Open Access
Add to BibSonomyAbstract
We describe a novel control approach for form accuracy of microlenses with continuous relief by control of exposure threshold. The approach can be achieved by analysis of the exposure distribution on photoresist and by deriving a relationship between the exposure distributions and the internal photoactive compound concentration (PAC) of the photoresist. The feature of parallel PAC curves for a specific value is determined in this way. We then analyze the development process and discover its critical effect on the approach. Finally we establish the relationship between the PAC distribution and the form accuracy of the relief. Not only is the fabricated relief height significantly increased to as high as 100 µm by use of this method, but we also realized effective fine control of the form accuracy of the continuous relief. With this approach we obtained micro-optic elements with 100-µm relief height and a form error (rms value) of less than 1 µm.
©2005 Optical Society of America
1. Introduction
Development of micro-optoelectromechanical systems (MOEMS) in recent years not only extends the application range of micro-optic elements (MOEs) [1–3], but also leads to higher and higher requirements of form accuracy for fabrication of MOEs. To maintain good control of exposure and development of photoresists, in the early 1970s Dill [3] divided photolithography into two processes, exposure and development, which eventually resulted in the famous Dill model and Mack model for exposure and development, respectively [4,5]. The Mack model has been improved, and some of the developed models with higher accuracy, e.g., the notch model and an enhanced notch model, have been reported [5,6]. The Dill model made a significant contribution to simulation of the resist exposure process because it can be used to describe the photoactive compound concentration (PAC) distribution after exposure precisely when reflection light from substrates is ignored. The developed model is used mainly to describe the development process of the photoresist. Experiments have demonstrated that the development model is in good agreement with the practical results for a relief height of approximately several micrometers. However, for a thick photoresist, the parameters of the developed model do not remain constant during the process because of the significant increase in reaction depth of the photoresist. Therefore, it is difficult to control the development process by use of theoretical models [7,8]. In addition, the development model determined the relationship only between the PAC and the developed velocity. A computer simulation must be performed before one can derive the final desired relief profile on the photoresist, which creates a complicated simulation for the development process. Moreover, accuracy of the measured parameters of the development model will strongly affect control of the accuracy of the relief form.
The exposure process means that exposure distribution on the photoresist is transferred to internal PAC images. The development process means that PAC images are transferred to microrelief structures in the photoresist. Control of the two above-mentioned transformations must be carried out before one can gain control of microrelief structures.
Here we analyze the exposure process and then deduce the relationship between the exposure distribution on the photoresist and the internal PAC. The rule of PAC distribution in the photoresist is concluded. In addition, we analyze the development process and discover its critical effect during the process. A novel control approach for the form accuracy of microlenses with continuous relief by control of the exposure threshold was put forth on the basis of the critical effect. The MOEs, with a relief height of 100 µm and a form error (rms value) of less than 1 µm, were obtained by use of this approach.
2. Analysis of exposure process
Dill derived the relationships of internal intensity of the photoresist and PAC percentage versus exposure time and propagation distance, respectively, according to the mechanism between the light and the photoresist [4]:
where I is the internal intensity distribution of the photoresist, M is the PAC percentage, and A, B, and C are the characteristic parameters of the photoresist. To determine the internal PAC clearly, we modified the Dill model as follows. First we integrated Eq. (2) and obtained Eq. (3):
Defining
we obtained
where k is the integral constant and Q(x,z,t) is the exposure function. From the initial condition of M|Q=0=1, we have
and k 0=1. Substituting Eq. (7) into Eq. (1), we obtained
Integrating Eq. (8) yields
From the initial condition of
Eq. (9) can be rewritten as
We obtained
Thus, after the exposure process, M versus Z can be expressed as
Because exposure and development cannot be expressed by use of normal mathematical models, we provide examples to analyze the characteristics of these processes. For example, for the AZ9260 photoresist, its characteristic parameters of A, B, and C are 0.2063 µm-1, 0.0214 µm-1, and 0.02 cm2/mJ, respectively. Exposure doses of 500–3000 mJ/cm2 were used on the surface of the photoresist. The PAC curves versus depth are shown in Fig. 1.
We defined the equalized PAC curves that have the same internal PAC values. Figure 1 shows that the PAC distributions have the following characteristics:
1) The exposure dose determines the initial value of M. Increasing the exposure dose causes the parallel movement of M(Z) curves toward the direction of increased Z.
