Manufacturing Apparatus of Optical Circuit and Manufacturing Method of Optical Circuit
20240085627 ยท 2024-03-14
Inventors
- Kenya Suzuki (Musashino-shi, Tokyo, JP)
- Keita Yamaguchi (Musashino-shi, Tokyo, JP)
- Ai Yanagihara (Musashino-shi, Tokyo, JP)
- Masashi Ota (Musashino-shi, Tokyo, JP)
Cpc classification
G03F7/0035
PHYSICS
C03B20/00
CHEMISTRY; METALLURGY
International classification
G03F7/00
PHYSICS
Abstract
An optical circuit to be manufactured on a wafer has a problem that characteristics are distributed (biased) in a wafer plane due to various causes in manufacturing. The present invention is characterized in that refractive index distribution of an upper cladding is adjusted on the basis of refractive index distribution of a lower cladding and a core film, a film thickness of the core film, and in-plane distribution such as an execution refractive index of an optical waveguide (calculated from a width of a core pattern).
Claims
1. An apparatus for manufacturing an optical circuit including a glass film, the apparatus comprising: a step of forming a lower cladding film and an apparatus configured to form a core film; an apparatus configured to form a core pattern by photolithography; and an apparatus configured to form an upper cladding film on the core pattern, wherein in the step of forming the upper cladding film, refractive index distribution of the upper cladding is adjusted on a basis of measurement data of refractive index distribution in a layer of the optical circuit before the step of forming the upper cladding film.
2. The apparatus for manufacturing the optical circuit according to claim 1, wherein the measurement data is refractive index distribution of the lower cladding in a wafer plane, refractive index distribution and/or a film thickness of the core film, and in-plane distribution of an effective refractive index of an optical waveguide calculated from a width of the core pattern.
3. The apparatus for manufacturing the optical circuit according to claim 1, wherein the refractive index distribution of the upper cladding is adjusted such that the optical circuit to be formed by a silica-based planar lightwave satisfies desired circuit characteristics.
4. The apparatus for manufacturing the optical circuit according to claim 2, wherein the refractive index distribution of the upper cladding is adjusted such that an effective refractive index of the optical waveguide becomes constant in a plane.
5. The apparatus for manufacturing the optical circuit according to claim 1, wherein a refractive index of the upper cladding is adjusted by one or both of P.sub.2O.sub.5 and B.sub.2O.sub.3.
6. The apparatus for manufacturing the optical circuit according to claim 1, wherein the refractive index of the upper cladding is adjusted by adding GeO.sub.2, TiO.sub.2, Ta.sub.2O.sub.5, HfO.sub.2, or ZrO.sub.2.
7. A method for manufacturing an optical circuit including a glass film, the method comprising: a step of forming a lower cladding film and a step of forming a core film; a step of forming a core pattern by photolithography; and a step of forming an upper cladding film on the core pattern, wherein in the step of forming the upper cladding film, refractive index distribution of the upper cladding is adjusted on a basis of measurement data of refractive index distribution in a layer of the optical circuit before the step of forming the upper cladding film.
8. The method for manufacturing the optical circuit according to claim 7, wherein the measurement data is refractive index distribution of the lower cladding in a wafer plane, refractive index distribution and/or a film thickness of the core film, and in-plane distribution of an effective refractive index of an optical waveguide calculated from a width of the core pattern.
9. The method for manufacturing the optical circuit according to claim 7, wherein the refractive index distribution of the upper cladding is adjusted such that the optical circuit to be formed by a silica-based planar lightwave satisfies desired circuit characteristics.
10. The method for manufacturing the optical circuit according to claim 8, wherein the refractive index distribution of the upper cladding is adjusted such that an effective refractive index of the optical waveguide becomes constant in a plane.
11. The method for manufacturing the optical circuit according to claim 7, wherein a refractive index of the upper cladding is adjusted by one or both of P.sub.2O.sub.5 and B.sub.2O.sub.3.
