JPH03276713A - Pattern forming material and pattern forming method - Google Patents

Abstract

PURPOSE:To improve the shape of accumulated energy profile which is formed as a latent image by electron beam lithography and to improve the shape of a pattern and resolution by performing the electron beam lithography and the projection of light within a specified wavelength range for resist at the same level. CONSTITUTION:In negative-type elecron-beam resit comprising novolak resin or p-hydroxystyrene resin, melamine compound and acid generating agent, the acid generating agent forms acid by the projection of the electron beam. With the acid as a catalyst, the resin and the melamine compound are bridged, and negatives property is obtained. In resist material, intense absorption is present in far infrared region. There is a window part where the absorbance becomes the minimum value in the vicinity of 240-260nm. In the p-hydroxystirene resin, the window is located in the vicinity of 248nm. In the vicinity of 265nm, epsilonbecomes large up to about 0.7mum<-1>. Then, the light is projected at this wavelength region. Thus the shape of a pattern is improved. The light is selectively projected on the wavelength region at the optimum value in the range of 0.5-1.2mum<-1> for epsilon of the resist material. Thus, the shape of the pattern is improved.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a technique for forming fine resist patterns in semiconductor device manufacturing technology.

[Conventional technology]

In recent years in the semiconductor industry, ASIC (apPl)
cation 5specified intergr.
Custom L represented by
Demand for SI is rapidly growing. Mass-produced LSIs, such as DRAM, are produced using optical lithography, but ASICs, which are in demand in small quantities and with many products,
Electron beam direct writing technology is also positioned as a useful pattern formation method. Electron beam lithography has already been put into practical use in the field of manufacturing masks for light exposure, and is a highly complete microfabrication technology. If the resist film thickness is made thinner, it is possible to form a pattern with a line width of 0.1 μm, and the resolution is basically higher than that of light exposure technology. In addition, it has features such as having a pattern creation function and not requiring a mask.
It is ideal for producing multiple items.

Generally, in the manufacture of devices such as LSIs, a substrate that has gone through a certain number of steps has a level difference of about 0.5 μm on the surface of the substrate due to wiring layers and the like. In order to cover such steps and still process the substrate, the resist film thickness must be 1 to 2 μm.
It is necessary to make it to a certain extent. However, when attempting to form a pattern using electron beam lithography on a resist with a film thickness of 1 to 2 μm with an aspect ratio of approximately 2, the proximity effect begins to significantly affect the pattern shape and resolution. In other words, the pattern shape is not rectangular but trapezoidal or triangular;
Resolution decreases. The proximity effect includes forward scattering of incident electrons within the resist film and back scattering from the substrate.

As the film thickness increases, due to the former effect, the latent image formed in the resist film takes on a shape that spreads toward the end, and the pattern after development reflects this shape. The drawing is shown in FIG. That is, FIG. 2 is a schematic diagram showing a cross-sectional shape of a resist pattern formed by a conventional pattern forming method. With a resist pattern having such a cross-sectional shape that widens toward the end, it is difficult to ensure dimensional accuracy when processing the substrate by dry etching. In order to process a substrate with high dimensional accuracy, a resist pattern having a rectangular cross-sectional shape is desirable.

It is well known that the multilayer resist method is useful as a method to avoid such deterioration of pattern shape.
There are problems in using it at a production level because the number of steps increases and it tends to become a source of dust. Regarding the improvement of the pattern shape of single-layer resist, for conventional photoresists etc., ■ Far ultraviolet irradiation [for example, Suga et al., Journal of Vacuum Science and Technology (J, Vac, Sci, Technol, ) Vol.
Volume 6, page 366 (1988)], ■ Soaking process [
For example, Ogawa et al., Microprocess Conference,
(Tokyo, 1988), p. 164], ■ forming an insoluble layer on the surface [e.g., Ogawa et al., Micro Process Conference, (Tokyo, 1988), p. 86], etc. has been reported.