2) Corresponding equalized PAC curves to different values of M have the same shape.
As a matter of fact, it can be seen from Eq. (13) that the characteristics are the common features for a photoresist after it has been exposed.
The relationship between the distribution of exposure dose and the PAC was established by use of Eq. (13). To achieve form control of the microrelief structures, it is necessary to transfer the internal PAC into the corresponding microrelief structures.
3. Development process
By analyzing the exposure process we derived the relationship between the exposure distribution on a photoresist surface and the internal PAC distribution. The AZ9260 photoresist was used as an example to simulate the internal PAC distribution for different exposure conditions, as shown in Fig. 1. We still use AZ 9260 as an example to analyze the development process of the photoresist herein. We substituted the PAC distribution, M(Z), and development parameters of AZ9620 into the notch model,
and obtained Rmax=173.82 nm/s, Rmin=0.075 nm/s, n=1.45, Mth_notch=0.765, and n_notch=11.33. Rmax and Rmin are the maximum and minimum velocities of development, n is the selectivity of the development model, Mth_notch is the PAC threshold value, and n_notch is the selectivity of the points of the notch.
Fig. 2. Reciprocal of developing velocity, 1/R, vs. photoresist exposure depth, Z (exposure dose ranging from 500 to 3000 mJ/cm2)
Figure 2 is the reciprocal of developing velocity 1/R versus photoresist exposure depth Z. It can be seen that a break exists in the 1/R versus M curve. We defined the break point (it is the point with a maximum value of a second-order differential coefficient) as the point of reflection (P) in the development curves. The curves in Fig. 1 with a similar shape were also used to determine the curves in Fig. 2 with a similar shape. The M-Z curves correspond to the same PAC value of Mp at point P. The development time is equal to the integration of the reciprocal of the development velocity 1/R to development depth Z and can be written as
where Z 0 is the development depth of the photoresist.
Fig. 3. Photoresist developing depth, Z0, vs. developing time(exposure dose ranging from 500 to 3000 mJ/cm2).
Figure 3 shows the relationship between development time T and development depth Z 0 in a photoresist. It can be seen that the T-Z 0 curves for the different exposure doses have a reflection point at M=Mp. When the development depth is smaller than the value of Z 0 at point P (M<Mp), 1/R approaches zero, and development time is minimal in this case. Similarly, when the development depth is larger than the value of Z 0 at point P (M > Mp), 1/R increases rapidly. The development time increases approximately linearly to 5×103 s with an increase in depth of 1 µm. It can be seen that the surface layer of the photoresist with the equalized PAC at M=Mp has the characteristic of preventing the process from further development, which we refer to as the critical effect because it is the synthesized result of the performances of both the exposure and the development. Our experiments demonstrate that similar critical effects were observed for different photoresists. When development takes a long time, the form of the microrelief structures overlap with the equalized PAC curve at M=Mp because of the existing critical effect during development and can be expressed as
where f(x) is the relief structure after development, and
is the equalized PAC curve at M=Mp. Equation (16) establishes the relationship between the internal PAC and the form of relief structures when there is sufficient development time.
4. Technique of form control by means of exposure threshold
Figure 4. is a flow chart of the technique of form control by means of exposure threshold control. The following three steps can achieve the control process:
1) Determination of the internal equalized PAC distribution in terms of the target form in Eq. (16) establishes the relationship between the equalized PAC curve and the form of relief structures. It can be seen from Eq. (16) that the form of the required equalized PAC curve is the same as the target form of the relief structure, that is, .
2) To derive the equalized PAC curve we calculated the required exposure dose Q(x,0) in terms of the relationship described in Eq. (13) after determination of parameters A, B, and C.
3) The required exposure dose on the surface of the photoresist was used to obtain the internal PAC distribution .
Finally the development stopped at the site of , which corresponds to the equalized PAC curve that is due to the critical effect, and the required relief structure that appeared at that time is the same as the target microstructure.
5. Experimental results and analysis
As an example, we used a parabolic concave microlens array with a sag height of 100 µm as the target form and AZ9260 as the photoresist material. The characteristic parameters of A, B, and C are 0.2063 µm-1, 0.0214 µm-1, and 0.02 cm2/mJ, respectively. The coating thickness of the photoresist is 120 µm, which was prepared by multiple spinning and baking processes. According to Eq. (16), the equalized PAC curve is the same as the target form. The required exposure distribution to obtain the equalized PAC curve can be calculated in terms of Eq. (13), as shown in Fig. 5.
