CN109212636B - Design method of free-form surface lens for DMD photoetching imaging system - Google Patents

Abstract

A free-form surface lens used in a DMD lithography imaging system and a design method thereof belong to the field of optical technology. ×21mm, thickness is 1mm, the front surface is flat, the back surface is free-form, the maximum distortion is 10.63μm, the method includes calculating the linear dislocation of the DMD single micromirror that can smooth the edge of the lithography pattern, and the design has a special The free-form surface lens with distortion characteristics, the modeling of the projection imaging system, and the invention can reduce the jagged edges of the DMD scanning lithography pattern to obtain the best lithography pattern quality.

Description

A design method of free-form surface lens for DMD lithography imaging system

technical field

The invention belongs to the field of optical technology, in particular to a free-form lens with special distortion which is applied in a lithography system based on a digital micromirror array to solve the problem of sawtooth on the edge of a DMD maskless scanning lithography pattern.

Background technique

With the rapid development of micro-optical devices, DMD-based maskless scanning lithography has received extensive attention. The photolithography process uses computer optimization to generate a series of "virtual" digital graphics, and controls projection exposure equipment to project the graphics onto the substrate one by one. In the lithography process, because the exposure energy in other directions is not superimposed in the scanning direction, the edge of the scribed line has the problem of jaggedness and is not smooth, which greatly reduces the quality of the DMD scanning lithography pattern.

At present, there are three main methods to reduce the jagged edges of DMD scanning lithography patterns:

(1) Grayscale writing technology, which controls the flipping time of a single micromirror by adjusting the pulse width to form different grayscale patterns to achieve the purpose of reducing the jagged edges of the lithography pattern. However, when writing complex patterns, the writing efficiency is limited due to the need to process and transmit complex data. (2) Improve the reduction magnification of the imaging lens, which improves the quality of the lithography pattern to a certain extent. However, with the increase of the reduction magnification of the imaging lens, the system is more difficult to focus, and the writing area of a single scan decreases sharply. The lithography efficiency is reduced. (3) Tilt the lithography platform or DMD so that the exposure energy of a single pixel is superimposed outside the scanning direction. However, there are problems such as difficulty in precise control of the inclination angle, and increased difficulty in the installation and adjustment of the system.

Therefore, how to improve the quality of the lithography pattern without changing the lithography efficiency and increasing the difficulty of system assembly and adjustment is an urgent problem to be solved.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a design method of a free-form surface lens used in a DMD lithography imaging system, which can reduce the jagged edges of the DMD scanning lithography pattern to obtain the best lithography pattern quality.

A method for designing a free-form surface lens for a DMD lithography imaging system, characterized in that it comprises the following steps, and the following steps are performed in sequence,

Step 1. Calculate the linear dislocation of the DMD single micromirror that can smooth the edge of the lithography pattern

The y direction is set as the lithography scanning direction, j and i are the row and column where the DMD single micromirror is located, the number of the DMD single micromirror is i×j, L is the side length of the DMD single micromirror, and S is the projection lens. Magnification, θ is the deflection angle formed by the line connecting the center of each micromirror in the corresponding column after the installation of the free-form lens and the imaging center of each micromirror in the corresponding column before installation. The linear misalignment of the DMD single micromirror perpendicular to the scanning direction is Δx _j , Δx _j =S×L×(j-1)×tanθ;

Step 2. Design a free-form surface lens with a maximum distortion of 10.68μm

Set the DMD single micromirror, free-form surface lens, projection imaging lens and lithography substrate in sequence from top to bottom according to the light path, establish a rectangular coordinate system, and obtain the unit direction vector parameters of the incident light. The Marquardt algorithm is used in Matlab software to perform polynomial After fitting, the maximum value of the sag height z of the free-form lens is less than 0.8236mm;

Step 3. Modeling of the projection imaging system

The free-form lens surface was imported into the optical software Zemax to obtain the free-form lens model.

The expression of the total exposure energy _En of the lithography pattern formed by the deflection angle θ formed by the center connection line after the imaging of each micromirror in the corresponding column before the installation of the free-form surface lens in the first step is:

where P _i,j is the central optical power of a single micromirror, t is the time integral variable, n is the number of pixels in the lithography pattern, and M is the number of single micromirrors in the scanning direction.