Ordinary resist materials have aromatic substituents,
Strongly absorbs deep ultraviolet light. The method of irradiating far ultraviolet rays before or after electron beam lithography exposes only the surface of the resist to form a hardly soluble layer on the resist surface. In the soaking method, an alkali-developable resist is immersed in a solvent such as an alkaline aqueous solution or chlorobenzene to modify the resist film surface and form a hardly soluble layer. A method of coating and forming an insoluble layer on the surface is, for example, by coating a thin layer of polymethylpentene sulfone (PMPS) on the resist surface to form a two-layer resist structure.
The electron beam drawing section utilizes self-development of PMPS, and the remaining PMPS functions in the undrawn section as an insoluble layer in the developer.

[Problem to be solved by the invention]

These surface hardly soluble layer forming treatment methods are found to be improved in terms of pattern shape improvement and resolution improvement when compared to untreated materials. However, the central part of the pattern cross section is often depressed, and it cannot be said that the pattern shape is necessarily suitable for substrate processing.

An object of the present invention is to provide a pattern forming material and a pattern forming method for achieving improved pattern shape and high resolution in direct electron beam writing.

[Means to solve the problem]

To summarize the present invention, the first aspect of the present invention relates to a pattern forming method, and the pattern forming method using a negative electron beam resist includes an electron beam drawing step, an extinction coefficient of the resist coating film, and a pattern forming method using a negative electron beam resist. It is characterized by including the steps of irradiating light in a wavelength range of 0.5 to 1.2 μm −1 and developing.

The second invention of the present invention relates to a resist material, which includes three essential components: a novolak resin or p-hydroxystyrene resin, a melamine compound, and an acid generator, and may also contain an ultraviolet absorber as a fourth component. In the negative electron beam resist which does not need to contain, the extinction coefficient of the resist coating film is 248 nm, 254 nm,
It is characterized in that it is 0.5 to 1.2 μm −1 for ultraviolet rays of 313 ohm, 365 nm or 436 nm.

In the pattern forming method of the present invention, other steps may be added in addition to the above three steps, and for example, heat treatment may be performed before the above development step.

Further, the electron beam drawing step and the light irradiation step may be performed in any order.

The present invention improves the shape of the stored energy profile formed as a latent image by electron beam lithography by performing electron beam lithography and light irradiation on the same layer of resist, thereby improving the pattern shape and resolution. This is intended to improve the quality of life.

The light incident on the resist film is attenuated according to the Lambert-Beer equation (Equation 1).

I (d) "IoX 10-" (1) where d = depth from the resist surface, I (d) UV intensity at depth d, ■. = incident ultraviolet light intensity, ε - resist extinction coefficient for irradiated ultraviolet light. Reflectance-R
When using a substrate with a resist film thickness of -T, the intensity distribution of ultraviolet light in the film thickness direction is 2
It can be expressed as the formula.

I (d) -1o X 1O-ed1Rx 1.
x 10G"2T) (2) The energy 8E absorbed by the resist film of Δd at depth d due to exposure for time t can be expressed as in equation 3.

△E= 2JO3xεxI(d)xtxΔd (3)
In the conventional method of making the surface insoluble by irradiating far ultraviolet rays, since the resist has a large extinction coefficient for far ultraviolet rays, the far ultraviolet rays attenuate steeply in the direction of the resist film thickness, and only the vicinity of the resist surface is strongly exposed. For this reason, the resist surface remains on the pattern after development, and the pattern tends to have a reverse tapered shape with a depression in the center. On the other hand, when the extinction coefficient is small, the effect of improving the pattern shape is small and the bottom of the resist film is exposed, which tends to appear as fog. As you can see from equations 2 and 3, the depth d
The energy given in is a function not only of the exposure amount but also of the extinction coefficient. This means that by controlling the extinction coefficient of the resist, the amount of light energy absorbed can be controlled in the film thickness direction. As a result of intensive study, the inventors of the present invention realized that the concept of improving the shape of the latent image profile includes the conventional surface treatment to make the surface insoluble, and completed the present invention. That is, by adding energy from ultraviolet irradiation as shown in FIG. 1b to the accumulated energy profile of a latent image formed by electron beam lithography as shown in FIG. 1-a, the accumulated energy profile is improved as shown in FIG. 1-c. A rectangular pattern as shown in FIG. 1-d is obtained.

