JP3152857B2 - Electrostatic chuck - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electrostatic chuck for processing and transporting a wafer by electrostatically attracting and holding it in a semiconductor manufacturing apparatus or the like.

[0002]

2. Description of the Related Art Conventionally, in a semiconductor manufacturing apparatus, it has been necessary to hold a silicon wafer or the like while forming and etching a semiconductor such as a silicon wafer while maintaining the flatness of the silicon wafer. Type, vacuum suction type, and electrostatic suction type have been proposed. Among these holding means, an electrostatic chuck capable of electrostatically holding a silicon wafer can easily realize the flatness and flatness of a processing surface required when processing a silicon wafer. Since silicon wafers can be processed in a vacuum, they are most frequently used in semiconductor manufacturing.

A conventional electrostatic chuck has an insulating layer made of alumina, sapphire, etc. formed on an electrode plate (Japanese Patent Laid-Open No. 60-261377). A conductive layer is formed on an insulating substrate, and a conductive layer is formed on the insulating layer. Having an insulating layer formed thereon (Japanese Unexamined Patent Publication No.
No. 4953) and a device in which a conductive layer is incorporated inside an insulating substrate (Japanese Patent Application Laid-Open No. 62-94953).

In recent years, as the degree of integration of integrated circuits of semiconductor devices has increased, the precision of electrostatic chucks has become higher, and a ceramic electrostatic chuck having excellent corrosion resistance, wear resistance and thermal shock resistance has been required. It has become In particular, since aluminum nitride is more excellent in plasma resistance than other ceramic materials, an electrostatic chuck using the same is being studied.

In general, the volume resistivity of an insulator tends to decrease as the temperature rises.

For example, in the case of aluminum nitride, the resistance value of 10 ¹⁶ Ω-cm at room temperature is reduced to 10 ¹² Ω-cm or less at 300 ° C., and a problem such as residual adsorption occurs and stable operation is obtained. Was difficult and the operating temperature was limited. Further, at room temperature or lower, since it has a resistance of 10 ¹⁶ Ω-cm or more, there is a problem that a practically required adsorption force cannot be obtained.

Therefore, Japanese Patent Application Laid-Open No. 2-160444 discloses that two or more insulating layers are laminated and electrodes, electric circuits, and switchings corresponding to the respective layers are provided so as to withstand use from room temperature to 400 ° C. A structure has been proposed. In Japanese Patent Application Laid-Open No. 4-300137, a temperature detector such as a heater and a thermocouple is mounted in an electrostatic chuck, and a control unit is provided outside to control a power supply unit in accordance with a temperature change to stabilize an attraction force. It has also been proposed to extend the operating temperature range. Further, Japanese Patent Application Laid-Open No. Hei 5-315435 proposes a method in which a dielectric layer is formed of a plurality of materials having different resistivities, and voltage application is switched according to a use temperature.

[0008]

Problems to be Solved by the Invention Aluminum nitride, alumina and the like have been mainly studied as a dielectric insulator for forming the surface of an electrostatic chuck. However, the method of changing the structure of the electrostatic chuck or expanding the temperature range that can be used by electrical control as described above also complicates the electric circuit,
Since the structure of the electrostatic chuck itself is complicated, the manufacturing process is complicated, and as a result, there are drawbacks in that the reliability of the product is reduced and the cost is increased.

Also, in the method of controlling the applied voltage by detecting the temperature of a built-in heater, a temperature detector such as a thermocouple is built in the electrostatic chuck. In this method, the properties of the ceramic material are not substantially changed, so that the range of use thereof is naturally limited.

[0010]

Means for Solving the Problems The present inventors have repeatedly studied the above problems with respect to the ceramic resistor layer forming the surface of the electrostatic chuck, particularly from the viewpoint of the material constituting the electrostatic chuck. As a result, a ceramic resistor layer having an aluminum nitride crystal phase as a main phase is formed on a predetermined substrate surface, and in the resistor layer, a periodic table 2b such as Zn or Cd is formed.
Group elements of the periodic table, such as S and Se, and a volume resistivity at 25 ° C. of 10 ⁷ to 10 ^13.
By forming a resistor layer of Ω-cm, it has been found that the resistance can be stabilized at least in a temperature range from 0 ° C. to 300 ° C., and the present invention has been achieved.

