JP5085396B2 - Simulation method and program - Google Patents

Description

  The present invention relates to a lithography simulation technique used for manufacturing a semiconductor device, and more particularly to a simulation method for simulating light intensity on a substrate in a lithography process. Furthermore, the present invention relates to a program for executing this simulation method by a computer.

  In the manufacture of a 45 nm node semiconductor device, when a lithography process using ArF light immersion and high NA is used, the size of the pattern on the mask is almost the same as the wavelength of ArF light. In this case, the waveguide effect by mask topography and the influence of shielding by oblique incident light cannot be ignored.

  Therefore, in lithography simulation for LSI design, for example, when simulating the intensity distribution of light irradiated onto the substrate surface through the mask, the thickness of the mask and the incident angle of light must be strictly considered. Don't be. That is, exact solution calculation of Maxwell's equations considering the mask three-dimensional structure is essential. However, in this case, it takes time on the order of 10 times to 100 times that of a simulation (thin film mask approximate calculation) performed with a thin film mask that is assumed to have no conventional thickness. In actual development, the speed of design is important, and such an increase in calculation time is a serious problem.

  In order to avoid this problem, the size of the translucent part and the transparent part when a three-dimensional mask pattern is expected from the light source is geometrically taken into consideration, and the plane mask pattern (thin film mask) is newly redefined. A method has been proposed in which an optical image that is almost the same as the strict consideration calculation is obtained in a short time (see, for example, Patent Document 1). However, in this type of method, the phase difference of the semi-transmissive part in the thin film mask approximate calculation is constant regardless of the incident angle of the illumination light, and there is a possibility that the prediction accuracy of the focus shift is low.

As described above, in the light intensity distribution simulation method for measuring the intensity distribution of light irradiated on the substrate surface through the mask, accurate measurement is possible with the exact solution calculation of the Maxwell equation considering the mask three-dimensional structure. There was a problem that enormous calculation time was required. On the other hand, as in Patent Document 1, in the thin film mask approximate calculation in which a three-dimensional mask pattern is newly redefined as a planar mask pattern, the calculation time can be shortened, but accurate measurement cannot be performed due to the influence of the semi-transmissive portion. was there.
JP 2007-273560 A

  The present invention has been made in consideration of the above circumstances, and the object of the present invention is to calculate the intensity distribution of light irradiated onto the substrate surface through a mask in a lithography simulation in a short time as in the thin film mask approximate calculation. It is an object of the present invention to provide a simulation method which can be measured by the above-described method and can be measured more accurately than the thin film mask approximate calculation.

One aspect of the present invention is to irradiate exposure light from an oblique direction on the surface of a three-dimensional mask having a thickness, and to calculate a light intensity distribution when a pattern formed on the mask is transferred onto a substrate by a projection optical system. This is a simulation method on the assumption that the three-dimensional mask is a thin thin mask, and is the same as the thin mask when a thin mask having a predetermined area ratio (ratio of openings in a predetermined mask region) is used. And a phase difference and an amplitude ratio between the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system in the transfer process in the case of using a three-dimensional mask having an area ratio of the shift amount of the phase difference and amplitude ratio from a thin mask to the three-dimensional mask advance acquired in advance respectively, of the projection optical system in the transfer process using the thin mask having an arbitrary area ratio Setting the phase difference and the amplitude ratio is calculated, the new phase difference obtained by adding the shift amount to the calculated the phase difference and the amplitude ratio and the amplitude ratio of the 0-order diffracted light and 1-order diffracted light on the surface The transfer process using the thin mask having the arbitrary area ratio is simulated.

In another aspect of the present invention, light is emitted when the surface of a three-dimensional mask having a thickness is irradiated with exposure light from an oblique direction and a pattern formed on the mask is transferred onto a substrate by a projection optical system. A computer-readable program for executing, using a computer, a method for simulating an intensity distribution on the assumption that a three-dimensional mask is a thin mask having no thickness, and having a predetermined area ratio (opening in a predetermined mask region) 0th order diffracted light on the pupil plane of the projection optical system in the transfer process , when a thin mask having a ratio of a portion) is used and when a three-dimensional mask having the same area ratio as the thin mask is used. When one procedure to calculate the phase difference and amplitude ratio of the diffracted light, reads each shift amount of the phase difference and amplitude ratio from a thin mask from the calculation result to the three-dimensional mask A procedure for calculating a phase difference and an amplitude ratio between the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system in the transfer process using a thin mask having an arbitrary area ratio; The computer executes a procedure for simulating a transfer process using the thin mask having the arbitrary area ratio in which a new phase difference and amplitude ratio obtained by adding the shift amount to the phase difference and amplitude ratio is set. It is characterized by making it.