From a chemical reaction theory, it is thought that the following photo/radiation chemical reactions proceed within the resist film. Let S be a sensitive compound or a sensitive group that contributes to negativeization in the electron beam resist. After being excited by electron beam irradiation (formula 4), S causes a chemical change and crosslinks the resist (formula 5). If the resist has appropriate absorption in the ultraviolet and deep ultraviolet regions,
S can also be excited by ultraviolet or deep ultraviolet light.

Even if the resist does not have appropriate absorption, it may be possible to impart photosensitivity by adding an appropriate spectral sensitizer. In such a case, first, the sensitizer is excited by light, and energy is transferred from the excited sensitizer molecule (Equation 6) to excite S (Equation 7).

Light D → D* (6) D"+S → D0S" (7) S* generated by formula 7 causes crosslinking according to formula 5. Here, D does not necessarily have to be a material additionally added to the electron beam resist, and may be a sensitizing group chemically introduced into the electron beam resist. Further, the wavelength of the light that excites D is not limited as long as it can cause the reactions of formulas 6 and 7.

The energy profile accumulated by the electron beam varies depending on the accelerating voltage of the electron beam, the thickness of the resist film, the material of the substrate, the composition of the resist, and the like. Therefore, the optimum extinction coefficient for improving the shape of the latent image profile by light irradiation differs depending on the conditions. When a silicon substrate was used, an accelerating voltage of 30 kV, a film thickness of -17 μm, and a pattern rule of 0.8 μm, a good pattern could be obtained by adjusting ε=0.7 μm−1.

Further, when the film thickness was 1 μm and the pattern rule was −0.5 μm, a good pattern was obtained by adjusting ε=1°2 μm−1. As a result of intensive study by the present inventors, the optimal value of ε is 0.5 to 1.2μ even if the writing conditions vary.
It was found that when ε is within the range of m-1 and takes the optimum value, the light energy is distributed in a well-balanced manner in the film thickness direction, and the pattern shape is good.

First, the pattern forming method of the present invention will be briefly explained. For example, when using chloromethylated polystyrene (CMS), a negative electron beam resist, which has ε1 μm−1 in the far ultraviolet region of 248 nm, after electron beam writing, Kr
By irradiating with light using a suitable light source such as P excimer laser, the pattern shape can be improved.

At this time, the light irradiation step may be performed before or after the electron beam lithography step. Further, in order to sensitize the resist, there is no problem in adding a suitable sensitizer. C
Using the example of MS, ε at 2540m is 0.2μ
Since it is small, about m-1, for example, by adding phenothiazine as a sensitizer and adjusting ε = 0.8 μm-1, it is possible to improve the pattern shape using an appropriate light source such as a low-pressure mercury lamp. can. Furthermore, instead of adding a sensitizer, a sensitizing group may be chemically introduced into the resist material. At this time, in order to control the distribution of light energy within the resist as shown in Equations 2 and 3, it is desirable that the exposure source be light with a wavelength as narrow as possible, and such light sources include bright lines and lasers. Alternatively, there is light that has been narrowed by an interference filter or the like. This also applies when a heat treatment step is performed before the development step.

An example of the method of the present invention will be briefly described below. In a negative electron beam resist consisting of a novolac resin or p-hydroxystyrene resin, a melamine compound, and an acid generator, the acid generator generates an acid by electron beam irradiation, which acts as a catalyst to generate an acid such as a phenol resin or p-hydroxystyrene. The resin and melamine compound crosslink and become negative.

Usually, these resist materials have a strong absorption in the deep ultraviolet region, but there is a window portion where the absorbance is minimal in the vicinity of 240 to 260 nm. Typically, a resist material made of a novolak resin, a melamine compound, and an acid generator has a thickness of about ε-0.4 μm −1 at around 25 Snm.

