CN114674534A - Method and device for extracting waveguide physical parameters, computer equipment and storage medium - Google Patents
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Abstract
A method, apparatus, computer device and storage medium for extracting waveguide physical parameters are provided. The method includes acquiring spectral information about a waveguide test structure. The waveguide test structure comprises a first main structure and a second main structure, and the frequency spectrum information comprises first frequency spectrum information and second frequency spectrum information corresponding to the first main structure and the second main structure. The first and second main structures each include a grating coupler pair and a MZI-based resonant structure. The method further includes determining link parameters of the waveguides of the waveguide test structure based on the first and second spectral information and a first link equation for the first master structure and a second link equation for the second master structure. The waveguide is an equivalent waveguide formed based on a waveguide test structure. The first and second link equations each represent spectral information of the corresponding main structure in a functional expression including a link parameter as an unknown number. The method further includes determining physical parameters of an equivalent waveguide of the waveguide test structure based on the link parameters and on a mapping relationship between the link parameters and the physical parameters.
Description
Technical Field
The present disclosure relates to the field of optoelectronics, in particular to the field of optical waveguide technology, and in particular to a method, an apparatus, a computer device, a computer-readable storage medium, and a computer program product for extracting a physical parameter of a waveguide.
Background
In recent years, with the rapid development of silicon-based optoelectronic chips based on silicon-based optoelectronic technologies, the silicon-based optoelectronic chips are widely applied to a plurality of emerging industries such as high-speed optical transmission (e.g. more than 100 Gbps), on-chip intelligent sensing (e.g. laser radar), photonic artificial intelligence, quantum computing and the like facing large data applications. The silicon-based optoelectronic chip combines the advantages of high-speed operation of an integrated circuit and high-speed transmission of a photonic integration technology, so that the silicon-based optoelectronic chip is continuously developed and applied in a series of innovation technologies.
Silicon-based optoelectronic chips may be fabricated by means of related well-established technologies such as integrated circuit CMOS processes. However, silicon optical devices (e.g., optical waveguides) have certain particularities in their own, including sensitivity to process errors and fluctuations, and the requirements of a particular process. Researches on how to evaluate the degree of the silicon optical device affected by the process, develop rapid process parameter extraction, further predict the device performance, analyze the yield and the like are still hot spots in the field.
Disclosure of Invention
The present disclosure provides a method, an apparatus, a computer device, a computer readable storage medium and a computer program product for extracting waveguide physical parameters.
According to an aspect of the present disclosure, a method for extracting waveguide physical parameters is provided. The method includes acquiring spectral information about a waveguide test structure. The spectral information describes the variation of the optical transmission performance of the waveguide test structure with wavelength. The waveguide test structure includes a first main structure and a second main structure. The first main structure and the second main structure each comprise a grating coupler pair for coupling an optical signal and a resonant structure based on a mach-zehnder interferometer (MZI). The MZI-based resonant structure includes a waveguide pair having a length difference and a multi-mode interference (MMI) power splitter disposed at both sides of the waveguide pair. The length difference between the two waveguides of the waveguide pair in the second main structure is larger than the length difference between the two waveguides of the waveguide pair in the first main structure. The spectrum information includes first spectrum information of the first master structure and second spectrum information of the second master structure. The method further includes determining link parameters of an equivalent waveguide of the waveguide test structure based on the first and second spectral information and pre-constructed first and second link equations for the first and second master structures. The first link equation and the second link equation each represent spectral information of the corresponding primary structure in a functional expression including a link parameter as an unknown number. The method further includes determining physical parameters of an equivalent waveguide of the waveguide test structure based on the link parameters and mapping relationships between the link parameters and the physical parameters that are pre-constructed by the waveguide model.
According to another aspect of the present disclosure, an apparatus for extracting waveguide physical parameters is provided. The device comprises an acquisition module, a first determination module and a second determination module. The acquisition module is configured to acquire spectral information about the waveguide test structure. The spectral information describes the variation of the optical transmission performance of the waveguide test structure with wavelength. The waveguide test structure includes a first main structure and a second main structure. The first main structure and the second main structure each comprise a grating coupler pair for coupling an optical signal and a MZI-based resonant structure. The MZI-based resonant structure includes a waveguide pair having a length difference and an MMI power splitter disposed on both sides of the waveguide pair. The length difference between the two waveguides of the waveguide pair in the second main structure is larger than the length difference between the two waveguides of the waveguide pair in the first main structure, and the spectrum information includes first spectrum information of the first main structure and second spectrum information of the second main structure. The first determination module is configured to determine link parameters of an equivalent waveguide of the waveguide test structure based on the first and second spectral information and pre-constructed first and second link equations for the first and second master structures. The first link equation and the second link equation each represent spectral information of the corresponding main structure in a functional expression including a link parameter as an unknown number. And the second determination module is configured to determine the physical parameters of the equivalent waveguide of the waveguide test structure based on the link parameters and the mapping relation between the link parameters and the physical parameters, which is pre-constructed through the waveguide model.
According to an aspect of the present disclosure, there is provided a computer device including: at least one processor; and a memory having a computer program stored thereon, wherein the computer program, when executed by the processor, causes the processor to perform the method as described above.
According to an aspect of the present disclosure, there is provided a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, causes the processor to carry out the method as described above.
According to an aspect of the disclosure, a computer program product is provided, comprising a computer program which, when executed by a processor, causes the processor to carry out the method as described above.
According to one or more embodiments of the present disclosure, physical parameters of a manufactured waveguide may be accurately extracted.
These and other aspects of the disclosure will be apparent from and elucidated with reference to the embodiments described hereinafter.
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Further details, features and advantages of the disclosure are disclosed in the following description of exemplary embodiments, taken in conjunction with the accompanying drawings, in which:
FIG. 1 shows a schematic diagram of a waveguide test structure according to an embodiment of the disclosure;
FIG. 2 shows a flow diagram of a method for extracting waveguide physical parameters according to an embodiment of the present disclosure;
fig. 3A and 3B illustrate examples of acquired spectrum information according to an embodiment of the present disclosure;
fig. 4A and 4B show examples of results of fitting a link equation to spectrum information;
FIG. 5 shows a schematic block diagram of an apparatus for extracting waveguide physical parameters according to an embodiment of the present disclosure; and
FIG. 6 illustrates an example configuration of a computer device that may be used to implement the methods described in this disclosure.
