Patent Application
20230327641
The present invention relates to an acoustic wave device.
Hitherto, acoustic wave devices are widely used in filters of mobile phones, and the like. International Publication No. 2018/151147 describes an example of the acoustic wave devices. In the acoustic wave device, an interdigital transducer electrode is provided on a multilayer substrate. In the multilayer substrate, a silicon substrate, a silicon oxide layer, a silicon nitride layer, and a piezoelectric substrate are laminated in this order. The plane orientation of the silicon substrate is set to (100), (110), or (111). Thus, a bulk wave spurious is reduced or prevented.
However, even when the plane orientation of the silicon substrate is set to (100), (110), or (111) as in the case of the acoustic wave device described in International Publication No. 2018/151147, it is difficult to sufficiently reduce ripple caused by higher-order modes.
Preferred embodiments of the present invention provide acoustic wave devices each capable of reducing higher-order modes in a wide band.
An acoustic wave device according to a preferred embodiment of the present invention includes a silicon substrate, a polysilicon layer provided on the silicon substrate, a silicon oxide layer directly or indirectly provided on the polysilicon layer, a piezoelectric layer directly or indirectly provided on the silicon oxide layer, and an interdigital transducer electrode provided on the piezoelectric layer. A plane orientation of the silicon substrate is any one of (100), (110), and (111). Where a wave length that is defined by an electrode finger pitch of the interdigital transducer electrode is λ, a thickness of the piezoelectric layer is less than or equal to about 1λ.
With the acoustic wave devices according to preferred embodiments of the present invention, higher-order modes are reduced in a wide band.
The above and other elements, features, steps, characteristics and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments with reference to the attached drawings.
Hereinafter, the present invention will be clarified by describing specific preferred embodiments of the present invention with reference to the drawings.
It should be noted that each of the preferred embodiments described in the specification is illustrative and that partial replacements or combinations of components are possible among different preferred embodiments.
As shown in
In the present preferred embodiment, the silicon substrate 2 is a silicon monocrystal substrate. The plane orientation of the silicon substrate 2 is (111). Of course, the plane orientation of the silicon substrate 2 may be any one of (100), (110), and (111).
Silicon oxides in the silicon oxide layer 5 are expressed by SiOx. x is a positive number. In the present preferred embodiment, the silicon oxide layer 5 is an SiO2 layer. Of course, x is not limited to two.
In the present preferred embodiment, the piezoelectric layer 7 is a lithium tantalate layer with a cut angle of 40°. Of course, the cut angle and material of the piezoelectric layer 7 are not limited thereto. For example, lithium niobate may be used as the material of the piezoelectric layer 7.
The interdigital transducer electrode 8 is provided on the piezoelectric layer 7. Acoustic waves are excited by applying an alternating-current voltage to the interdigital transducer electrode 8. As shown in
As shown in
The interdigital transducer electrode 8 includes a multilayer metal film. More specifically, in the multilayer metal film, a Ti layer, an AlCu layer, and a Ti layer are laminated in this order. The reflector 14 and the reflector 15 are also made of a material similar to that of the interdigital transducer electrode 8. Of course, the materials of the interdigital transducer electrode 8, the reflector 14, and the reflector 15 are not limited thereto. Alternatively, the interdigital transducer electrode 8, the reflector 14, and the reflector 15 may be made up of a single-layer metal film.
Where a wave length that is defined by the electrode finger pitch of the interdigital transducer electrode 8 is A, the thickness of the piezoelectric layer 7 is less than or equal to about 1λ, for example. The electrode finger pitch is an electrode finger center-to-center distance between adjacent electrode fingers. The electrode finger pitch is, specifically, a distance connecting central points of adjacent electrode fingers in the acoustic wave propagation direction, that is, the X direction. When the electrode finger center-to-center distance is not constant, the electrode finger pitch is assumed as an average value of the electrode finger center-to-center distance.
A protective film may be provided on the piezoelectric layer 7 so as to cover the interdigital transducer electrode 8. In this case, the interdigital transducer electrode 8 is less likely to break. An appropriate dielectric may be used as the protective film. When, for example, a silicon oxide is used as the protective film, frequency-temperature characteristics (TCF) are increased. When a silicon nitride is used as the protective film, frequency is easily adjusted by adjusting the thickness of the protective film. Of course, the protective film does not need to be provided.
Some of the unique features of the present preferred embodiment are that, in the multilayer substrate 9, the silicon substrate 2, the polysilicon layer 3, the silicon oxide layer 5, and the piezoelectric layer 7 are laminated, and the thickness of the piezoelectric layer 7 is less than or equal to about 1λ, for example. Thus, higher-order modes are reduced in a wide band. The details of the advantageous effects will be described below together with the definition and the like of crystallographic axes and plane orientation.
As shown in
As described above, the plane orientation of the silicon substrate 2 according to the present preferred embodiment is (111). The fact that the plane orientation is (111) means that a substrate or a layer is cut along the (111) plane orthogonal to the crystallographic axes represented by Miller indices [111] in the crystal structure of silicon having a diamond structure. The (111) plane is a plane shown in
On one hand, the fact that the plane orientation is (100) means that a substrate or a layer is cut along the (100) plane orthogonal to the crystallographic axes represented by Miller indices [100] in the crystal structure of silicon having a diamond structure. There is a four-fold symmetry in the (100) plane, and an equivalent crystal structure is obtained by 90° rotation. The (100) plane is a plane shown in
On the other hand, the fact that the plane orientation is (110) means that a substrate or a layer is cut along the (110) plane orthogonal to the crystallographic axes represented by Miller indices [110] in the crystal structure of silicon having a diamond structure. There is a two-fold symmetry in the (110) plane, and an equivalent crystal structure is obtained by 180° rotation. The (110) plane is a plane shown in
Here, the present preferred embodiment and a first comparative example are compared with each other to demonstrate that higher-order modes are reduced in a wide band according to the present preferred embodiment. The first comparative example differs from the present preferred embodiment in that, in the multilayer substrate, a silicon nitride layer is laminated instead of the polysilicon layer.
As indicated by the arrow A in
The reason will be described by using a first reference example and a second reference example. In the first reference example, a multilayer substrate is a multilayer body of a silicon substrate, a silicon oxide layer, and a piezoelectric layer. The plane orientation of the silicon substrate in the first reference example is (111). In the second reference example, a multilayer substrate is a multilayer body of a polysilicon substrate, a silicon oxide layer, and a piezoelectric layer. The piezoelectric layer according to the first reference example and the piezoelectric layer according to the second reference example are lithium tantalate layers.
