Bonded body of piezoelectric material substrate and supporting substrate

Abstract

A bonded body includes a supporting substrate; a piezoelectric material substrate composed of a material selected from the group consisting of lithium niobate, lithium tantalate and lithium niobate-lithium tantalate; and a bonding layer bonding the supporting substrate and the piezoelectric material substrate and contacting a main surface of the piezoelectric material substrate. It is provided that at least one of a bonding surface of the supporting substrate and a bonding surface of the piezoelectric material substrate is measured by X-ray reflectivity method and that 1 is assigned to a signal intensity in the case of total reflection. A relative intensity I of a reflected light from the bonding surface is approximated by the following formula (1) in a range of 1.0×10.sup.−4 or larger and 1.0×10.sup.−1 or smaller.
I=a(2θ).sup.−b  (1)
(θ represents an incident angle of an X-ray with respect to the bonding surface, a is 1.0×10.sup.−5 or larger and 2.0×10.sup.−3 or smaller, and b is 5.0 or larger and 9.0 or smaller.)

Claims

1. A bonded body comprising: a supporting substrate; a piezoelectric material substrate comprising a material selected from the group consisting of lithium niobate, lithium tantalate and lithium niobate-lithium tantalate; and a bonding layer bonding said supporting substrate and said piezoelectric material substrate, wherein at least one of a bonding surface of said supporting substrate and a bonding surface of said piezoelectric material substrate has a relative intensity I of a reflected light from said bonding surface in a range of 1.0×10.sup.−4 or larger and 1.0×10.sup.−1 or smaller when measured by an X-ray reflectivity method and 1 is assigned to a signal intensity in the case of total reflection, as calculated by the following formula (1):
I=a(2θ).sup.−b  (1) where θ represents an incident angle of an X-ray with respect to said bonding surface, a is 1.0×10.sup.−5 or larger and 2.0×10.sup.−3 or smaller, and b is 5.0 or larger and 9.0 or smaller, the bonded body further comprising a surface denatured region adjacent said at least one bonding surface, said surface denatured region disposed to being subjected to said X-ray reflectivity method when I is measured.

2. The bonded body of claim 1, wherein said at least one bonding surface adjacent said surface denatured region has a roughened surface.

3. The bonded body of claim 1, wherein the bonded body has a spurious value of 4.8 dB or less.

4. The bonded body of claim 1, wherein said bonding layer comprises a material selected from the group consisting of silicon oxide, silicon nitride, aluminum nitride, alumina, tantalum pentoxide, mullite, niobium pentoxide and titanium oxide.

5. The bonded body of claim 1, wherein said supporting substrate comprises a material selected from the group consisting of silicon, quartz, sialon, mullite, sapphire and translucent alumina.

6. The bonded body of claim 5, wherein said supporting substrate comprises silicon.

7. The bonded body of claim 1, wherein said supporting substrate comprises said at least one bonding surface adjacent said surface denatured region.

8. The bonded body of claim 1, wherein said at least one bonding surface adjacent said surface denatured region is provided by grinding with grinding stones, by blast processing with micro media or by ion beam processing.

9. The bonded body of claim 8, wherein said at least one bonding surface adjacent said surface denatured region is provided by grinding with grinding stones, by blast processing with micro media or by ion beam processing of a mirror surface.

10. The bonded body of claim 8, wherein said at least one bonding surface adjacent said surface denatured region is provided by grinding with grinding stones of #6000 to #8000.

11. The bonded body of claim 8, wherein said at least one bonding surface adjacent said surface denatured region is provided by blast processing with micro media comprising alumina or silicon nitride.

12. The bonded body of claim 8, wherein said at least one bonding surface adjacent said surface denatured region is provided by ion beam processing with colliding Ar ions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a model chart showing the relationship between an incident angle θ and relative density I of a reflected light.

(2) FIG. 2(a) shows the state that a bonding surface of a supporting substrate is processed, FIG. 2(b) shows the state that a bonding layer is provided on the bonding surface of the supporting substrate, and FIG. 2(c) shows the state that plasma is irradiated onto a bonding surface of the bonding layer to activate the surface.

(3) FIG. 3(a) shows a piezoelectric material substrate, and FIG. 3(b) shows the state that a bonding surface of the piezoelectric material substrate is activated.

