Patent Grant
10573492
This application claims priority to foreign French patent application No. FR 1755863, filed on Jun. 27, 2017, the disclosure of which is incorporated by reference in its entirety.
The invention relates to a method for calibrating small elementary patterns (“shots”) in variable-shaped-beam electron-beam lithography, and to the application of such a calibration to the preparation of electron-beam-lithography data.
Electron-beam lithography is used to transfer, to a substrate, with a high resolution, geometric patterns forming a layout. An electron beam is used to expose a resist deposited on the substrate according to the layout to be transferred. The exposed resist undergoes a chemical transformation that allows it to be selectively removed, uncovering certain regions of the substrate that may then be etched or undergo a deposition or an ion implantation (alternatively, it is the unexposed resist that is selectively removed).
The main application of electron-beam lithography is the manufacture of the photolithography masks that are used to produce integrated circuits. Other applications are the direct manufacture of integrated circuits, of photonic or electronic components, and of nanostructures.
The resist may be exposed point by point, by means of a very narrow electron beam, but this takes a lot of time. For this reason, recourse is generally made to another technique, called the variable-shaped-beam (VSB) technique, the principle of which is illustrated in
In fact, the shape and dimensions of the elementary pattern actually transferred to the substrate does not correspond exactly to those of the beam, and also depend on nearby patterns (for this reason “proximity effects” are spoken of). This is mainly due to scattering of the electrons in the resist and to backscattering thereof by the substrate.
To determine the pattern actually transferred to the substrate, the following are applied to a “nominal” pattern:
a physical model, which represents the spread of the electrons in the resist, generally by means of a point spread function (PSF), and
a model of the resist—generally a simple threshold-based model: the resist is considered to be exposed if the electron dose that it receives exceeds a threshold.
As is known per se, this allows the corrections that must be made to the nominal pattern to ensure the transferred pattern is as close as possible to that desired to be determined. “Data preparation” is spoken of because this operation results in the creation of a data file that is delivered to the VSB machine to control the execution of the lithography process in order to obtain the transfer of the sought-after pattern.
Typically, VSB machines allow rectangular or square, or even right-isosceles-triangle-shaped elementary patterns having an orientation of 0°, ±45° or 90° with respect to a reference direction to be obtained. These various elementary shapes are illustrated in
Now, it is known that when elementary patterns of very small dimensions (typically 100 nm or less) are produced by variable-shaped-beam electron-beam lithography, the dimensions of the patterns actually transferred to the substrate differ from those expected from physical model and model of the resist alone. For example,
This effect is known to the scientific literature:
However, there is no method allowing the errors associated with the use of “small” elementary patterns, i.e. elementary patterns smaller than the critical dimension of the pattern be transferred, to be systematically and simply corrected.
The invention aims to overcome this limitation of the prior art. More precisely, it aims to provide a method for calibrating elementary patterns, in variable-shaped-beam electron-beam lithography, that may be used, in the preparation of data, to substantially decrease the errors associated with the use of “small” elementary patterns. It also aims to provide at least one such method for preparing data.
Moreover, the inventors have also realized that the errors associated with the use of “small” elementary patterns unfavourably affects the estimation of the physical model of the spread of electrons (PSF). One embodiment of the invention allows this problem, which has remained overlooked up till now, to be remedied.
One subject of the invention is therefore a method for calibrating elementary patterns in variable-shaped-beam electron-beam lithography, comprising the following steps:
a. producing, by variable-shaped-beam electron-beam lithography, at least one calibration pattern comprising geometric figures each having a nominal critical dimension, said figures being divided into elementary patterns of smaller dimensions than each said nominal critical dimension, the elementary patterns of each geometric figure having dimensions that are identical and those of other geometric figures having different dimensions;
b. measuring the actual critical dimension of each said geometric figure; and
c. applying a regression method on the basis of the actual critical dimensions thus determined to construct a mathematical model expressing:
According to particular embodiments of such a method:
c1. determining an expression for said variation in dimensions of said elementary patterns or said dose error as a function of the dimensions of the elementary patterns and of a plurality of parameters to be evaluated;
c2. calculating the values of said parameters to be evaluated by minimizing a function representative of an average deviation between the dimensions measured in step b and those calculated using the expression determined in substep c1.
The geometric figures of a given calibration pattern may be straight lines that are parallel to one another.