12. The method for manufacturing the optical circuit according to claim 7, wherein the refractive index of the upper cladding is adjusted by adding GeO.sub.2, TiO.sub.2, Ta.sub.2O.sub.5, HfO.sub.2, or ZrO.sub.2.
Description
BRIEF DESCRIPTION OF DRAWINGS
[0020]
[0021]
[0022]
[0023]
[0024]
[0025]
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[0027]
[0028]
[0029]
[0030]
[0031]
[0032]
DESCRIPTION OF EMBODIMENTS
[0033] Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings.
Basic Configuration
[0034] A manufacturing method according to an embodiment of the present invention includes: measuring components or characteristics of an optical device formed in one step in a manufacturing step at that time and adjusting or correcting manufacturing conditions in a subsequent step on the basis of the measurement data (hereinafter, this scheme will be referred to as a feedforward system). The feedforward system makes it possible to obtain desired optical characteristics for the finally obtained optical device, in which variations in the optical characteristics of the optical device are reduced.
[0035]
[0036] For example, a refractive index and a thickness of a lower cladding film formed in step 1 of lower cladding deposition, and a refractive index and a thickness of a core layer deposited in step 2 of core deposition are measured. On the basis of the measurement results, final optical characteristics of the device manufactured with standard (nominal) design values are estimated. Then, on the basis of this estimation, intensity or a period of etching is controlled in step 6 of etching which is a subsequent step.
[0037] Specifically, an ideal core width of a pattern for satisfying performance required as an optical device is estimated (predicted) on the basis of the measured film thickness and refractive index of the core layer and the refractive index of the cladding film. Then, in step 6 of etching, etching is performed on the basis of the prediction value. For example, in a case of prediction information that a waveguide width after core processing is increased, and desired performance cannot be satisfied with the standard (nominal) design values, correction is performed to narrow the core width to be formed in the etching step. As an adjustment method in this event, a method in which the core width is made narrower than a standard (nominal) value by increasing a period of etching or increasing intensity of etching can be considered. Furthermore, it is also possible to measure the width and a level difference of the core in the pattern of the waveguide formed in step 6 of etching, control the refractive index, and the like, of the upper cladding film formed in step 8 of upper cladding deposition on the basis of the measurement result and adjust the optical characteristics of the finally obtained optical waveguide.
[0038] As described above, in the feedforward system of the present embodiment, shapes, characteristics, and the like, of the components of the formed optical device are measured during or after the preceding step among a plurality of steps of manufacturing the optical device, and the manufacturing conditions are adjusted or corrected in the subsequent step on the basis of the measurement result such that performance of the finally completed device satisfies desired conditions.
[0039]
[0040] In
[0041] The prediction value derived by the measurement data processing unit 31 is passed to the control data processing unit 32. The control data processing unit 32 obtains manufacturing conditions in step j, which is a subsequent step, on the basis of the prediction value. When step j is executed, the control data processing unit 32 supplies control data for step j set in the manufacturing apparatus according to the obtained manufacturing conditions. The control data based on the preceding step supplied when the subsequent step j is executed may be only the control data based on the preceding step i or may be a plurality of types of control data based on some of the preceding steps. It is a matter of course that a form of the control data is determined according to conditions of an actually configured manufacturing apparatus and an object to be manufactured.
Example 1
[0042] n the following, specific examples of waveguide manufacturing by the above-described feedforward system will be described. The following example relates to a configuration for obtaining control data for step 8 of upper cladding deposition (step k) on the basis of measurement data obtained in step 6 of etching (step i).
[0043]
[0044]
[0049] The core of the optical waveguide is processed by the dry etching apparatus 1013 illustrated in
[0050] The measurement result in the dry etching step can be fed forward to the FHD step, for example.
[0051] The measurement data obtained above is subjected to the following processing by the measurement data processing unit 31. Specifically, the measurement data processing unit 31 performs prediction by calculating a nominal model of the optical characteristics .sub.nom(x, y) as an optical device according to the following Formula 1 on the basis of the time-series value of each measurement data.
