Methods and related products for optimizing lithographic processes

Abstract

The invention provides a method for optimizing a photolithographic process and a related product. The method comprises the following steps: acquiring two critical dimension curves of upper and lower limit offset values of a critical dimension, performing tangent modeling with a process window curve, constructing two groups of offset tangent equations, calculating a plurality of calculated values of focal depths at tangent positions based on a given value of exposure dose tolerance, and taking the minimum value as a target value, the method comprises the steps of obtaining a curve of a target process window, judging whether the target process window is tangent to the critical dimension curve or not, and taking the target process window as the maximum process window if the target process window is tangent to the critical dimension curve. According to the method, traditional numerical iteration is replaced with the tangent problem of the mathematical analysis quadratic function and the ellipse, the calculation efficiency is remarkably improved, and compared with an exhaustion method in the prior art, the theoretical optimal solution is directly solved through the mathematical tangent condition, and the algorithm precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor manufacturing technology, and particularly to a method, a computer program product, a computer-readable storage medium, and a computer device for optimizing a lithography process. Background Art

[0002] In some optical lithography systems, the imaging quality of critical dimensions (CD, Critical Dimension) is affected by the depth of focus and the allowable deviation of the exposure dose. Under the current lithography process requirements, the allowable critical dimension deviation is usually ±10%. To determine the optimal process conditions, it is necessary to find the elliptical process window with the largest area within the region formed by two quadratic curves describing the change of critical dimensions. The two major axes of this ellipse respectively correspond to the depth of focus (abbreviation: DOF) and the allowable change range of the exposure dose. Currently, the exhaustive method is usually used to optimize the process window. First, a set of combinations of focus positions and exposure doses is fixed as the center point of the ellipse, and the corresponding parameter matching range is calculated; then, all possible center points within the feasible region are repeatedly calculated, and finally, the optimal process window is determined by comparing the areas of each ellipse. However, the above-mentioned exhaustive method has great limitations in the process of finding the process window with the largest area. For example, it takes a long time when the number of traversed points is too large, and the optimal window may be missed when the number of traversed points is too small. Summary of the Invention

[0003] In view of the above problems, the present invention is proposed to provide a method for optimizing a lithography process that overcomes the above problems or at least partially solves the above problems.

[0004] An object of the present invention is to solve the problem that the existing exhaustive method takes too much time when the number of traversed points is large, and achieve the purpose of shortening the time for finding the process window with the largest area.

[0005] Specifically, according to one aspect of the present invention, there is provided a method for optimizing a lithography process, including:

[0006] Obtaining a preset tangent equation set, where the tangent equation set is used to characterize the relationship between the depth of focus and the exposure dose tolerance under the tangent condition of the process window curve and the critical dimension curve, the process window curve is represented by an ellipse, and the critical dimension curve is represented by a quadratic function curve;

[0007] Respectively offset the critical dimension curve based on two different offset values to obtain two offset tangent equation sets;

[0008] Obtaining a given value of the exposure dose tolerance, and solving a plurality of calculated values of the depth of focus through the two offset tangent equation sets;

[0009] Determining the smallest one among all the calculated values of the depth of focus as the target value;

[0010] Determine whether the target process window is tangent to the critical dimension curve, where the central coordinate of the target process window is a given value, the semi-minor axis is a given value of the exposure dose tolerance, and the semi-major axis is a target value of the depth of focus;

[0011] If they are tangent, use the target process window as the maximum process window.

[0012] Optionally, the step of determining the target value includes:

[0013] Determine the minimum value among the calculated values of the depths of focus corresponding to each of the offset tangent equation systems, and denote it as the extreme value between groups;

[0014] Compare the extreme values between groups corresponding to the two offset tangent equation systems, and use the smaller one of the two as the target value.

[0015] Optionally, the step of obtaining the tangent equation system includes:

[0016] Obtain the simultaneous expression of the tangent equations of the process window curve and the critical dimension curve at the tangent point coordinates (x0, y0):

[0017]

[0018] Based on the simultaneous expression of the tangent equations, obtain an expression for characterizing the relationship between the tangent point coordinates and the exposure dose tolerance:

[0019]

[0020] Based on the simultaneous expression of the tangent equations, obtain an expression for characterizing the relationship between the tangent point coordinates and the depth of focus:

[0021]

[0022] Wherein, a represents the depth of focus, b represents the exposure dose tolerance, x represents variables, d represents the coefficient determining the opening direction and opening width of the critical dimension curve, e represents the coefficient related to the symmetry axis position of the critical dimension curve, and f represents the ordinate of the intersection point of the critical dimension curve and the vertical axis.

[0023] Optionally, determining whether the target process window is tangent to the critical dimension curve includes:

[0024] Calculate the number of intersection points between the target process window and the critical dimension curve;

[0025] Judge whether the number of intersection points is less than or equal to 1;

[0026] If it is less than or equal to 1, the target process window is tangent to the critical dimension curve.

