JP2014041182A - Method of calculating the number of electron beam irradiation and drawing time - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of precisely estimating time needed to draw a relatively large drawing region while keeping a shot size of a beam in an electron beam lithography appropriately.SOLUTION: A method of calculating the number of irradiation of an electron beam (shot number) needed for manufacturing a photomask from a shot size of the electron beam in an electron beam drawing device and photomask data which specify a radiation region of the electron beam includes the steps of virtually dividing an irradiated region on the photomask data into a plurality of rectangular regions, calculating the total number y(k) of rectangles having a short side in the range of knm≤p<(k+1)nm by k (k=0, 1, 2, ..., n), where p is a length of the short side of rectangles, and calculating the total number Y of shots of the electron beam by Y=Σk2y(k).

Description

  The present invention relates to a method for preliminarily estimating an electron beam irradiation frequency and a writing time necessary for printing a wiring pattern on a resist on a silicon wafer using an EB drawing apparatus.

  In the semiconductor manufacturing process, a photomask that controls transmission of ultraviolet light is used to print a circuit pattern necessary for a semiconductor on a resist applied to a silicon wafer. Since the circuit pattern is too fine, it is difficult to draw 1: 1 with a 1x photomask. Usually, UV light is transmitted using a photomask that is 4 times the size to be baked on the resist, and then transmitted. The resist is irradiated with the optical pattern optically reduced to ¼.

Although the photomask has a submicron order pattern even though it has been magnified four times, the ultraviolet rays used in the semiconductor manufacturing process are naturally not used, and an electron beam drawing method capable of forming a finer resist pattern is adopted. The
Electron beam drawing methods are roughly classified into the following three types.

(1) Spot beam (point beam)
The electron beam emitted from the electron gun (emitter or cathode) has a circular cross-sectional shape, and pattern drawing is performed by continuous irradiation in synchronization with the movement of the deflector (deflector) and the XY stage. And In this method, the beam diameter of the electron beam can be changed, but the beam irradiation area per shot is smaller than that of the rectangular beam, so the throughput is poor. However, fine pattern drawing from several tens of nm to several nm is possible.

(2) Variable shaped beam (rectangular beam)
An electron beam emitted from an electron gun (emitter) is passed through several rectangular holes called shaping apertures to change the electron beam shape to a rectangle, and is continuously irradiated in synchronization with the movement of the XY stage to draw a pattern. It is characterized by performing. Although a fine pattern cannot be drawn as compared with a spot beam, the drawing area per shot is variable, so the throughput is good, and it is used for reticle production for mass production processes of reticles and LSIs for mass production.

(3) Character-Projection (CP) beam
Non-variable molding that reduces the number of shots and increases the speed by using a mask with multiple apertures of a specific shape as an aperture and exposing the same shape pattern used in various places in the mask with a low acceleration electron beam. This is a beam exposure method. By combining with a variable shaped beam, the throughput of exposure to the wafer can be increased, which is called a partial batch exposure method (block exposure / block drawing method).

  In the methods (2) and (3), when the electron beam diameter having a full width at half maximum of about 8 μm is adopted, the opening of the first aperture is about 4 μm square. The electron beam transmitted through the first aperture is further restricted by the second aperture. In the variable rectangle drawing method, the opening of the second aperture is also rectangular, and in the block drawing method, various shapes are formed. The variable rectangle is easier to deal with the required variety of drawing patterns, but if the drawing unit is set too small, the number of beam irradiations (number of shots) increases. Since block drawing uses an aperture with a fixed shape, the pattern followability is low, but the number of beam irradiations tends to be small. Actually, an aperture control method that analyzes the drawing pattern and combines the two seems to be used.

  By the way, the drawing time required to manufacture one photomask using the EB drawing apparatus is several tens of hours, and this prediction / estimation of the drawing time manages the production of the photomask. It becomes an important problem. The resist writing time is approximately proportional to the number of times of irradiation (hereinafter referred to as the number of shots) if the irradiation time of one electron beam is constant. If the drawing time actually spent is T and the total number of shots is Y, it can be approximated as T = αY. The proportionality constant α is an average value determined from the time required for position adjustment of the apertures and stage movement required before and after the beam shot.