Through the above-mentioned design scheme, the present invention can bring the following beneficial effects: a free-form surface lens used in a DMD lithography imaging system and a design method thereof, which can reduce the jagged edges of the DMD scanning lithography pattern to obtain the best lithography pattern quality.

Description of drawings

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:

FIG. 1 is a schematic diagram of the normal and linear dislocation arrangement of the DMD single micromirror of the present invention.

Fig. 2 is the exposure effect diagram of the single pixel and the scribed line when the linear dislocation Δx ₁₀₁ of the DMD single micromirror of the present invention is different;

FIG. 3 is a working principle diagram of the free-form surface lens of the present invention in the DMD projection imaging system.

FIG. 4 is a surface profile diagram of a free-form surface lens of the present invention.

FIG. 5 is a model diagram of a free-form surface lens of the present invention.

FIG. 6 is an effect diagram of an embodiment of the present invention.

In the figure, 1-DMD single micromirror, 2-free-form surface lens, 3-projection imaging lens, 4-lithography substrate.

Detailed ways

A free-form surface lens for a DMD lithography imaging system, characterized in that the distance between the DMD single micromirror and the free-form surface lens is 1mm, the material of the free-form surface lens is silicon crystal, the outer contour size is 12mm×21mm, and the thickness is 1mm, the front surface profile is a plane, the back surface profile is a free-form surface, and the maximum distortion is 10.68μm.

A method for designing a free-form surface lens for a DMD lithography imaging system, characterized in that it comprises the following steps, and the following steps are performed in sequence,

Step 1. Calculation of linear dislocation of DMD single micromirror that can smooth the edge of lithography pattern

Aiming at the problem that the edge of the lithography pattern has sawtooth outside the scanning direction, the linear dislocation form of the single micromirror as shown in Fig. 1 is proposed. If the y direction is set as the lithography scanning direction (the scanning direction below is the same direction), j and i are the row and column where the single micromirror is located, the number of single micromirrors of the DMD is i×j, and L is the single micromirror , the magnification of the projection lens is S, and the linear displacement of the DMD single micromirror in the direction perpendicular to the scanning direction is Δx _j . The deflection angle formed by the line is θ, then the expression of Δx _j is shown in (1):

Δx _j =S×L×(j-1)×tanθ.......(1)

The expression of the total exposure energy _En of the lithography pattern is:

where P _i,j is the central optical power of a single micromirror, t is the time integral variable, n is the number of pixels in the lithography pattern, and M is the number of single micromirrors in the scanning direction. When the exposure threshold of the photoresist is E ₀ , the number of single micromirrors in the scanning direction is 101, and E _n ≥ 101E ₀ , the exposure effect of a single pixel and a scribed line is shown in Figure 2, from left to right Δx ₁₀₁ 0, 0.5L and L in order. The sawtooth values of the reticle are shown in Table 1 below.

Table 1 Values of the serrations of the graticule

It can be seen from Table 1 that when Δx ₁₀₁ is taken as L(0.9En), the value of the line length and line width of the scribed line is taken as the line connecting the center points of the micromirror, and the jagged edge of the horizontal line is reduced from 0.14 pixels to 0 pixels. , the slash edge aliasing is reduced from 0.338 pixels to 0.115 pixels. The width of the oblique line increases greatly but does not affect the shape of the graph. Here, the line width and length of the horizontal line and the vertical line shall prevail. The change of the line length and line width of the horizontal line is 0.04 and 0.126 pixels respectively. The changes in length and line width are -0.063 and 0.046 pixels, respectively. Both Figure 2 and Table 1 illustrate that the edge of the lithography pattern can be smoothed by means of linear dislocation of a single micromirror.

Step 2. Design of free-form surface lens with special distortion characteristics

The laser light source is set to 405nm, the pixel side length of DMD (1080×1920) is 10.68μm, the overall size is 11.664mm×20.732mm, and the magnification of the projection imaging lens is 1. The parameters of the free-form surface lens with special distortion can be obtained. ,As shown in table 2.