[0027] Optionally, the calculating step of the intersection number includes:

[0028] Obtain a preset intersection expression:

[0029] a 2 d 2 x 4 +2dea 2 x 3 +(a 2 (e 2 +2d(f - k)) + b 2 )x 2 +(2a 2 e(f - k) - 2b 2 h)x + a 2 (f - k) 2 +b 2 h 2 -a 2 b 2 = 0;

[0030] where h and k represent the central coordinates of the target process window, a represents the depth of focus, b represents the exposure dose tolerance, x represents a variable, d represents a coefficient determining the opening direction and opening width of the critical dimension curve, e represents a coefficient related to the position of the axis of symmetry of the critical dimension curve, and f represents the ordinate of the intersection of the critical dimension curve and the vertical axis;

[0031] Based on the intersection expression, calculate the intersection number of the target process window and the critical dimension curve.

[0032] Optionally, the two offset values are the products of the given coefficients of the critical dimension curve and two ratio values respectively, and both of the two ratio values are in the range of -10% to +10%.

[0033] Optionally, the step of determining the target value includes:

[0034] Obtain all the calculated values of the depth of focus corresponding to the two offset tangent equation systems;

[0035] Compare all the calculated values of the depth of focus, and take the smallest one as the target value.

[0036] According to another aspect of the present invention, there is also provided a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method for optimizing a lithography process as described in any one of the above are performed.

[0037] According to another aspect of the present invention, there is also provided a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, it performs the steps of the method for optimizing a lithography process according to any one of the above.

[0038] According to still another aspect of the present invention, there is also provided a computer device, including a memory, a processor, and a computer program stored on the memory, wherein the processor executes the computer program to implement the steps of the method for optimizing a lithography process according to any one of the above.

[0039] The method of the present invention is a method for optimizing a lithography process. It obtains two critical dimension curves of upper and lower limit offset values of critical dimensions, performs a tangent modeling with a process window curve, constructs two sets of offset tangent equations, transforms the optimization problem of the process window curve into a tangency problem between a quadratic function and an ellipse. Based on a given value of exposure dose tolerance, it calculates calculated values of multiple focal depths at the tangent position and takes the minimum value thereof as the target value to obtain a curve of the target process window, and determines whether the target process window is tangent to the critical dimension curve. By performing mathematical analysis to calculate the number of intersection points, when the number of intersection points meets the tangency condition, the target process window is taken as the maximum process window. By solving the tangency problem between the process window curve based on a set of center points and the critical dimension curve, and seeking the process window with the largest area within the feasible region, it avoids the process of repeatedly calculating all possible center points within the feasible region and then comparing the areas of the process window curves to determine the optimal process window. This method uses mathematical analysis of the tangency problem between a quadratic function and an ellipse to replace the traditional numerical iteration, significantly improving the calculation efficiency. Compared with the exhaustive method of the prior art that can only give an approximate solution within a fixed step range near the exact solution by continuously reducing the fixed step size, the present invention directly obtains the theoretical optimal solution through strict mathematical tangency conditions, improving the algorithm accuracy.

[0040] From the following detailed description of specific embodiments of the present invention in conjunction with the accompanying drawings, those skilled in the art will become more clear about the above and other objects, advantages, and features of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Some specific embodiments of the present invention will be described in detail hereinafter with reference to the accompanying drawings in an exemplary but non-limiting manner. The same reference numerals in the drawings denote the same or similar components or parts. Those skilled in the art should understand that these drawings are not necessarily drawn to scale. In the drawings:

[0042] Figure 1 is a flowchart showing a method for optimizing a lithography process according to an embodiment of the present invention;

[0043] Figure 2It is a schematic flow chart of a method for optimizing a lithography process according to an embodiment of the present invention;

[0044] Figure 3 It is a schematic flow chart of a method for optimizing a lithography process according to an embodiment of the present invention;

[0045] Figure 4 It is a schematic flow chart of a method for optimizing a lithography process according to an embodiment of the present invention;

[0046] Figure 5 It is a schematic flow chart of a method for optimizing a lithography process according to an embodiment of the present invention;

[0047] Figure 6 It is a schematic diagram showing the relationship between the depth of focus and the exposure dose tolerance under the tangency condition of the process window curve and the critical dimension curve according to an embodiment of the present invention;

[0048] Figure 7 It is a diagram showing the positional relationship between the critical dimension curve and the process window curve according to an embodiment of the present invention, which shows two process window curves tangent to the same critical dimension curve;

[0049] Figure 8 It is a schematic diagram of a computer program product according to an embodiment of the present invention;

[0050] Figure 9 It is a schematic diagram of a computer-readable storage medium according to an embodiment of the present invention; and

[0051] Figure 10 It is a schematic diagram of a computer device according to an embodiment of the present invention. Detailed implementation manners

[0052] Obviously, the accompanying drawings in the following description are only some examples or embodiments of the present application. For those of ordinary skill in the art, without creative efforts, the present application can also be applied to other similar scenarios based on these drawings. In addition, it can also be understood that although the efforts made in this development process may be complex and lengthy, for those of ordinary skill in the art related to the content disclosed in the present application, some design, manufacturing or production changes based on the technical content disclosed in the present application are only conventional technical means and should not be understood that the content disclosed in the present application is insufficient.