Fig. 5. Exposure distribution on photoresist surface with parameters of A=0.2063µm-1,B=0.0214µm-1, C=0.02cm2/mJ,
Fig. 6. Calculated internal PAC distribution by employing the exposure distribution as shown in Fig.5.
In our experiments first we designed the required mask pattern according to the exposure distribution shown in Fig. 5 and then exposed the photoresist by use of the mask-moving method [9]. After employing the exposure distribution of Fig. 5, we obtained the internal PAC distribution, as shown in Fig. 6. The stable form of the microlens array was achieved after 12 min of development. Figure 7 is the binary moving mask that we used during the exposure process.
The two-dimensional profile of the microlens array was obtained with the Alpha-Step 500 profilometer, as shown in Fig. 8. It can be seen that the sag height reached 100 µm. For comparison, we transferred the measured data from the profilometer and replotted it together with the target profile, as shown in Fig. 9. It can be seen that the actual profile is in good agreement with the target form. The statistical results show that the mean square root (rms) is less than ±1 µm.
Fig. 8. Measure two-dimensional profile of the concave microlensarray by use of the profilometer, Alpha Step 500.
6. Summary
In summary, we have achieved control of microrelief structures by virtue of the critical effect during the development process. Therefore, it is free of accurate control of characteristic parameters of development, and any fine control of the development process is not required. The relief form after development approaches the target form automatically after sufficient development time, as long as the required equalized PAC curve in photoresist is formed by means of the designed distribution of exposure doses.
Unstable factors of the microrelief form during development were degraded in this way. Thus the control of a microrelief form can be achieved by a combination of exposure methods such as a gray-level mask and mask moving.
Acknowledgments
This research was supported by the Innovation Foundation of the Chinese Academy of Sciences and the Foundation of the State Key Laboratory of Optical Technologies for Microfabrication. The authors thank their colleagues for their experimental and measurement contributions to this research.
References and links
1. M. He, X. Yuan, and J. Bu, “Sample-inverted reflow technique for fabrication of a revolved-hyperboloid microlens array in hybrid solgel glass,” Opt. Lett. 29, 2004–2006 (2004). [CrossRef] [PubMed]
2. Y. Oppliger, P. Sixt, J.M. Stauffer, J. M. Mayor, P. Regnault, and G. Voirin, “One-step 3D shaping using a gray-tone mask for optical and microelectronic applications,” Microelectron. Eng. 23, 449–454 (1994). [CrossRef]
3. F. H. Dill, W. P. Hornberger, P. S. Hauge, and J. M. Shaw. “Characterization of positive photoresist,” IEEE Trans. Electron Devices 22, 445–452 (1975). [CrossRef]
4. C. A. Mack, M. J. Maslow, A. Sekiguchi, and R. A. Carpio , “New model for the effect of developer temperature on photoresist dissolution,” in Advances in Resist Technology and Processing XV, W. Conley, ed., Proc. SPIE3333, 1218–1231 (1998).
5. G. G. Arthur, C. Wallace, and B. Martin , “Comparison of recent development models in optical lithography simulation,” in Metrology, Inspection, and Process Control for Microlithography XII, B. Singh, ed., Proc. SPIE3332, 538–549 (1998).
6. C. A. Mack and G. Arthur, “Notch model for photoresist dissolution,” Electrochem. Solid-State Lett. 1, 86–88 (1998). [CrossRef]
7. C. L. Henderson, S. Pancholi, S. A. Chowdhury, C. G. Wilson, and R. R. Dammel, “Photoresist characterization for lithography simulation: II. Exposure parameter measurements,” in Advances in Resist Technology and Processing XIV, R. G. Tarascon-Auriol, ed., Proc. SPIE3049, 816–828 (1997).
8. C. L. Henderson, P. C. Tsiartas, S. Pancholi, S. A. Chowdhury, K. D. Dombrowski, C. G. Wilson, and R. R. Dammel , “Photoresist characterization for lithography simulation: III. Development parameter measurements,” in Advances in Resist Technology and Processing XIV, R. G. Tarascon-Auriol, ed., Proc. SPIE3049, 805–815 (1997).
9. C. Du, X. Dong, C. Qiu, Q. Deng, and C. Zhou, “Profile control technology for high performance microlens array,” Opt. Eng. 43, 2595–2602 (2004). [CrossRef]