Detailed Description
It will be understood that, although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer or section from another element, component, region, layer or section. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the present disclosure.
Spatially relative terms such as "below …," "below …," "lower," "below …," "above …," "upper," and the like may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that these spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "below" or "beneath" or "under" other elements or features would then be oriented "above" the other elements or features. Thus, the exemplary terms "below …" and "below …" may encompass both an orientation above … and below …. Terms such as "before …" or "before …" and "after …" or "next" may similarly be used, for example, to indicate the order in which light passes through the elements. The devices may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. In addition, it will also be understood that when a layer is referred to as being "between" two layers, it can be the only layer between the two layers, or one or more intervening layers may also be present.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items, and the phrase "at least one of a and B" refers to a alone, B alone, or both a and B.
It will be understood that when an element or layer is referred to as being "on," "connected to," "coupled to" or "adjacent to" another element or layer, it can be directly on, connected to, coupled to or adjacent to the other element or layer or intervening elements or layers may be present. In contrast, when an element is referred to as being "directly on," "directly connected to," "directly coupled to," or "directly adjacent to" another element or layer, there are no intervening elements or layers present. However, neither "on … nor" directly on … "should be construed as requiring that one layer completely cover an underlying layer in any event.
Embodiments of the present disclosure are described herein with reference to schematic illustrations (and intermediate structures) of idealized embodiments of the present disclosure. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments of the present disclosure should not be construed as limited to the particular shapes of regions illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. Thus, the regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the actual shape of a region of a device and are not intended to limit the scope of the present disclosure.
Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and/or the present specification and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
As used herein, the term "substrate" may refer to a substrate of a diced wafer, or may refer to a substrate of an unslit wafer. Similarly, the terms chip and die (die) may be used interchangeably unless such interchange causes a conflict. It should be understood that the term "layer" includes films and, unless otherwise specified, should not be construed as indicating a vertical or horizontal thickness.
In the related art, in order to evaluate the process-affected degree, predict the performance, analyze the yield, etc. of a silicon optical device such as an optical waveguide, it is generally required to first know the structural dimensions of the optical waveguide manufactured through the process, i.e. the physical parameters including the width and the height of the optical waveguide, and then perform subsequent evaluation, prediction, analysis, etc. according to the physical parameters. That is, it is necessary to extract the physical parameters of the fabricated optical waveguide first.
Current methods for extracting physical parameters, in particular height, generally involve the use of SEM (scanning electron microscope). However, the measurement by SEM scanning of the device is highly demanding for dicing, which is destructive to the device. Meanwhile, the imaging quality may be low due to the silicon material itself, and thus the measurement accuracy of the SEM method is difficult to guarantee. In summary, the current extraction of physical parameters by SEM methods may be inefficient.
To this end, according to an aspect of an embodiment of the present disclosure, a method for extracting a waveguide physical parameter is proposed. Embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.
Before explaining the method according to an embodiment of the present disclosure in detail, a waveguide test structure according to an embodiment of the present disclosure is first described in conjunction with fig. 1. Instead of the traditional SEM method, embodiments of the present disclosure enable the extraction of waveguide physical parameters by means of optical measurements based on a waveguide test structure.
It should be noted that the terms "optical waveguide" and "waveguide" are used interchangeably or alternatively herein and are understood by those skilled in the art to refer to a medium for guiding the propagation of light waves.
Fig. 1 shows a schematic diagram of a waveguide test structure 100 according to an embodiment of the present disclosure.
As shown in fig. 1, the waveguide test structure 100 includes a first main structure 110 and a second main structure 120. The first main structure 110 includes a first grating coupler pair 112 and a mach-zehnder interferometer (MZI) based first resonant structure 114 (hereinafter, also simply referred to as "first MZI resonant structure"). The second main structure 120 includes a second grating coupler pair 122 and a second resonating structure 124 based on MZI (hereinafter, also simply referred to as "second MZI resonating structure").
In the first main structure 110, the first grating coupler pair 112 is configured to couple an optical signal, wherein the optical signal is input through one grating coupler of the first grating coupler pair 112 (e.g., the grating coupler on the left side of the first grating coupler pair 112) and output from the other grating coupler of the first grating coupler pair 112 (e.g., the grating coupler on the right side of the first grating coupler pair 112).
The first MZI resonant structure 114 includes a waveguide pair composed of two waveguides 1142, 1144 having a length difference, and multimode interference (MMI) power splitters 1140, 1146 disposed on both sides of the waveguide pair. The MMI power splitter 1140 on one side is connected to the MMI power splitter 1146 on the other side via waveguides 1142, 1144. The waveguides 1142, 1144 each have a length l11And l12. In the example shown in FIG. 1, the length l of the waveguide 114412Greater than length l of waveguide 114211And the length difference between the two is delta l1. The waveguides 1142, 1144 may each have a bend for adjusting the length of the waveguides (e.g., the number of bends and/or the bend radius of the waveguides 1142 and 1144 may be the same). The first grating coupler pair 112 may be connected to M by, for example, a straight waveguideMI power dividers 1140, 1146.
Similar to the first main structure 110, in the second main structure 120, the second grating coupler pair 122 is configured to couple an optical signal, wherein the optical signal is input through one grating coupler of the second grating coupler pair 122 (e.g., the grating coupler on the left side of the second grating coupler pair 122) and output from the other grating coupler of the second grating coupler pair 122 (e.g., the grating coupler on the right side of the second grating coupler pair 122).