[0053] References to "embodiments" in this application mean that the specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of this application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in this application can be combined with other embodiments without conflict.

[0054] Unless otherwise defined, the technical terms or scientific terms involved in this application shall have the ordinary meaning as understood by those of ordinary skill in the technical field to which this application belongs. The words "a", "an", "one", "the", and the like involved in this application do not indicate a limitation in quantity and can mean singular or plural. The terms "comprising", "including", "having", and any variations thereof involved in this application are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or modules (units) is not limited to the listed steps or units, but may further include steps or units not listed, or may further include other steps or units inherent to these processes, methods, products, or devices.

[0055] In this application, some features and their corresponding English abbreviations and explanations are as follows:

[0056] Critical Dimension: English abbreviation: CD, English full name: Critical Dimension, Explanation: Refers to the minimum feature size that must be precisely controlled during chip manufacturing;

[0057] Depth of Focus: English abbreviation: DOF, English full name: Depth of Focus, Explanation: In an optical system, when the image plane (such as the surface of the photoresist) moves along the optical axis (longitudinally), the maximum allowable range within which the image can still remain clearly distinguishable;

[0058] Exposure Latitude: English abbreviation: EL, English full name: Exposure Latitude, Explanation: Represents the maximum range of allowable exposure dose (Energy Dose) fluctuations on the premise of ensuring the pattern quality (such as critical dimension CD, line edge roughness LER, etc.);

[0059] Exposure Dose: English abbreviation: Dose, English full name: Exposure Dose, Explanation: Refers to the total amount of light energy received by the photoresist per unit area during the exposure process;

[0060] Focus: English full name: Focus, Explanation: Refers to the vertical distance deviation between the surface of the silicon wafer during actual exposure and the best focal plane of the optical system;

[0061] The above features are given for the convenience of understanding the present application based on the English names and explanations.

[0062] Please refer to Figure 1 , an embodiment of the present invention provides a method for optimizing a lithography process, including the following steps:

[0063] S100: Obtain a preset tangent equation system, which is used to characterize the relationship between the depth of focus and the exposure dose tolerance under the tangency condition of the process window curve and the critical dimension curve. The process window curve is represented by an ellipse, and the critical dimension curve is represented by a quadratic function curve.

[0064] The process window curve is an ellipse, and the center of the ellipse is the determined values of defocus and exposure dose, that is, the center of the process window curve is determined. The semi-major axis of the elliptical process window is the depth of focus, and the semi-minor axis is the exposure dose tolerance.

[0065] The critical dimension curve is a quadratic function curve, and this quadratic function describes the variation law of defocus and exposure dose when the critical dimension is given. In this quadratic function, x is the defocus and y is the exposure dose, where:

[0066] There is a functional relationship among the critical dimension, defocus, and exposure dose, and the critical dimension changes with defocus and exposure dose.

[0067] When the exposure dose is fixed, the critical dimension and defocus usually have a quadratic relationship, and the formula is:

[0068] cd(x) = px 2 + qx + r; (1)

[0069] In the above expression (1): The variable x is the defocus, and p, q, and r are function parameters, which are used to characterize the variation relationship between the two when establishing the quadratic function of the critical dimension and defocus.

[0070] When the defocus is fixed, the critical dimension and exposure dose have a linear relationship, and the formula is:

[0071] cd(y) = my + n; (2)

[0072] In the above expression (2): The variable y is the exposure dose, and m and n are function parameters and are used to characterize the variation relationship between the two when establishing the linear function of the critical dimension and exposure dose.

[0073] Then there is a functional relationship among the critical dimension, defocus, and exposure dose, and the formula is:

[0074] cd(x,y) = dx 2 + ex + fy + gxy + h; (3)

[0075] In the above expression (3): the variable x is the defocus amount, the variable y is the exposure dose, and d, e, f, g, and h are function parameters and are used to characterize the variation relationship between them when establishing the binary quadratic function of the critical dimension, defocus amount, and exposure dose.

[0076] After ignoring the cross term xy, it is simplified to:

[0077] cd(x,y) = ax 2 + bx + cy + d; (4)

[0078] In the above expression (4): the variable x is the defocus amount, the variable y is the exposure dose, and a, b, c, and d are the function parameters after the simplification of expression (3).

[0079] Since the critical dimension is already given, the fitting coefficients are used to construct a quadratic function with x as the defocus amount and y as the exposure dose as the quadratic function curve of the critical dimension curve. The formula is:

[0080] dx 2 + ex + f = y; (5)

[0081] In the above expression (5): the variable x is the defocus amount, the independent variable y is the exposure dose, and d, e, and f are function parameters and are used to establish the quadratic function between the defocus amount and the exposure dose when the critical dimension is given, and to characterize the variation relationship between the defocus amount and the exposure dose. Among them, d represents the coefficient that determines the opening direction and opening width of the quadratic curve of formula (5), e represents the coefficient related to the symmetry axis position of the quadratic curve of formula (5), and f represents the ordinate of the intersection point of the quadratic curve of formula (5) and the vertical axis. d, e, and f can also be called the given coefficients of the critical dimension curve.