Even if this area is irradiated with light, the effect of improving the pattern is small. However, at 248nm, ε=0.9μm
Since it is about -1, the pattern shape can be improved by irradiating light in this wavelength range. Also 026
Even in the vicinity of 5 mm, since ε=0.8 μm−1, a similar effect can be obtained. Furthermore, in the case of p-hydroxystyrene resin, the window is around 248 nm, and ε is as small as about 0.2 μm −1 . However, 265
Since ε increases to about 0.7 μm-1 in the vicinity of nm, the pattern shape can be improved by irradiating light in this wavelength range. In this way, in this example, the pattern shape is improved by selectively irradiating light in the wavelength range of the optimum value within the range of ε of the resist material from 0.5 to 1.2 μm l. It is. Note that the heat treatment step is performed to promote the negative conversion reaction.

Also in this specific example, the light irradiation step may be performed before or after the electron beam lithography step.

Hereinafter, one example of the resist material of the present invention, that is, the second invention of the present invention will be briefly described.

4. There are not many light sources that have an appropriate output for uniformly irradiating the entire surface of the substrate. In the present invention, the material is prepared so that ε is 0.5 to 1.2 μm −1 for a specific wavelength. Here, the specific wavelength is 2
48 nm (KrF excimer laser) or 254
nm (bright line of low pressure mercury lamp) or 313 nm (bright line of high pressure mercury lamp) or 365 nm (bright line of ultra high pressure mercury lamp) or 436 nm (bright line of ultra high pressure mercury lamp)
And so. The extinction coefficient of novolak resin and p-hydroxystyrene resin can be adjusted by the synthesis method, the mixing ratio of isomers, etc. Furthermore, the extinction coefficient may be adjusted by adding a suitable sensitizer. The sensitizer is not specified as long as it is a compatible material when mixed to form a resist coating film.

In one example of a pattern forming method using the resist material of the second invention, in the step of drawing an electron beam in a pattern, ε is set to 0.
．． This is carried out by irradiating the entire surface of the substrate with light in the wavelength range adjusted to 5 to 1.2μ, a heat treatment step, and a development step. You can go before or after.

〔Example〕

EXAMPLES Hereinafter, the present invention will be explained in more detail with reference to Examples, but the present invention is not limited to these Examples.

Example I CMS was dissolved in chlorobenzene to form a coating film with a thickness of 2 μm. Extinction coefficient at 248 nm is 1.0μ
It was m-1.

1 at acceleration voltage -30kV, exposure amount = 3 μC/cm2
．． A line and space pattern of 0 μm was drawn, and then 248 nm light was irradiated at 3 mJ/cm 2 using a KrF excimer laser. Methyl isobutyl ketone (
MIBK) for 2 minutes to obtain a pattern. Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved. Furthermore, even when the order of light irradiation and electron beam writing was changed, and light irradiation was performed first and electron beam writing was performed afterwards, a similar improvement in pattern shape was observed.

Example 2 CMS was dissolved in chlorobenzene, phenothiazine was added, and the amount of phenothiazine was adjusted so that the extinction coefficient at 254 nm was 0.8 μm −1 . This resist was spin-coded onto a silicon substrate and prebaked at 85° C. for 2 minutes to form a coating film with a thickness of 1.7 μm. Acceleration voltage -30kV, exposure amount = 4 μC/cm2, 0.8
A line and space pattern of μm was drawn, then irradiated with 254 nm light and developed with MIBK.

Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved.

Example 3 A pyrenyl group was introduced into CMS by reacting the chloromethyl group of CMS with 1-pyrenemagnesium bromide. The amount of pyrenyl group introduced was adjusted so that the absorbance at 340 nm was 0.8 per 1 μm of the coating film. This resist was coated with a quick pin on a silicon substrate, prebaked at 85°C for 1 minute, and
A coating film with a thickness of μm was formed. The entire surface was irradiated with 365 nm light, and then a 0.8 μm line and space pattern was drawn with an electron beam. A pattern was obtained by developing with MIBK for 2 minutes. Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved.