(4) FIG. 4(a) shows a bonded body of the supporting substrate and piezoelectric material substrate, FIG. 4(b) shows the state that a piezoelectric material substrate of a bonded body is thinned, and FIG. 4(c) shows an acoustic wave device.

(5) FIG. 5(a) shows the piezoelectric material substrate, and FIG. 5(b) shows the state that a bonding surface of an intermediate layer on the piezoelectric material substrate is activated.

(6) FIG. 6(a) shows a bonded body of the supporting substrate and piezoelectric material substrate, FIG. 6(b) shows the state that the piezoelectric material substrate of a bonded body is thinned by processing, and FIG. 6(c) shows an acoustic wave device.

(7) FIG. 7 is a chart showing reflection characteristics of a surface acoustic wave device of the inventive example.

(8) FIG. 8 is a chart showing reflection characteristics of a surface acoustic wave device according to a comparative example.

MODES FOR CARRYING OUT THE INVENTION

(9) Embodiments of the present invention will be described in detail below, appropriately referring to the drawings.

(10) First, as shown in FIG. 2(a), a supporting substrate 1 having a pair of main surfaces 1a and 1b is prepared. Processing A is then performed on the main surface (bonding surface) 1a to roughen the surface. Then, as shown in FIG. 2(b), a bonding layer 2 is film-formed on the main surface 1a of the supporting substrate 1. The surface 2a of the bonding layer 2 is subjected to CMP polishing for obtaining a mirror surface. Then, as shown in FIG. 2(c), plasma is irradiated onto the surface 2a of the bonding layer 2 to obtain a surface-activated bonding surface 2b.

(11) Further, as shown in FIG. 3(a), a piezoelectric material substrate 3 having a main surface 3a is prepared. Plasma is irradiated onto the main surface of the piezoelectric material substrate 3 as arrows C to activate the surface to form a surface-activated bonding surface 3b.

(12) The activated bonding surface 2b of the bonding layer 2 on the supporting substrate and the activated bonding surface 3b of the piezoelectric material substrate 3 are contacted with each other and subjected to direct bonding, to obtain a bonded body 5 shown in FIG. 4(a).

(13) At this stage, electrodes may be provided on the piezoelectric material substrate 3. However, preferably, as shown in FIG. 4(b), the main surface 3c of the piezoelectric material substrate 3 is processed to thin the substrate 3 to form a thinned piezoelectric material substrate 3A so that a bonded body 5A is provided. 9 represents a processed surface. Then, as shown in FIG. 4(c), predetermined electrodes 10 may be formed on the processed surface 9 of the piezoelectric material substrate 3A of the bonded body 5A to obtain an acoustic wave device 6.

(14) Further, an intermediate layer may be provided between the bonding layer 2 and the piezoelectric material substrate 3. FIGS. 5 and 6 relate to this embodiment.

(15) According to the present example, as shown in FIG. 2(a), a supporting substrate 1 having a pair of main surfaces 1a and 1b is prepared. Processing A is then performed on the main surface (bonding surface) la for roughening. Then, as shown in FIG. 2(b), a bonding layer 2 is film-formed on the main surface 1a of the supporting substrate 1. The surface of the bonding layer 2 is subjected to CMP polishing for obtaining a mirror surface. Then, as shown in FIG. 2(c), plasma is irradiated onto the bonding surface of the bonding layer 2 as arrows B to obtain a surface-activated bonding surface 2b.

(16) Further, as shown in FIG. 5(a), a piezoelectric material substrate 3 having a main surface 3a is prepared. Then, as shown in FIG. 5(b), an intermediate layer 12 is formed on the main surface (bonding surface) 3a of the piezoelectric material substrate 3, and plasma is irradiated onto the surface of the intermediate layer 12 as arrows C to perform the surface activation to form a surface-activated bonding surface 12a.

(17) Then, the activated surface 2b of the bonding layer 2 on the supporting substrate and the activated bonding surface 12a of the intermediate layer 12 on the piezoelectric material substrate 3 are contacted with and directly bonded with each other, to obtain a bonded body 15 shown in FIG. 6(a).