As indicated by the arrow A in
On the other hand, as indicated by the arrow B in
In contrast, in the first preferred embodiment, the multilayer substrate 9 includes both the silicon substrate 2 and the polysilicon layer 3, and the plane orientation of the silicon substrate 2 is (111). In addition, the thickness of the piezoelectric layer 7 is less than or equal to about 1λ. With this configuration, as shown in
Incidentally, in the first preferred embodiment, the polysilicon layer 3 and the silicon oxide layer 5 are provided between the silicon substrate 2 and the piezoelectric layer 7. The inventor of the present application discovered that, even in such a case, higher-order modes were further reliably reduced by defining the relationship between the plane orientation of the silicon substrate 2 and the crystallographic axes of the piezoelectric layer 7. Here, a directional vector that is defined in accordance with the direction of crystallographic axes of the piezoelectric layer 7 is assumed as k. An angle that is defined in accordance with the relationship between the crystallographic axes of the piezoelectric layer 7 and the plane orientation of the silicon substrate 2 is assumed as α. The directional vector k is any one of three vectors k111, k110, and k100. The angle α is any one of three angles α111, α110, and α100. k111 and α111, k110 and α110, and k100 and α100 respectively correspond to the plane orientations (111), (110), and (100). Hereinafter, the details of the directional vector k and the angle α will be described.
Here, as shown in
As shown in
On one hand, in a silicon substrate of which the plane orientation is (110), a directional vector obtained by projecting the ZP-axis onto the (110) plane of the silicon substrate is assumed as kilo. The angle α110 is an angle between the directional vector kilo and the [001] direction of silicon that is a component of the silicon substrate. From the symmetry of silicon, the [001] direction, a [100] direction, and a [010] direction are equivalent.
On the other hand, in a silicon substrate of which the plane orientation is (100), a directional vector obtained by projecting the ZP-axis onto the (100) plane of the silicon substrate is assumed as k100. The angle α100 is an angle between the directional vector k100 and the [001] direction of silicon that is a component of the silicon substrate.
Regardless of whether the silicon substrate is laminated directly on the piezoelectric layer or laminated indirectly on the piezoelectric layer with another layer interposed therebetween, the definition of the directional vector k and the angle α is the same.
As described above, the plane orientation of the silicon substrate 2 is not limited to (111). The plane orientation of the silicon substrate 2 may be any one of (100), (110), and (111). The angle α is any one of three angles, that is, the angle α100, the angle α110, and the angle α111. More specifically, when the plane orientation of the silicon substrate 2 is (100), the angle α is the angle α100. When the plane orientation of the silicon substrate 2 is (110), the angle α is the angle α110. When the plane orientation of the silicon substrate 2 is (111), the angle α is the angle α111.
Here, an example of the phase characteristics of an acoustic wave device that has a similar configuration to the first preferred embodiment and in which the angle α111 is defined will be described. The design parameters of the acoustic wave device are as follows.
As shown in
Incidentally, as shown in
The present preferred embodiment differs from the first preferred embodiment in that a silicon nitride layer 26 is provided between the silicon oxide layer 5 and the piezoelectric layer 7. The present preferred embodiment further differs from the first preferred embodiment in that a protective film 29 is provided on the piezoelectric layer 7 so as to cover the interdigital transducer electrode 8. Other than the above points, the acoustic wave device according to the present preferred embodiment has a similar configuration to the acoustic wave device 1 according to the first preferred embodiment.
Here, an example of the phase characteristics of an acoustic wave device that has a similar configuration to the present preferred embodiment and in which the angle α111 is defined will be described. The design parameters of the acoustic wave device are similar to those of the acoustic wave device according to the first preferred embodiment in which the phase characteristics shown in
As shown in
The present preferred embodiment differs from the first preferred embodiment in that the silicon nitride layer 26 is provided between the polysilicon layer 3 and the silicon oxide layer 5. The present preferred embodiment further differs from the first preferred embodiment in that the protective film 29 is provided on the piezoelectric layer 7 so as to cover the interdigital transducer electrode 8. Other than the above points, the acoustic wave device according to the present preferred embodiment has a similar configuration to the acoustic wave device 1 according to the first preferred embodiment.
Here, an example of the phase characteristics of an acoustic wave device that has a similar configuration to the present preferred embodiment and in which the angle α111 is defined will be described. The design parameters of the acoustic wave device are similar to those of the acoustic wave device according to the first preferred embodiment in which the phase characteristics shown in
As shown in
The present preferred embodiment differs from the second preferred embodiment in that a titanium oxide layer 36 is provided between the silicon oxide layer 5 and the piezoelectric layer 7. A multilayer substrate 39 is a multilayer body of the silicon substrate 2, the polysilicon layer 3, the silicon oxide layer 5, the titanium oxide layer 36, and the piezoelectric layer 7. Other than the above points, the acoustic wave device according to the present preferred embodiment has a similar configuration to the acoustic wave device according to the second preferred embodiment.
Here, an example of the phase characteristics of an acoustic wave device that has a similar configuration to the present preferred embodiment and in which the angle α111 is defined will be described. The design parameters of the acoustic wave device are similar to those of the acoustic wave device according to the second preferred embodiment in which the phase characteristics shown in
As shown in
Here, in each of the acoustic wave devices respectively having the multilayer substrates according to the first, second, and fourth preferred embodiments, the phase of a higher-order mode was measured while the parameters such as the angle α were changed. Thus, conditions in which the phase of a higher-order mode was reduced to less than or equal to about −70[deg.] or less than or equal to about −80[deg.] were obtained. In each of the acoustic wave devices, the protective film 29 shown in
In the configuration of the first preferred embodiment shown in
There is a four-fold symmetry in the (100) plane of a silicon substrate, and an equivalent crystal structure is obtained by 90° rotation. Thus, when the plane orientation of the silicon substrate 2 is (100), the angle α100 is set to α100=α100+90×n. n is an integer (0, ±1, ±2, . . . ).
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, the equation 1 that was a relational expression between the parameters and the phase of a higher-order mode was derived. The angle α is assumed as Si_psi[deg.], the thickness of the piezoelectric layer 7 is assumed as t_LT[λ], the thickness of the silicon oxide layer 5 is assumed as t_SiO2[λ], the thickness of the polysilicon layer 3 is assumed as t_Si2[λ], and the phase of a higher-order mode is assumed as y[deg.]. In the equation 1, Si_psi[deg.] is the angle α100. In the equations in the specification, unit [deg.] represents the same meaning as unit [°].