[0082] The tangent equation system is the tangent equation system constructed at the tangent point position of the process window curve and the quadratic function curve.

[0083] S200: Offset the critical dimension curve respectively based on two different offset values to obtain two offset tangent equation systems. That is to say, first obtain two offset critical dimension curves, as shown by curve 1 and curve 2 in Figure 6 , and construct two offset tangent equation systems at the respective tangent point positions through the two offset critical dimension curves and the elliptical process window. Among them, the process window curve is an elliptical curve, as shown by curve 3 in Figure 6 .

[0084] Each offset value can have a corresponding offset amount. Therefore, based on two different offset values, two curves of the critical dimension can be obtained. These two curves of the critical dimension are respectively:

[0085] The curve y1(x) of the first critical dimension: corresponding to the critical dimension CD + the first offset, i.e., y1(x) = dx 2 + ex + f + the first offset; as shown by curve 1 in Figure 6 .

[0086] The curve y2(x) of the second critical dimension: corresponding to the critical dimension CD + the second offset, i.e., y2(x) = dx 2 + ex + f + the second offset; as shown by curve 2 in Figure 6 .

[0087] S300: Obtain the given value of the exposure dose tolerance, and solve for the calculated values of multiple focal depths through two offset tangent equation systems.

[0088] After obtaining the combined equation system of the two tangent equations in step S200, solve the combined equations of the two sets of tangent equations respectively. Since the center of the elliptical process window is determined, and the given exposure dose tolerance is the value of the semi-minor axis in the elliptical process window, that is, the value of the semi-minor axis is equal to the given value of the exposure dose tolerance, what needs to be solved is the semi-major axis of the elliptical process window. And since the semi-major axis of the elliptical process window is the focal depth, what needs to be solved is also the focal depth.

[0089] When solving, multiple solutions for the semi-major axis of the elliptical process window can be obtained. Taking curve 1 as an example to explain the reason for obtaining multiple semi-major axes: as shown in Figure 7 , since the elliptical process window may be tangent to the critical dimension curve on the left side of the critical dimension curve, as shown in Figure 7 where curve 1 is tangent to the smaller curve 3, that is, the tangent point is on the left side; and, the elliptical process window may also be tangent to the critical dimension curve on the right side of the critical dimension curve, as shown in Figure 7 where curve 1 is tangent to the larger curve 3, that is, the tangent point is on the right side. Obviously, there are two tangent point positions. Therefore, the tangent point position between the elliptical process window and the critical dimension curve is not unique, and a solution can be obtained at each tangent point position, that is, a semi-major axis of the elliptical process window is obtained. As shown in Figure 7 , for the smaller elliptical process window tangent to curve 1, the corresponding semi-major axis is L1, and for the larger elliptical process window tangent to curve 1, the corresponding semi-major axis is L2. Since there are multiple tangent point positions, multiple semi-major axes of the elliptical process window are obtained, such as Figure 7 L1 and L2 in, that is, multiple values of the focal depth can be obtained, which means multiple values of the focal depth are calculated.

[0090] S400: Determine the minimum of all calculated values ​​of the depth of focus as the target value to obtain a target process window, wherein the center coordinate of the target process window is a given value, the semi-minor axis is a given value of the exposure dose tolerance, and the semi-major axis is a target value of the depth of focus.

[0091] S500: Determine whether the target process window is tangent to the critical dimension curve. If so, proceed to step S600: Use the target process window as the maximum process window.

[0092] After the target value semi-major axis is calculated in step S400, the equation of the elliptical process window is obtained based on the given center coordinates and semi-minor axis of the elliptical process window. Then, the intersection of the elliptical process window and each curve offset based on the offset value of the critical dimension curve is determined respectively, and whether the target process window is tangent to the critical dimension curve is determined according to the intersection. In other words, it can be said that the target value determined in step S400, that is, the determined semi-major axis / focal depth, is determined according to the intersection to determine whether it meets the requirements of the target value / semi-major axis / focal depth.

[0093] The judgment standard is that the number of intersections is ≤1. That is, the number of intersections between the first critical dimension curve y1(x) and the elliptical process window is N1; the number of intersections between the second critical dimension curve y2(x) and the elliptical process window is N2; if N1≤1 and N2≤1, the target process window is tangent to the critical dimension curve, so the target process window is the maximum process window. Figure 6 As shown, Figure 6 The number of intersections between the elliptical process window and the curves of the two critical dimensions is less than or equal to 1, that is, Figure 6 The elliptical process window (curve 3) is the maximum process window. Figure 6 The MaxDof in the formula represents the semi-major axis / focal depth of the maximum process window. Obtaining the maximum process window can also be said to be to obtain a given value of the exposure dose tolerance and a semi-major axis / focal depth that meets the requirements. In other words, Figure 6 The MaxDof in the figure indicates the semi-major axis / depth of focus that meets the requirements.