(18) At this stage, electrodes may be provided on the piezoelectric material substrate 3. However, preferably, as shown in FIG. 6(b), the main surface 3c of the piezoelectric material substrate 3 is processed to thin the substrate 3 to form a thinned piezoelectric material substrate 3A so that a bonded body 15A is provided. 9 represents a processed surface. Then, as shown in FIG. 6(c), predetermined electrodes 10 may be formed on the processed surface 9 of the piezoelectric material substrate 3A of the bonded body 15A to obtain an acoustic wave device 16.

(19) Alternatively, after the bonding layer 2 is film-formed, the intermediate layer 12 may be subsequently film-formed on the bonding layer 2. In this case, CMP processing is performed on the surface of the intermediate layer 12 to obtain a bonding surface (mirror surface). Plasma is irradiated onto the thus obtained bonding surface to activate the surface. The surface of the supporting substrate is then subjected to plasma activation and directly bonded with the bonding surface of the intermediate layer.

(20) According to the present invention, b is 5.0 or larger. Further, b is 9.0 or smaller and is preferably 7.0 or smaller. Further, according to the present invention, a is 1.0×10.sup.−5 or larger, and is preferably 1.0×10.sup.−4 or larger. Further, a is 2.0×10.sup.−3 or smaller and is preferably 1.0×10.sup.−3 or smaller.

(21) According to a preferred embodiment, a and b satisfy the following formula (2).
−0.713.Math.ln(a)+0.5≤b≤−0.713.Math.ln(a)+0.7  (2)

(22) According to another preferred embodiment, a and b satisfy the following formula (3).
b==−0.713.Math.ln(a)+0.6  (3)

(23) The measurement condition for the X-ray reflectivity method is as follows.

(24) TABLE-US-00001 Measurement system: ″SmartLab″ supplied by Rigaku Corporation Measurement condition: X-ray generating part: Anti-cathode; Cu    : Output power; 5kV 200mA Detecting part: Semiconductor detector Incident optical system: Ge (111) Unsymmetrical beam condensation crystal Solar slit: incident side; −   Reception side: 5.0° Slit: Reception side: IS=0.05 (mm)  : Longitudinal limit 5 (mm)  : Reception side: RS1=0.1 RS2=0.1 (mm) Scanning condition: Scanning axis; 2θ/ω    Scanning mode: continuous scanning    Scanning speed: 0.2° /min    Step width: 0.002°    Analysis range: 0.3~3.0° It is preferred to apply the following processing

(25) It is preferred to apply the following processing method for controlling the measurement results by the X-ray reflectivity method of the bonding surfaces of the piezoelectric material substrate and supporting substrate as described above.

(26) As to the method for roughening the surfaces, a mechanical processing method such as grinding process by grinding stones or blast processing by micro media such as alumina or silicon nitride, and ion beam processing of colliding ions at a high speed may be used.

(27) Respective constituents of the present invention will be described further in detail below.

(28) Although the material of the supporting substrate 1 is not particularly limited, the material is preferably selected from the group consisting of silicon, quartz, sialon, mullite, sapphire and translucent alumina. It is thus possible to further improve the temperature characteristics on frequency of the acoustic wave device 6 or 16.

(29) Although the film-forming method of the bonding layer or intermediate layer is not particularly limited, a sputtering method, a chemical vapor deposition (CVD) method or a vapor deposition method may be used.

(30) Although the material of the bonding layer 2 is not particularly limited as far as the surface activation process is concerned, a metal oxide film is preferred, and the material may preferably be selected from the group consisting of silicon oxide, silicon nitride, aluminum nitride, alumina, tantalum pentoxide, mullite, niobium pentoxide and titanium oxide. Further, as the surface activation method, an appropriate method may be selected depending on the material used for the bonding layer. Such a surface activation method includes plasma activation or FAB (Ar atomic beam).

(31) Although the material of the intermediate layer 12 is not particularly limited as far as the surface activation processing is concerned, a metal oxide film is preferred, and a material selected from the group consisting of silicon oxide, silicon nitride, aluminum nitride, alumina, tantalum pentoxide, mullite, niobium pentoxide and titanium oxide is particularly preferred. Further, it is preferred to select the material of the intermediate layer to be different from that of the bonding layer.

(32) The thickness of the bonding layer 2 is preferably 0.05 μm or larger, more preferably 0.1 μm or larger and most preferably 0.2 μm or larger. Further, the thickness of the bonding layer 2 is preferably 3 μm or smaller, more preferably 2 μm or smaller and further preferably 1 μm or smaller.