y[deg.]=(−72.1492542241195)+0.627588217157224×(Si_psi[deg]−21.7083333333333)+(−1.93347870945237)×(t_Si2[λ]−0.4525)+72.3846086764674×(t_LT[λ]−0.160833333333333)+(−67.3219584197057)×(t_SiO2[λ]−0.16625)+0.0000655654050315201×((Si_psi[deg.]−21.7083333333333)×(Si_psi[deg.]−21.7083333333333)−25.2065972222222)+(−2.34857364418332)×((Si_psi[deg.]−21.7083333333333)×((t_Si2[λ]−0.4525))+37.0048979126418×((t_Si2[λ]−0.4525)×((t_Si2[λ]−0.4525)−0.0360354166666667)+7.0771357128953×((Si_psi[deg.]−21.7083333333333)×((t_LT[λ]−0.160833333333333))+(−10.057857939681)×((t_Si2[λ]−0.4525)×(t_LT[λ]−0.160833333333333))+1.50716777611893×((Si_psi[deg.]−21.7083333333333)×(t_SiO2[λ]−0.16625))+426.86632497558×(((t_Si2[λ]−0.4525)×((t_SiO2[λ])−0.16625))+925.280868396996×((t_LT[λ]−0.160833333333333)×(t_SiO2[λ]−0.16625))+988.798729044457×((t_SiO2[λ]−0.16625)×(t_SiO2[λ]−0.16625)−0.000871354166666668) Equation 1
Si_psi[deg.], t_LT[λ], t_SiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 1 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70 [deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In the configuration of the first preferred embodiment, the plane orientation of the silicon substrate 2 was set to (110), and the phase of a higher-order mode was measured while the parameters were changed. The design parameters and the variable ranges of the design parameters were similar to those when the equation 1 was derived except the angle α.
There is a two-fold symmetry in the (110) plane of a silicon substrate, and an equivalent crystal structure is obtained by 180° rotation. Thus, when the plane orientation of the silicon substrate 2 is (110), the angle α110 is set to α110=α110+180×n. n is an integer (0, ±1, 2, . . . ).
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, the equation 2 that was a relational expression between the parameters and the phase of a higher-order mode was derived. In the equation 2, Si_psi [deg.] is the angle α110.
y[deg.]=(78.1876454049157)+(−0.182894322081067)×(Si_psi[deg.]−28.1088082901554)+6.18390256271178×(t_Si2[λ]−0.39961139896373)+116.669335737855×(t_LT[λ]−0.169948186528498)+10.3573467893808×(t_SiO2[λ]−0.144041450777202)+0.0110735958981267×((Si_psi[deg.]−28.1088082901554)×(Si_psi[deg.]−28.1088082901554)−189.946709978791)+(−0.246858144090431)×((Si_psi[deg.]−28.1088082901554)×(t_Si2[λ]−0.39961139896373)+22.031016276383×((t_Si2[λ]−0.39961139896373)×(t_Si2[λ]−0.39961139896373)−0.0484389681602191)+(−X.0545756011518778)×((Si_psi[deg.]−28.1088082901554)×(t_LT[λ]−0.169948186528498))+(−32.427969747408)×((t_Si2[λ]−0.39961139896373)×((t_LT[λ]−0.169948186528498))+(−2.62164982026802)×((Si_psi[deg.]−28.1088082901554)×(t_SiO2[λ]−0.144041450777202))+(−112.759047075747)×((t_Si2[λ]−0.39961139896373)×((t_SiO2[λ]−0.144041450777202))+(−604.832727678973)×((t_LT[λ]−0.169948186528498)×((t_SiO2[λ]−0.144041450777202))+326.415587634024×((t_SiO2[λ]−0.144041450777202)×((t_SiO2[λ]−0.144041450777202)−0.00120154232328385) Equation 2
Si_psi[deg.], t_LT[λ], t_SiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 2 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70 [deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In the configuration of the first preferred embodiment, the plane orientation of the silicon substrate 2 was set to (111), and the phase of a higher-order mode was measured while the parameters were changed. The design parameters and the variable ranges of the design parameters were similar to those when the equation 1 was derived except the angle α.
There is a three-fold symmetry in the (111) plane of a silicon substrate, and an equivalent crystal structure is obtained by 120° rotation. Thus, when the plane orientation of the silicon substrate 2 is (111), the angle α111 is set to α111=α111+120×n. n is an integer (0, ±1, 2, . . . ).
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, the equation 3 that was a relational expression between the parameters and the phase of a higher-order mode was derived. In the equation 3, Si_psi [deg.] is the angle α111.
y[deg.]=(77.9109394183719)+(−0.0492368384201428)×(Si_psi[deg.]−45.2068126520681)+0.525124426223863×(t_Si2[λ]−0.426216545012165)+117.400884406373×(t_LT[λ]−0.174330900243311)+(−2.62484877324049)×(t_SiO2[λ]−0.15139902676399)+0.00307563131201403×((Si_psi[deg.]−45.2068126520681)×(Si_psi[deg.]−45.2068126520681)−182.925598356629)+(−0.0261801752592506)×((Si_psi[deg.]−45.2068126520681)×(t_Si2[λ]−0.426216545012165))+23.8987529211434×((t_Si2[λ]−0.426216545012165)×(t_Si2[λ]−0.426216545012165)−0.0481296027432942)+1.52616542281399×((Si_psi[deg.]−45.2068126520681))×(t_LT[λ]−0.174330900243311))+(−129.002027283367)×((t_Si2[λ]−0.426216545012165)×((t_LT[λ]−0.174330900243311))+(−1.22761778451819)×((Si_psi[deg.]−45.2068126520681)×((t_SiO2[λ]−0.15139902676399))+(−42.6041784800926)×((t_Si2[λ]−0.426216545012165)×(t_SiO2[λ]−0.15139902676399))+(−468.84116493048)×((t_LT[λ]−0.174330900243311)×(t_SiO2[λ]−0.15139902676399))+(−8.20635607220859)×((t_SiO2[λ]−0.15139902676399)×(t_SiO2[λ]−0.15139902676399)−0.0012830183932134) Equation 3
Si_psi[deg.], t_LT[λ], t_SiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 3 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70 [deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In addition, conditions in which the phase of a higher-order mode was reduced to less than or equal to about −80[deg.] were obtained in each of a case where the plane orientation of the silicon substrate 2 was (100), a case where the plane orientation of the silicon substrate 2 was (110), and a case where the plane orientation of the silicon substrate 2 was (111). In these cases, the relational expression between the parameters and a higher-order mode differs from the equation 1, the equation 2, or the equation 3. More specifically, to obtain the conditions, an equation 4, an equation 5, and an equation 6 were derived while the parameters were changed within the range in which the phase of a higher-order mode was greater than or equal to −90[deg.] and less than or equal to about −70[deg.].