  On the other hand, the total number of shots Y is the shape of the electron beam of one shot (hereinafter referred to as the shot size or basic figure in the region to which the electron beam is to be irradiated. It can be regarded as proportional to the total number N of squares (basic figures) when they are laid out so that there is no overlap and no gaps (Y∝N). Conventionally, the proportionality constant in this case is calculated from the drawing results so far, the number of shot sizes (basic figures) included in the drawing pattern of the photomask is estimated, and the drawing time is calculated using this as N. .

  However, in order to approximate that the total number of shots of the electron beam is substantially equal to the total number N of basic figures in the photomask data that determines the drawing area, the size of each figure constituting the photomask data must be It needs to be small enough compared to the size (same as the basic figure). If it is not sufficiently small, the total number N of basic figures includes an error. Therefore, the proportional constant or the drawing time required for the future production of the photomask is estimated from the data in which the error N and the actually measured drawing time corresponding to the error N are associated with each other. In a normal case, all the figures constituting the photomask data are rarely less than the shot size.

  Therefore, the shot size (basic figure) should be made sufficiently small to estimate the total number N of basic figures, and a drawing experiment was conducted. From the result, the proportionality constant was estimated using the relational expression of T∝N. The error can be reduced as much as possible, but the smaller the shot size, the more the total number of shots increases geometrically and the drawing time becomes longer.

JP 2011-44464 A Japanese Patent No. 4867163

  Therefore, the present invention has an object to provide a method for accurately estimating the time required for drawing a drawing region having a relatively larger area while maintaining an appropriate beam shot size in electron beam drawing. did.

In order to achieve the above object, the invention described in claim 1 is directed to an electron necessary for manufacturing a photomask from photomask data specifying an electron beam shot size and an electron beam irradiation area in an electron beam lithography apparatus. A method of calculating the number of beam irradiations (number of shots),
Virtually dividing the irradiated area on the photomask data into a plurality of rectangular areas;
The total length y (k) of rectangles having short sides in the range of knm ≦ p <(k + 1) nm is set to k (k = 0, 1, 2,..., N) where the length of the rectangular short side is p. A step of calculating
A step of calculating the total number of shots Y of the electron beam by Equation 1,
This is a method of calculating the number of times of electron beam irradiation characterized by having

According to the second aspect of the present invention, the total number of shots Y (k) necessary for manufacturing the kth photomask calculated by the method according to the first aspect and the drawing time actually required are represented by T (K) to (Y (k), T (k)), the process of accumulating up to n-th pair data (k = 1, 2,..., N),
Calculating the total number of shots Y (n + 1) required for manufacturing the (n + 1) -th photomask by the method according to claim 1;
Assuming that the writing time T (n + 1) required for manufacturing the (n + 1) th photomask is proportional to the total number of shots Y (n + 1), calculating a proportionality constant α from the pair data;
A step of calculating a writing time T (n + 1) required for manufacturing the (n + 1) -th photomask using a total shot number Y (n + 1) and a proportionality constant α. This is a calculation method.

  The invention described in claim 3 is the electron beam writing time calculation method according to claim 2, wherein the proportionality constant α is calculated using the following formula 2.

  The invention according to claim 4 is characterized in that the proportionality constant α is calculated from the pair data of (Y (k), T (k)) by using the least square method. This is a method for calculating the beam writing time.

  According to the first aspect of the present invention, an approximate calculation method for the total number of shots necessary for drawing is given by setting an area irradiated with one electron beam as a shot size. The shot size is a basic figure, and the drawing area is virtually divided by various rectangles determined by the outer shape of the drawing area, and the number of basic figures contained in this rectangle is the length of the short rectangle It is calculated by weighting accordingly. If all the rectangles are square and can be divided so that the length of one side is an integral multiple of the length of one side of the basic figure, there is an effect of giving an accurate number of shots.

  The invention of claim 2 provides a method for accurately estimating the writing time required for manufacturing a new photomask from the relationship between the total number of shots and the corresponding actual writing time. The method for calculating the number of shots according to claim 1 includes errors when all the rectangles are squares and the length of one side is not an integral multiple of the length of one side of the basic figure, and the drawing area is such Very few. The present invention has an effect of improving the estimation accuracy of the drawing time by reducing the error by using a plurality of drawing results.

