Design and Simulation of Eccentric Holes Off-axis Illumination EUVL Miniature Projection Objectives Lin Qiang, Jin Chunshui, Xiang Peng, Ma Yueying, Yan Shu, Cao Jianlin (Chinese Academy of Sciences Changchun Institute of Optics, Fine Mechanics and Physics Institute of Applied Optics National Focus, Photolithography Mask That is, the object surface of the system; the silicon wafer is the image plane of the system; and M 2 is the mirror coated with the EUV reflective multilayer film.
(4). Poor and astigmatism. Appropriately select the radius of curvature R2 and R2 of the two spherical surfaces, the system satisfies 1, and considering that the radius of curvature of the two spherical surfaces is too small, it will bring certain difficulties to the uniform coating, and appropriately select their values. Since the target is better than 100 nm, the optimization process mainly considers the transfer function with a spatial frequency greater than 5000/mm. 1 Using zamax software to set up i and count 6 to obtain the parameters of the miniature projection objective, the results are shown in Table 2.
Table 2 EUVL miniature projection objective structure parameters surface annotation radius of curvature thickness mirror type diameter object eccentric light 阑 light reflection mirror surface image where STP marks the pupil Stop is eccentric, eccentric distance is y-axis direction 2. 25mm.3 mark times The center of the mirror M2 has a clear aperture of <12 mm.
The transfer function curve for the system (where T, representing the meridian and sagittal directions, respectively). After optimization, a resolution better than 100 nm is obtained in the image field of <0. 14 mm, and the transfer function of each field of view point is deviated from the transfer function of the diffraction limit. The final system image square aperture NA=0.082, the reduction ratio is 0.1, the back focal length is 22.95mm, the total length of the imaging system (object-to-image surface distance) is 283.64mm, and the design residual is smaller than the result of the optical system adjustment, mainly It is described by the wave aberration of the exit position reflecting the performance of the system. The smaller the wave aberration, the closer to the ideal design value, the smaller the error of the adjustment. As long as the system's offset is obtained from the relationship between wave aberrations and system structural parameters, the purpose of the adjustment is achieved.
3.1 Wave aberration vector and sensitive matrix The wave aberration is expressed as Zemike coefficient form to form the wave aberration vector Z. The mathematical model of wave aberration is the functional relationship Z=Z composed of the structural parameter vector and the wave aberration vector. X). Describe the best imaging quality of the system is to minimize Z. So finding a structural form X to minimize Z is equivalent to optimizing the optical design process. Since the relationship between Z(X) and X is nonlinear and the structural parameters are cross-correlated, this causes a problem of ill-posedness in solving Z-min. That is to say, when solving by least squares, there are many approximate solutions. Newton iteration method based on singular value decomposition (SVD) can solve the above problems better.
Assuming that there is a slight correction condition for the structural parameters, so that the optical system is in an unbalanced state, and the aberration vector is Z (X + Desire), then the offset of the solution system is obtained by Z(X+DX) = 0 Solution. It is developed by the Tylor formula: where / is the sensitive matrix, and it reflects the high-order term of the sensitive one (2) generation net table DX affected by the offset wave of the hostile wave aberration z.
3.2 Solving Offsets When using Newton's iterative method to solve the (3) offset DX, only the linear term is ignored, and the high-order term is ignored. Firstly, the sensitivity matrix is ​​first obtained. J. The optical system design is used to design the initial optical system structure and calculate The initial aberration Zernike coefficient Z... artificially changes a slight increment DX to an initial structural parameter, calculates the Zernike coefficient Zi, and the amount of change DZi=Zi-Z., then the corresponding Jij=secret/desire, repeat the process Then J can be calculated and then the sensitive matrix J is decomposed into SVD: the interferometer is used to detect the wavefront aberration at the 瞳 position, and the wave aberration vector Z(X) expressed in the form of Zernike coefficient is obtained.
Find the pseudo-inverse of the matrix of (7), substitute (6), and finally get the offset DX: Since (6) is only the approximate solution of the ideal (5), it needs to be solved multiple times until the wave image The difference reaches the design residual requirement.
4 Modulation Simulation 4.1 Compensator and Correction of the aberration Generally, for the spherical surface, the rotation amounts H and Q are equivalent to the translational quantities Ay and Ax, respectively. In the designed Schwarzschild structure consisting of two spherical mirrors, two degrees of freedom of translation Ax, Ay, Az are selected to adjust, and M2 is fixed, and finally the object sides Az, Ml-Ax, Ml-Ay, Ml-Az are selected. And like the side Az as a compensator.
In the process of adjusting the system, since the high-level aberration is always the same, only the primary aberration is corrected. The system uses only a single wavelength K = 13 nm, and is a total reflection system, so there is no chromatic aberration portion. Image plane tilt does not affect the imaging quality of the system for small fields of view, so it is not considered. As long as the coma is corrected in the system, the astigmatism is corrected. Therefore, defocus, coma, and spherical aberration are selected as correction targets.
4.2 Description of the Modulation Simulation Section 2 Calculate the Sensitive Matrix J and its SVD Matrix U, W, V. Use the Zemax Optical Design Software to give a random disturbance to the structural parameters, and calculate the wave image represented by the Zernike coefficient at the image plane position. The difference is selected from four coefficients of Z4 (defocus), Z7 and Z8 (å½— difference), and Z9 (spherical aberration) reflecting the correction target, and constitutes a wave aberration vector Z(X). Then calculate the offset amount DX according to (8) to correct the system by the obtained offset amount, and recalculate the wave aberration. Repeat this process until the wave aberrations meet the requirements of the system design.
As shown, it is the result of a random disturbance. Before the iteration, a residual of 30 KRMS is generated (K = 13 nm), that is, a value of about 0.62 KRMS at a wavelength of 632.8 nm, which is achievable under rough adjustment. After two iterations, the residual is controlled in the 1/14K range, as in (a), and the amount of offset that needs to be corrected is getting smaller and smaller, as in (b). This shows that the iterative process is a process of gradual convergence. A number of simulation experiments have been carried out and both have been obtained. It can be seen that when the disturbance of the structure is controlled within a certain range, the adjustment system is always converged by this method.
5 Conclusion The EUVL projection objective imaging system with eccentric aperture off-axis illumination is optimized. The numerical aperture of the system is 0. 082, the reduction ratio is 0.1, and the design residual is less than 1/14KRMS (A=13nm). And the system is simulated and adjusted several times, which proves that the method can be used in the precise adjustment of the system.
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