That is, in the electrostatic chuck of the present invention, the surface of the substrate on which the electrodes are provided is made of an aluminum nitride crystal phase as a main component and at least one selected from Group 2b elements of the periodic table and Group 6b elements excluding oxygen. Contains one element and 25 ° C
Wherein a ceramic resistor layer having a volume resistivity of 10 ⁷ to 10 ¹³ Ω-cm is formed.

In particular, when the doping element in the ceramic resistor layer is a Group 2b element of the periodic table, the element is contained at a ratio of 0.01 to 20 atomic%, and the lattice constant of the resistor layer is reduced. It has a value shifted from the lattice constant of the element-free aluminum nitride single phase by 0.003 to 0.020 ° on the a-axis and 0.005 to 0.040 ° on the c-axis. When the element is a Group 6b element of the periodic table, it is contained at a ratio of 0.01 to 20 atomic%,
From the lattice constant of the aluminum nitride single phase containing no doping element, the lattice constant of the resistor layer is 0.004 to 0.5 in the a-axis.
013 ° and a value shifted by 0.005 to 0.018 ° on the c-axis.

Hereinafter, the present invention will be described in detail. FIG. 1 shows an example of the electrostatic chuck of the present invention. According to the electrostatic chuck shown in FIG. 1, an electrode 2 to which a voltage is applied is provided on a surface of a substrate 1 made of an insulator having a volume resistivity of 10 ¹⁴ Ω-cm or more at room temperature. A thin layer 3 made of a resistor (hereinafter, referred to as a ceramic resistor layer) is formed. The ceramic resistor layer 3 is formed on at least the mounting surface of the silicon wafer 4 or the entire base surface exposed in the semiconductor manufacturing apparatus. Further, a heater 5 may be built in the base 1 as shown in FIG. 1, and a cooling medium flow path may be provided to cool the electrostatic chuck. Further, a groove 6 may be formed on the surface of the ceramic resistor layer 3 in order to improve the heat uniformity of the silicon wafer 4. The electrode 2 can be used as a high-frequency electrode by connecting to a high-frequency power supply.

In the present invention, the ceramic resistor layer 3
Is composed mainly of an aluminum nitride crystal phase, and contains, in the crystal phase, a Group 6b element of the Periodic Table or oxygen other than oxygen.
It contains a group b element. These elements are doped in the aluminum nitride crystal. Further, the ceramic resistor layer 3 in the present invention is formed by doping with the above element.
A volume resistivity at 5 ° C. of 10 ⁷ to 10 ¹³ Ω-cm,
In particular, it has characteristics in the range of 10 ⁸ to 10 ¹² Ω-cm. The Group 2b element of the periodic table or the Group 6b element other than oxygen is for imparting conductivity to aluminum nitride and controlling the volume resistivity in the above range.

When the doping element is a Group 2b element of the periodic table, it is contained at a ratio of 0.01 to 20 atomic%. If the content is less than 0.01 at%, it is not enough to lower the volume resistivity, and if it exceeds 20 at%, the properties as aluminum nitride change, and the volume resistivity becomes 10%.
^It becomes lower than ⁷ Ω-cm and cannot be used as an electrostatic chuck. As the elements of Group 2b of the periodic table, Zn,
Among them, Cd and Hg can be mentioned. Among them, Zn is inexpensive and the film formation can be easily controlled.

On the other hand, when the doping element is a Group 6b element of the periodic table other than oxygen, it is contained at a ratio of 0.01 to 20 atomic%. If this content is less than 0.01 atomic%, it is not enough to lower the volume resistivity, and if it is less than 20 atomic%.
If it exceeds, the characteristics as aluminum nitride change, the volume resistivity becomes lower than 10 ⁷ Ω-cm, and it cannot be used as an electrostatic chuck. Examples of the Group 6b elements of the periodic table include S, Se, and Te. Among these, S is inexpensive and the control of film formation is easy.