Said elementary patterns may be chosen from rectangular patterns and triangular patterns.
Said elementary patterns may be right-isosceles-triangle shaped, and the geometric figures of a given calibration pattern may be straight lines that are parallel to one another and to a right line of said elementary patterns.
Each said geometric shape may be divided into identical elementary patterns that are juxtaposed without overlap.
Said elementary patterns may be right-isosceles-triangle shaped, said geometric figures may be straight lines that are parallel to one another and to a side of the corresponding elementary patterns, and said calibration pattern may comprise:
lines formed from two subassemblies of identical elementary patterns of right-isosceles-triangle shape, said elementary patterns being juxtaposed without overlap, said subassemblies being superposed with a spatial offset; and
lines formed from elementary patterns of right-isosceles-triangle shape having complementary orientations, said elementary patterns being juxtaposed without overlap.
Said mathematical model may be a polynomial model.
Another subject of the invention is a method for preparing data for variable-shaped-beam electron-beam lithography, comprising a step of correcting a variation in dimensions of at least one elementary pattern of a layout to be transferred to a substrate by variable-shaped-beam electron-beam lithography, said step being implemented using a mathematical model expressing said variation, or an exposure-dose error producing an effect equivalent to said variation, as a function of the dimensions of said elementary pattern.
According to particular embodiments:
Said mathematical model may express said variation in dimensions of at least one elementary pattern as a function of its dimensions, the method comprising the following steps:
i. receiving, by way of input datum, a layout to be transferred to a substrate by variable-shaped-beam electron-beam lithography;
ii. dividing said layout into elementary patterns and using a physical model of the spread of the electrons to make a correction to the geometry and/or to the exposure dose of each said elementary pattern;
iii. applying said mathematical model to calculate a variation in dimensions of each said elementary pattern;
iv. calculating, for each said elementary pattern, a corrected exposure dose taking into account the corresponding variation in dimensions; and
v. applying the corrected exposure doses calculated in step iv to the corrected elementary patterns, such as determined at the end of step ii.
Said mathematical model may express said variation in dimensions of at least one elementary pattern as a function of its dimensions, the method comprising the following steps:
I. receiving, by way of input datum, a geometric pattern to be transferred to a substrate by variable-shaped-beam electron-beam lithography;
II. dividing said geometric pattern into elementary patterns and using a physical model of the spread of the electrons to make a correction to the geometry and/or exposure dose of each said elementary pattern;
III. applying said mathematical model to calculate a variation in dimensions of each said elementary pattern, and modifying said elementary patterns to correct this variation;
IV. reapplying said mathematical model to recalculate a new variation in dimensions of each said elementary pattern, taking into account the correction made in step III;
V. calculating, for each said elementary pattern, a corrected exposure dose taking into account the corresponding variation in dimensions calculated in step IV; and
VI. applying the corrected exposure doses calculated in step V to the elementary patterns such as modified in step III.
Said mathematical model may express an exposure-dose error producing an equivalent effect to a variation in dimensions of at least one elementary electron-beam-lithography pattern as a function of its dimensions, the method comprising a step of correcting said exposure-dose error.
Yet another subject of the invention is a method for transferring a layout to a substrate by variable-shaped-beam electron-beam lithography, comprising:
a step of preparing data, which step is implemented using a method such as defined above; and
a step of variable-shaped-beam electron-beam lithography using the elementary-pattern dimensions and exposure doses obtained using said method.
Yet another subject of the invention is a method for estimating a physical model of the spread of electrons in a variable-shaped-beam electron-beam lithography method, comprising:
A. transferring a layout to a substrate by means of said variable-shaped-beam electron-beam lithography method, said layout being composed of a plurality of elementary patterns;
B. estimating said physical model of the spread of electrons by comparing simulated dimensions and measured dimensions of said layout transferred to the substrate;
C. implementing a calibrating method such as defined above to construct a mathematical model expressing a variation in dimensions of said elementary patterns as a function of said dimensions; and
D. calculating new simulated dimensions of the layout transferred to the substrate by applying said mathematical model; and steps B. to D. being implemented iteratively.