Math. 1
.sub.nom(x, y)=f.sub.xy(W, F.sub.1, F.sub.2, L, P, V) (Formula 1)
[0052] In Formula 1, x and y are coordinates in a wafer plane. .sub.nom is optical characteristics. For example, in a case of an arrayed waveguide grating, .sub.nom is a transmission center wavelength, a crosstalk, a polarization dependent loss, a wavelength dependent loss, a polarization dependent transmission wavelength, wavelength dispersion, polarization mode dispersion, or the like.
[0053] The nominal model f.sub.xy(W, F.sub.1, F.sub.2, L, P, V) can be expressed as, for example, a power sum of each parameter. In other words, in a case where an average value of the optical characteristics over a plurality of times K-1 of manufacturing before certain K-th manufacturing is set as .sup.Avg(x, y), and averages of the measured values are set as W.sub.avg, F.sub.1avg, F.sub.2avg, L.sub.avg, P.sub.avg, and V.sub.avg, the nominal model can be expressed as:
[0054] Here, coefficients C.sub.w, C.sub.F1, C.sub.F2, C.sub.L, C.sub.P, and C.sub.V are determined for each coordinate (x, y) in the wafer. In addition, it can be assumed that each measurement value in the K-th manufacturing has small deviation from the average of previous measurement values, and thus, each sum may be obtained by adding the first terms. In addition, while it is assumed here that change from the average value of each measurement value is minute and each measurement value is independent, a formula f.sub.xy(W, F.sub.1, F.sub.2, L, P, V) of a nominal model assuming a case where each measurement value is dependent may be defined. For example, if the gas flow rates F.sub.1 and F.sub.2 change, the degree of vacuum V also changes, and thus, the nominal model may include the product of both and light relating to V(F.sub.1, F.sub.2). In addition to the power sum, the coefficients may be obtained by machine learning, or the like.
[0055] Noe that the coefficients may be obtained by AI/machine learning on the basis of the inspection result performed in the middle of the manufacturing step of the optical waveguide, and the final device characteristics may be predicted. As training data of AI, data in which step inspection results and device characteristics of optical waveguides manufactured so far are combined can be utilized.
[0056] In addition, in the embodiment described above, the reading W of the RF power, the readings F.sub.1 and F.sub.2 of the mass flowmeter, the reading (wavelength) L of the emission detector, the (intensity) P, and the reading V of the vacuum gauge are used as measurement items, but other measurement values, for example, an emission spectrum obtained from the emission detector, a temperature, humidity, an atmospheric pressure, weather, a timing of overhaul of the apparatus, the number of times of processing from the overhaul, and the like, may be added.
[0057] An example using FHD will be described below.
[0058]
[0059] Oxygen and hydrogen (not illustrated) are simultaneously supplied to the burner. The source gas is hydrolyzed in an oxyhydrogen flame to produce glass microparticles, which are deposited on the wafer. The burner 2003 moves in a radial direction above the turntable 2002 rotating at the angular velocity Q. Thus, as illustrated in
[0060] Here, as control values, [0061] rotation angular velocity of turntable: [0062] readings of mass flow meter: F21, F22, F23, and [0063] movement speed of the burner in the radial direction: v are defined. These control values are observable. In the following description, it is assumed that the upper cladding layer is formed by the FHD method after the core processing.
[0064] The nominal model of the optical characteristics .sub.nom(x, y) as the optical device in step 8 of upper cladding deposition is described as:
Math. 3
.sub.nom(x, y)=f.sub.xy(, F.sub.21, F.sub.22, F.sub.23, v) Formula (3).
[0065] Here, x and y in Formula (3) are coordinates in the wafer plane. .sub.nom is optical characteristics. For example, in a case of an arrayed waveguide grating, .sub.nom is a transmission center wavelength, a crosstalk, a polarization dependent loss, a wavelength dependent loss, a polarization dependent transmission wavelength, wavelength dispersion, polarization mode dispersion, or the like. In a case of an optical switch, examples of the optical characteristics can include a loss, an extinction wavelength, a crosstalk, a polarization dependent loss, and the like.