[0094] In the calculation method for determining the number of intersections between a quadratic function curve and an elliptical process window, the elliptical process window and the quadratic function curve are simultaneously eliminated and organized into a quartic equation about x, and the number of intersections is determined using the discriminant method. In particular, the number of intersections here refers to the number of real roots of the equation.

[0095] The discriminant method: the discriminant of the quartic equation Δ is judged by the size of 0 and the nature of the root:

[0096] If Δ is greater than 0, it indicates that there are 4 real roots. It is still necessary to further determine whether there are 2 pairs of multiple roots or 2 pairs of conjugate complex roots among the 4 root values. If not, the number of intersection points is 4; if so, the number of intersection points is determined to be 0.

[0097] If Δ is equal to 0, it indicates that there are multiple roots, and it is determined that the ellipse is tangent to the quadratic curve, and the number of intersection points is determined to be 1.

[0098] If Δ is less than 0, it indicates that there are 2 different real roots and 2 conjugate complex roots, then the number of intersection points is determined to be 2.

[0099] In the embodiments of the present invention, the curve of the first key dimension and the curve of the second key dimension form a feasible region, and the elliptical process window is included in this feasible region. The method of the present invention, by solving the tangency problem between the process window curve based on a set of center points and the key dimension curve, and seeking the process window with the largest area within the feasible region, avoids the process of repeatedly calculating all possible center points within the feasible region and then comparing the areas of the process window curves to determine the optimal process window. This method uses the tangency problem of mathematical analytical quadratic functions and ellipses to replace the traditional numerical iteration, significantly improving the calculation efficiency. Compared with the exhaustive method of the prior art that can only give an approximate solution within a fixed step range near the exact solution by continuously reducing the fixed step size, the present invention directly obtains the theoretical optimal solution through strict mathematical tangency conditions, improving the algorithm accuracy.

[0100] In some embodiments of the present invention, referring to Figure 2 , step S100, the obtaining step of the tangent equation system includes the following steps:

[0101] S110: Obtain the combined expression of the tangent equations of the process window curve and the key dimension curve at the tangent point coordinates (x0, y0):

[0102]

[0103] S120: Based on the combined expression (6) of the tangent equations, obtain an expression for characterizing the relationship between the tangent point coordinates (x0, y0) and the exposure dose tolerance b:

[0104]

[0105] S130: Based on the combined expression (6) of the tangent equations, obtain an expression for characterizing the relationship between the tangent point coordinates (x0, y0) and the depth of focus:

[0106]

[0107] Among them, in expressions (6), (7), and (8), a represents the depth of focus, b represents the exposure dose tolerance, x represents a variable, usually the defocus amount, d represents the coefficient that determines the opening direction and opening width of the critical dimension curve, e represents the coefficient related to the position of the symmetry axis of the critical dimension curve, and f represents the vertical coordinate of the intersection of the critical dimension curve and the vertical axis.

[0108] In the embodiment of the present invention, by establishing the simultaneous expression of the tangent equations at the tangent point coordinates (6), the possible coordinates of x0 when the ellipses are tangent are solved using formula (7), and then substituting them into formula (8), different x0 can be obtained, and then different focal depth values ​​corresponding to different x0 can be obtained. This method of establishing the tangent equation group combines the rigor of mathematical modeling and engineering practicality, ensuring the accuracy of the results.

[0109] In some embodiments of the present invention, reference Figure 3 In step S110, the specific process of obtaining the tangent equation simultaneous expression (6) can be:

[0110] S111, the standard equation for an ellipse is defined as:

[0111]

[0112] S112, assuming that the tangent point has coordinates (x0, y0), the tangent line equation of the above ellipse standard equation (9) is:

[0113]

[0114] S113, the equation defining the quadratic function is:

[0115] dx 2 +ex+f=y; (11)

[0116] In the quadratic function: independent variable (x): defocus; dependent variable (y): exposure dose, d, e, f are fitting coefficients and given coefficients, determined by experimental data. The quadratic function describes the change law of the key dimension with defocus and exposure dose.

[0117] S114, the equation of the tangent line of the quadratic function (11) passing through the tangent point with coordinates (x0, y0) is:

[0118] y=(2dx0+e)x-dx0+f; (12)

[0119] S115, compare the tangent equation (10) and the tangent equation (12), the expression after the coefficient comparison is the tangent equation joint expression (6), thereby obtaining the tangent equation joint expression.

[0120] In an embodiment of the present invention, by fitting the coefficients at the tangent point positions of the elliptical process window and the critical dimension curve, a tangent equation expression is established. This method combines the rigor of mathematical modeling and lays a foundation for subsequent digital modeling.

[0121] In some embodiments of the present invention, the offset value is used to offset a given coefficient, that is, to change d, e, and f. When changing d, the changed d can be: d + offset value; when changing e, the changed e can be: e + offset value; when changing f, the changed f can be: f + offset value. In step S200, the two offset values are the products of the given coefficients of the critical dimension curve and the two ratio values respectively.