The second MZI resonant structure 124 includes a waveguide pair composed of two waveguides 1242, 1244 having a length difference, and MMI power splitters 1240, 1246 provided on both sides of the waveguide pair. The MMI power splitter 1240 on one side is connected to the MMI power splitter 1246 on the other side via waveguides 1242, 1244. The waveguides 1242, 1244 each have a length l21And l22. In the example shown in FIG. 1, the length l of the waveguide 124422Greater than length l of waveguide 124221And the length difference between the two is delta l2. In addition, the length difference Δ l2Greater than the aforementioned difference in length Δ l1. The waveguides 1242, 1244 may each have a bend for adjusting the length of the waveguide (e.g., the number of bends and/or the bend radius of the waveguides 1242 and 1244 may be the same). The second grating coupler pair 122 may be connected to the MMI power splitters 1240, 1246 by, for example, straight waveguides.
In an example, Δ l may be divided1And Δ l2Set to, for example, 4 μm and 120 μm, respectively. Those skilled in the art will appreciate that the above values are only one example of an embodiment of the present disclosure and that other values are possible. Generally speaking, setting the value to be relatively short can be avoided because the subsequent fitting process may be affected, and also can be avoided because the area burden may be caused.
Additionally, the waveguide test structure 100 may further include an auxiliary structure 130. The auxiliary structure 130 includes a third grating coupler pair 132. The optical signal is input through one grating coupler of the third grating coupler pair 132 (e.g., the grating coupler on the left side of the third grating coupler pair 132) and output from the other grating coupler of the third grating coupler pair 132 (e.g., the grating coupler on the right side of the third grating coupler pair 132). In the example shown in fig. 1, the third grating coupler pairs 132 may be interconnected by, for example, a straight waveguide. The third grating coupler pair 132 is arranged identical to the first grating coupler pair 112 and the second grating coupler pair 122.
According to an embodiment of the present disclosure, since the respective sub-structures (i.e., the first main structure 110, the second main structure 120, and additionally, the auxiliary structure 130) inside the waveguide test structure 100 may be disposed to be small in size and/or pitch, the waveguide test structure 100 may be equivalent to one waveguide as a whole, i.e., an equivalent waveguide. The method according to the disclosed embodiments can perform the extraction of the physical parameters for the equivalent waveguide. In addition to this, the extracted parameters can also be applied as "samples" in subsequent statistical methods.
Fig. 2 shows a flow diagram of a method 200 for extracting waveguide physical parameters according to an embodiment of the disclosure. In the following description of the method 200, the waveguide test structure referred to may be the waveguide test structure 100 described in connection with fig. 1. Accordingly, for clarity of illustration, reference numerals as shown in FIG. 1 are still used in the following description.
As shown in fig. 2, in step 202, spectral information about the waveguide test structure 100 is obtained. The spectral information describes the optical transmission performance of the waveguide test structure 100 as a function of wavelength. Here, the waveguide test structure 100 includes a first main structure 110 and a second main structure 120, as described in connection with fig. 1. The first main structure 110 includes a first grating coupler pair 112 and a first MZI resonant structure 114 for coupling optical signals. The second main structure 120 comprises a second grating coupler pair 122 for coupling an optical signal and a second MZI resonant structure 124. The first MZI resonant structure 114 comprises a waveguide 1142, 1144 having a length difference Δ l1And MMI power splitters 1140, 1146 disposed on either side of the waveguide pair. The second MZI resonant structure 124 comprises a length difference Δ l made up of waveguides 1242, 12442Of the waveguidePair, and MMI power splitters 1240, 1246 disposed on either side of the waveguide pair. The difference in length Δ l between the two waveguides 1242, 1244 of a waveguide pair in the second main structure 1202Greater than the difference in length Δ l between the two waveguides 1142, 1144 of the waveguide pair in the first main structure 1101. Accordingly, the spectrum information includes first spectrum information of the first master structure 110 and second spectrum information of the second master structure 120.
According to some embodiments, due to the difference in length difference of the waveguide pairs in the first main structure 110 and the second main structure 120, the first spectral information may exhibit a relatively lower resonance order and spectral curve complexity and the second spectral information may exhibit a relatively higher resonance order and spectral curve complexity within the measurement range.
In step 204, link parameters of the waveguides of the waveguide test structure are determined based on the first and second spectral information acquired in step 202, and the pre-constructed first link equation with respect to the first main structure 110 and the second link equation with respect to the second main structure 120. The waveguide herein refers to an equivalent waveguide formed based on the waveguide test structure 100. The first link equation represents the first spectrum information of the first main structure 110 in a functional expression including a link parameter as an unknown number. The second link equation represents the second spectrum information of the second main structure 120 in a functional expression including the link parameter as an unknown number.
In step 206, physical parameters of the equivalent waveguide of the waveguide test structure 100 are determined based on the link parameters determined in step 204 and mapping relationships between the link parameters and the physical parameters, which are pre-constructed by the waveguide model.
According to the method for extracting the waveguide physical parameters, the waveguide physical parameters can be extracted in an optical measurement mode based on the waveguide test structure, and therefore the traditional SEM method is replaced. As described in connection with fig. 1, the waveguide test structure can be regarded as equivalent to a waveguide, since it can form an equivalent waveguide, which makes it possible to extract physical parameters based on the waveguide test structure. Meanwhile, the two-stage MZI resonant structure with different length differences is used, so that the MZI resonant order can be accurately determined, and the physical parameters can be accurately extracted. Furthermore, by virtue of the mapping relationship between the link parameters and the physical parameters, which is known with the aid of the additionally modeled waveguide, the corresponding physical parameters of the waveguide test structure can be deduced, thereby enabling the extraction of the physical parameters of the actually manufactured waveguide.
Various aspects of a method 200 for extracting waveguide physical parameters according to an embodiment of the present disclosure are described in detail below.
In step 202, the first spectrum information of the first master structure 110 and the second spectrum information of the second master structure 120 may be previously measured by the relevant testing equipment. In other words, the acquiring step in step 202 may include receiving or retrieving measured spectrum information.
According to some embodiments, the waveguide test structure 100 may be fabricated on a wafer. Accordingly, the first spectrum information and the second spectrum information may be obtained by measuring the spectrum associated with the first master structure 110 and the spectrum associated with the second master structure 120 by the wafer level test equipment, respectively.