Table 2 Freeform lens parameters

The working principle of the free-form surface lens is shown in FIG. 3 . From top to bottom, there are a DMD single micromirror 1 , a free-form surface lens 2 , a projection imaging lens 3 and a lithography substrate 4 . Among them, z is the direction of the optical axis, and θ is the deflection angle formed by the line connecting the imaging center of each micromirror in the corresponding column after the free-form surface lens is installed. The incident ray I is parallel to the optical axis z, and the free-form surface lens makes the surface A of the DMD micromirror array form a virtual object B after the micromirror array is linearly displaced, and the distance d from the virtual object B to the DMD is given by the following formula

d=(n _i -1)×h...(3)

n _i and h are the refractive index and thickness of the free-form surface lens, respectively.

The virtual object B is finally imaged on the lithography substrate by the projection imaging system. Due to the action of the free-form surface lens, the DMD micromirror array is linearly dislocated after imaging. The deflection angle formed by the line connecting the rear of the free-form surface lens and the imaging center of each micromirror in the corresponding column before installation is θ.

After the establishment of the rectangular coordinate system, the acquisition of parameters such as the unit direction vector of the incident light, according to the linear dislocation analysis of the single micromirror, the Snell's law of space optics, and the knowledge of multivariate differential mathematics, the initial data of the free-form lens surface can be obtained. In Matlab After polynomial fitting using the Levenberg-marquardt algorithm in the software, the surface shape of the free-form lens can be obtained as shown in Figure 4, and the maximum value of the lens sag z is close to 0.8236mm.

Step 3. Modeling of the projection imaging system

The free-form lens surface shape was imported into the optical software Zemax to obtain the lens model, as shown in Figure 5. Taking the long side of the DMD chip size as the height of the object surface and the short side as the width of the object surface, an ideal imaging lens group with a magnification of 1 is used to form an aberration-free double-telecentric optical system, which performs 1:1 imaging on the image plane.

Figure 6 shows the smoothing result of the free-form surface lens simulation simulation on the edge of the scribed line designed by the present invention for the DMD lithography imaging system.

Take the total exposure energy as I, the side length of a single micromirror as L, the number of single micromirrors in the scanning direction as 101, and the magnification of the projection imaging lens as 1, taking the lithography pattern "tree" as an example to simulate the installation The exposure effect of the "tree" before and after the free-form lens, Figure 6 is the edge map of the "tree" before and after installing the free-form lens.

Claims (2)

1. A design method of a free-form surface lens for a DMD photoetching imaging system is characterized by comprising the following steps: comprises the following steps which are sequentially carried out,

step one, calculating linear dislocation of DMD single micromirror capable of smoothing edge of photoetching pattern

Setting the y direction as the photoetching scanning direction, j and i as the rows and columns of DMD single micromirrors, i × j as the number of DMD single micromirrors, L as the side length of DMD single micromirrors, S as the magnification of projection lens, and theta as the deflection angle formed by the central connecting line after installing the free-form surface lens and after imaging each micromirror in the corresponding column before installing to obtain the angle perpendicular to the scanning directionLinear misalignment of DMD micromirrors is Δ x_j，Δx_j＝S×L×(j-1)×tanθ；

Step two, designing a free-form surface lens with the maximum distortion of 10.68 mu m

The method comprises the steps that a DMD single micromirror, a free-form surface lens, a projection imaging lens and a photoetching substrate are sequentially arranged from top to bottom according to a light path, a rectangular coordinate system is established, unit direction vector parameters of incident light are obtained, and after polynomial fitting is carried out in Matlab software by adopting a Marquardt algorithm, the maximum value of the rise z of the free-form surface lens is smaller than 0.8236 mm;

step three, modeling of projection imaging system

The free-form surface lens model is obtained by introducing the free-form surface lens shape into the optical software Zemax.

2. The method of claim 1, wherein the free-form surface lens comprises: in the first step, the total exposure energy E of the photoetching pattern with the deflection angle theta formed by the central connecting line after the free-form surface lens is installed and after the imaging of each micromirror in the corresponding row before installation_nThe expression of (a) is:

in the formula, P_i,jThe central optical power of the single micromirror, t is the time integral variable, n is the number of pixels of the lithography pattern, and M is the number of single micromirrors in the scanning direction.

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