In terms of characteristics as an electrostatic chuck, if the resistance of this ceramic resistor layer is less than 1 × 10 ⁷ Ω-cm, the leakage current becomes large, and 1 × 10 ¹³ Ω-cm
If it is larger than the above range, the suction force may be reduced and a residual suction force may be generated.
Volume resistivity at ~ 300 ° C is 1 × 10 ⁷ Ω-cm ~ 1
It is desirable to be in the range of × 10 ¹³ Ω-cm. The electrostatic chuck of the present invention exhibits a substantially constant volume resistivity from 0 ° C. to 300 ° C. within this range. Considering the response to leakage current and voltage application, 1 × 10 ⁸ to
5 × 10 ¹² Ω-cm is 1 ×
Most preferably, it is 10 ^{9 to} 5 × 10 ¹¹ Ω-cm.

Further, in order to perform a stable operation as an electrostatic chuck, a temperature range of use, for example, 25 ° C. to 300 ° C.
The volume resistivity change in the temperature range of ° C. should be within 3 digits, preferably within 2 digits. If the volume resistivity at 25 ° C. is R (25 ° C.) and the volume resistivity at 300 ° C. is R (300 ° C.),

[0019]

(Equation 1)

The resistance change ΔR represented by
It means the following. In addition, -100
Similar results can be expected at temperatures between 300C and 300C.

Further, according to the present invention, the periodic table 2
The addition of a group b element or a group 6b element changes the lattice constant of the aluminum nitride crystal phase, which is the main phase. According to the measurement by the present inventors, the positive side,
The shift to the negative side changes, but the lattice constant of the aluminum nitride single phase (may change depending on the measurement equipment, etc., but the measurement by the present inventors has shown that the a-axis 3.120 °, c
The axis was 4.994 °. ), It is 0.003 to 0.020 ° on the a-axis and 0.00 on the c-axis in the case of the Group 2b element.
It has a value shifted by 5 to 0.040 °, and in the case of a Group 6b element, it has a value shifted by 0.004 to 0.013 ° on the a-axis and 0.005 to 0.018 ° on the c-axis.
Therefore, when this lattice constant shifts at a level smaller than the above range or shifts beyond the above range,
In any case, it is difficult to obtain desired electric characteristics.

As described above, an AlN ceramic resistor layer containing elements other than Al and N and having the above-mentioned electrical characteristics can be easily produced by a vapor phase synthesis method. Specific film formation methods include sputtering,
Physical vapor synthesis (PVD) such as ion plating
Method), plasma CVD, optical CVD, MO (Metal)
-Organic) Chemical vapor synthesis (CV) such as CVD
D method), and among them, the CVD method is preferable.

For example, when Zn is selected as an element to be contained and a film is formed by a CVD method, N ₂ gas, NH ₃ gas, Zn (CH ₃ ) ₂ and AlC
l ₃ gas, and the flow ratio of these gases is N ₂ / AlC
l ₃ = 5-70, Zn (CH ₃ ) ₂ / NH ₃ = 0.00
1 to 5, NH ₃ / AlCl ₃ = 1 to 10, and the film formation temperature is set at a relatively high value of 850 ° C. or higher. In addition, when an element of Group 2b of the periodic table is contained, in addition to the above Zn (CH ₃ ) ₂ , Z
n (C ₂ H ₅ ) ₂ , Cd (CH ₃ ) ₂ , Cd (C
₂ H ₅ ) ₂ , Hg (CH ₃ ) _2, etc. can be used in the same manner.

When an element of Group 6b of the periodic table is contained, for example, when S (sulfur) is contained, N ₂ gas, NH ₃ gas, H ₂ S and AlC
l ₃ gas, and the flow ratio of these gases is N ₂ / AlC
l ₃ = 5-70, H ₂ S / NH ₃ = 0.001-5, N
H ₃ / AlCl ₃ = 1 to 10; film forming temperature 850 ° C.
It can be manufactured by setting the above relatively high. In addition, when an element of Group 6b of the periodic table is contained, in addition to the above H ₂ S, H ₂ Se, Se (C
H ₃ ) ₂ , Se (C ₂ H ₅ ) ₂ , H ₂ Te, Te (CH
₃ ) ₂ , Te (C ₂ H ₅ ) _{2 and the} like.