  The invention of claim 3 provides a method of calculating a proportionality constant when a proportional relationship is assumed between the drawing time and the total number of shots. The invention of claim 4 calculates two constants assuming a linear relationship between the drawing time and the total number of shots. With these calculations, the drawing time can be estimated.

  If the accuracy of estimating the drawing time is improved, it becomes easier to make a production plan for the photomask, and planned production becomes possible. As a result, it is possible to reduce the idle time of the apparatus, deterioration due to the waiting time of the material / sub-material, and the production of defective masks. There is also an effect that the drawing time can be estimated regardless of the data format for manufacturing the photomask.

(A) It is drawing which shows typically an example which divides the drawing area irradiated with an electron beam into a plurality of rectangles. (B) It is a figure which shows typically the electron beam shot size relative to the pattern of (a).

  According to the present invention, when a photomask is manufactured using an EB drawing apparatus, the drawing time is predicted with high accuracy from the drawing pattern data in which the electron beam is irradiated on the resist on the substrate. This is to help make an efficient production plan for a large number of photomasks based on this drawing time prediction.

  As for prediction, if the shot size of the electron beam is sufficiently small, the drawing time can be calculated from the total number of basic figures in units of basic figures (for example, 4 μm square) whose side length is about half the width of the shot size or less. Guess and calculate. However, if the basic unit (shot size) is too small (for example, 2 μm □), the drawing time becomes long and it is not economically practical, so it needs to be set to a moderate size. Then, since the drawing pattern is not sufficiently smaller than the shot size, an error occurs in the calculation of the total number of figures.

There is also a problem with the figure counting itself. As shown in FIG. 1A, the drawing area 1 is mostly regarded as a collection of a large number of rectangles 2 having different sizes, but the basic figure 6 shown in FIG. The drawing area is divided into a plurality of rectangles 2 and calculated from the length of the rectangular short side 3 as follows.
Rectangular short side length 0 to 1 nm Number of basic figures 1
1nm ~ 2nm Number of basic figures 2
2 nm or more Number of basic figures 0 However, it is clear that the total figure number is not correctly counted by this calculation method.

In the present invention, appropriate weighting is performed for each length of the rectangular short side 3 in the above calculation method.
In particular,
Length of rectangular short side 0 to 1 nm Total figure number y (1) Weight 1
Total figure number of 1-2nm y (2) Weight 4
Number of total figures of 2 to 3 nm y (3) Weight 9
・ ・
・ ・
・ ・
Total number of figures (n-1) to n (nm) y (n) Weight n ²
It was. The length of the rectangular short side 3 (n-1) ~n (nm , nanometers) in which given a weight of ^{n 2} to figures. The total figure number Y in this case is given by the following equation.

This rectangle short side length of n (nm) Tosureba the number basic figure of the rectangle intended to approximate the n ^2, the length of one side rectangle in square basic shape of one side length of If it is an integer multiple, the approximation accuracy is high, but if the rectangle that covers the drawing area is generally a rectangle or the side length is an integer multiple, Y will be the lower limit of the total number of figures. Conceivable. In that sense, it can be said that it is preferable to virtually divide the drawing area into rectangles with a rectangle close to a square without any gaps.

The approximation of Equation 1 can be said to have improved the approximation accuracy as a method of calculating the total number of figures compared to the conventional method with a weight of 1. However, in view of the fact that the total number of figures includes an error, the present invention further A device is added to the calculation of a constant indicating the linear relationship between the total number of figures and the drawing time.
In general, Y depends on the method of covering the drawing area with a rectangle (the method of division). For example, the total figure number Y may be different depending on whether the drawing area 1 in FIG. 1A is divided by a rectangle 2 indicated by diagonal lines or a line indicated by a broken line 4.