Example 4 Anisyl was added to a negative resist prepared by adding a diazide compound to a novolac resin as a photosensitizer, and the amount of anisyl added was adjusted so that the absorption intensity at 313 nm was 1.2 per 1 μm thick coating film. . A resist having this composition was spin-coded onto a silicon substrate and prebaked at 85° C. for 2 minutes to form a coating film with a thickness of 1.0 μm. Accelerating voltage 30
Draw a 0.6 μm line and space pattern at kV, ill light intensity = 30 μC/cm2, and then
It was irradiated with 13 nm light. A pattern was obtained by developing with a 3% aqueous solution of tetramethylammonium hydroxide (TMAH). Compared to the purple 8 sample in the reference experiment that was not exposed to external radiation, the cross-sectional shape of the pattern was made rectangular, the resolution was improved, and the power was suppressed.

Example 5 The extinction coefficient at 248 nm of a negative electron beam resist consisting of three components: a novolac resin, a melamine compound, and an acid generator was 0.9 μm −1 . The resist was spin-coded onto a silicon substrate, prebaked at 85°C for 2 minutes, and then
．． A coating film with a thickness of 2 μm was formed. Acceleration voltage = 30kV,
A 0.6 μm line and space pattern was drawn at an exposure dose of 4.8 μC/cm 2 , and then 248 nm light from a KrF excimer laser was irradiated at 6 mJ/cm'.

Heat treatment was performed at 105° C. for 2 minutes, and development was performed with a 3% TMAH aqueous solution. Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved.

Example 6 265 nm negative electron beam resist consisting of three components: p-hydroxystyrene resin, melamine compound, and acid generator
The extinction coefficient at was 1.0 μm 19 . The resist was spin-coded onto a silicon substrate and prebaked at 85° C. for 2 minutes to form a coating film with a thickness of 1.0 μm. Acceleration voltage 30kVS exposure amount = 3.2
A line and space pattern of 0.6 μm was drawn using μC7cm 2 and irradiated with 265 nm light. The 265 nm light was obtained by monochromating far ultraviolet light from a xenon-mercury lamp using an interference filter. Heat treatment was performed at 105° C. for 2 minutes, and development was performed with a 3% TMAH aqueous solution. Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved.

Example 7 Phenazine was added to a negative electron beam resist consisting of three components: a novolak resin, a melamine compound, and an acid generator.
So that the extinction coefficient at 65 nm is 0.5 μm-1,
The amount of phenazine added was adjusted. A resist having this composition was spin-coded onto a silicon substrate and prebaked at 85° C. for 2 minutes to form a coating film with a thickness of 2.0 μm. A 1.00 μm line and space pattern was drawn at an accelerating voltage of −30 kV and an exposure amount of −10 μC 7 cm 2 , and then 2.5 J 7 cm” of 365 nm light was irradiated.

Heat treatment was performed at 105°C for 2 minutes. A pattern was obtained by developing with a 3% TMAH aqueous solution. Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved.

Example 8 Anisyl was added to SAL601ER7 (Silapray), and the amount of anisyl added was adjusted so that the extinction coefficient at 313 nm was 1.2 μm −1 .

A resist having this composition was spin-coded onto a silicon substrate and prebaked at 85° C. for 2 minutes to form a coating film with a thickness of 0.8 μm. Acceleration voltage 30kV, exposure amount = 10μ
A 0.4 μm line and space pattern was drawn with C7 cm”, and then 313 nm light was irradiated.1
Heat treatment was performed at 05°C for 2 minutes. A pattern was obtained by developing with a 3% TMAR aqueous solution. Compared to the sample in the reference experiment which was not exposed to ultraviolet rays, rectangularization of the cross-sectional shape of the pattern1 and improvement of resolution were observed.

Example 9 A negative electron beam resist material consisting of three components: a novolak resin, a melamine compound, and an acid generator was used. By adjusting the mixing ratio of cresol isomers in the novolak resin, the extinction coefficient at 254 nm of the resist material was adjusted to 0.7 μm.
It was hot. spin-coding the resist onto a silicon substrate using 2-ethoxyethyl acetate as a coating solvent;
Prebaking was performed at 85° C. for 2 minutes to form a coating film with a thickness of 1.7 μm. Accelerating voltage = 30kV, ji light amount -4μC/
Draw a line and space pattern of 0.8 μm in cm2, and then apply 254 nm light at 6 mJ/cm.
2 irradiations were performed. After heat treatment at 105℃, 3% T
It was developed with an MAH aqueous solution to obtain a negative pattern. Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved. Further, even when the order of light irradiation and electron beam drawing was changed, and light irradiation was performed first and electron beam drawing was performed afterwards, a similar improvement in the pattern 2 shape was observed.