When the plane orientation of the silicon substrate 2 is (100), the equation 4 was derived as described above.
y[deg.]=(−75.3156232479379)+0.63547968892276×(Si_psi[deg]−20.9090909090909)+(−2.02838142816204)×(t_Si2[λ]−0.439772727272727)+90.1874317877843×(t_LT[λ]−0.151136363636364)+(−71.2997621594781)×(t_SiO2[λ]−0.171590909090909)+0.108397383766316×((Si_psi[deg.]−20.9090909090909)×(Si_psi[deg.]−20.9090909090909)−13.9462809917355)+(−3.76982864951476)×((Si_psi[deg.]−20.9090909090909)×(t_Si2[λ]−0.439772727272727))+37.3378798744213×((t_Si2[λ]−0.439772727272727)×(t_Si2[λ]−0.439772727272727)−0.0358613119834711)+(−23.7942425679855)×((Si_psi[deg.]−20.9090909090909)×(t_SiO2[λ]−0.171590909090909))+462.018905986831×((t_Si2[λ])−0.439772727272727)×(t_SiO2[λ]−0.171590909090909))+1223.13016730739×(((t_SiO2[λ]−0.171590909090909)×(t_SiO2[λ]−0.171590909090909)−0.000641787190082645) Equation 4
Si_psi[deg.], t_LT[λ], t_SiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 4 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
When the plane orientation of the silicon substrate 2 is (110), the equation 5 was derived as described above.
y[deg.]=(81.4138269086073)+(−0.100532115186538)×(Si_psi[deg.]−29.1379310344828)+0.845708574223377×(t_Si2[λ]−0.385689655172414)+87.6682874459356×(t_LT[λ]−0.166724137931034)+(−0.137780433371857)×(t_SiO2[λ]−0.145)+0.00337749443465239×((Si_psi[deg.]−29.1379310344828)×(Si_psi[deg.]−29.1379310344828)−127.877526753864)+(−0.116548121456389)×((Si_psi[deg.]−29.1379310344828)×(t_Si2[λ]−0.385689655172414))+11.8893452691356×((t_Si2[λ]−0.385689655172414)×(t_Si2[λ]−0.385689655172414)−0.0448900416171225)+0.333200244545922×((Si_psi[deg.]−29.1379310344828)×(t_LT[λ]−0.166724137931034))+55.2630600466406×((t_Si2[λ]−0.385689655172414)×(t_LT[λ]−0.166724137931034))+(−0.296582437395607)×((Si_psi[deg.]−29.1379310344828)×(t_SiO2[λ]−0.145))+(−67.4578937630203)×((t_Si2[λ]−0.385689655172414)×(t_SiO2[λ]−0.145))+(−376.292315976729)×((t_LT[λ])−0.166724137931034)×(t_SiO2[λ]−0.145))+48.6290874437329×((t_SiO2[λ]−0.145)×((t_SiO2[λ]−0.145)−0.00120775862068966) Equation 5
Si_psi[deg.], t_LT[λ], t_SiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 5 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
When the plane orientation of the silicon substrate 2 is (111), the equation 6 was derived as described above.
y[deg.]=(−79.8924944284088)+0.033261334588906×(Si_psi[deg.]−39.3173431734317)+3.93783296791666×(t_Si2[λ]−0.416974169741698)+80.6680077909648×(t_LT[λ]−0.17140221402214)+13.2276438709535×(t_SiO2[λ]−0.148431734317343)+(−0.00907764275073328)×((Si_psi[deg.]−39.3173431734317)×(Si_psi[deg.]−39.3173431734317)−21.2129464468077)+0.000540095694459618×((Si_psi[deg.]−39.3173431734317)×(t_Si2[λ]−0.416974169741698))+5.79698263968963×((t_Si2[λ]−0.416974169741698)×(t_Si2[λ]−0.416974169741698)−0.0400439808826132)+(−0.136650035849863)×((Si_psi[deg.]−39.3173431734317)×(t_LT[λ]−0.17140221402214))+(−20.3328823416631)×((t_Si2[λ]−0.416974169741698)×(t_LT[λ]−0.17140221402214))+(−2.22480760136672)×((Si_psi[deg.]−39.3173431734317)×(t_SiO2[λ]−0.148431734317343))+(−13.0975601885972)×((t_Si2[λ]−0.416974169741698)×(t_SiO2[λ]−0.148431734317343))+(−511.743077543129)×((t_LT[λ]−0.17140221402214)×(t_SiO2[λ]−0.148431734317343))+137.213612130809×((t_SiO2[λ]−0.148431734317343)×(t_SiO2[λ]−0.148431734317343)−0.00135593537669694) Equation 6
Si_psi[deg.], t_LT[λ], t_SiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 6 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
Subsequently, in the configuration having a multilayer substrate similar to that of the second preferred embodiment shown in
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, an equation 7 that was a relational expression between the parameters and the phase of a higher-order mode was derived. The thickness of the silicon nitride layer 26 is set to t_SiN[λ]. In the equation 7, Si_psi[deg.] is the angle α100.
y[deg.]=(−67.7782730918073)+0.0667732718475358×(Si_psi[deg.]−25.6259314456036)+(−6.71256568714434)×(t_Si2[λ]−0.426192250372578)+177.355083873051×(t_LT[λ]−0.16602086438151)+(−64.7093491078986)×(t_SiN[λ]−0.0465201192250378)+1.0890884781807×(t_SiO2[λ]−0.155793591654245)+0.000179985859065592×(Si_psi[deg.]−25.6259314456036)×(Si_psi[deg.]−25.6259314456036)−130.38317256758)+(−0.329348427439478)×((Si_psi[deg.]−25.6259314456036)×(t_Si2[λ]−0.426192250372578))+(−33.1084698932093)×((t_Si2[λ]−0.426192250372578)×(t_Si2[λ]−0.426192250372578)−0.0504801359160987)+1.52146775761601×((Si_psi[deg.]−25.6259314456036)×(t_LT[λ]−0.16602086438151))+14.59741625744683×((t_Si2[λ]−0.426192250372578)×(t_LT[λ]−0.16602086438151))+0×((t_LT[λ]−0.16602086438151)×(t_LT[λ]−0.16602086438151)−0.000544375123544922)+(−4.94058423048505)×((Si_psi[deg.]−25.6259314456036)×((t_SiN[λ]−0.0465201192250378))+138.799085167873×((t_Si2[λ]−0.426192250372578)×(t_SiN[λ]−0.0465201192250378))+1746.7447498235×((t_LT[λ]−0.16602086438151)×(t_SiN[λ]−0.0465201192250378))+2167.04168685901×((t_SiN[λ]−0.0465201192250378)×(t_SiN[λ]−0.0465201192250378)−0.000465274930537198)+(−0.931372972560935)×((Si_psi[deg.]−25.6259314456036)×(t_SiO2[λ]−0.155793591654245))+(−79.4377446578721)×((t_Si2[λ]−0.426192250372578)×(t_SiO2[λ]−0.155793591654245))+(−86.9697272546991)×((t_LT[λ]−0.16602086438151)×(t_SiO2[λ]−0.155793591654245))+1966.46522796354×((t_SiN[λ]−0.0465201192250378)×(t_SiO2[λ]−0.155793591654245))+169.040605778099×((t_SiO2[λ]−0.155793591654245)×(t_SiO2[λ]−0.155793591654245)-0.00164210493657841) Equation 7
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_SiN[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 7 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70[deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In the configuration having a multilayer substrate similar to that of the second preferred embodiment, the plane orientation of the silicon substrate 2 was set to (110), and the phase of a higher-order mode was measured while the parameters were changed. The design parameters and the variable ranges of the design parameters were similar to those when the equation 7 was derived except the angle α.