  According to the present invention, the intensity distribution of light irradiated on the substrate surface through the mask can be measured in a short time as in the thin film mask approximate calculation, and more accurately than the thin film mask approximate calculation. it can.

  The details of the present invention will be described below with reference to the illustrated embodiments.

  FIG. 1 is a schematic block diagram showing an example of a projection exposure apparatus used in an embodiment of the present invention. 11 is a light source, 12 is a mask, 13 is a projection optical system, and 14 is a wafer (substrate). .

This example is an oblique illumination method using second illumination as the light source 11. For this reason, the light from the light source 11 (point light source A) is irradiated obliquely with respect to the mask plane, and the 0th-order diffracted light and the 1st-order diffracted light from the mask 12 are converged by the projection optical system 13 and connected to the wafer 14. It has come to be imaged. Here, the positions of the zero-order diffracted light and the first-order diffracted light on the pupil plane of the projection optical system 13 are separated by a distance corresponding to the pattern pitch on the mask, and the distance x is HP, If the wavelength of the exposure light is λ, x = λ / (2 · HP)
It is represented by

  When such a projection exposure apparatus is used, the light intensity distribution on the wafer 14 is obtained by simulation. A desired pattern can be formed on the wafer 14 by correcting the pattern of the mask 12 based on the simulation result.

  As described above, the calculation considering the mask three-dimensional structure can be measured accurately but takes a lot of time. Therefore, as in (Patent Document 1), a thin film mask definition using a shadow model has been studied.

  First, as shown in FIG. 2, a mask 21 having a three-dimensional structure is newly defined as a planar mask 31 in consideration of only a shadow effect due to oblique incidence. In the figure, θ is the incident angle of the exposure light (angle formed by the optical axis direction of the irradiated light and the incident direction of the irradiated light on the mask), and d is the thickness of the light shielding portion (including the translucent portion) 22. is there.

  For example, in order to resolve a 1: 1 contact hole pattern with a pitch of 100 nm, the illumination condition is 1.3 NA, the fourth illumination, the distance σ = 0.8 from the optical axis to the center of the fourth illumination eye, the exposure Assuming that the reduction ratio of the apparatus is Mag = 4, the light incident angle from the point light source at the center of each eye of the fourth illumination to the mask is determined as follows.

sinθ = NA × σ / Mag = 0.26 ∴θ = 15.07deg
For simplification, it is assumed that a portion that is shaded by light irradiation from a direction inclined by θ from the optical axis shields illumination light (including semi-transmission).

The newly set size w ′ of the opening (mask pattern) is tan θ = 0.269260 when the size w of the original opening of the mask pattern is 70 nm.
w ′ = w−d · tan θ = 65.29 nm
It becomes.

  Here, in order to consider the phase difference in the mask opening peripheral portion 32 where the irradiation light from each eye of the fourth illumination is shaded (including transflective) by the mask side surface and becomes a shadow, as shown in FIG. A method has been proposed in which a constant transmittance / phase is given to the shadowed portion 32 (fringe) for calculation. However, in such mask calculation, the phase distribution of the diffracted light transmitted through the fringe 32 is uniquely determined.

  FIG. 4 shows the half-pitch (HP) dependence of the phase difference between the 0th-order diffracted light and the 1st-order diffracted light with a 1: 1 periodic pattern. From this figure, it can be seen that as HP increases, the phase difference between the 0th order diffracted light and the 1st order diffracted light becomes smaller. Such a phase difference of diffracted light greatly affects the simulation accuracy.

  Therefore, the conventional method is insufficient, and it is necessary to correctly incorporate the effect of the phase difference distribution between the diffracted lights in order to perform accurate simulation. Considering this point, it is necessary not to fix the phase in the fringe but to consider the phase difference distribution between the diffracted lights according to various parameters.