In an example, the waveguide test structure 100 may have an area on the order of hundreds of microns square. Thus, tens, hundreds, or even thousands of waveguide test structures 100 may be randomly arranged in a die, with one die (die) on the wafer having an area of, for example, about 20mm by 20 mm. In addition, each of several dies (e.g., about 40) on the wafer may employ the above arrangement. The above arrangement may be performed on a layout for manufacturing via tape-out.
In this manner, the waveguide test structure 100 may be randomly fabricated within an active area on a wafer, thereby facilitating an assessment of process impact that waveguides fabricated at different locations may be subjected to, thereby facilitating waveguide performance prediction and analysis yield. For example, where the effects of process errors are such as experienced, the measured spectra for waveguides fabricated at different locations may not be consistent, and thus physical parameters may be derived according to the methods of embodiments of the present disclosure to infer or predict the effects of process errors.
In addition, since the waveguide test structure 100 is fabricated on a wafer, the spectrum associated with the first main structure 110 and the spectrum associated with the second main structure 120 may also be automatically measured directly by wafer-level test equipment, which may facilitate fast and batch measurements of the spectra.
Here, examples of the acquired spectrum information according to embodiments of the present disclosure are shown in fig. 3A and 3B, where fig. 3A shows a measured example spectrum associated with the first main structure 110 and fig. 3B shows a measured example spectrum associated with the second main structure 120. Due to the waveguide pair length difference Δ l of the first MZI resonant structure 114 in the first main structure 1101(FIG. 3A by Δ l14 μm as an example) and the second MZI resonant structure 124 in the second main structure 120 by the waveguide pair length difference Δ l2(FIG. 3B is given by Δ l 2120 μm as an example), and thus exhibits different degrees of resonance on the frequency spectra as shown in fig. 3A and 3B. By the MZI principle, the larger the length difference, the more intense the resonance. Therefore, at the length difference Δ l2Greater than Δ l1The resonance exhibited on the spectrum shown in fig. 3B is more severe than that of fig. 3A.
As previously described, using a waveguide having different waveguide pair length differences Δ l1、Δl1The two-stage MZI resonant structures 114, 124 of (a) can help to accurately determine the MZI resonant order. Accordingly, the frequency spectrum associated with the first master structure 110 and the frequency spectrum associated with the second master structure 120 may be measured separately to obtain the required frequency spectrum information.
Returning now to fig. 2, in step 204, the first link equations for the first main structure 110 and the second link equations for the second main structure 120 may be pre-constructed according to the respective link structures of the first main structure 110 and the second main structure 120, respectively, and may be obtained for use before the method 200 is performed or before step 204 is performed. The first link equation and the second link equation constructed with the functional expressions are used in order to fit them to the first spectrum information and the second spectrum information that are actually measured, thereby determining the link parameters as unknowns in the link equations.
According to some embodiments, the first link equation and the second link equation may each be expressed as a product of a frequency domain equation for the respective grating coupler pair, a frequency domain equation for the respective MMI power splitter, and a frequency domain equation for the respective waveguide pair.
Here, the frequency domain equation is also a functional expression to express the spectrum information. In the three-part frequency domain equation described above, the respective function expressions are constructed with the wavelength parameters as arguments. Further, since the link parameters relate to portions of the waveguide pairs, the frequency domain equation for the waveguide pairs may be a functional expression including the link parameters as unknowns.
Depending on the link structure of the first main structure 110, the first link equation may be expressed as a product of the frequency domain equation of the first grating coupler pair 112, the frequency domain equation of the MMI power splitter 1140, 1146, and the frequency domain equation of the waveguide pair consisting of the two waveguides 1142, 1144, as shown in equation 1 below:
wherein, Pmzi1(λ) represents a first link equation; p isgc1(∑iaiλi)2Frequency domain equation, a, representing the first grating coupler pair 112iRepresenting coefficients in a multi-order polynomial, i representing an order; pmmi1(∑jbjλj)2Frequency domain equation representing MMI power splitter 1140, 1146, bjRepresenting coefficients in a multi-order polynomial, j representing an order;
representing the frequency domain equation, n, for a waveguide pair consisting of two waveguides 1142, 1144effAnd ngRespectively representing the effective and group refractive indices,/, of11And l12The length of the two waveguides 1142, 1144, respectively; λ represents a wavelength. Upper part ofEquation 1 above can be obtained ignoring MMI power splitter splitting non-uniformities. One skilled in the art will appreciate that equation 1 may also be optimized to account for this spectral non-uniformity.
Similarly, depending on the link structure of the second main structure 120, the second link equation may be expressed as a product of the frequency domain equation of the second grating coupler pair 122, the frequency domain equation of the MMI power splitters 1240, 1246, and the frequency domain equation of the waveguide pair formed by the two waveguides 1242, 1244, as shown in equation 2 below:
wherein, Pmzi2(λ) represents a second link equation; pgc2(∑iaiλi)2Frequency domain equation, a, representing the second grating coupler pair 122iRepresenting coefficients in a multi-order polynomial, i representing an order; pmmi2(∑jbjλj)2Equation in the frequency domain, b, representing the MMI power splitters 1240, 1246jRepresenting coefficients in a multi-order polynomial, j representing an order;
representing the frequency domain equation, n, for a waveguide pair consisting of two waveguides 1242, 1244effAnd ngRespectively representing the effective and group refractive indices,/, of21And l22The length of the two waveguides 1242, 1244, respectively; λ represents a wavelength.
In this way, corresponding link equations may be constructed for the two stages of MZI resonant structures 114, 124, respectively, to facilitate accurate determination of the MZI resonant orders in the fitting process.
According to some embodiments, as described in connection with fig. 1, since the waveguide test structure 100 may further include the auxiliary structure 130 (the auxiliary structure 130 includes the third grating-coupler pair 132), third spectral information of the auxiliary structure 130, that is, third spectral information of the third grating-coupler pair 132, may also be acquired in step 202. In addition, since the third grating coupler pair 132 is provided to be identical to the first grating coupler pair 112 and the second grating coupler pair 122, both the frequency domain equation of the first grating coupler pair 112 and the frequency domain equation of the second grating coupler pair 122 can be determined by fitting the third spectral information by a multi-order polynomial, i.e., determining coefficients in the multi-order polynomial.