α110: changed in increments of 10° in the range greater than or equal to 0° and less than or equal to 90°
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, an equation 8 that was a relational expression between the parameters and the phase of a higher-order mode was derived. In the equation 8, Si_psi [deg.] is the angle α110.
y[deg.]=(−75.0174122935603)+(−0.00810936153116664)×(Si_psi[deg.]−42.0340722495895)+1.98135617767495×(t_Si2[λ]−0.385026683087027)+143.173790020328×(t_LT[λ]−0.17306034482757)+16.4148627328736×(t_SiN[λ]−0.04207922824302)+50.4122771861205×(t_SiO2[λ])−0.144909688013139)+0.00619821963137332×((Si_psi[deg.]−42.0340722495895)×(Si_psi[deg.]−42.0340722495895)−514.232829229589)+0.020323078287526×((Si_psi[deg.]−42.0340722495895)×(t_Si2[λ]−0.385026683087027))+1.15443318031007×((t_Si2[λ]−0.385026683087027)×(t_Si2[λ]−0.385026683087027)−0.0477966331139576)+0.472662465737381×((Si_psi[deg.]−42.0340722495895)×(t_LT[λ]−0.17306034482757))+(−105.2996012677)×((t_Si2[λ]−0.385026683087027)×(t_LT[λ]−0.17306034482757))+(−1.29517116632701)×((Si_psi[deg.]−42.0340722495895)×(t_SiN[λ]−0.04207922824302))+(−26.1801037669841)×((t_Si2[λ]−0.385026683087027)×(t_SiN[λ])−0.04207922824302))+168.1334353773×((t_LT[λ]−0.17306034482757)×(t_SiN[λ]−0.04207922824302))+2120.76431830662×((t_SiN[λ]−0.04207922824302)×(t_SiN[λ]−0.04207922824302)−0.000508197335364991)+(−0.687562974959064)×((Si_psi[deg.]−42.0340722495895)×(t_SiO2[λ]−0.144909688013139))+15.3482271106745×((t_Si2[λ]−0.385026683087027)×(t_SiO2[λ]−0.144909688013139))+(−358.720795782422)×((t_LT[λ]−0.17306034482757)×(t_SiO2[λ]−0.144909688013139))+1062.30534015379×((t_SiN[λ]−0.04207922824302)×(t_SiO2[λ]−0.144909688013139))+248.937429294479×((t_SiO2[λ]−0.144909688013139)×(t_SiO2[λ]−0.144909688013139)−0.00162330875671721) Equation 8
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_SiN[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 8 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70[deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In the configuration having a multilayer substrate similar to that of the second preferred embodiment, the plane orientation of the silicon substrate 2 was set to (111), and the phase of a higher-order mode was measured while the parameters were changed. The design parameters and the variable ranges of the design parameters were similar to those when the equation 7 was derived except the angle α. α111: changed in increments of 5° in the range greater than or equal to 0° and less than or equal to 60°
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, an equation 9 that was a relational expression between the parameters and the phase of a higher-order mode was derived. In the equation 9, Si_psi [deg.] is the angle α111.
y[deg.]=(−77.5405307874512)+0.00496521862619995×(Si_psi[deg.]−44.3479880774963)+(−3.07514699616305)×(t_Si2[λ]−0.395628415300543)+115.725430166886×(t_LT[λ]−0.173919523099848)+75.6109484741613×(t_SiN[λ]−0.0387729756582212)+29.9143205043822×(t_SiO2[λ]−0.145404868355688)+0.00452378218877289×((Si_psi[deg.]−44.3479880774963)×(Si_psi[deg.]−44.3479880774963)−147.519490487682)+(−0.127045459018856)×((Si_psi[deg.]−44.3479880774963)×(t_Si2[λ]−0.395628415300543))+10.135015813019×((t_Si2[λ]−0.395628415300543)×(t_Si2[λ]−0.395628415300543)−0.0544331992323139)+0.267609205446981×((Si_psi[deg.]−44.3479880774963)×(t_LT[λ]−0.173919523099848))+(−151.966315117959)×((t_Si2[λ]−0.395628415300543)×(t_LT[λ]−0.173919523099848))+1.1818941610908×((Si_psi[deg.]−44.3479880774963)×(t_SiN[λ]−0.0387729756582212))+(−19.0228093275549)×((t_Si2[λ]−0.395628415300543)×(t_SiN[λ]−0.0387729756582212))+25.2693219567039×((t_LT[λ]−0.173919523099848)×(t_SiN[λ])−0.0387729756582212))+1545.52112794945×((t_SiN[λ]−0.0387729756582212)×(t_SiN[λ]−0.0387729756582212)−0.000519520243356094)+(−0.39161225199813)×((Si_psi[deg.]−44.3479880774963)×(t_SiO2[λ]−0.145404868355688))+22.0391330835907×((t_Si2[λ]−0.395628415300543)×(t_SiO2[λ]−0.145404868355688))+(−297.764935637906)×((t_LT[λ]−0.173919523099848)×(t_SiO2[λ]−0.145404868355688))+982.324171494675×((t_SiN[λ]−0.0387729756582212)×(t_SiO2[λ]−0.145404868355688))+420.570041600812×((t_SiO2[λ]−0.145404868355688)×(t_SiO2[λ]−0.145404868355688)−0.00124068307615005) Equation 9
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_SiN[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 9 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70[deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In addition, conditions in which the phase of a higher-order mode was reduced to less than or equal to about −80[deg.] were obtained in each of a case where the plane orientation of the silicon substrate 2 was (100), a case where the plane orientation of the silicon substrate 2 was (110), and a case where the plane orientation of the silicon substrate 2 was (111). More specifically, to obtain the conditions, an equation 10, an equation 11, and an equation 12 were derived while the parameters were changed within the range in which the phase of a higher-order mode was greater than or equal to −90[deg.] and less than or equal to about −70[deg.].