[0066] The nominal model f.sub.xy(, F.sub.21, F.sub.22, F.sub.23, and v) can be expressed as, for example, a power sum of each parameter. In other words, in a case where an average value of optical characteristics over a plurality of times K-1 of manufacturing before certain K-th manufacturing is set as .sup.Avg(x, y), and averages of measurement values of control values are set as .sub.avg, F.sub.21avg, F.sub.22avg, F.sub.23avg, and v.sub.avg, the nominal model can be expressed as:
[0067] As described above, the formula of the nominal model may be in a form other than the power sum. In the formula of the nominal model, , F.sub.21, F.sub.22, F.sub.23, and v are measurement values and control values.
[0068] he measurement data including the measurement values and the control data including the control values may be accumulated in a database.
[0069] The control data processing unit 32 generates control data as follows. For example, taking a silica-based planar lightwave circuit as an example, as illustrated in
Math. 5
[.sub.nom(x, y).sub.target(x, y)]+[.sub.nom(x, y).sub.target(x, y)]=0 Formula (5) [0070] is satisfied at each position (x, y) in the wafer plane. As a result, it is possible to obtain desired optical characteristics .sub.target(x, y) of an optical device with no distribution of optical characteristics.
[0071] In feedforward correction, a controllable parameter (upper , F21, 22, . . . , etc.) may be controlled so as to satisfy Formula (5). The above formula of the nominal model is expressed to represent controllability. In other words, the left side of Formula (5) is an evaluation function, and if Formulas (1) and (3) are substituted into Formula (5), the evaluation function is expressed by the sum of powers of the controllable parameters for each step. It is only necessary to perform manufacturing while adjusting each control parameter so that the evaluation function becomes zero. The control may be performed by selecting one of the control parameters that most efficiently satisfies the evaluation function.
[0072] A method described below is means for obtaining data to be output. In deriving the control parameters to be output, first, the measurement values of the known control parameters obtained in step 6 of etching are substituted into the formula obtained by substituting Formula (1) and (3) into Formula (5). The control parameters .sub.avg, F.sub.21avg, F.sub.22avg, F.sub.23avg, and v.sub.avg in step 8 of upper cladding deposition are variables of the same formula, but each parameter can be determined using a method such as a hill-climbing method, a method using a genetic algorithm, and Particle Swarm Optimization. In a case where Formula (3) is linear, each parameter can also be determined by using a simple method such as linear programming.
[0073] Specific description will be given. For example, the center wavelength of the arrayed waveguide grating is expressed as:
Math. 6
.sub.0=n.sub.effdL/m Formula (6).
[0074] Here, n.sub.eff is an effective refractive index of the arrayed waveguide, dL is an optical path length difference between the waveguides of the arrayed waveguide, and m is diffraction order. In other words, the center wavelength of the arrayed waveguide grating depends on the effective refractive index n.sub.eff. The effective refractive index neff increases as the width and height of the waveguide core increase and increases as the refractive index of the cladding increases.
Math. 7
f.sub.xy(, F.sub.21, F.sub.22, F.sub.23, v) right side of Formula (3), [0075] the above is achieved by increasing the flow rate of BCl.sub.3 that lowers the refractive index of the glass.
[0076] Although the method in which the deviation of distribution in the wafer plane from a target value in the core processing is compensated for at the time of the upper cladding deposition has been described as an example, it is obvious that the deviation can be compensated for between other steps. For example, it is also possible to correct the distribution during the deposition of the core film in subsequent steps, for example, a photolithography step, a core processing step, and an upper cladding film formation step (step 8 of upper cladding film formation), and it is also possible to correct the distribution during the photolithography in the core processing step and the upper cladding film formation step. Furthermore, it is obvious that the distribution at the time of core deposition can be corrected by combining the photolithography step and the core processing.
[0077] Here, the center wavelength of the arrayed waveguide grating has been described as an example, but similarly, a crosstalk and polarization dependence may be corrected as optical characteristics, or an extinction wavelength and a loss of an optical switch by a Mach-Zehnder interferometer may be corrected. Furthermore, a plurality of indexes among them may be corrected.