[0122] Specifically, the two ratio values are respectively defined as the first ratio value and the second ratio value. The expression of the critical dimension curve after offset based on the first ratio value, that is, the first critical dimension curve, is:

[0123] y = (d + d * first ratio value)x 2 + (e + e * first ratio value)x + (f + f *

[0124] first ratio value) = dx 2 + ex + f + first ratio value * (dx 2 + ex + f).

[0125] Then the first offset of the first critical dimension curve is: first ratio value * (dx 2 + ex + f).

[0126] The expression of the critical dimension curve after offset based on the second ratio value, that is, the second critical dimension curve, is:

[0127] y = (d + d * second ratio value)x 2 + (e + e * second ratio value)x + (f + f *

[0128] second ratio value) = dx 2 + ex + f + second ratio value * (dx 2 + ex + f).

[0129] Then the second offset of the second critical dimension curve is: second ratio value * (dx 2 + ex + f).

[0130] In some embodiments of the present invention, both ratio values are in the range of -10% to +10%. In the actual process, we define the allowable error range for the critical dimension as ±10% error (i.e., critical dimension CD ±10%). Here, the two ratio values are selected as +10% and -10% respectively. Therefore, two curves of the critical dimension, y1(x) and y2(x), will be generated, which are respectively:

[0131] The first curve of the critical dimension y1(x) = d*(1 + 10%)x 2 + e*(1 + 10%)x + f*(1 + 10%).

[0132] The second curve of the critical dimension y2(x) = d*(1 - 10%)x 2 + e*(1 - 10%)x + f*(1 - 10%).

[0133] In the embodiments of the present invention, the ratio values +10% and -10% are common ratio data in the lithography field itself. The corresponding offsets are converted into mathematical constraints, and the process fluctuation range is covered by mathematical means to avoid hidden failures during mass production.

[0134] In some embodiments of the present invention, in step S300, the specific steps for calculating the depth of focus are as follows: after obtaining the joint equations of the two tangent equations in step S200 and after obtaining the exposure dose tolerance, where d, e, and f are fitting coefficients / given coefficients determined by experimental data, substitute the known b, d, e, and f into formula (7) to solve for the possible x0 coordinates when the elliptical process window is tangent to the corresponding critical dimension curve.

[0135] After obtaining multiple values of x0 coordinates, substitute them into formula (8) to obtain the corresponding depth of focus values.

[0136] Among them, two sets of offset tangent equation systems respectively solve for multiple calculated values of the depth of focus.

[0137] In the embodiments of the present invention, by using mathematical analysis to solve the tangency problem, the obtained values are more accurate, providing algorithm accuracy.

[0138] In some embodiments of the present invention, in step S400, the method for determining the target value includes the steps of: determining the minimum value among the multiple calculated values of the depth of focus corresponding to each offset tangent equation system, denoted as the extreme value between groups; comparing the extreme values between groups corresponding to the two offset tangent equation systems, and taking the smaller of the two as the target value.

[0139] For example, corresponding to two critical dimension curves y1(x) and y2(x), multiple values of the semi-major axis of the elliptical process window are obtained through step S300. The minimum values corresponding to the two parabolas are taken as the first semi-major axis and the second semi-major axis respectively, and the smaller value of the first semi-major axis and the second semi-major axis is taken as the above-mentioned target value. The smaller the target value, the greater the possibility that the corresponding ellipse is within the feasible region formed by the first critical dimension curve and the second critical dimension curve. And since it is tangent to at least one of the two critical dimension curves, it indicates that the corresponding ellipse is the largest ellipse within the feasible region formed by the first critical dimension curve and the second critical dimension curve. That is to say, this target value is the largest semi-major axis with the ellipse center fixed and the determined semi-minor axis within the feasible region formed by y1(x1) and y2(x2).

[0140] That is to say, the ellipse represented by the semi-major axis obtained in step S300 is only tangent to a certain side of the quadratic function, and it does not guarantee that the ellipse is completely wrapped by the quadratic function, that is, it does not guarantee that the corresponding ellipse is completely within the feasible region formed by the first critical dimension curve and the second critical dimension curve. In order to make the ellipse completely wrapped by the quadratic function as much as possible, it is necessary to obtain the smallest semi-major axis as the target value.

[0141] In some other embodiments of the present invention, it is also possible to obtain all the calculated values of the focal depth corresponding to two offset tangent equation systems; compare all the calculated values of the focal depth, and take the smallest one as the target value. In the embodiments of the present invention, the process of obtaining the minimum value of the above target only needs to be compared once, avoiding repeated comparisons, saving computing power and having high accuracy.

[0142] In some embodiments of the present invention, referring to Figure 4 , in step S500, determining whether the target process window is tangent to the critical dimension curve includes the steps of:

[0143] S510: Calculate the number of intersection points between the target process window and the critical dimension curve.

[0144] S520: Determine whether the number of intersection points is less than or equal to 1.

[0145] S530: If it is less than or equal to 1, then the target process window is tangent to the critical dimension curve.