FIG. 5 is a schematic diagram showing the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system when a pattern having different HPs HP1, HP2, and HP3 is illuminated from a point light source on the optical axis. is there. The diffracted light is represented by an arrow, the magnitude of the arrow represents the amplitude of the diffracted light, and the angle formed by the arrow with the light source direction of the optical axis being positive represents the phase. The three first-order diffracted lights indicate that diffracted lights appear at different positions when patterns having different HPs HP1, HP2, and HP3 are illuminated from a point light source on the optical axis. Here, the relationship of each HP is HP1 <HP2 <HP3. From FIG. 4, the smaller the HP is, the larger the phase difference between the 0th order diffracted light and the 1st order diffracted light. Further, the distances x1, x2, and x3 between the 0th-order diffracted light and the 1st-order diffracted light corresponding to each pattern are x = λ / (2 · HP)
Accordingly, the relationship of x1>x2> x3 is established.

  Therefore, it is possible to give the phase difference Δφ as a variable having the 0th-order diffracted light-1st-order diffracted light interval x on the pupil plane as a variable.

FIG. 6 is a diagram showing the 0th-first order phase difference Δφ at the position on the pupil plane. The phase difference Δφ is
Δφ = f (x, bias, θinc, d)
x: Distance between 0th-order diffracted light and 1st-order diffracted light on the pupil plane
bias: difference amount between the pattern size of the periodic mask pattern and HP θinc: incident angle of illumination light d: expressed as the film thickness of the mask shielding part, and takes different values depending on the difference of bias, θinc, d. Each graph is different. It takes a lot of time to calculate different phase differences depending on these conditions, and calculating at the time of simulation causes a reduction in the speed of the simulation.

  Therefore, if the phase difference under various lithography conditions is calculated in advance and the result is stored in a database (DB) or converted into a function, the phase difference required at the time of simulation can be extracted from the DB. However, with this method, it takes a long time to create the DB.

  Therefore, in the present embodiment, the phase difference and the amplitude ratio between the 0th-order diffracted light and the 1st-order diffracted light of the three-dimensional mask corresponding to the thin mask under one lithography condition are calculated in advance, and for masks with different lithography conditions, The phase difference and the amplitude ratio are set based on the relationship obtained by the above calculation. As a lithography condition at this time, a bias value that is an area ratio in the periodic pattern (ratio of openings in the periodic pattern) is used.

  FIG. 7 is a diagram showing fluctuations in the diffracted light balance due to the mask stereo effect when a 1: 1 L / S pattern is used. In contrast to the thin mask (TMA), the amplitude of the 0th-order diffracted light changes greatly in the three-dimensional mask (TOI), and the amplitude of the 1st-order diffracted light does not change much. Further, the phase of the 0th-order diffracted light does not change, and the phase of the 1st-order diffracted light slightly changes. Such fluctuations in amplitude and phase are due to the effect of the waveguide and the oblique incidence effect of the illumination light.

  FIG. 8 is a diagram showing the result of calculating the bias dependence based on the relationship shown in FIG. In the calculation results of FIG. 8, the conditions such as the film thickness and pitch of the pattern, which are conditions other than the bias, are constant. The vertical axis represents the phase difference between the 1st order diffracted light and the 0th order diffracted light, the horizontal axis represents the amplitude ratio between the 1st order diffracted light and the 0th order diffracted light, and the horizontal axis represents a logarithmic scale.

  Here, as shown in FIG. 9, the L / S pattern is, for example, a pattern with a pitch of 80 nm on the mask, and a plurality of thin masks are patterns having different bias values. The bias value is a ratio (area ratio) of openings in the periodic pattern. FIGS. 9A to 9C are L / S patterns having the same pitch L. For example, FIG. 9A shows an L / S pattern with an area ratio of 0.8, and FIG. (1: 1 L / S pattern), FIG. 9C is an L / S pattern with an area ratio of 1.2. In FIG. 8, the difference in bias value is indicated by the line size of the pattern.

  As shown in FIG. 8, the three-dimensional mask (TOI) has a larger phase difference and intensity ratio between the 0th-order diffracted light and the 1st-order diffracted light than the thin mask (TMA). At this time, the method of changing the phase difference and the intensity ratio is very similar for different biases, and the straight line of change from TMA to TOI is shifted in parallel by the difference of the bias.

  Accordingly, the diffracted light amplitude ratio (first-order diffracted light) on the pupil of TMA (thin film approximate calculation) and TOI (accurate calculation of oblique incident light and mask three-dimensional structure) having the same pitch and line dimensions indicated by ◯ in FIG. Amplitude / 0th order diffracted light amplitude) and phase difference (1st order diffracted light phase−0th order diffracted light phase) on the scatter diagram, if the bias is changed, even if the corresponding point in the TMA calculation is known, Without actually performing TOI calculation, the amplitude ratio and phase difference of diffracted light can be predicted from the initial positional relationship.