(33) The piezoelectric material substrate 3 used in the present invention is composed of lithium tantalate (LT) single crystal, lithium niobate (LN) single crystal, or lithium niobate-lithium tantalate solid solution. As the materials have a high propagation speed of an acoustic wave and a large electromechanical coupling factor, they are suitable for a surface acoustic wave device of a high frequency and wide-band frequency application.

(34) Further, although the normal line direction of the main surface 3a of the piezoelectric material substrate 3 is not particularly limited, for example, in the case that the piezoelectric material substrate 3 is made of LT, it is preferred to use the substrate rotated from Y-axis toward Z-axis by 32 to 55°, (180°, 58 to 35°, 180°) on Euler angle representation, around X-axis, which is a direction of propagation of a surface acoustic wave, because of a low propagation loss. In the case that the piezoelectric material substrate 3 is made of LN, (i) it is preferred to use the substrate rotated from Z axis toward Y-axis by 37.8°, (0°, 37.8°, 0°) on Euler angle representation, around X-axis, which is the direction of propagation of the surface acoustic wave, because of a larger electromechanical coupling factor. Alternatively, (ii) it is preferred to use the substrate rotated from Y-axis toward Z-axis by 40 to 65°, (180°, 50 to 25°, 180°) on Euler angle representation, around X-axis, which is the direction of propagation of the surface acoustic wave, because of a high sound velocity. Further, although the size of the piezoelectric material substrate 3 is not particularly limited, for example, the diameter may be 100 to 200 mm and thickness may be 0.15 to 1 μm.

(35) Plasma is then irradiated onto the bonding surfaces of the bonding layer 2 on the supporting substrate 1, piezoelectric material substrate 3 and intermediate layer 12 on the piezoelectric material substrate 3 at a temperature of 150° C. or lower, to activate the bonding surfaces. Although it is preferred to irradiate nitrogen plasma, it is possible to obtain the inventive bonded body even when oxygen plasma is irradiated.

(36) The pressure during the surface activation is preferably 100 Pa or lower and more preferably 80 Pa or lower. Further, the atmosphere may be composed of nitrogen only, oxygen only or mixture of nitrogen and oxygen.

(37) The temperature during plasma irradiation is 150° C. or lower. It is thus possible to obtain a bonded body having a high bonding strength without deterioration of crystallinity. The temperature during the plasma irradiation is 150° C. or lower, and is preferably 100° C. or lower.

(38) Further, the energy of the plasma irradiation is preferably 30 to 150 W. Further, the product of the energy and irradiation time duration of the irradiated plasma is preferably 0.12 to 1.0 Wh.

(39) The plasma-treated bonding surfaces of the piezoelectric material substrate and bonding layer are contacted with each other at room temperature. The treatment may be performed in vacuum and the contact is preferably performed in atmosphere.

(40) When the activation of the surfaces is performed using the argon atomic beam, it is preferred to use a system described in Japanese patent publication No. 2014-086400A to generate the argon atomic beam, which is irradiated. That is, a high-speed atomic beam source of saddle field type is used as the beam source. Then, inert gas is introduced into the chamber and a high voltage is applied onto electrodes from a direct current electric source. By this, an electric field of saddle field type is generated between the electrode (positive electrode) and a housing (negative electrode) causing motion of electrons, e, so that argon atomic and ion beams are generated. Among the beams reached at the grid, the ion beam is neutralized at the grid, and the beam of argon atoms is emitted from the high-speed atomic beam source. In the activation step by beam irradiation, the voltage is preferably 0.5 to 2.0 kV, and the current is preferably 50 to 200 mA.

(41) According to a preferred embodiment, before the surface activation treatment, the bonding surfaces of the bonding layer on the supporting substrate, of the piezoelectric material substrate and of the intermediate layer on the piezoelectric material substrate are subjected to a flattening process. The method of flattening the respective surfaces includes lapping, chemical mechanical polishing (CMP) and the like. Further, the flattened surfaces preferably have an Ra of 1 nm or lower and more preferably 0.3 nm or lower.

(42) Then, the bonding surface of the bonding layer on the supporting substrate and the bonding surface of the piezoelectric material substrate 3 or bonding surface of the intermediate layer are contacted and bonded with each other. Thereafter, it is preferred to improve the bonding strength by performing annealing treatment. The temperature for the annealing treatment is preferably 100° C. or higher and 300° C. or lower.