Other features, details and advantages of the invention will become apparent on reading the description that is given with reference to the appended drawings, which are given by way of example and show, respectively:
The left-hand part of
ΔW0=ΔW(W0,H0)
ΔH0=ΔH(W0,H0) (1)
It is assumed that the functions expressing the dimensional deviations as a function of the nominal dimensions depend on a finite number of parameters. For example, the functions ΔW(W,H) and ΔH(W,H) may be considered to be polynomials of degree N, and hence it is possible to write:
where χ0 and Λ0 are respectively the two (N×N) matrices of coefficients of the polynomial relationships of degree N, defining what may be called the “elementary-pattern model” for the case of a rectangle of 0° orientation.
The case of a rectangular elementary pattern oriented at 45° with respect to the reference direction (
ΔL(L0)=Σi=0NΓiL0i (3)
where Γ is a vector of coefficients of dimension N. In fact, there are four possible orientations for a triangular elementary pattern (see the bottom part of
Thus, for a VSB electron-beam-lithography apparatus employing the elementary patterns of
The choice of a polynomial model is not exclusive. Moreover, various VSB machines may employ elementary patterns that are different from those of
It is also possible to not directly consider the dimensional variations ΔW, ΔH, ΔL, but rather equivalent variations ΔD in the dose D, i.e. dose variations that would indirectly induce the same dimensional variations. In the case of a triangular elementary pattern for example, it is then possible to write:
ΔD(L0)=Σi=0NδiL0i (4)
the parameters δi forming a vector of 8 to N components. The case of rectangular patterns is entirely similar except that, as in Equation 2, the model comprises N2 parameters.
In any case, a model expressing a dimensional variation, or an equivalent dose variation, as a function of the nominal dimensions of an elementary pattern, of its shape and of a finite number of parameters is obtained. The problem of estimating these parameters therefore arises.
To do this, it is necessary to transfer, to the substrate, calibration patterns obtained from elementary patterns the nominal critical dimensions of which are identical within a given calibration pattern. In the embodiments described below, the calibration patterns all have identical nominal critical dimensions, but this is not essential.
Different calibration patterns are used for various elementary patterns.
For rectangular elementary patterns with an orientation of “0°” (see
In contrast, the height (H) or width (W) of the elementary patterns of a horizontal or vertical line, respectively, is not subject to any specific quantification constraint. The maximum height and width of the elementary patterns are however limited by the VSB machine. It is advantageous to choose a CD0 value such that the discretization of the width or height of the elementary patterns is as fine as possible. For example, for a CD0 of 120 nm, the integer widths of possible elementary patterns are [120, 60, 40, 30, 24, 20, 15, 12, 10, 8, 6, 5, 4, 3, 2, 1] nm. In practice, elementary patterns the width of which is proportional to the minimum grid pitch of an input layout of the VSB machine will be employed. It will be noted that the larger the CD0 of the calibration pattern, the larger the number of different possible elementary patterns meeting the preceding criteria.
For rectangle-shaped elementary patterns oriented at 45°, line-shaped calibration patterns MCO having the same orientation are used.
The case of triangle-shaped elementary patterns is more complex. Specifically, a straight line constructed from identically oriented identical right triangles would only be half filled (see the left-hand part of
More generally, a calibration pattern comprises lines the direction of which corresponds to an orientation of the elementary patterns producible by the VSB apparatus to be calibrated. Such a line may be constructed solely from elementary patterns of the same type (having the same shape, the same orientation and identical nominal dimensions) or elementary patterns of the same shape and dimensions, but possibly having different, and in particular opposite, orientations.
The calibration patterns are first transferred to the resist, then their actual critical dimensions are measured using known methods, for example electron microscopy or atomic force microscopy. For example,
The next step of the process for calibrating the small-elementary-pattern model consists in calculating the expected, or “theoretical”, critical dimension of the calibration patterns. To do this, it is first necessary to calculate the dose field, i.e. the spatial spread of the electrons; this requires the physical model to be used; next the critical dimension is obtained by applying the resist model.
In principle, the dose field D(r) for a calibration pattern is given by the sum, over all the elementary patterns, of the product of convolution of an elementary pattern MEi and the point spread function (PSF) (which is assumed to be the same for all the elementary patterns):
D({right arrow over (r)})=D0Σi∫ME
where D0 is the exposure dose of each elementary pattern, and {right arrow over (r)} and {right arrow over (r)}s position vectors. When the PSF is expressed by a sum of Gaussian curves (this frequently being the case), its convolution with a rectangular elementary pattern may be calculated analytically. In other cases, a finite-element calculational approach is used, i.e. the convolution integral is estimated by a discrete sum over the sub-elements of each elementary pattern.
