 193nm CAR were simulated with the various Dill exposure parameters and the results were analyzed by response surface model. The response surface methodology (RSM) approach was used to analyze the influence of independent factors on a dependent response, and to optimize each process. A method of steepest ascent was utilized to produce first-order models, which were verified by lack of fit testing. As optimum operation points were approached, a second-order model was fitted and analyzed. The Dill exposure parameter C affects critical dimension greatly whereas A and B have much less effect. Among parameters other than exposure parameters, PEB time and PEB temperature are great factors to affect critical dimension. Even small change of them can make great critical dimension changes. Process optimization for the target response value as well as process latitude was possible through the use of the response surface.

Effect of temperature variation during post exposure bake on 193 nm chemically amplified resist simulation

We measured the temperature change of 193 nm chemically amplified resist during post exposure bake and investigated the effects of these variations on photoresist (PR) simulation. The effects of the variations were studied for various baking and cooling methods. The effective PEB time was determined by considering the temperature variation during PEB. The effective PEB times were used in simulation and the resulting PR profiles were compared with the experimental results. The resulting profiles showed a significant variation in line width depending on bake conditions. Careful PEB temperature consideration is necessary since the resulting line width is strongly dependent on the resist temperature rising and cooling rate. The effective bake time with proper consideration of the temperature change during PEB should be used in the simulation to depict experimental profile correctly.

CD prediction by threshold energy resist model (TERM)

In the step of developing lithography devices, VTRM (Variable Threshold Resist Model), aerial image based simulation, is useful to get feedback for a resist process margin. VTRM is also used to compensate for the mask patterns OPE (Optical Proximity Effect) and to optimize the optical system rather than the full simulation method that requires all the process parameters. However, VTRM has shown some problems that the exposure dose and focus should be fixed in one special condition to improve the prediction accuracy and cannot be combined together in one equation for patterns size and type variation. In this paper, a new simulation method that has more accuracy and wider applicability than the VTRM method was suggested. The new simulation method can represent the photolithography process with simple formula. The parameters of this formula are composed of exposure dose and defocus as input components, CD as output component, and all the resist processes are kept constant to keep consistency for other resist processes. The first technical improvement of this equation is to use process-matched aerial image derived from the fact that the aerial images at the top resist surface cannot represent the bulk resist energy distribution. The second one is to introduce a new concept TERM (Threshold Energy Resist Model). The energy threshold level is used instead of the aerial images intensity threshold level in order to predict CDs. Energy threshold level can be simply found by the simple equation and an experiment. The simple equation consists of a mask edge opening energy, the mask edge image intensity, and a process factor.

Threshold energy resist model for CD prediction

The threshold resist model based on only aerial image is less time consuming and is sometimes more efficient than the full simulation model based on mathematically analyzing the whole complicated process of photolithography. But this model still contains a disadvantage that the prediction is limited in various situations. In this paper, the new threshold resist model to predict the Critical Dimension (CD) on the wafer is presented. This model has a functional form consisted of the aerial image intensity and its slope. More than 90% of prediction accuracy in various patterns with respect to pattern sizes is obtained by using the new model for 248 nm.

Resist develop prediction by Monte Carlo simulation

Various resist develop models have been suggested to express the phenomena from the pioneering work of Dills model in 1975 to the recent Shipleys enhanced notch model. The statistical Monte Carlo method can be applied to the process such as development and post exposure bake. The motions of developer during development process were traced by using this method. We have considered that the surface edge roughness of the resist depends on the weight percentage of protected and de-protected polymer in the resist. The results are well agreed with other papers. This study can be helpful for the developing of new photoresist and developer that can be used to pattern the device features smaller than 100 nm.

Threshold energy resist model for critical dimension prediction

The threshold energy resist model based on the aerial image is less time consuming and sometimes more efficient than the full simulation model based on mathematical analysis of the whole complicated photolithography process. Moreover, this model still contains a disadvantage that its prediction is limited in various situations. In this paper, we report the new threshold resist model to predict the critical dimension (CD) on the wafer is presented. This model has a functional form that is consisted of the aerial image intensity and its slope. The contours of a resist pattern are determined from the aerial image contours of the process matched by using a functional form. High prediction accuracy in various patterns with respect to pattern sizes is obtained by using the new model.

Simple optical system parameter optimization method by comparing the critical dimension

Resolution enhancement technology will play a crucial role in the future of optical lithography. The only question is how much the resolution limit can be extended. The better critical dimension (CD) uniformity is demanded as pattern size is decreased. In our previous work, we had made a simulation tool which can find the optimum illumination system such as numerical aperture, wavelength, and illumination shape for best CD control. In order to improve better CD control, the mask size, assist feature size and placement are modified by the simulated annealing (SA) algorithm. However, in this method, the effects of post exposure bake or development process are not considered to predict the real CD, since the results are obtained only with the aerial image which can be precisely calculated. To consider these elements that affect CD profile, threshold energy resist model (TERM) model was suggested previously. However, TERM model still has a weak point in extracting necessary parameters for the transfer function. Therefore, we made a simulation tool using Monte Carlo method that extracts the necessary parameters with the experimental data. The experimental data include the exposure energy, measured line CD on a mask, wafer line CD after development. Finally, the predicted line CDs are compared to the empirical data under a different optical system condition to verify the extracted parameters. The simulation results matching the actual process can be obtained by using these methods.

Simulation parameter effects on critical dimension and sensitivity of 193 nm Chemically Amplified Resist

It is helpful in lithography process and developing resist to know the relationship between the critical dimension variation and simulation parameters such as aerial image parameters, the Dill exposure parameters, PEB (Post Exposure Bake) parameters, and development parameters. In this paper the profiles of a 193 nm CAR (Chemically Amplified Resist) were simulated with those various parameter, and those results were analyzed by the response surface methodology (RSM) approach to know the influence of independent factors on a dependent response and to optimize each process. Both the parameter effects of each process and the simulation process effects of the whole process were described about critical dimension and side wall angle so that the sensitivity of lithography process could be assumed. The development parameters were modified with those of flood exposure experiment according to the pattern density and pattern size for more accurate lithography simulation. Also those effects on critical dimension and side wall angle were analyzed. For the validity of our results the quantitative comparison between our results and those of a commercial tool was shown.

Line Width Variation due to Global Topography

To obtain the spun-on resist surface profile around a topographical feature, the analytical solution of an equation derived from mass continuity and the Navier-Stokes equation using the lubrication approximation was used. The final resist thickness profile was obtained by applying our previous experimental result of resist thickness reduction due to the soft bake process. We found that the difference in resist thickness could induce severe critical dimension variation. Since the resist height differences between above and far from the feature could be greater than the focus margin, a 180 nm line and space pattern could not be obtained for the entire area within the process latitude. To overcome this problem, we applied mask bias and an edge phase-shift mask. As a result, the desired line and space pattern was obtained for the entire global topographical area.