[0078] Further, in correction of an oscillation wavelength of a distributed Bragg reflector (DBR) type semiconductor laser, an oscillation wavelength Ao of the Gragg grating is expressed as:
Math. 8
.sub.0=2n.sub.eff(Formula 7).
[0079] Thus, n.sub.eff can be corrected between steps in a similar manner. In the manufacturing step of the semiconductor laser, a refractive index of an epitaxially grown InP waveguide varies depending on composition. Deviation of the refractive index from the absolute value or the distribution in the wafer plane generated in the growth step may be corrected using the parameters W, F.sub.1, F.sub.2, L, P, and V at the time of etching as control values.
[0080] Although the FHD has been described above as an example, other methods such as chemical phase vapor deposition (CVD) and physical phase vapor deposition (PVD) may be used. In a method such as CVD and PVD, a glass film is collectively formed on the entire surface of the wafer without scanning a wafer position with a burner. In this case, as described above, the optical characteristics may be corrected on the basis of (Formula 1) for each apparatus calculated on the basis of the time-series values W(t), F1(t), F2(t), L(t), P(t), and V(t) of reading of each measurement apparatus of the manufacturing apparatus.
[0081] The present embodiment discloses an optical device manufacturing system including M (M is an integer of 2 or more) steps, the optical device manufacturing system including at least one measurement data processing unit configured to input and process measurement data from a manufacturing apparatus or a measurement apparatus in an i-th step and at least one control data processing unit configured to process the measurement data and output the processed measurement data to a manufacturing apparatus in a j-th step, where M is an integer of 2 or more, i is a natural number, j is an integer of 2 or more, and i<j. With this optical device manufacturing system, in manufacturing an optical waveguide component including a plurality of steps, in a certain step (j-th step), conditions of the step (j-th step) can be adjusted using the measurement data from the manufacturing apparatus or the measurement apparatus in a step (i-th step) before the step.
Example 2
[0082] In the present embodiment, correction of the upper cladding (overcladding) will be described.
[0083] In photolithography, there is a case where a target pattern width does not be a desired width due to causes such as in-plane distribution of a resist film thickness, distribution of a degree of development caused by deterioration of a developer due to a pattern density, and distribution of illuminance in a plane of an exposure apparatus. The deviation of the circuit pattern width from the target value due to these causes can be corrected in a subsequent step. In other words, by correcting the distribution of the effective refractive index in the film formation step (upper cladding deposition) 8 of the upper cladding 19 in the manufacturing step of the standard silica-based planar lightwave circuit in
[0084] In the present embodiment, the in-plane distribution of width dimension of the core pattern 18 is measured after the photoresist pattern 17 is removed in step 7 in
[0085]
[0086] As illustrated in
[0087]
[0088] In the present embodiment, the refractive index distribution of the upper cladding is adjusted on the basis of the refractive index distribution of the lower cladding and the core film, the film thickness of the core film, and the in-plane distribution such as an execution refractive index of the optical waveguide (calculated from the width of the core pattern). An optical circuit to be manufactured by a glass film forming method by a flame deposition method, the optical circuit being manufactured by a step of forming a lower cladding film, a step of forming a core film, and a step of forming a core pattern by photolithography, in which refractive index distribution of the lower cladding in a wafer plane, refractive index distribution of the core film, a film thickness, and in-plane distribution of an effective refractive index of an optical waveguide calculated from a width of the core pattern are fed forward to manufacturing of an upper cladding, so that there is an effect of reducing distribution (bias) of characteristics in the wafer plane of a silica-based planar lightwave circuit.
Example 3
[0089] The effective refractive index may be adjusted by providing in-plane distribution to the refractive index of the upper cladding so that the circuit characteristics in the wafer plane maintain desired values. As described above, it is possible to control the in-plane distribution of the in-plane upper cladding at the time of upper cladding deposition. Thus, the refractive index of the upper cladding may be controlled in order to obtain desired optical circuit characteristics.