In the example described previously, the frequency domain equation P for the first grating coupler pair 112gc1(∑iaiλi)2And frequency domain equation P for the second grating coupler pair 122gc2(∑iaiλi)2May be represented by a multi-order polynomial. Thus, by fitting the equation to third spectral information, the coefficient a in the multi-order polynomial may be determinedi。
Since the process results of the grating coupler pairs can be considered to be substantially identical in the case of close proximity, by means of this equivalent process, the frequency domain equation of the first grating coupler pair 112 and the frequency domain equation of the second grating coupler pair 122 can be determined indirectly by means of the auxiliary structure 130 comprising the third grating coupler pair 132.
According to some embodiments, the frequency domain equation of the MMI power splitter may be constructed as a multi-order polynomial. In this way, fitting of the link equations to the spectral information may be facilitated.
In the example described previously, the frequency domain equation P for the MMI power dividers 1140, 1146mmi1(∑jbjλj)2And frequency domain equation P for MMI power splitters 1240, 1246mmi2(∑jbjλj)2May be constructed as a multi-order polynomial. The multi-order polynomial may be a unitary multi-order polynomial about wavelength. In fitting the first link equation to the first spectral information and the second link equation to the second spectral information, coefficients b in the corresponding multi-order polynomials may be determinedj。
According to some embodiments, the frequency domain equation for a waveguide pair may be expressed as
Wherein wg1Function sum wg2The functions correspond to the first waveguide and the second waveguide in the waveguide pair, respectively, and wg1The function is expressed as
wg2The function is expressed as
Wherein λ represents the wavelength, λ0Represents a center wavelength, neffRepresents lambda0Effective refractive index of (a), ngRepresents the group refractive index,/1Represents the length of the first waveguide,/2Representing the length of the second waveguide.
The expression for the frequency domain equation may be applied to each of the waveguide pair consisting of the two waveguides 1142, 1144 and the waveguide pair consisting of the two waveguides 1242, 1244.
According to some embodiments, the link parameters may include an effective index and a group index (also referred to as group velocity). Accordingly, in step 204, determining the link parameter may include: fitting a second link equation to the second spectral information to determine a second effective index and a second group index; and fitting a first link equation substituted into the second effective refractive index and the second group refractive index to the first spectral information to determine a corrected second effective refractive index. The corrected second effective index and second group index are such that the first link equation has a best fit to the first spectral information.
By the mode, the two-stage MZI resonant structures 114 and 124 with different waveguide pair length differences can be used for accurately determining the MZI resonant order, so that the required link parameters can be accurately determined, and accurate extraction of waveguide physical parameters is facilitated.
According to the analysis of the fitting error principle, the first effective refractive index may be more accurate (because the resonance order is not selected by mistake) and the first group refractive index may have a larger error (because the curve complexity is low) among the first effective refractive index and the first group refractive index determined in the case of fitting the first link equation to the first spectrum information. In the case of fitting the second link equation to the second spectral information, the second effective refractive index may have a larger error, and the second group refractive index may be more accurate, since the resonance order of the second MZI resonant structure 124, which resonates more intensely, is more likely to be selected incorrectly to cause the error.
As an example, fig. 4A and 4B show the result of fitting a link equation to spectrum information. FIG. 4A shows an example result of fitting a first link equation to first spectral information (waveguide pair length difference Δ l of the first MZI resonant structure 1141Take 4 μm). A first effective index and a first group index corresponding to the first link equation may be determined by the fitting process. In this case, as mentioned above, the first effective refractive index may be more accurate, and the first group refractive index may have a larger error. FIG. 4B shows an example result of fitting a second link equation to second spectral information (waveguide pair length difference Δ l of the second MZI resonant structure 124)2Take 120 μm). A second effective index and a second group index corresponding to a second link equation may be determined by the fitting process. In this case, as mentioned above, the second effective refractive index may have a larger error, and the second group refractive index may be more accurate.
In an example, the fitting process described above may be performed based on a differential evolution algorithm or a genetic algorithm. In addition, it is also possible to set the range of each of the first and second effective refractive indices to, for example, a numerical range [2.0-2.5], and the range of each of the first and second group refractive indices to, for example, a numerical range [4.0-4.5], in order to speed up the algorithm convergence time, because the above numerical range may be a typical range of the effective refractive index and the group refractive index of the waveguide.
As mentioned above, the second effective refractive index with larger error may be caused by misselecting the resonance order of the second MZI resonant structure 124 during fitting. Thus, to accurately determine the resonance order, the second effective index and the second group index may be substituted into the first link equation to be re-fitted with the first spectral information. In this refitting process, the resonance order of the second MZI resonant structure 124 may be shifted until the lowest fitting error is obtained. At this time, the second effective refractive index determined by the refitting is corrected, that is, corrected. In other words, the corrected second effective refractive index and second group refractive index enable the first link equation to have a best fit to the first spectral information. Here, there is also a best fit to the second spectral information, since only the resonance order is shifted by itself.
According to some embodiments, the corrected second effective refractive index may be represented as neff2+Δm*λ0Δ l, where neff2Represents the second effective refractive index, Δ l represents the waveguide pair length difference in the second main structure 120, Δ m represents the relative resonance order, and λ0Representing the center wavelength.
In this way, the calculation method of the corrected second effective refractive index is quantified. In case the resonance order is accurately determined by the above-mentioned re-fitting procedure, the accurate link parameters can be obtained accordingly via the above-mentioned formula.
Returning again to fig. 2, in step 206, the mapping between the link parameters and the physical parameters previously constructed by the modeled waveguides may be obtained for use prior to execution of the method 200 or prior to execution of step 206.