When the plane orientation of the silicon substrate 2 is (100), the equation 10 was derived as described above.
y[deg.]=(−78.3557914112162)+(−0.00785147182473267)×(Si_psi[deg.]−24.9802110817942)+(−1.32878861667394)×(t_Si2[λ]−0.429221635883905)+(−41.7937386863014)×(t_LT[λ]−0.150923482849606)+35.6722090195008×(t_SiN[λ]−0.0500263852242746)+18.7743164986736×(t_SiO2[λ]−0.145646437994723)+(−0.000765722206063909)×((Si_psi[deg.]−24.9802110817942)×(Si_psi[deg.]−24.9802110817942)−153.396706024045)+(−0.0463379291760545)×((Si_psi[deg.]−24.9802110817942)×(t_Si2[λ]−0.429221635883905))+(−17.7293821535291)×((t_Si2[λ]−0.429221635883905)×(t_Si2[λ]−0.429221635883905)−0.0593208981070862)+(−1.3441873888418)×((Si_psi[deg.]−24.9802110817942)×(t_LT[λ]−0.150923482849606))+(−417.636233521175)×((t_Si2[λ]−0.429221635883905)×(t_LT[λ]−0.150923482849606))+(−0.487351707638102)×((Si_psi[deg.]−24.9802110817942)×(t_SiN[λ]−0.0500263852242746))+(−25.3025544220714)×((t_Si2[λ]−0.429221635883905)×(t_SiN[λ]−0.0500263852242746))+1666.3381560311×((t_LT[λ]−0.150923482849606)×(t_SiN[λ]−0.0500263852242746))+233.559062145034×((t_SiN[λ]−0.0500263852242746)×(t_SiN[λ]−0.0500263852242746)−0.000389115398806747)+(−0.148028298904273)×((Si_psi[deg.]−24.9802110817942)×(t_SiO2[λ]−0.145646437994723))+(−63.9722673973965)×((t_Si×[λ]−0.429221635883905)×(t_SiO2[λ]−0.145646437994723))+1197.10044921435×((t_LT[λ]−0.150923482849606)×(t_SiO2[AX]−0.145646437994723))+450.45656510444×((t_SiN[λ]−0.0500263852242746)×(t_SiO2[AX])−0.145646437994723))+(−37.7857111587959)×((t_SiO2[λ]−0.145646437994723)×(t_SiO2[AX]−0.145646437994723)−0.0017158749939084) Equation 10
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_SiN[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 10 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
When the plane orientation of the silicon substrate 2 is (110), the equation 11 was derived as described above.
y[deg.]=(−79.9409825800918)+0.00367175250563163×(Si_psi[deg.]−42.1225309675259)+(−1.19942177285592)×(t_Si2[λ]−0.381570137261466)+91.8359644721651×(t_LT[λ]−0.164596585202533)+58.8431912005245×(t_SiN[λ]−0.0395698024774026)+16.9153289429696×(t_SiO2[λ]−0.13875125544024)+0.00130491910714855×((Si_psi[deg.]−42.1225309675259)×(Si_psi[deg.]−42.1225309675259)−385.786124427809)+0.0745672315210127×((Si_psi[deg]−42.1225309675259)×(t_Si2[λ]−0.381570137261466))+2.6699307571413×((t_Si2[λ]−0.381570137261466)×(t_Si2[λ]−0.381570137261466)−0.0456605075514713)+(−0.377889849052574)×((Si_psi[deg.]−42.1225309675259)×(t_LT[λ]−0.164596585202533))+(−43.4148735553507)×((t_Si2[λ]−0.381570137261466)×(t_LT[λ]−0.164596585202533))+(−0.378387168121428)×((Si_psi[deg.]−42.1225309675259)×(t_SiN[λ]−0.0395698024774026))+(−20.545088460627)×((t_Si2[λ]−0.381570137261466)×(t_SiN[λ]−0.0395698024774026))+232.919108783203×((t_LT[λ]−0.164596585202533)×(t_SiN[λ]−0.0395698024774026))+840.791113736585×((t_SiN[λ]−0.0395698024774026)×(t_SiN[λ]−0.0395698024774026)−0.000464855104179262)+0.190837727117146×((Si_psi[deg.]−42.1225309675259)×(t_SiO2[λ]−0.13875125544024))+0.695837098714372×((t_Si2[λ]−0.381570137261466)×(t_SiO2[λ]−0.13875125544024))+(−184.621593720628)×((t_LT[λ]−0.164596585202533)×(t_SiO2[λ]−0.13875125544024))+607.033426600094×((t_SiN[λ]−0.0395698024774026)×(t_SiO2[λ]−0.13875125544024))+142.721242732228×((t_SiO2[λ]−0.13875125544024)×(t_SiO2[λ]−0.13875125544024)−0.00152562510304392) Equation 11
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_SiN[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 11 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
When the plane orientation of the silicon substrate 2 is (111), the equation 12 was derived as described above.
y[deg.]=(−79.8683540124538)+0.0118371753456289×(Si_psi[deg.]−44.4595052524568)+(−1.99138796522555)×(t_Si2[λ]−0.413673331074209)+88.0775643151379×(t_LT[λ]−0.167705862419511)+46.4734172707698×(t_SiN[λ]−0.0351321585903086)+14.4134894109961×(t_SiO2[λ]−0.142222975262623)+0.00167085752221365×((Si_psi[deg.]−44.4595052524568)×(Si_psi[deg.]−44.4595052524568)−128.282924729805)+(−0.0463012101323173)×((Si_psi[deg.]−44.4595052524568)×(t_Si2[λ]−0.413673331074209))+4.58192618035487×((t_Si2[λ]−0.413673331074209)×(t_Si2[λ]−0.413673331074209)−0.05167257915661)+0.524887931323933×((Si_psi[deg]−44.4595052524568)×(t_LT[λ]−0.167705862419511))+(−71.7492658390069)×((t_Si2[λ]−0.413673331074209)×(t_LT[λ]−0.167705862419511))+0.73863390529294×((Si_psi[deg.]−44.4595052524568)×(t_SiN[λ]−0.0351321585903086))+(−42.8957552454222)×((t_Si2[λ]−0.413673331074209)×(t_SiN[λ]−0.0351321585903086))+(−411.839865840595)×((t_LT[λ]−0.167705862419511)×(t_SiN[λ]−0.0351321585903086))+982.235412331017×((t_SiN[λ]−0.0351321585903086)×(t_SiN[λ]−0.0351321585903086)−0.000477142818756284)+(−0.236509133242243)×((Si_psi[deg.]−44.4595052524568)×(t_SiO2[λ]−0.142222975262623))+17.2370398551984×((t_Si2[λ]−0.413673331074209)×(t_SiO2[λ]−0.142222975262623))+(−469.933137492789)×((t_LT[λ]−0.167705862419511)×(t_SiO2[λ]−0.142222975262623))+541.748349798792×((t_SiN[λ]−0.0351321585903086)×(t_SiO2[λ]−0.142222975262623))+226.311489477246×((t_SiO2[λ]−0.142222975262623)×(t_SiO2[λ]−0.142222975262623)−0.00116579711361478) Equation 12
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_SiN[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 12 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
Subsequently, in the configuration having the multilayer substrate 39 similar to that of the fourth preferred embodiment shown in
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, an equation 13 that was a relational expression between the parameters and the phase of a higher-order mode was derived. The thickness of the titanium oxide layer 36 is set to t_TiO2[λ]. In the equation 13, Si_psi[deg.] is the angle α100.