[0090]
Another Example 1
[0091] As a method using a secondary measurement value, a method (referred to as selective exposure) described in detail below will be described. Here, an example of a silica-based planar lightwave circuit will be described.
[0092] In the first embodiment described above, an example has been described in which the measurement data processing unit predicts the optical characteristics from the measurement data of the control values of the manufacturing apparatus, and the control data processing unit generates the measurement values of the control data for controlling the manufacturing apparatus in the next and subsequent steps. However, as described below, it is also possible to separately acquire characteristic data of the wafer using the measurement apparatus for the wafer in process during each manufacturing step and perform correction using the manufacturing apparatus and method for performing correction.
[0093] Here, a method for manufacturing a silica-based planar lightwave circuit will be described with reference to a manufacturing step of an optical waveguide device illustrated in
[0094] A silica-based planar lightwave circuit is mechanically and chemically stable and is applied to a functional device such as a wavelength filter and an optical switch by an interferometer, and typical interference devices include an arrayed waveguide grating. The center wavelength of the arrayed waveguide grating is expressed as:
Math. 9
.sub.0=n.sub.effdL/m Formula (6).
[0095] The manufacturing stability depends on the effective refractive index n.sub.eff. By the way, in the FHD method to be used in the film formation of the core 13 in step 2 in
[0096] In the present embodiment, a method will be described in which the film thickness and the distribution of the refractive index of the wafer in the plane after the film formation of the core 13 are measured using a measurement apparatus, measurement data is acquired, and the distribution is corrected in the photolithography step in step 4. In general, an optical waveguide device to be manufactured on a wafer is manufactured by disposing a plurality of chips Shot 1 to 16 on the wafer. The core 13 has distribution in the refractive index and the film thickness in the wafer plane, and thus, each chip has optical characteristics reflecting the distribution. Thus, in the present embodiment, as illustrated in
[0097] First, after the film formation of a core in step 2, the film thickness and refractive index distribution of the core film are measured by a method such as ellipsometry. In the measurement, as illustrated in
Math. 10
n(x,y)=.sub.k=0.sup.K.sup.
[0098] Here, a.sub.k, b.sub.k, c.sub.k, and d.sub.k are coefficients and are obtained using a least squares method, or the like. In correcting the optical characteristics for each chip, n(x, y) and t(x, y) at each arrangement place are calculated using the above approximate formula. For example, in a case where an arrayed waveguide grating is assumed as an optical circuit type to be manufactured, n(x.sub.p, y.sub.p), t(x.sub.p, y.sub.p) in an arrayed waveguide portion (x.sub.p, y.sub.p) which is an interferometer portion is obtained.
[0099] Three effective refractive index correction methods will be described below.
[0100] In the first distribution correction method, patterns having different optical path length differences of the arrayed waveguides are arranged. The effective refractive index of the optical waveguide greatly depends on the refractive index of the core pattern 18 as described above, and thus, the refractive index of the bulk of the core may be mainly considered in the first order approximation. Thus, the effective refractive index n.sub.eff(x.sub.p, y.sub.p) at the arrayed waveguide position (x.sub.p, y.sub.p) of the effective refractive index is expressed as a function of n(x, y), t(x, y), w.sub.norm:
Math. 11
n.sub.eff(x.sub.p, y.sub.p)=f(n(x.sub.p, y.sub.p), t(x.sub.p, y.sub.p), w.sub.norm) Formula (9) [0101] by setting the nominal value of the finished width of the core pattern 18 as w.sub.norm. A function
Math. 12
f() [0102] is a function expressed by a Marquarry method, an imaginary axis propagation method, an equivalent refractive index method, or the like. Assuming that a target range of the center wavelength of the arrayed waveguide grating is set as .sub.norm with respect to n.sub.eff(x.sub.p, y.sub.p) obtained by the above formula, if the arrayed waveguide pattern has the optical path length difference dL between the arrays satisfying:
Math. 13
dL=m(.sub.norm)/n.sub.eff(x.sub.p, y.sub.p) Formula (10), [0103] an arrayed waveguide grating having a desired center wavelength can be obtained. Thus, as illustrated in
[0104] and perform exposure. In the present example, the arrayed waveguide grating pattern is selected, and exposure is performed.