[0146] In some embodiments of the present invention, referring to Figure 5 , in step S510, the calculation steps for determining the number of intersection points include:

[0147] S511: Obtain the general equation of the ellipse:

[0148]

[0149] S512: Obtain the general equation of the quadratic function:

[0150] dx 2 + ex + f = y; (14).

[0151] S513: Combine formula (13) and (14) to establish a quartic equation expression about x:

[0152] a 2 d 2 x 4 + 2dea 2 x 3 +(a 2 (e 2 + 2d(f - k)) + b 2 )x 2 +(2a 2 e(f - k) -

[0153] 2b 2 h)x + a 2 (f - k) 2 + b 2 h 2 - a 2 b 2 = 0; (15).

[0154] Where h and k represent the center coordinates of the target process window, a represents the depth of focus, b represents the exposure dose tolerance, x represents variables, d represents the coefficient determining the opening direction and width of the critical dimension curve, e represents the coefficient related to the position of the axis of symmetry of the critical dimension curve, and f represents the ordinate of the intersection point of the critical dimension curve and the vertical axis;

[0155] S514: Based on the intersection point expression (14), calculate the number of intersection points between the target process window and the critical dimension curve. The determination of the number of intersection points can be carried out by using the discriminant method described above.

[0156] In summary, the method of the present invention is a method for optimizing the lithography process, obtaining two critical dimension curves of the upper and lower limit offset values of the critical dimension, performing tangent modeling with the process window curve, constructing two sets of offset tangent equations, transforming the optimization problem of the process window curve into the tangent problem of the quadratic function and the ellipse, based on the given value of the exposure dose tolerance, calculating the calculated values of multiple depths of focus at the tangent position and taking the minimum value as the target value, obtaining the curve of the target process window, determining whether the target process window is tangent to the critical dimension curve, and calculating the number of intersection points through mathematical analysis. When the number of intersection points meets the tangent condition, the target process window is used as the maximum process window.

[0157] The method of the present invention seeks the process of the process window with the largest area within the feasible region by solving the tangency problem between the process window curve and the critical dimension curve based on a set of center points, avoiding the process of repeatedly calculating all possible center points within the feasible region and then comparing the areas of the process window curves to determine the optimal process window. This method uses the mathematical analysis of the tangency problem between quadratic functions and ellipses to replace the traditional numerical iteration, significantly improving the calculation efficiency. Compared with the exhaustive method of the prior art that can only give an approximate solution within a fixed step range near the exact solution by continuously reducing the fixed step size, the present invention directly obtains the theoretical optimal solution through strict mathematical tangency conditions, improving the algorithm accuracy.

[0158] The flowchart provided in this embodiment is not intended to indicate that the operations of the method will be performed in any specific order, or that all operations of the method are included in every case. In addition, the method may include additional operations. Within the scope of the technical idea provided by the method of this embodiment, additional changes may be made to the above method.

[0159] It should be understood that in some embodiments, each part may be implemented by hardware, software, firmware, or a combination thereof. In the above embodiment, multiple steps or methods may be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system.

[0160] This embodiment also provides a computer program product 10, a computer-readable storage medium 20, and a computer device 30. Figure 8 It is a schematic diagram of a computer program product 10 according to an embodiment of the present invention. Figure 9 It is a schematic diagram of a computer-readable storage medium 20 according to an embodiment of the present invention. Figure 10 It is a schematic diagram of a computer device 30 according to an embodiment of the present invention. The computer program product 10 includes a computer program 11, and when the computer program 11 is executed by a processor 32, it implements the steps of any one of the above methods for optimizing the lithography process. The computer-readable storage medium 20 stores the above computer program 11, and when the computer program 11 is executed by the processor 32, it implements the method for optimizing the lithography process according to any one of the above embodiments. The computer device 30 may include a memory 31, a processor 32, and a computer program 11 stored on the memory 31 and running on the processor 32.

[0161] The computer program 11 for performing the operations of the present invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, configuration data of an integrated circuit, or source code or object code written in any combination of one or more programming languages and procedural programming languages. The computer program 11 may be executed entirely on the user's computer, partially on the user's computer, executed as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer. In some embodiments, in order to perform aspects of the present invention, an electronic circuit, including, for example, a programmable logic circuit, a field-programmable gate array (FPGA), or a programmable logic array (PLA), may execute computer-readable program instructions by utilizing the state information of the computer-readable program instructions to personalize the electronic circuit.

[0162] For the description of this embodiment, the computer program product 10 is a related product containing the computer program 11.

[0163] For the description of this embodiment, the computer-readable storage medium 20 is a tangible device capable of retaining and storing the computer program 11, which may be any device that can contain, store, communicate, propagate, or transport the computer program 11 for use by or in connection with an instruction execution system, apparatus, or device. More specific examples (non-exhaustive list) of the computer-readable storage medium 20 include the following: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital versatile disc (DVD), memory stick, floppy disk, mechanically encoded device, and any suitable combination of the above.