On the other hand, the substrate of the electrostatic chuck on which the ceramic resistor layer is formed is not particularly limited. For example, Al ₂ O ₃ , AlON, Si ₃ N ₄ , AlN, diamond, mullite, ZrO _2, etc. The main ceramic materials may be mentioned. Among them, a sintered body mainly composed of aluminum nitride in view of excellent plasma resistance at the time of semiconductor production and excellent adhesion with the ceramic resistor layer, or 800 to 800 from room temperature. Thermal expansion coefficient up to 4.0 ° C
8.0 × 10 ⁻⁶ / ° C., especially 4.8 to 6.7 × 10 ⁻⁶ / ° C.
Is preferable in consideration of the adhesion to the resistor film.

Further, a well-known metal material can be applied to the electrode 2 to which a voltage is applied, for example, W, Mo, Mo-M
Any of n and Ag can be used. In addition, a conductive ceramic material, for example, TiN, SiC, WC, carbon, or a Si semiconductor material (n-type or p-type) can also be used as the electrode material. In addition, there is a case where the electrode 2 does not exist and the substrate itself has an electrode function.
It may be formed of a conductive ceramic mainly composed of iC, TiN, WC, or the like, a simple metal such as W or Mo, an alloy thereof, or carbon. In that case, it can be used as an electrostatic chuck by directly applying a voltage to the conductive substrate itself. When the heater is built in the insulating base, Mo, W, WC,
Mo-Mn, TiC, TiN or the like is used.

In order to electrostatically adsorb a silicon wafer by the electrostatic chuck having the above-described configuration, electrostatic adsorption is performed by applying a voltage of about 0.2 to 2.0 kV to an electrode or a conductive substrate. be able to.

[0028]

[Action] Normally, aluminum nitride has a volume resistivity of 10 ¹⁴
Although it is a high insulator of Ω-cm or more, in the aluminum nitride crystal, a 2b group element of the periodic table such as Zn and Cd,
It is considered that when an element of Group 6b of the periodic table, such as S or Se, is substituted with aluminum or nitrogen, it becomes a semiconductor, that is, an excess or deficiency of electrons occurs, which contributes to conductivity and increases the conductivity of the crystal. By controlling the volume resistivity at 25 ° C. to be in the range of 10 ⁷ to 10 ¹³ Ω-cm, excellent electrostatic attraction characteristics can be obtained under the operating conditions of the electrostatic chuck. In addition, this resistor layer has a small resistance change with temperature, for example, from 25 ° C. to 300 ° C.
Resistance change to temperature change up to ° C is as small as 3 digits or less. As a result, the wafer chucking characteristics in this temperature range are stabilized, and an electrostatic chuck free of residual suction force can be obtained.

Further, according to the present invention, it is not necessary to take a particularly complicated structure as the electrostatic chuck, and the use of the material of the present invention simplifies the structure of the electrostatic chuck itself, and enables a low cost and wide range. The device can be used in the temperature range, the device itself including the electric circuit can be simplified, and the reliability and long-term stability of the electrostatic chuck are guaranteed.

[0030]

【Example】

Example 1 After an alloy of Mo and Mn was metallized as an electrode on the surface of a substrate made of an aluminum nitride sintered body, an AlN film was formed on the surface of the substrate including the electrode by a chemical vapor deposition method. The formation of the AlN film is performed by using an external heat method for the substrate.
In a furnace heated to 00 ° C., the nitrogen gas was kept constant at 8 SLM, the ammonia gas was kept constant at 1 SLM, the gas containing a Group 2b element in the periodic table was changed to the flow rate shown in Table 1, and the furnace pressure was set at 4 SLM.
0 torr. And aluminum chloride (AlC
l ₄ ) at a flow rate of 0.3 SLM to start the reaction.
A ceramic resistor layer having a thickness of 00 μm was formed. The volume resistivity at -100 ° C, 0 ° C, 25 ° C and 300 ° C of the obtained resistor layer was measured. The results are shown in Table 1.

The angle of the obtained film was corrected by X-ray diffraction measurement using Si (SRM640b) as a standard sample, and the lattice constant was calculated by the peak top method.
Table 1 shows the difference from the lattice constant of the o.1 sample. The measurement surface indices are (100), (002), (101), and (1).
02), (110), (103), (112), (00)
4).