Example 10 SAL601ER7 (Silapray) had an extinction coefficient of 0.4 μm −1 at 254 nm. Phenothiazine was added to this SAL to adjust the extinction coefficient to 0.7 μm-1. This was spin-coded onto a silicon substrate and heated to 85°C.
This was prebaked for 2 minutes to form a coating film with a thickness of 1.7 μm. Acceleration voltage - 30kVXi Light intensity - 3.5μC 7cm
2 to draw a 0.8 μm line and space pattern,
Thereafter, 254 nm light was irradiated at 5 mJ/cm2.

A heat treatment was performed at 105° C., and a pattern was obtained by developing with MF622 developer for 20 minutes. Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved. A similar improvement in pattern shape was observed when 2-nitronaphthol, 2-methoxyphenothiazine, phenazine, or pyrene was used instead of phenothiazine as the ultraviolet absorber.

Example 11 A resist material consisting of three components: p-hydroxystyrene resin, methylolmelamine, and acid generator was prepared, and the absorbance at 248 nm was 0.25 per μm of coated film. By adding phenothiazine to this material, coating film 1
The absorbance per μm was adjusted to 0.6. This was spin-coded onto a silicon substrate and prebaked at 85° C. for 2 minutes to form a coating film with a thickness of 2.0 μm. Acceleration voltage = 30
kV, exposure amount = 6 μC 7 cm2 to draw a 1.0 μm line and space pattern, then 248
6 mJ/cm'' of light was irradiated.

It was sensitized by heat treatment at 105°C. 0.8% of TMAH
A pattern was obtained by developing with an aqueous solution for 10 minutes.

Compared to the sample in the reference experiment which was not exposed to ultraviolet light, it was observed that the cross-sectional shape of the pattern was rectangular and the resolution was improved. Even if novolak resin, anisyl, 2-nitronaphthol, 2methoxyphenothiazine, phenazine, pyrene, etc. are used instead of phenothiazine, the absorbance at 248 nm can be adjusted, and a pattern shape similar to that of phenothiazine can be obtained. Improvement was observed.

〔Effect of the invention〕

As described above, according to the present invention, it is possible to improve the shape of a fine pattern formed by electron beam drawing technology, and this invention is useful in semiconductor device manufacturing.

[Brief explanation of drawings]

Figure 1-a is a schematic diagram showing the stored energy contour lines formed as a latent image on the resist film by electron beam lithography, and Figure 1-b is a schematic diagram showing the stored energy contour lines formed as a latent image on the resist film by full-surface irradiation with ultraviolet rays. Schematic diagram showing,
FIG. 1-c is a schematic diagram showing the accumulated energy contour lines formed as a latent image in the resist film by a combination of electron beam lithography and full-surface ultraviolet irradiation, FIG. 1-d is a schematic diagram showing the cross-sectional shape of the resist pattern, and FIG. 1 is a schematic diagram showing a cross-sectional shape of a resist pattern formed by a conventional pattern forming method. 5 Sauce at the register -78- Figure/-C Figure

Claims (1)

[Scope of Claims] 1. In a pattern forming method using a negative electron beam resist, in the step of electron beam drawing, a wavelength range in which the extinction coefficient of the resist coating film is 0.5 to 1.2 μm^-^1 1. A pattern forming method comprising the steps of irradiating with light and developing. 2. In a negative electron beam resist that requires three components: a novolac resin or p-hydroxystyrene resin, a melamine compound, and an acid generator, and may or may not contain an ultraviolet absorber as a fourth component, resist coating. The extinction coefficient of the film is 248 nm, 254 nm, 313 nm, 3
0.5 to 1 for ultraviolet rays of 65 nm or 436 nm
．． A resist material characterized by having a thickness of 2 μm^-^1.