  That is, if the conditions such as the film thickness and the pitch of the pattern are the same, by calculating only one of the above relationships, the amplitude ratio and level of the three-dimensional mask corresponding to the thin mask with respect to the different bias patterns are calculated. The phase difference can be easily obtained.

  Specifically, the phase difference and amplitude ratio between the 0th-order diffracted light and the 1st-order diffracted light are calculated in advance when a thin mask having a certain bias is used and when a three-dimensional mask having the same bias is used. Then, based on the calculation result, the phase difference and the shift amount of the amplitude ratio from the thin mask to the three-dimensional mask are obtained. Then, assuming that the three-dimensional mask having a predetermined bias used in the lithography simulation in this embodiment is a thin mask, the phase difference and the amplitude ratio between the 0th-order diffracted light and the first-order diffracted light using the thin mask are calculated and calculated. The phase difference and amplitude ratio of the three-dimensional mask corresponding to the thin mask are set by shifting the shift amount of the phase difference and amplitude ratio obtained in advance with respect to the phase difference and amplitude ratio. By performing a simulation using a thin mask based on the set phase difference and amplitude ratio, an accurate simulation can be performed. In addition, it is not necessary to perform strict calculation using a three-dimensional mask, and measurement can be performed in a short time as in the thin film mask approximate calculation. Here, it is not necessary to set the film thickness and pitch of the 3D mask applied to the simulation and the 3D mask used to calculate the shift amount, but it is more accurate by setting the film thickness and pitch to the same. Simulation may be possible.

  Also, unlike creating a database by performing calculations for a large number of masks with various biases, it is only necessary to perform calculations for one bias, so pre-processing for simulation preparation is extremely difficult. There is an advantage of being easy.

  In addition, this invention is not limited to embodiment mentioned above. In the embodiment, the example of the pattern dimension design for the L / S pattern has been shown, but even a contact hole can be designed in a short time by the same method.

  If there are patterns with different pitches on the mask, the phase difference and amplitude ratio between the 0th-order diffracted light and the 1st-order diffracted light in the three-dimensional mask corresponding to the thin mask are calculated in advance for each different pitch. That's fine. That is, for different conditions other than the bias, it is only necessary to perform calculation for one bias for each condition.

  In this embodiment, a simulation using a mask having a periodic pattern is performed. However, it is not always necessary to use a mask having a periodic pattern. For example, the pupil plane of the projection optical system in a transfer process using a thin mask having a predetermined area ratio (bias, that is, a ratio of openings in a predetermined mask surface area) and a three-dimensional mask having the same area ratio as the thin mask. The phase difference between the 0th-order diffracted light and the 1st-order diffracted light and the shift amount of the amplitude ratio are acquired, and an arbitrary area ratio (the ratio of the opening in the mask surface area having the same area as the predetermined mask surface area may be used. The zero-order diffracted light and the first-order diffracted light on the pupil plane of the projection optical system in a transfer process using a thin mask having a mask surface region having an area different from the predetermined mask surface region may be used. Based on the phase difference and amplitude ratio set by calculating the phase difference and amplitude ratio, and adding the shift amount to the calculated phase difference and amplitude ratio, the transfer using a thin mask having an arbitrary area ratio is performed. It is possible to simulate the process.

  In this embodiment, the phase difference and the amplitude ratio shift amount between the thin film approximate calculation (TMA) and the mask three-dimensional structure exact calculation (TOI) using obliquely incident light are obtained. It is also possible to provide a step of obtaining the phase difference and the amplitude ratio of the diffracted light on the pupil plane due to the vertically incident light on the mask while strictly considering only the mask three-dimensional structure. That is, the shift amount is determined by considering the mask three-dimensional structure by the phase difference and amplitude ratio calculated by the normal incident light from the phase difference and amplitude ratio obtained by the thin film approximate calculation and the mask three-dimensional structure by the normal incident light. The phase difference and amplitude ratio obtained by calculation are decomposed into the phase difference and amplitude ratio shift amount obtained by rigorous calculation of the mask three-dimensional structure using obliquely incident light, and these shift amounts are applied in order, and the thin film You may obtain | require the phase difference and amplitude ratio by oblique incidence light and mask three-dimensional structure exact calculation from the phase difference and amplitude ratio of diffracted light by approximate calculation.