[0164] The computer device 30 can be, for example, a server, a desktop computer, a laptop computer, a tablet computer, or a smart phone. In some examples, the computer device 30 can be a cloud computing node. The computer device 30 can be described in the general context of computer system executable instructions, such as program modules, executed by a computer system. Generally, program modules can include routines, programs, object programs, components, logic, data structures, etc. that perform particular tasks or implement particular abstract data types. The computer device 30 can be implemented in a distributed cloud computing environment where tasks are performed by remote processing devices linked through a communication network. In a distributed cloud computing environment, program modules can be located on local or remote computing system storage media including storage devices.

[0165] The computer device 30 can include a processor 32 adapted to execute stored instructions and a memory 31 that provides temporary storage space for the operation of the instructions during operation. The processor 32 can be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. The memory 31 can include random access memory (RAM), read-only memory, flash memory, or any other suitable storage system.

[0166] The computer device 30 can also include a network adapter / interface and an input / output (I / O) interface. The I / O interface allows data to be input and output with external devices that can be connected to the computer device. The network adapter / interface can provide communication between the computer device and a network, which is generally shown as a communication network.

[0167] At this point, those skilled in the art should recognize that although multiple exemplary embodiments of the present invention have been shown and described in detail herein, many other variations or modifications consistent with the principles of the present invention can still be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the present invention. Therefore, the scope of the present invention should be understood and construed to cover all such other variations or modifications.

Claims

1. A method for optimizing a photolithography process, characterized in that: include: Obtaining a preset tangent equation group, wherein the tangent equation group is used to characterize the relationship between the depth of focus and the exposure dose tolerance of the process window curve and the critical dimension curve under a tangent condition, wherein the process window curve is represented by an ellipse, and the critical dimension curve is represented by a quadratic function curve; The key dimension curve is offset based on two different offset values ​​respectively to obtain two offset tangent equation groups; Obtaining a given value of the exposure dose tolerance, and solving a plurality of calculated values ​​of the focal depth by using the two offset tangent equation groups; Determine the smallest of all the calculated values ​​of the focal depth as the target value; Determining whether a target process window is tangent to the critical dimension curve, wherein the center coordinate of the target process window is a given value, the semi-minor axis is a given value of the exposure dose tolerance, and the semi-major axis is a target value of the depth of focus; If they are tangent, the target process window is used as the maximum process window.

2. The method according to claim 1, characterized in that The step of determining the target value comprises: Determine the smallest value among the plurality of calculated values ​​of the focal depth corresponding to each of the offset tangent equation groups, and record it as an inter-group extreme value; The inter-group extreme values ​​corresponding to the two offset tangent equation groups are compared, and the smaller one of the two is taken as the target value.

3. The method according to claim 1, characterized in that The step of obtaining the tangent equation group comprises: Get the simultaneous expressions of the tangent equations of the process window curve and the critical dimension curve at the tangent point coordinates (x0, y0): Based on the simultaneous expressions of the tangent equations, an expression for characterizing the relationship between the tangent point coordinates and the exposure dose tolerance is obtained: Based on the simultaneous expressions of the tangent equations, an expression for characterizing the relationship between the tangent point coordinates and the focal depth is obtained: Among them, a represents the focal depth, b represents the exposure dose tolerance, x represents a variable, d represents the coefficient that determines the opening direction and opening width of the critical dimension curve, e represents the coefficient related to the position of the symmetry axis of the critical dimension curve, and f represents the vertical coordinate of the intersection of the critical dimension curve and the vertical axis.

4. The method according to claim 1, characterized in that: Determining whether the target process window is tangent to the critical dimension curve includes: Calculating the number of intersections between the target process window and the critical dimension curve; Determine whether the number of intersections is less than or equal to 1; If it is less than or equal to 1, the target process window is tangent to the critical dimension curve.

5. The method according to claim 4, characterized in that The step of calculating the number of intersections comprises: Get the preset intersection expression: a 2 d 2 x 4 +2dea 2 x 3 +(a 2 (e 2 +2d(f-k))+b 2 )x 2 +(2a 2 e(f-k)-2b 2 h)x+a 2 (f-k) 2 +b 2 h 2 -a 2 b 2 =0; Wherein g and k represent the center coordinates of the target process window, a represents the focal depth, b represents the exposure dose tolerance, x represents a variable, d represents a coefficient that determines the opening direction and opening width of the critical dimension curve, e represents a coefficient related to the position of the symmetry axis of the critical dimension curve, and f represents the ordinate of the intersection of the critical dimension curve and the ordinate axis; Based on the intersection expression, the number of intersections between the target process window and the critical dimension curve is calculated.

6. The method according to claim 1, characterized in that The two offset values ​​are the products of the given coefficients of the critical dimension curve and two proportional values, respectively, and both of the proportional values ​​are in the range of -10% to +10%.

7. The method according to claim 1, characterized in that The step of determining the target value comprises: Obtaining calculated values ​​of all the focal depths corresponding to the two offset tangent equation groups; All the calculated values ​​of the focal depths are compared, and the smallest one among them is taken as the target value.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer device, characterized in that: The method comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

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