More precisely, for a rectangular geometry, each elementary pattern may be divided into virtual sub-elements of area dx·dy. The size of the mesh in question must be chosen such that the variation in the PSF within each cell of the mesh is negligible. In the case where the width or height of an elementary pattern is not a multiple of the grid pitch, the sub-elements located on the borders of the pattern are made smaller in order to prevent them from protruding.
The dose density is written as a double sum over the elementary patterns MEi and over their sub-elements j:
D({right arrow over (r)})=D0Σi,jMEijPSF(∥{right arrow over (r)}−{right arrow over (rij)}∥) (6)
where MEij corresponds to the area of sub-element j of the elementary pattern i and {right arrow over (rij)} the position vector of a point of this sub-element taken as origin. In the case of a triangular elementary pattern, the dose field may be calculated numerically by discretization of the elementary pattern into triangular or rectangular sub-elements the characteristic size of which is small with respect to the variation in the PSF.
Once the dose field has been calculated, the resist model is applied. The latter is more often than not of the threshold type; it is then a question of determining the outline defined by D({right arrow over (r)})=Dthreshold, where Dthreshold is the exposure threshold, above which the resist is considered to be perfectly exposed.
Because of the division of the calibration pattern, this outline is generally not straight, but presents undulations; the theoretical critical dimension CDtheo is therefore obtained by calculating the average width of the pattern over the entire length of the line (or, at least, over a length much larger than the scale of the undulations).
In the calculation of the theoretical critical dimension CDtheo, it is not necessary to limit consideration to the nominal elementary patterns, but to apply thereto the dimensional variations introduced by the small-elementary-pattern model to be calibrated, in order to find, via a regression method, the optimal values of the parameters of this model—i.e. those that minimize the deviation between the theoretical and measured critical dimensions. More precisely, the calculation of CDtheo must be repeated for all the nominal dimensions of the elementary patterns used in the experimental part of the calibration method and, for each nominal dimension or combination of nominal dimensions (for example W0 and H0), various values attributed to the parameters of the small-elementary-pattern model. Thus, in the case of rectangular elementary patterns, for each pair of nominal dimensions (W0, H0) used to produce the calibration patterns, it is necessary to explore the parameter space (χ, Λ), to calculate the dimensional variations ΔW, ΔH corresponding to each set of parameters, and then the corresponding critical dimension CDtheo. Most often, a complete sampling of the parameter space would to be too costly in terms of calculation time. Thus, preferably, conventional methods, such as a gradient-descent algorithm, will be used to partially and optimally scan this space (for example, in the case of a gradient-descent approach only parameters in the vicinity of a convergence path are taken into account).
Typically, a cost function such as an average quadratic error is minimized. In the case of rectangular elementary patterns, the calibration then consists in finding the matrices of coefficients χ and Λ that minimize:
where the index i designates an elementary pattern of a specific calibration pattern.
The polynomial relationships of the model may be constrained on the basis of physical considerations, thereby allowing the optimization problem to be better framed:
The model relates to small elementary patterns. There is therefore a reference size Wref×Href from which the measured critical dimension is entirely explained by the physical model. It is therefore possible to consider that for a size W0≥Wref and H0≥Href, the variations ΔW and ΔH are zero.
An additional constraint amounts to setting the derivative of the relationships ΔW(W0) and ΔH(H0) to zero at the reference sizes Wref and Href.
For triangular patterns, it is possible to proceed in an entirely equivalent way using the calibration pattern of
The case of an elementary-pattern model that is expressed in terms of dimensional variations is considered here. In the case of a model expressed in terms of dose variation (Equation (4)), it is enough to replace, in the Equation (5) or (6), the dose value D0 with that delivered by the elementary-pattern model and expressed as a function of the parameters to be determined.
When the small-elementary-pattern model is expressed in terms of dose variation (Equation (4)), it delivers directly a dose correction that must be taken into account in the application of the physical model. More precisely, for each elementary pattern, the dose actually applied via the small-elementary-pattern model is D0+ΔD, ΔD depending on geometric parameters. To correct this effect it is therefore enough to assign, to each elementary pattern, the dose D0−ΔD.