In an example, the waveguide may first be modeled using physical simulation software such as COMSOL or the like. The modeled waveguide may be an 85 degree trapezoid in cross-section, and the cladding materials above and below the waveguide may be based On the selected SOI (Silicon-On-Insulator) wafer substrate and Silicon dioxide (SiO) wafer substrate2) The film growth process. After the waveguide is modeled, link parameter values corresponding to each set of height and width values may be obtained by scanning the height of the waveguide over a range of values and scanning the width of the waveguide over a range of values. In an example, the value interval for scanning can be selected as appropriate according to the physical size of the actual waveguide, process fluctuation and the likeA scanning interval. Here, the width may be selected according to a definition in simulation, and may refer to a width corresponding to a half position of the height, for example.
In other words, a mapping relationship between link parameters and physical parameters associated with the modeled waveguide may be obtained. The mapping relationship may be expressed as f (width) or (n)eff，ng) Where width and thickness represent the width and height, respectively, of the modeled waveguide, and neffAnd ngThe effective and group indices of the modeled waveguide are represented separately.
Then, the mapping relationship f (width, thickness) may be transformed to (n)eff，ng) To obtain a transformed mapping g (n) of the independent variables and the dependent variables (e.g. inverse matrix)eff，ng) Width (thick). In this case, the link parameters of the waveguides of the waveguide test structure 100 determined in step 204 may be substituted into the mapping g (n)eff，ng) To determine the physical parameters of the waveguides of the waveguide test structure 100.
In an example, the process of steps 202-206 may also be repeated for a number of waveguide test structures 100 randomly fabricated on a wafer. Therefore, the process influence on the waveguides manufactured at different positions can be evaluated through a statistical method, and the waveguide performance prediction and the analysis yield are facilitated.
According to some embodiments, the pre-constructed mapping relationship between the link parameters and the physical parameters may be determined based on the link parameters when the lowest order mode is transmitted in the modeled waveguide. Thus, the mapping relation can be constructed quickly and easily.
In an example, the effective index and the group index at the time of transmission of the lowest order mode in the waveguide (which may be a single mode waveguide in general, only one mode) can be recorded while scanning the height and width of the modeled waveguide. In addition, since the scanning results are discrete numerical points, the fitting between the height and width parameters and the effective refractive index and group refractive index parameters can be performed through an equation, wherein the equation for fitting can adopt twoA polynomial of a multiple degree (generally, the higher the order of the polynomial, the higher the fitting accuracy, but at the same time, the complexity is also increased, and here, for example, three orders may be used). Accordingly, the equation may represent the mapping relationship f (width, thickness) — (n) as described aboveeff，ng)。
As described above, according to the method for extracting the waveguide physical parameter of the embodiment of the present disclosure, the extraction of the waveguide physical parameter can be achieved by performing optical measurement based on the waveguide test structure, thereby replacing the conventional SEM method. Since the waveguide test structure can form an equivalent waveguide, it can be regarded as equivalent to one waveguide, which makes it possible to extract physical parameters based on the waveguide test structure. Meanwhile, the two-stage MZI resonant structure with different length differences is used, so that the MZI resonant order can be accurately determined, and the physical parameters can be accurately extracted. Furthermore, by means of the mapping relationship between the link parameters and the physical parameters known with the aid of the additionally modeled waveguide, the corresponding physical parameters of the waveguide test structure can be deduced, thereby enabling the extraction of the physical parameters of the actually manufactured waveguide.
Fig. 5 shows a schematic block diagram of an apparatus 500 for extracting waveguide physical parameters according to an embodiment of the present disclosure. In the following description of the apparatus 500, the waveguide test structure referred to may be the waveguide test structure 100 described in connection with fig. 1. Therefore, for clarity of explanation, the reference numerals shown in FIG. 1 are still used in the following description.
As shown in fig. 5, the apparatus 500 includes an obtaining module 502, a first determining module 504, and a second determining module 506.
The acquisition module 502 is configured to acquire spectral information about the waveguide test structure 100. The spectral information describes the optical transmission performance of the waveguide test structure 100 as a function of wavelength. Here, the waveguide test structure 100 includes a first main structure 110 and a second main structure 120, as described in connection with fig. 1. The first main structure 110 includes a first grating coupler pair 112 for coupling an optical signal and a first MZI resonant structure 114. The second main structure 120 comprises a second grating for coupling the optical signalA coupler pair 122 and a second MZI resonant structure 124. The first MZI resonant structure 114 comprises a length difference Δ l made up of waveguides 1142, 11441And MMI power splitters 1140, 1146 disposed on either side of the waveguide pair. The second MZI resonant structure 124 comprises a length difference Δ l made up of waveguides 1242, 12442And MMI power splitters 1240, 1246 arranged on both sides of the waveguide pair. Accordingly, the spectrum information includes first spectrum information of the first master structure 110 and second spectrum information of the second master structure 120.
The first determining module 504 is configured to determine link parameters of the waveguides of the waveguide test structure based on the first and second spectrum information acquired at the acquiring module 502, and the pre-constructed first link equations regarding the first main structure 110 and the second link equations regarding the second main structure 120. The waveguide is an equivalent waveguide formed based on the waveguide test structure 100. The first link equation represents the first spectrum information of the first main structure 110 in a functional expression including a link parameter as an unknown number. The second link equation represents the second spectrum information of the second main structure 120 in a functional expression including the link parameter as an unknown number.
The second determination module 506 is configured to determine physical parameters of the equivalent waveguides of the waveguide test structure 100 based on the link parameters determined in step 204 and mapping relationships between the link parameters and the physical parameters, which are pre-constructed by the waveguide model.
It should be understood that the various modules of the apparatus 500 shown in fig. 5 may correspond to the various steps in the method 200 described with reference to fig. 2. Thus, the operations, features and advantages described above with respect to the method 200 are equally applicable to the apparatus 500 and the modules comprised thereby. Certain operations, features and advantages may not be described in detail herein for the sake of brevity.
Although specific functionality is discussed above with reference to particular modules, it should be noted that the functionality of the various modules discussed herein may be divided into multiple modules and/or at least some of the functionality of multiple modules may be combined into a single module. Performing an action by a particular module as discussed herein includes the particular module itself performing the action, or alternatively the particular module invoking or otherwise accessing another component or module that performs the action (or performs the action in conjunction with the particular module). Thus, a particular module that performs an action can include the particular module that performs the action itself and/or another module that the particular module invokes or otherwise accesses that performs the action.