[0105] By the way, as the plurality of circuit patterns to be prepared, it is preferable to overlap ranges of the optical path length differences dL of the arrayed waveguides to some extent in consideration of the influence of manufacturing fluctuation in a subsequent step. For example, in a case where d is a positive value, and a target center wavelength is expressed as follows:
Math. 15
.sub.0d.sub.0.sub.0+dFormula (12), [0106] an optical path length difference dL.sub.0 of the arrayed waveguide when a core film with ideal (nominal value) effective refractive index
[0108] In the second correction method, circuit patterns having different waveguide widths are arranged. As described above, the effective refractive index n.sub.eff(x.sub.p, y.sub.p) is a function of n(x.sub.p, y.sub.p), t(x.sub.p, y.sub.p) in (x.sub.p, y.sub.p) and the width W. Thus, as illustrated in
[0109] In the second correction method, optical characteristics other than the center wavelength described above can be corrected. In general, in a multiple beam interferometer such as an arrayed waveguide grating, a phase error between beam fluxes limits its definition. In other words, the phase error determines crosstalk performance of different wavelengths in optical communication. Thus, in a case where there is distribution of the effective refractive index inside a region where the arrayed waveguide exists, an arrayed waveguide grating having a width for correcting the deviation of the effective refractive index from the desired value may be prepared for each point (x.sub.pi, y.sub.pi) inside the region.
[0110]
[0111] A plurality of circuits having different arrayed waveguide distribution is arranged in the photomask. In the figure, as illustrated on the right side, arrayed waveguide gratings having different waveguide width distribution are arranged in a matrix of 33 for the arrayed waveguide numbers. The matrix is laid out such that, in the arrayed waveguide gratings in the left column, widths of arrayed waveguides having younger numbers are wider, in the arrayed waveguide gratings in the right column, widths of arrayed waveguides of older numbers are wider, and in the arrayed waveguide gratings in the middle column, a waveguide at the center of the arrayed waveguide is wide and has second-order distribution. Furthermore, in the upper row, an absolute value of the gradient of the distribution is large, in the middle row, the absolute value is moderate, and in the lower row, the absolute value is small. Here, a combination of 33 has been described, and a combination in which the gradient of the thickness of the arrayed waveguide is first order or second order has been described. However, a combination having thickness distribution expressed by a general polynomial may be arranged in the photomask.
[0112] In the third distribution correction method, the distribution is corrected by adjusting an exposure period. Generally, the width of the waveguide can be changed by changing the exposure period, a development period, and concentration of a developer. Thus, the exposure period may be changed for each arrayed waveguide grating circuit present at each point (x.sub.p, y.sub.p). In addition, in a case where it is desired to change the width of the waveguide over the entire wafer, for example, in a case where the core film is formed to have a large or small refractive index over the entire wafer, it is also possible to adjust the width of the waveguide over the entire wafer by changing the concentration of the developer or the development period.
[0113] Although the arrayed waveguide grating has been described above as an example, the present invention is also applicable to an interferometer typified by a matrix switch using two-beam interference such as a Mach-Zehnder interferometer or a filter such as a Bragg diffraction grating. In addition, in a spot size converter, or the like, to be used to reduce a connection loss between an optical waveguide and an optical fiber, a field system of an optical wave affects characteristics thereof. The effective refractive index of the field system is one of the parameters, and thus, it is clear that the above method can be applied.
[0114] The refractive index distribution of the upper cladding 11 in step 8 of deposition of the upper cladding 19 which is the subsequent step can be adjusted using the measurement data of the refractive index distribution in the wafer plane of the lower cladding 19, the refractive index distribution of the core film, and/or the film thickness of the core film, and the in-plane distribution of the effective refractive index of the optical waveguide calculated from the width of the core pattern 18.