(43) The bonded bodies 5, 5A, 15 and 15A of the present invention can be appropriately used for the acoustic wave devices 6 and 16. That is, an acoustic wave device having the bonded body of the present invention and an electrode provided on the piezoelectric material substrate is provided.

(44) Specifically, as the acoustic wave devices 6 and 16, a surface acoustic wave device, Lamb wave-type device, thin film resonator (FBAR) and the like are known. For example, the surface acoustic wave device is produced by providing input side IDT (Interdigital transducer) electrodes (also referred to as comb electrodes or interdigitated electrodes) for an oscillating surface acoustic wave and IDT electrodes on the output side for receiving the surface acoustic wave on the surface of the piezoelectric single crystal substrate. By applying a high frequency signal on the IDT electrodes on the input side, an electric field is generated between the electrodes, so that the surface acoustic wave is oscillated and propagated on the piezoelectric substrate. Then, the propagated surface acoustic wave is drawn as an electrical signal from the IDT electrodes on the output side provided in the direction of the propagation.

(45) The material forming the electrodes 10 on the piezoelectric material substrate 3A is preferably aluminum, aluminum alloy, copper or gold and more preferably aluminum or aluminum alloy. The aluminum alloy used is preferably Al doped with 0.3 to 5 weight percent of Cu. In this case, Ti, Mg, Ni, Mo, or Ta may be used instead of Cu.

EXAMPLES

Inventive Example 1

(46) An acoustic wave device 6 shown in FIG. 4(c), according to the method described referring to FIGS. 2 to 4 was produced.

(47) Specifically, one main surface 3c of a 42Y-cut X-propagation LiTaO.sub.3 substrate (piezoelectric material substrate) 3 having a thickness of 250 μm was polished into mirror surface and the other main surface 3a was subjected to lapping with GC #1000. Further, a Si(100) substrate (supporting substrate) 1 having a thickness of 0.23 mm and high resistance (>2kΩ.Math.cm) was prepared. The sizes of the respective substrates were 150 mm.

(48) The bonding surface of the supporting substrate was then subjected to processing into a roughened surface. According to the present example, a grinding process using grinding stones of number of #6000 was performed. The amount of the processing was about 3 μm.

(49) By using the X-ray reflectivity method of the bonding surface of the supporting substrate and the relative signal intensity was approximated based on the formula (1), values of a of 9.2×10.sup.−4 and b of 5.55 were obtained.

(50) A silicon oxide film 2 was the film-formed in 0.7 μm on the bonding surface 1a of the supporting substrate 1, and the surface was polished by CMP (chemical mechanical polishing) in about 0.2 um for the flattening. Then, the bonding surface 3b of the piezoelectric material substrate 3 and bonding surface of the silicon oxide film 2 were activated by N.sub.2 plasma, respectively, and then bonded with each other in atmosphere. Specifically, as the surface roughness of the bonding layer after the polishing was measured by AFM (Atomic force Microscope), it was confirmed that a mirror surface having an Ra of 0.4 nm could be obtained sufficient for the bonding.

(51) Then, the bonding surface 3b of the piezoelectric material substrate 3 and bonding surface 2b of the bonding layer 2 were subjected to cleaning and surface activation. Specifically, ultrasonic cleaning by pure water was performed and the substrate surface was dried by spin drying. Then, the supporting substrate after the cleaning was introduced into a plasma activation chamber and the bonding surface of the bonding layer was activated at 30° C. by nitrogen plasma. The piezoelectric material substrate 3 was similarly introduced in the plasma activation chamber and subjected to surface activation by nitrogen plasma at 30° C. The time period of the surface activation was 40 seconds, and the energy was 100 W. The ultrasonic cleaning and spin drying were performed again as described above, for removing particles adhered during the surface activation.

(52) The positions of the respective substrates were then adjusted so that the bonding surfaces of the respective activated substrates were contacted with each other at room temperature. The piezoelectric material substrate 3 was positioned on the upper side when the substrates were contacted. As a result, the state (so-called bonding wave) was observed and that the adhesion of the substrates was spreading to prove that good preliminary bonding was accomplished. The bonded body was then charged into an oven filled with nitrogen atmosphere and held at 130° C. for 40 hours, for improving the bonding strength.