y[deg.]=(−47.9946211404703)+1.21901050350713×(Si_psi[deg.]−19.0566037735849)+4.12041154986452×(t_Si2[λ]−0.408490566037736)+228.432202102143×(t_TiO2[λ]−0.0288364779874214)+(−33.1253993677708)×(t_SiO2[λ]−0.160062893081761)+0.140472008263765×((Si_psi[deg,]−19.0566037735849)×(Si_psi[deg.]−19.0566037735849)−38.1037142518096)+(−5.44594625372052)×((Si_psi[deg.]−19.0566037735849)×(t_Si2[λ]−0.408490566037736))+114.747133042737×((t_Si2[λ]−0.408490566037736)×(t_Si2[λ]−0.408490566037736)−0.0406983505399312)+10.4171695197979×((Si_psi[deg.]−19.0566037735849)×(t_TiO2[λ]−0.0288364779874214))+(−526.442885320397)×((t_Si2[λ]−0.408490566037736)×(t_TiO2[λ]−0.0288364779874214))+(−298.795469471375)×((t_TiO2[λ]−0.0288364779874214)×(t_TiO2[λ]−0.0288364779874214)−0.000424904078161465)+(−50.1009078768921)×((Si_psi[deg.]−19.0566037735849)×(t_SiO2[λ]−0.160062893081761))+1038.08065133921×((t_Si2[λ])−0.408490566037736)×(t_SiO2[λ]−0.160062893081761))+(−1286.74436136556)×((t_TiO2[λ]−0.0288364779874214)×(t_SiO2[λ]−0.160062893081761))+4158.8148931551×((t_SiO2[λ]−0.160062893081761)×(t_SiO2[λ]−0.160062893081761)−0.00134527906332819) Equation 13
Si_psi[deg.], t_SiO2[λ], t_TiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 13 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70 [deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In the configuration having a multilayer substrate 39 similar to that of the fourth preferred embodiment, the plane orientation of the silicon substrate 2 was set to (110), and the phase of a higher-order mode was measured while the parameters were changed. The design parameters and the variable ranges of the design parameters were similar to those when the equation 13 was derived except the angle α.
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, an equation 14 that was a relational expression between the parameters and the phase of a higher-order mode was derived. In the equation 14, Si_psi [deg.] is the angle α110.
y[deg.]=(−66.0681190864303)+(−0.0323391014318074)×(Si_psi[deg.]−35.9295352323838)+0.997507104337367×(t_Si2[λ]−0.394527736131933)+155.754971155735×(t_TiO2[λ]−0.0378860569715143)+(−27.4736558331949)×(t_SiO2[λ]−0.149887556221888)+0.00791197424152189×((Si_psi[deg.]−35.9295352323838)×(Si_psi[deg.]−35.9295352323838)−256.81962242267)+0.212504000649305×((Si_psi[deg.]−35.9295352323838)×(t_Si2[λ]−0.394527736131933))+88.6294722534935×((t_Si2[λ]−0.394527736131933)×(t_Si2[λ]−0.394527736131933)−0.0392241772666888)+0.636412965393882×((Si_psi[deg.]−35.9295352323838)×(t_TiO2[λ]−0.0378860569715143))+157.120610191294×((t_Si2[λ]−0.394527736131933)×(t_TiO2[λ]−0.0378860569715143))+544.188337615988×((t_TiO2[λ]−0.0378860569715143)×(t_TiO2[λ]−0.0378860569715143)−0.000522930045472021)+0.408031229502175×((Si_psi[deg.]−35.9295352323838)×(t_SiO2[λ]−0.149887556221888))+(−46.0736528123303)×((t_Si2[λ]−0.394527736131933)×(t_SiO2[R]−0.149887556221888))+(−1322.9465191866)×((t_TiO2[λ]−0.0378860569715143)×(t_SiO2[λ]−0.149887556221888))+359.098768522305×((t_SiO2[λ])−0.149887556221888)×(t_SiO2[λ]−0.149887556221888)−0.00163979245384803) Equation 14
Si_psi[deg.], t_SiO2[λ], t_TiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 14 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70 [deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In the configuration of the fourth preferred embodiment, the plane orientation of the silicon substrate 2 was set to (111), and the phase of a higher-order mode was measured while the parameters were changed. The design parameters and the variable ranges of the design parameters were similar to those when the equation 13 was derived except the angle α.
The phase of a higher-order mode was measured while the parameters were changed as described above. Thus, an equation 15 that was a relational expression between the parameters and the phase of a higher-order mode was derived. In the equation 15, Si_psi [deg.] is the angle α111.
y[deg.]=(−69.4030815485713)+(−0.269371737613053)×(Si_psi[deg.]−33.8730694980695)+(−4.68577968707475)×(t_Si2[λ]−0.440745656370656)+176.177168052005×(t_LT[λ]−0.168858590733587)+73.1412385401181×(t_TiO2[λ]−0.0300916988416992)+(−12.3739066281753)×(t_SiO2[λ]−0.154983108108108)+0.00777703537774127C((Si_psi[deg.]−33.8730694980695)×(Si_psi[deg.]−33.8730694980695)−508.406668570442)+0.121265989497045×((Si_psi[deg.]−33.8730694980695)×(t_Si2[λ]−0.440745656370656))+17.8168374568741×((t_Si2[λ]−0.440745656370656)×(t_Si2[λ]−0.440745656370656)−0.0493816592475423)+1.34130425597794×((Si_psi[deg.]−33.8730694980695)×(t_LT[λ]−0.168858590733587))+(−5.11032690396319)×((t_Si2[λ]−0.440745656370656)×(t_LT[λ]−0.168858590733587))+2.48016332864734×((Si_psi[deg.]−33.8730694980695)×(t_TiO2[λ]−0.0300916988416992))+77.8145877606436×((t_Si2[λ]−0.440745656370656)×(t_TiO2[λ]−0.0300916988416992))+2112.87481803881×((t_LT[λ]−0.168858590733587)×(t_TiO2[λ]−0.0300916988416992))+196.040518466468×((t_TiO2[λ]−0.0300916988416992)×(t_TiO2[λ]−0.0300916988416992)−0.000562395066225887)+(−0.969575065396993)×((Si_psi[deg.]−33.8730694980695)×(t_SiO2[λ]−0.154983108108108))+(−138.70694337489)×((t_Si2[λ]−0.440745656370656)×(t_SiO2[λ]−0.154983108108108))+(−1100.04408119143)×((t_LT[λ]−0.168858590733587)×(t_SiO2[λ]−0.154983108108108))+74.9944030678128×((t_TiO2[λ]−0.0300916988416992)×(t_SiO2[λ]−0.154983108108108))+117.812778429437×((t_SiO2[λ]−0.154983108108108)×(t_SiO2[λ]−0.154983108108108)−0.00117057162586093) Equation 15
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_TiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 15 is less than or equal to about −70. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −70[deg.]. Therefore, higher-order modes are further reliably and effectively reduced.