The case of a small-elementary-pattern model that is expressed in terms of dimensional variations (Equations (2) and (3)) is more complex. Two embodiments will be described with reference to
In the embodiment in
A computer file describing the layout to be transferred to a substrate is delivered as input datum (step i).
The patterns from which this layout is formed are divided into elementary patterns having predefined nominal dimensions, and the physical model is used, in an entirely conventional way, to make a first geometry and dose correction (step ii). This correction leads to a corrected layout consisting of a set of patterns to be exposed the dimensions of which differ from those of the “nominal” patterns provided as input, and to a dose distribution {D0} associated with each elementary pattern.
The elementary-pattern model is then applied, so as to determine the geometry of the patterns that are actually exposed (step iii).
The geometric modifications affect the dose distribution in a way that may be calculated (step iv). The “actual” dose D1 of an elementary pattern may be related to the initial dose D0 by the law of conservation of energy: D1=D0(S0/S1), where S0/S1 corresponds to the ratio of the areas of an initial elementary pattern (taking into account only corrections intended to compensate for proximity effects) and the same pattern such as modified in step iii.
This law of conservation of energy is natural in order to keep long-range proximity effects unchanged. Specifically, the dose field far from the elementary pattern in question is the same in the case of a change of geometry or dose respecting the equation of conservation of energy. In contrast, for structures that are small with respect to the spatial variation in the PSF, for example contact-type structures, simply applying the law of conservation of energy does not achieve satisfactory results. It is therefore necessary to have recourse to a global correction taking into account neighbouring elementary patterns. This global correction of the dose of the elementary patterns may be carried out in step iv). It may use an algorithm similar to that implemented in step ii), but modifying only the dose and leaving the geometry unchanged.
The last step (v) consists in applying the dose D1 to the elementary patterns “to be exposed”, i.e. the patterns determined in step ii. Formally, this consists in carrying out a geometric transformation that is the inverse of that applied in step iii, but in practice it is not necessary to calculate this transformation because the target geometry is already known.
The method of
A computer file describing the layout to be transferred to the substrate is provided as input datum (step I, equivalent to step i of the method of
The layout to be transferred is divided into elementary patterns and the physical model is used, in an entirely conventional way, to make a first correction of geometry and dose (step II, equivalent to step ii of the method of
The elementary-pattern model is used to calculate and to apply a correction to the provisional elementary patterns, so as to obtain the patterns to be exposed (step III). Typically, if a “provisional” elementary pattern has a dimension H0, a corrected elementary pattern (“to be transferred”) of dimension H0−ΔH0 will be used, such that the dimension of the pattern actually transferred to the substrate, which dimension is given by the elementary-pattern model, will be H0. In practice, the dimension H0−ΔH0 of the corrected elementary pattern is rounded to the closest multiple of the minimum grid pitch of an input layout of the VSB machine.
Next, the elementary-pattern model is applied, so as to determine the geometry of the patterns that will actually be exposed (step IV, equivalent to step iii of the method of
At this point, the actual dose D1 is calculated as in step iv of the method of
Next, this dose D1 is applied to the patterns determined in step III (VI).
In a VSB machine, the input data may be re-divided at the borders of the field zones of the machine. In a standard data-preparation flow, based only on a PSF model, this step of post-division does not adversely affect the correction. In contrast, in the case of the small-elementary-pattern model, the post-division of the elementary patterns may lead to correction errors. It is therefore preferable to take into account this “machine division”. This may be done by introducing a correction “in advance”, which correction is integrated into step ii) of the method of
The method for preparing data of
To mitigate this drawback, the invention proposes to perform an iterative estimation of the PSF, as illustrated in
Firstly, the PSF is estimated conventionally, by comparing the simulation of a “nominal” first calibration layout (layout 1) with measurements taken on the layout actually transferred to a substrate. The PSF thus obtained is used to carry out a calibration of the elementary-pattern model as was described in detail above, using a second calibration layout (layout 2). The elementary-pattern model thus obtained is applied to the first calibration layout. The first calibration layout modified to take into account the effects of the small elementary patterns is used to calculate a new estimation of the PSF, and so on until convergence.
Once the data have been prepared, the pattern is transferred to the substrate in a conventional way, using the geometries and doses calculated according to the invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 17 55863 | Jun 2017 | FR | national |
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| Number | Date | Country | |
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| 20180374677 A1 | Dec 2018 | US |