Then, the surface of the ceramic resistor layer after the vapor phase growth is polished so that the surface roughness Ra becomes 0.02 mm, and then 25 ° C. as an electrostatic chuck when a voltage of 400 V is applied to the electrodes. And the voltage was applied for 30 minutes, and the presence or absence of the residual adsorption force immediately after stopping the voltage application was measured in vacuum. Further, in the change of the adsorption force from 25 ° C. to 300 ° C., the rate of change was within 10% was evaluated as ○, and the rate of change was evaluated as ×. The results of these measurements are shown in Table 1.

[0033]

[Table 1]

As is clear from the results shown in Table 1, the amount of the element belonging to Group 2b of the periodic table and the lattice constant of the resistor layer change depending on the flow rate of the gas containing the element belonging to Group 2b of the periodic table. In the case where no element-containing gas is introduced and the oxygen atomic weight is 0.0001 atomic%, which is the impurity level (Sample No. 1), the resistance value is 5.9 × 10 ¹⁵ Ω-cm at room temperature and the insulating property is high. However, when the flow rate of the gas containing a Group 2b element in the periodic table was gradually increased, the volume resistivity at room temperature also decreased. However, when the element of Group 2b of the periodic table exceeded 20 atomic% (Sample No. 10), the volume resistivity was lower than 10 ⁷ Ω-cm, and the leak current was so large that the adsorption power could not be measured. In addition, the obtained resistor layer was obtained from X-ray diffraction measurement (00
The AlN film was oriented in 2).

FIG. 2 shows the measurement results of the temperature dependence of the volume resistivity of the electrostatic chuck of Sample No. 4, and FIG.
The electrostatic chuck of FIG. 1 is configured using the AlN film of o.4,
FIG. 3 shows the measurement results of the temperature dependence of the attraction force when a voltage of 400 V was applied to the electrodes. As is clear from FIGS. 2 and 3, the volume resistivity is 3.5 × 10 ^{10 to} 6.0 × 1 in the entire temperature range of −100 ° C. to 300 ° C.
It was in the range of 0 ¹⁰ Ω · cm, and the adsorbing power was constant in this temperature range as shown in FIG.

On the other hand, in the case of an electrostatic chuck (sample No. 1) in which the AlN film contains only the element of Group 2b of the periodic table at an impurity level, the measured temperature is from 25 ° C. to 300 ° C.
With the change to ° C, the volume resistance changes from 10 ¹⁵ Ω-cm to 10
^It rapidly changed to ¹¹ Ω-cm. Therefore, 150 ℃,
At 200 ° C., the time required for the adsorption force to stabilize was long, and residual adsorption force was observed. Samples No. 1 and 2 having a resistance at 25 ° C. exceeding 10 ¹³ Ω-cm had low adsorption power, and sample No. 10 had a leak current, and could not be measured.

Example 2 An alloy made of Mo and Mn was metallized as an electrode on the surface of a substrate made of an aluminum nitride sintered body, and an AlN film was formed on the surface of the substrate including the electrode by a chemical vapor deposition method. The formation of the AlN film is performed by using an external heat method for the substrate.
The reactor was placed in a furnace heated to 00 ° C., the nitrogen gas was kept constant at 8 SLM, the ammonia gas was kept constant at 1 SLM, the gas containing a Group 6b element in the periodic table was changed to the flow rate shown in Table 1, and the furnace pressure was set at 4 SLM.
0 torr. And aluminum chloride (AlC
l ₄ ) at a flow rate of 0.3 SLM to start the reaction.
A ceramic resistor layer having a thickness of 00 μm was formed. The volume resistivity at -100 ° C, 0 ° C, 25 ° C and 300 ° C of the obtained resistor layer was measured. The results are shown in Table 2.

The lattice constant of the obtained film was calculated in the same manner as in Example 1, and the difference from the lattice constant of Sample No. 1 is shown in Table 1.

Then, the surface of the ceramic resistor layer after the vapor phase growth was polished so that the surface roughness Ra became 0.02 mm. The change in the adsorption power at 300 ° C. to 300 ° C. was evaluated. The results of these measurements are shown in Table 2.