  The drawing time can be calculated assuming that the way of division is set as rationally as possible and Y is calculated and the drawing time T is proportional to this (T∝Y), but this requires the value of the proportionality constant α. Since the time required for drawing is accurately stored and stored in the EB drawing apparatus, the proportionality constant α can be estimated empirically from the drawing time corresponding to Y, but the present invention makes this estimation multiple times in the past. Refined based on the trial results.

  Assuming that an EB drawing process is the kth trial, the total number of figures calculated using the square weight is Y (k), and the actual drawing time at that time is T (k), pair data (Y (k) , T (k)). Assuming a proportional relationship to these, it is possible to write T (k) = α (k) × Y (k) and to obtain α (k). As described above, this is a value including an error depending on the shape of the rectangle and how it is divided. Therefore, if the EB drawing process is performed n times (k = 1, 2,..., N), there should be n data accumulation in α. Alternatively, different Y (k) may be obtained by changing the division method even in the same drawing, and the same actual drawing time may be associated with this.

  From the pair data (T (k), Y (k)) relating to the past EB drawing for a plurality of times, a proportional constant α for the (n + 1) th EB drawing to be performed again is determined by the following equation.

Here, Σ is the sum up to k = 1, 2,..., N.
Since the total figure number Y (n + 1) can be calculated using the above-mentioned square weight, if the drawing time of the (n + 1) -th EB drawing is written as α (n + 1), T (n + 1) = α (n + 1) ) × Y (n + 1).
Here, the EB drawing corresponding to k = 1, 2,... Does not have to be the subsequent EB drawing, and simply by numbering a number of EB drawing processes in any order. Good. However, (n + 1) is an EB drawing process different from them.

  More precisely, it is preferable to assume a linear relationship between T (k) and Y (k). With T (k) as the horizontal axis and Y (k) as the vertical axis, the slope α and the y-intercept b are calculated using the method of least squares. Here, as n, it is preferable to select a pair in which Y (k) is widely dispersed from a small value to a large value as much as possible and includes Y (n + 1). In the least square method, α and b are given by the following equations.

_{α = nΣT k Y k -ΣT k} ΣY k / (nΣT k 2 - (ΣT k) 2)
b = ΣT _k ² ΣY _k −ΣT _k Y _k ΣT _k / (nΣT _k ² − (ΣT _k ) ² )
Here, the subscript k is used instead of (k), and Σ is the sum of 1 to n for k.
The gradient α determined by the least square method is α (n + 1), and the current drawing time is calculated as T (n + 1) = α (n + 1) × Y (n + 1) + b.

1, drawing area 2, rectangle (area)
3, rectangular short side 4, broken line 5 showing another division example, undivided drawing area 6, basic figure (shot size)

Claims (4)

A method for calculating the number of electron beam irradiations (number of shots) necessary for manufacturing a photomask from photomask data specifying an electron beam shot size and an electron beam irradiation area in an electron beam lithography apparatus,
Virtually dividing the irradiated area on the photomask data into a plurality of rectangular areas;
The total length y (k) of rectangles having short sides in the range of knm ≦ p <(k + 1) nm is set to k (k = 0, 1, 2,..., N) where the length of the rectangular short side is p. A step of calculating
A step of calculating the total number of shots Y of the electron beam by the following formula 1,
A method for calculating the number of electron beam irradiations.
The total number of shots Y (k) required for manufacturing the k-th photomask calculated by the method according to claim 1 and the drawing time actually required from T (k) (Y (k ), T (k)) to accumulate the nth pair data (k = 1, 2,..., N),
Calculating the total number of shots Y (n + 1) required for manufacturing the (n + 1) -th photomask by the method according to claim 1;
Assuming that the writing time T (n + 1) required for manufacturing the (n + 1) th photomask is proportional to the total number of shots Y (n + 1), calculating a proportionality constant α from the pair data;
A step of calculating a writing time T (n + 1) required for manufacturing the (n + 1) -th photomask using a total shot number Y (n + 1) and a proportionality constant α. Calculation method. 3. The electron beam writing time calculation method according to claim 2, wherein the proportionality constant [alpha] is calculated using the following equation (2).
  3. The electron beam writing time calculation method according to claim 2, wherein the proportionality constant α is calculated from a pair data of (Y (k), T (k)) using a least square method.