It should also be appreciated that various techniques may be described herein in the general context of software, hardware elements, or program modules. The various modules described above with respect to fig. 5 may be implemented in hardware or in hardware in combination with software and/or firmware. For example, the modules may be implemented as computer program code/instructions configured to be executed in one or more processors and stored in a computer-readable storage medium. Alternatively, the modules may be implemented as hardware logic/circuitry. For example, in some embodiments, one or more of the acquisition module 502, the first determination module 504, and the second determination module 506 may be implemented together in a System on Chip (SoC). The SoC may include an integrated circuit chip (which includes one or more components of a Processor (e.g., a Central Processing Unit (CPU), microcontroller, microprocessor, Digital Signal Processor (DSP), etc.), memory, one or more communication interfaces, and/or other circuitry), and may optionally execute received program code and/or include embedded firmware to perform functions.
According to an aspect of the disclosure, a computer device is provided that includes a memory, a processor, and a computer program stored on the memory. The processor is configured to execute the computer program to implement the steps of any of the method embodiments described above.
According to an aspect of the present disclosure, a non-transitory computer-readable storage medium is provided, having stored thereon a computer program which, when executed by a processor, implements the steps of any of the method embodiments described above.
According to an aspect of the present disclosure, a computer program product is provided, comprising a computer program which, when executed by a processor, performs the steps of any of the method embodiments described above.
Illustrative examples of such computer devices, non-transitory computer-readable storage media, and computer program products are described below in connection with FIG. 6.
Fig. 6 illustrates an example configuration of a computer device 600 that may be used to implement the methods described in this disclosure. The above-described means 500 for extracting waveguide physical parameters may be implemented in whole or at least in part by a computer device 600 or similar device or system.
The computer device 600 may be a variety of different types of devices. Examples of computer device 600 include, but are not limited to: a desktop computer, a server computer, a notebook or netbook computer, a mobile device (e.g., a tablet, a cellular or other wireless telephone (e.g., a smartphone), a notepad computer, a mobile station), a wearable device (e.g., glasses, a watch), an entertainment device (e.g., an entertainment appliance, a set-top box communicatively coupled to a display device, a gaming console), a television or other display device, an automotive computer, and so forth.
The computer device 600 may include at least one processor 602, memory 604, communication interface(s) 606, display device 608, other input/output (I/O) devices 610, and one or more mass storage devices 612, capable of communicating with each other, such as through a system bus 614 or other suitable connection.
Memory 604 and mass storage device 612 are examples of computer readable storage media for storing instructions that are executed by processor 602 to implement the various functions described above. By way of example, memory 604 may generally include both volatile and nonvolatile memory (e.g., RAM, ROM, and the like). In addition, mass storage device 612 may generally include a hard disk drive, solid state drive, removable media, including external and removable drives, memory cards, flash memory, floppy disks, optical disks (e.g., CDs, DVDs), storage arrays, network attached storage, storage area networks, and the like. The memory 604 and mass storage device 612 may both be referred to collectively herein as memory or computer-readable storage medium and may be non-transitory media capable of storing computer-readable, processor-executable program instructions as computer program code that may be executed by the processor 602 as a particular machine configured to implement the operations and functions described in the examples herein.
A number of programs may be stored on the mass storage device 612. These programs include an operating system 616, one or more application programs 618, other programs 620, and program data 622, which can be loaded into memory 604 for execution. Examples of such applications or program modules may include, for instance, computer program logic (e.g., computer program code or instructions) for implementing the following components/functions: an acquisition module 502, a first determination module 504, and a second determination module 506, and/or further embodiments described herein.
Although illustrated in fig. 6 as being stored in memory 604 of computer device 600, modules 616, 618, 620, and 622, or portions thereof, may be implemented using any form of computer-readable media that is accessible by computer device 600. As used herein, "computer-readable media" includes at least two types of computer-readable media, namely computer-readable storage media and communication media.
Computer-readable storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer-readable storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, Digital Versatile Disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information for access by a computer device. In contrast, communication media may embody computer readable instructions, data structures, program modules, or other data in a modulated data signal, such as a carrier wave or other transport mechanism. Computer-readable storage media, as defined herein, does not include communication media.
One or more communication interfaces 606 are used to exchange data with other devices, such as over a network, direct connection, and the like. Such communication interfaces may be one or more of the following: any type of network interface (e.g., a Network Interface Card (NIC)), wired or wireless (such as IEEE 802.11 Wireless LAN (WLAN)) wireless interface, worldwide interoperability for microwave Access (Wi-MAX) interface, Ethernet interface, Universal Serial Bus (USB) interface, cellular network interface, BluetoothTMAn interface, a Near Field Communication (NFC) interface, etc. The communication interface 606 may facilitate communication within a variety of networks and protocol types, including wired networks (e.g., LAN, cable, etc.) and wireless networks (e.g., WLAN, cellular, satellite, etc.), the internet, and so forth. The communication interface 606 may also provide for communication with external storage devices (not shown), such as in storage arrays, network attached storage, storage area networks, and so forth.
In some examples, a display device 608, such as a monitor, may be included for displaying information and images to a user. Other I/O devices 610 may be devices that receive various inputs from a user and provide various outputs to the user, and may include touch input devices, gesture input devices, cameras, keyboards, remote controls, mice, printers, audio input/output devices, and so forth.
The techniques described herein may be supported by these various configurations of the computer device 600 and are not limited to specific examples of the techniques described herein. For example, the functionality may also be implemented in whole or in part on a "cloud" using a distributed system. The cloud includes and/or represents a platform for resources. The platform abstracts underlying functionality of hardware (e.g., servers) and software resources of the cloud. The resources may include applications and/or data that may be used when performing computing processes on servers remote from the computer device 600. Resources may also include services provided over the internet and/or over a subscriber network such as a cellular or Wi-Fi network. The platform may abstract resources and functionality to connect the computer device 600 with other computer devices. Thus, implementations of the functionality described herein may be distributed throughout the cloud. For example, the functionality may be implemented in part on the computer device 600 and in part by a platform that abstracts the functionality of the cloud.