[0040]

[Table 2]

As is clear from the results shown in Table 2, the amount of the element belonging to Group 6b of the periodic table and the lattice constant of the resistor layer change depending on the flow rate of the gas containing the element belonging to Group 6b of the periodic table. When the element-containing gas was not introduced at all and the impurity level was 0.0001 atomic% (sample No. 18), the resistance was 8.8 × 10 ¹⁵ Ω-cm at room temperature, but the insulation was high. When the flow rate of the group 6b element-containing gas in the periodic table was gradually increased, the volume resistivity at room temperature also decreased. However, Sample No. 2 in which Group 6b element of the periodic table exceeds 20 atomic%
In Nos. 4 and 30, peeling of the film occurred. This is probably because the internal stress in the film increased. Sample No. 19, which had a volume resistivity at 25 ° C. of more than 10 ¹³ Ω-cm, had a low adsorption power. The obtained resistor layer was an AlN film oriented to (002) by X-ray diffraction measurement.

FIG. 4 shows the measurement results of the temperature dependence of the volume resistivity of the electrostatic chuck of Sample No. 23, and the electrostatic chuck of FIG. 1 was constructed using the AlN film of Sample No. 23. FIG. 5 shows the measurement results of the temperature dependence of the attraction force when a voltage of 400 V was applied to the electrodes. As apparent from FIGS. 4 and 5, the volume resistivity is 2.0 × 10 ^{11 to} 2.3 over the entire temperature range of −100 ° C. to 300 ° C.
It was in the range of × 10 ¹⁰ Ω · cm, and the adsorbing power was constant in this temperature range, as shown in FIG.

On the other hand, in the case of the electrostatic chuck (sample No. 18) in which the AlN film contains only the element of group 6b of the periodic table at the impurity level, the measured temperature is from 25 ° C. to 30 ° C.
With the change to 0 ° C., the volume resistance changed from 10 ¹⁵ Ω-cm to 1
It rapidly changed to 0 ¹¹ Ω-cm. Therefore, 150
At 200 ° C. and 200 ° C., the time required for the adsorption force to stabilize was long, and residual adsorption force was observed.

[0044]

As described in detail above, the electrostatic chuck of the present invention has high plasma resistance, high suction power during semiconductor manufacturing, and stable suction characteristics over a wide temperature range. Thus, excellent reliability and long-term stability as an electrostatic chuck can be obtained, and the manufacturing cost of the electrostatic chuck can be reduced.

[Brief description of the drawings]

FIG. 1 is a sectional view showing a structure of an electrostatic chuck according to the present invention.

FIG. 2 is a diagram showing the temperature dependence of the volume resistance value of the ceramic resistor layer of Sample No. 4 of Example 1.

FIG. 3 is a diagram showing the temperature dependence of the attraction force of an electrostatic chuck having a ceramic resistor layer of Sample No. 4 of Example 1.

FIG. 4 is a diagram showing the temperature dependence of the volume resistance value of the ceramic resistor layer of Sample No. 23 of Example 2.

FIG. 5 is a diagram showing the temperature dependence of the attraction force of an electrostatic chuck having a ceramic resistor layer of Sample No. 23 of Example 2.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Base 2 Electrode 3 Ceramic resistor layer 4 Silicon wafer

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int. Cl. ⁷ , DB name) H01L 21/68 B23Q 3/15 H01C 7/00

Claims (3)

(57) [Claims] 1. A surface of a substrate on which an electrode is provided, comprising, on a surface of an aluminum nitride crystal phase, at least one element selected from Group 2b elements other than Group 2b and oxygen of the periodic table, and Volume resistivity at 25 ° C. of 10 ⁷ to
An electrostatic chuck having a ceramic resistor layer of 10 ¹³ Ω-cm formed thereon. 2. The ceramic resistor layer contains a Group 2b element of the periodic table excluding oxygen at a ratio of 0.01 to 20 atomic%, and the lattice constant of the resistor layer does not include a doping element. From the lattice constant of aluminum nitride single phase, 0.00
2. The electrostatic chuck according to claim 1, wherein the electrostatic chuck has a value of 3 to 0.020 ° and a value shifted by 0.005 to 0.040 ° on the c-axis. 3. An aluminum nitride monolayer containing a Group 6b element of the periodic table at a rate of 0.01 to 20 atomic% in the ceramic resistor layer, wherein the lattice constant of the resistor layer does not contain a doping element. From the lattice constant of the phase, 0.004 to 0.0 on the a-axis.
The electrostatic chuck according to claim 1, wherein the electrostatic chuck has a value shifted by 0.005 to 0.018 ° on the c-axis at 13 °.