  Thus, for example, when the mask pattern is not changed and the light incident angle changes with the change of the illumination shape, the phase difference from the mask three-dimensional structure consideration calculation by the normal incident light to the mask three-dimensional structure exact calculation by the oblique incident light It is only necessary to recalculate only the shift amount of the amplitude ratio, and the analysis of the phase difference and the amplitude ratio in the exact calculation of the mask three-dimensional structure by the oblique incident light becomes easy.

  In addition, various modifications can be made without departing from the scope of the present invention.

The schematic block diagram which shows an example of the projection exposure apparatus used for one Embodiment of this invention. The figure which shows the example which defined the mask of a solid structure as a mask of a planar structure newly considering only the shadow effect by oblique incidence. The figure which shows the method of giving a fixed transmittance | permeability and a phase to the part (fringe) used as the shadow around an opening part, and calculating. The figure which shows HP dependence of the phase difference of the 0th-order diffracted light of a L / S pattern of 1: 1, and a 1st-order diffracted light. The figure which shows the phase difference of the 0th-order diffracted light and the 1st-order diffracted light in the pupil plane of a projection lens. The figure which shows 0th-1st phase difference (DELTA) phi in the position on the pupil of a projection lens. The figure which shows the fluctuation | variation of the diffracted light balance by a mask three-dimensional effect. The figure which shows the bias dependence of the diffracted light balance by a mask three-dimensional effect. The figure which shows the difference in the bias (area ratio) in a L / S pattern.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Light source 12 ... Mask 13 ... Projection optical system 14 ... Wafer (substrate)
DESCRIPTION OF SYMBOLS 21 ... Three-dimensional structure mask 22 ... Light-shielding part 31 ... Planar structure mask 32 ... The part used as the shadow around an opening part (fringe)

Claims (5)

Light intensity distribution when irradiating exposure light from the oblique direction to the surface of a three-dimensional mask having a thickness and transferring a pattern formed on the mask onto a substrate by a projection optical system, a thin three-dimensional mask with no thickness A simulation method assuming a mask,
In the case of using a thin mask having a predetermined area ratio (ratio of openings in a predetermined mask region) and in the case of using a three-dimensional mask having the same area ratio as the thin mask , the transfer process The phase difference and amplitude ratio between the 0th order diffracted light and the 1st order diffracted light on the pupil plane of the projection optical system are calculated, and the phase difference and the shift amount of the amplitude ratio from the thin mask to the three-dimensional mask are obtained in advance from the calculation results , respectively. Aside,
Calculating a phase difference and an amplitude ratio between the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system in the transfer process using a thin mask having an arbitrary area ratio;
A simulation of a transfer process using a thin mask having the arbitrary area ratio set with a new phase difference and amplitude ratio obtained by adding the shift amount to the calculated phase difference and amplitude ratio is performed. Simulation method.   The simulation method according to claim 1, wherein the area ratio is a ratio of openings in the periodic pattern.   The simulation method according to claim 2, wherein the thin mask and the three-dimensional mask used for acquiring the shift amount and the thin mask used for the simulation have a periodic pattern with the same pitch.   4. The simulation according to claim 1, wherein the simulation is a simulation of a light intensity distribution of a transfer process using a three-dimensional mask having the same thickness as the three-dimensional mask used for acquiring the shift amount. The simulation method described in 1. Light intensity distribution when irradiating exposure light from the oblique direction to the surface of a three-dimensional mask having a thickness and transferring a pattern formed on the mask onto a substrate by a projection optical system, a thin three-dimensional mask with no thickness A computer readable program for executing a simulation method assuming a mask using a computer,
In the case of using a thin mask having a predetermined area ratio (ratio of openings in a predetermined mask region) and in the case of using a three-dimensional mask having the same area ratio as the thin mask , the transfer process A procedure for calculating the phase difference and amplitude ratio between the 0th-order diffracted light and the 1st-order diffracted light on the pupil plane of the projection optical system , and reading out the phase difference and the shift amount of the amplitude ratio from the thin mask to the three-dimensional mask from the calculation results , respectively. When,
A procedure for calculating a phase difference and an amplitude ratio between the zero-order diffracted light and the first-order diffracted light on the pupil plane of the projection optical system in the transfer process using a thin mask having an arbitrary area ratio;
A procedure for performing a simulation of a transfer process using a thin mask having the arbitrary area ratio set with a new phase difference and amplitude ratio obtained by adding the shift amount to the calculated phase difference and amplitude ratio;
A program that causes a computer to execute.

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