While the disclosure has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative and exemplary and not restrictive; the present disclosure is not limited to the disclosed embodiments. Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed subject matter, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps not listed, the indefinite article "a" or "an" does not exclude a plurality, the term "a" or "an" means two or more, and the term "based on" should be construed as "based at least in part on". The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.
Claims (13)
1. A method for extracting waveguide physical parameters, comprising:
obtaining spectral information about a waveguide test structure, wherein the spectral information describes a variation of an optical transmission performance of the waveguide test structure with wavelength, the waveguide test structure comprises a first main structure and a second main structure, the first main structure and the second main structure each comprising a grating coupler pair for coupling an optical signal and a resonant structure based on a Mach-Zehnder interferometer (MZI), the MZI-based resonant structure comprises a waveguide pair having a length difference and a multi-mode interference (MMI) power splitter disposed on either side of the waveguide pair, a length difference between two waveguides of the waveguide pair in the second main structure is larger than a length difference between two waveguides of the waveguide pair in the first main structure, and the spectrum information comprises first spectrum information of the first primary structure and second spectrum information of the second primary structure;
determining link parameters of an equivalent waveguide of the waveguide test structure based on the first and second spectrum information, and a pre-constructed first link equation about the first main structure and a second link equation about the second main structure, wherein the first and second link equations each represent spectrum information of the corresponding main structure in a function expression including the link parameters as unknowns; and
and determining the physical parameters of the equivalent waveguide of the waveguide test structure based on the link parameters and mapping relations between the link parameters and the physical parameters, which are pre-constructed through a waveguide model.
2. The method of claim 1, wherein the waveguide test structure is fabricated on a wafer, and the first and second spectral information are obtained by measuring a spectrum associated with the first master structure and a spectrum associated with the second master structure, respectively, by a wafer-level test apparatus.
3. The method of claim 1 or 2, wherein the first link equation and the second link equation are each expressed as a product of a frequency domain equation for the respective grating coupler pair, a frequency domain equation for the respective MMI power splitter, and a frequency domain equation for the respective waveguide pair.
4. The method of claim 3, wherein the waveguide test structure further comprises an auxiliary structure comprising a same auxiliary grating coupler pair as the grating coupler pair, and the obtaining spectral information about the waveguide test structure further comprises obtaining third spectral information of the auxiliary structure comprising the auxiliary grating coupler pair,
wherein the frequency domain equation of the grating coupler pair is determined by fitting the third spectral information by a multi-order polynomial.
5. The method of claim 3, wherein the frequency domain equation of the MMI power splitter is constructed as a multiple order polynomial.
6. The method of claim 3, wherein the frequency domain equation for the waveguide pair is expressed as
Wherein wg1Function sum wg2The functions correspond to the first waveguide and the second waveguide of the waveguide pair, respectively, and wg1The function is expressed as
wg2The function is expressed as
Wherein λ represents the wavelength, λ0Represents a center wavelength, neffRepresents lambda0Effective refractive index of (a), ngRepresents the group refractive index,/1Represents the length of the first waveguide,/2Representing the length of the second waveguide.
7. The method of claim 1 or 2, wherein the link parameters comprise an effective index and a group index, and wherein the determining link parameters for an equivalent waveguide of the waveguide test structure comprises:
fitting the second link equation to the second spectral information to determine a second effective index and a second group index; and
fitting the first link equation substituted into the second effective refractive index and the second group refractive index to the first spectral information to determine a corrected second effective refractive index, wherein the corrected second effective refractive index and the second group refractive index are such that the first link equation has a best fit to the first spectral information.
8. The method of claim 7, wherein the corrected second effective refractive index is represented as neff2+Δm*λ0,/Δ l, where neff2Represents the second effective refractive index, Δ l represents a length difference of the waveguide pair in the second main structure, Δ m represents a relative resonance order, and λ0Representing the center wavelength.
9. The method according to claim 1 or 2, wherein the mapping relation between the link parameter and the physical parameter, which is pre-constructed by the waveguide model, is determined based on the link parameter when the lowest order mode is transmitted in the waveguide model.
10. An apparatus for extracting waveguide physical parameters, comprising:
an acquisition module configured to acquire spectral information about a waveguide test structure, wherein the spectral information describes a variation of an optical transmission performance of the waveguide test structure with wavelength, the waveguide test structure comprises a first main structure and a second main structure, the first main structure and the second main structure each comprising a grating coupler pair for coupling an optical signal and a resonant structure based on a Mach-Zehnder interferometer (MZI), the MZI-based resonant structure includes a waveguide pair having a length difference and a multi-mode interference (MMI) power splitter disposed on both sides of the waveguide pair, a length difference between two waveguides of the waveguide pair in the second main structure is larger than a length difference between two waveguides of the waveguide pair in the first main structure, and the spectrum information comprises first spectrum information of the first primary structure and second spectrum information of the second primary structure;
a first determination module configured to determine link parameters of an equivalent waveguide of the waveguide test structure based on the first and second spectrum information, and a pre-constructed first link equation regarding the first main structure and a second link equation regarding the second main structure, wherein the first and second link equations each represent spectrum information of the corresponding main structure in a function expression including the link parameters as unknowns; and
a second determination module configured to determine the physical parameters of the equivalent waveguide of the waveguide test structure based on the link parameters and mapping relationships between the link parameters and the physical parameters, which are pre-constructed by a waveguide model.
11. A computer device, comprising:
at least one processor; and
a memory having a computer program stored thereon,
wherein the computer program, when executed by the at least one processor, causes the at least one processor to perform the method of any one of claims 1 to 9.
12. A computer-readable storage medium, on which a computer program is stored which, when executed by a processor, causes the processor to carry out the method of any one of claims 1 to 9.
13. A computer program product comprising a computer program which, when executed by a processor, causes the processor to carry out the method of any one of claims 1 to 9.
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