In addition, conditions in which the phase of a higher-order mode was reduced to less than or equal to about −80[deg.] were obtained in each of a case where the plane orientation of the silicon substrate 2 was (110) and a case where the plane orientation of the silicon substrate 2 was (111). More specifically, to obtain the conditions, an equation 16 and an equation 17 were derived while the parameters were changed within the range in which the phase of a higher-order mode was greater than or equal to −90[deg.] and less than or equal to about −70 [deg.].
When the plane orientation of the silicon substrate 2 is (110), the equation 16 was derived as described above.
y[deg.]=(−77.5229944626225)+(−0.0245637365901893)×(Si_psi[deg.]−34.5205479452055)+(−1.18326432300356)×(t_Si2[λ]−0.408904109589041)+131.275052857081×(t_TiO2[λ]−0.0160045662100456)+(−18.9167659640434)×(t_SiO2[λ]−0.150228310502283)+0.00233031321934999×((Si_psi[deg.]−34.5205479452055)×(Si_psi[deg.]−34.5205479452055)−75.9116782385689)+(−0.0809397438263331)×((Si_psi[deg.]−34.5205479452055)×(t_Si2[λ]−0.408904109589041))+43.1653284334043×((t_Si2[λ]−0.408904109589041)×(t_Si2[λ]−0.408904109589041)−0.0169869268780884)+(−0.255179621676294)×((Si_psi[deg.]−34.5205479452055)×(t_TiO2[λ])−0.0160045662100456))+(−101.438420329361)×((t_Si2[λ]−0.408904109589041)×(t_TiO2[λ]−0.0160045662100456))+(−834.553397134957)×((t_TiO2[λ]−0.0160045662100456)×(t_TiO2[λ]−0.0160045662100456)−0.000126844728008173)+0.935627393438751×((Si_psi[deg.]−34.5205479452055)×(t_SiO2[λ])−0.150228310502283))+(−21.1152350576513)×((t_Si2[λ]−0.408904109589041)×(t_SiO2[λ]−0.150228310502283))+(−41.8110780477077)×((t_TiO2[λ]−0.0160045662100456)×(t_SiO2[λ]−0.150228310502283))+263.939639423742×((t_SiO2[λ]−0.150228310502283)×(t_SiO2[λ]−0.150228310502283)−0.00160953691541044) Equation 16
Si_psi[deg.], t_SiO2[λ], t_TiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 16 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
When the plane orientation of the silicon substrate 2 is (111), the equation 17 was derived as described above.
y[deg.]=(−78.9096176038851)+0.034903516437231×(Si_psi[deg.]−45.8453473132372)+(−2.02533584474356)×(t_Si2[λ]−0.421068152031454)+81.4363661536651×(t_LT[λ]−0.156225425950199)+71.7903756668229×(t_TiO2[λ]−0.0334862385321101)+(−3.53261283561548)×(t_SiO2[λ]−0.149606815203146)+0.00246176329064131×((Si_psi[deg.]−45.8453473132372)×(Si_psi[deg.]−45.8453473132372)−143.191023568758)+(−0.0293712406566626)×((Si_psi[deg.]−45.8453473132372)×(t_Si2[AX]−0.421068152031454))+0.972512275661977×((t_Si2[λ]−0.421068152031454)×(t_Si2[λ]−0.421068152031454)−0.0430997109516307)+0.30260322985253×((Si_psi[deg.]−45.8453473132372)×(t_LT[λ]−0.156225425950199))+(−23.2249863870645)×((t_Si2[λ]−0.421068152031454)×(t_LT[λ]−0.156225425950199))+0.513496313876766×((Si_psi[deg.]−45.8453473132372)×(t_TiO2[λ]−0.0334862385321101))+(−143.065209527507)×((t_Si2[λ]−0.421068152031454)×(t_TiO2[λ]−0.0334862385321101))+(−324.329178613173)×((t_LT[λ]−0.156225425950199)×(t_TiO2[λ]−0.0334862385321101))+(−98.4001544132927)×((t_TiO2[λ]−0.0334862385321101)×(t_TiO2[λ]−0.0334862385321101)−0.000480867110753061)+(−1.15889670547368)×((Si_psi[deg.]−45.8453473132372)×(t_SiO2[λ]−0.149606815203146))+(−50.3263112114924)×((t_Si2[λ]−0.421068152031454)×(t_SiO2[λ]−0.149606815203146))+(−209.199256641353)×((t_LT[λ]−0.156225425950199)×(t_SiO2[λ]−0.149606815203146))+90.23187502294813×((t_TiO2[λ]−0.0334862385321101)×(t_SiO2[λ]−0.149606815203146))+347.448658314796×((t_SiO2[λ]−0.149606815203146)×(t_SiO2[λ]−0.149606815203146)−0.00114008131659363) Equation 17
Si_psi[deg.], t_LT[λ], t_SiO2[λ], t_TiO2[λ], and t_Si2[λ] each are preferably a value within a range with which y in the equation 17 is less than or equal to about −80. With this configuration, the phase of a higher-order mode is further reliably set to less than or equal to about −80[deg.]. Therefore, higher-order modes are further reliably and further reduced.
In the above description, an example in which the piezoelectric layer 7 is a lithium tantalate layer has been described. Hereinafter, an example in which the piezoelectric layer 7 is a lithium niobate layer will be described with reference to
A fifth preferred embodiment of the present invention differs from the second preferred embodiment in that the piezoelectric layer 7 is a lithium niobate layer. Other than the above points, the acoustic wave device according to the fifth preferred embodiment has a similar configuration to the acoustic wave device according to the second preferred embodiment.
Here, the phase characteristics of the acoustic wave device having the configuration of the fifth preferred embodiment were measured. The design parameters of the acoustic wave device are as follows.
Here, the present preferred embodiment and a second comparative example are compared with each other to demonstrate that higher-order modes are reduced in a wide band according to the present preferred embodiment. The second comparative example differs from the present preferred embodiment in that, in the multilayer substrate, a silicon nitride layer is laminated instead of the polysilicon layer.
As shown in
While preferred embodiments of the present invention have been described above, it is to be understood that variations and modifications will be apparent to those skilled in the art without departing from the scope and spirit of the present invention. The scope of the present invention, therefore, is to be determined solely by the following claims.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2020-169095 | Oct 2020 | JP | national |
This application claims the benefit of priority to Japanese Patent Application No. 2020-169095 filed on Oct. 6, 2020 and is a Continuation Application of PCT Application No. PCT/JP2021/035803 filed on Sep. 29, 2021. The entire contents of each application are hereby incorporated herein by reference.
| Number | Date | Country | |
|---|---|---|---|
| Parent | PCT/JP2021/035803 | Sep 2021 | US |
| Child | 18124592 | US |