(53) The surface 3c of the piezoelectric material substrate 3 of the bonded body after the heating was subjected to grinding, lapping and CMP processing so that the thickness of the piezoelectric material substrate 3A reached 7 μm.

(54) Then, for confirming the effects of the present invention, a comb-shaped electrode made of aluminum metal was formed on the piezoelectric material substrate of the bonded body, to produce a resonator of a surface acoustic wave device. The specification of the device is as follows.

(55) TABLE-US-00002 IDT period:  6 μm IDT opening length: 300 um Number of IDT lines:  80 lines Number of lines of reflector:  40 lines

(56) As the reflection characteristics of the resonator were measured by a network analyzer, spurious wave was hardly observed in a range higher than an anti-resonance frequency, as shown in FIG. 7. The value of the spurious wave was 2.7 dB.

(57) The results are shown in Table 1.

Inventive Example 2

(58) The resonator of the surface acoustic wave device was produced according to the same procedure as that in Inventive Example 1, and the reflection characteristics of the resonator were measured by the network analyzer. However, the processing of the bonding surface of the supporting substrate was performed by grinding the bonding surface by grinding stones of #8000.

(59) As spectrum of the bonding surface of the supporting substrate was obtained by the X-ray reflectivity method and the relative signal intensity was approximated by the formula (1), values of a of 7.1×10.sup.−4 and b of 5.80 were obtained. The magnitude of the spurious wave was 3.2 dB.

Inventive Example 3

(60) The resonator of the surface acoustic wave device was produced according to the same procedure as Inventive Example 1, and the reflection characteristics of the resonator were measured by the network analyzer. However, the processing of the bonding layer of the supporting substrate was performed by blasting of the whole surface of the substrate with silicon nitride particles. The amount of the processing was evaluated and was as small as 10 nm.

(61) As spectrum of the bonding surface of the supporting substrate was obtained by the X-ray reflectivity method and the relative signal intensity was approximated by the formula (1), values of a of 2.2×10.sup.−5 and b of 8.84 were obtained. The magnitude of the spurious wave was 4.8 dB.

Inventive Example 4

(62) The resonator of the surface acoustic wave device was produced according to the same procedure as that of Inventive Example 1, and the reflection characteristics of the resonator were measured by the network analyzer. However, the processing of the bonding surface of the supporting substrate was performed by charging the supporting substrate in an ion processing machine and by colliding Ar ions accelerated at 0.5 keV.

(63) As spectrum of the bonding surface of the supporting substrate was obtained by the X-ray reflectivity method and the relative signal intensity was approximated by the formula (1), values of a of 5.6×10.sup.−5 and b of 7.63 were obtained. The magnitude of the spurious wave was 3.3 dB.

Inventive Example 5

(64) The resonator of the surface acoustic wave device was produced according to the same procedure as that of Inventive Example 1, and the reflection characteristics of the resonator were measured by the network analyzer. However, the processing of the bonding surface was performed by charging the supporting substrate in an ion processing machine and by colliding Ar ions accelerated at 1.0 keV.

(65) As spectrum of the bonding surface of the supporting substrate was obtained by the X-ray reflectivity method and the relative signal intensity was approximated by the formula (1), values of a of 1.8×10.sup.−3 and b of 5.12 were obtained. The magnitude of the spurious wave was 3.5 dB.

Comparative Example 1

(66) The resonator of the surface acoustic wave device was produced according to the same procedure as that of Inventive Example 1, and the reflection characteristics of the resonator was measured by the network analyzer. However, as the bonding surface of the supporting substrate was made a mirror surface, the Ra was 0.02 nm and the approximation by the formula (1) could not be made. Spurious wave was observed in the reflection characteristics, as shown in FIG. 8. The magnitude of the spurious wave was 12 dB.

(67) TABLE-US-00003 TABLE 1 a B Spurious Inventive 9.2 × 10.sup.−4 5.55 2.7 Example 1 Inventive 7.1 × 10.sup.−4 5.80 3.2 Example 2 Inventive 2.2 × 10.sup.−5 8.84 4.8 Example 3 Inventive 5.6 × 10.sup.−5 7.63 3.3 Example 4 Inventive 1.8 × 10.sup.−3 5.12 3.5 Example 5 Comparative — — 12 Example 1