Title of Invention: MASK BLANK SUBSTRATE, SUBSTRATE WITH MULTILAYER REFLECTION FILM, TRANSMISSIVE MASK BLANK, REFLECTIVE MASK BLANK, TRANSMISSIVE MASK, REFLECTIVE MASK, AND SEMICONDUCTOR DEVICE FABRICATION METHOD Abstract: Disclosed is a mask blank substrate for use in lithography, wherein a main surface of the substrate satisfies a relational equation of (BA70−BA30)/(BD70−BD30)≧350 (%/nm), and has a maximum height (Rmax)≦1.2 nm in a relation between a bearing area (%) and a bearing depth (nm) obtained by measuring, with an atomic force microscope, an area of 1 μm×1 μm in the main surface on the side of the substrate where a transfer pattern is formed, wherein BA30 is defined as a bearing area of 30%, BA70 is defined as a bearing area of 70%, and BD70 and BD30 are defined to respectively represent bearing depths for the bearing area of 30% and the bearing area of 70%. Detailed Description: CROSS REFERENCE TO RELATED APPLICATIONS This is a Continuation of application Ser. No. 14/348,349 filed Mar. 28, 2014, claiming priority based on International Application No. PCT/JP2013/059200 filed Mar. 28, 2013, claiming priority based on Japanese Patent Application No. 763-583-1812 filed Mar. 30, 2012, the contents of all of which are incorporated herein by reference in their entirety. TECHNICAL FIELD The present invention relates to a mask blank substrate, a substrate with a multilayer reflective film, a transmissive mask blank, a reflective mask blank, a transmissive mask, a reflective mask, and a method of manufacturing a semiconductor device, which ensure suppression of false defects (pseudo defects, nuisance defects) originating from the surface roughness of a substrate and a film in defect inspection using a high-sensitivity defect inspection apparatus, and facilitate the detection of critical defects such as foreign matters and scratches. BACKGROUND ART Generally, in the process of manufacturing a semiconductor device, fine patterns are formed using photolithography. A number of transfer masks called photomasks are normally used in forming the fine patterns. This transfer mask is generally a fine pattern formed by a metal thin film or the like and provided on a transparent glass substrate, and photolithography is also used in the fabrication of the transfer mask. A mask blank having a thin film (e.g., a light shielding film (an opaque film)) for forming a transfer pattern (a mask pattern) on a transparent substrate such as a glass substrate is used in fabricating the transfer mask by photolithography. The drawing a desired pattern on a resist film formed on the mask blank, a developing process of developing the resist film after drawing to form a desired resist pattern, an etching process of etching the thin film as a mask, and a process of stripping and removing the remaining resist pattern with the resist pattern used as a mask. In the developing process, after the desired pattern is drawn on the resist film formed on the mask blank, a developer is supplied to the resist film to dissolve a portion of the resist film which is soluble in the developer, thereby forming the resist pattern. In the etching step, with the resist pattern used as a mask, an exposed portion of the thin film where the resist pattern is not formed is removed by wet etching or dry etching, thereby forming a desired mask pattern on the transparent substrate. The transfer mask is finished in this way. A phase shift mask, as well as a binary mask having a light shielding film pattern of a chromium-based material on a conventional transparent substrate, is known as the types of a transfer mask. The phase shift mask is configured to have a phase shift film on a transparent substrate. The phase shift film has a predetermined phase difference, and is made of, for example, a material containing molybdenum silicide compound. Further, a binary mask using a material containing a silicide compound of a metal such as molybdenum for a light shielding film is being used. These binary mask and phase shift mask are generally called a transmissive mask herein, and a binary mask blank and a phase shift mask blank, which are used as a master for a transfer mask, are generally called a transmissive mask blank herein. In recent years, higher integration of semiconductor devices in the semiconductor industry requires fine patterns beyond the transfer limit of the conventional photolithography using ultraviolet light. To enable formation of such fine patterns, EUV lithography which is an exposure technique using extreme ultraviolet (hereafter referred to as “EUV”) is promising. EUV light refers to light in the waveband of the soft X-ray region or the vacuum ultraviolet region, specifically, light with a wavelength of about 0.2 to 100 nm. A reflective mask has been proposed as a transfer mask for use in the EUV lithography. Such a reflective mask has a multilayer reflective film formed on a substrate to reflect exposure light, and an absorber film patterned on the multilayer reflective film to absorb exposure light. As described above, as a demand for miniaturization in the lithography process increases, problems in the lithography process are becoming prominent. One of the problems concerns defect information on a mask blank substrate or the like, which are used in the lithography process. The mask blank substrate is demanded to have a higher flatness from the viewpoints of an improvement on the defect quality needed with the recent miniaturization of patterns and the optical characteristics needed for transfer masks. The conventional surface processing methods for mask blank substrates are described in, for example, Patent Literatures 1 to 3. Patent Literature 1 describes a glass-substrate polishing method of polishing the surface of a glass substrate essentially comprising SiO2 by using a polishing slurry containing colloidal silica with an average primary particle size of 50 nm or less, acid, and water, and adjusted to have a pH of 0.5 to 4, in such a way that the surface roughness, Rms, as measured with an atomic force microscope becomes not more than 0.15 nm. Patent Literature 2 describes a polishing agent for the synthetic quartz glass substrate, which contains a suppressive colloidal solution and an acidic amino acid to suppress the formation of defects to be detected by a high-sensitivity defect inspection apparatus on the surface of a synthetic quartz glass substrate. Patent Literature 3 describes a method of controlling the flatness of a quartz glass substrate by placing the quartz glass substrate in a hydrogen radical etching apparatus, and causing hydrogen radicals to act with the quartz glass substrate, so that the flatness can be controlled in the sub-nanometer order. Patent Literature 1: JP-A-2006-35413 Patent Literature 2: JP-A-2009-297814 Patent Literature 3: JP-A-2008-94649 With the rapid miniaturization of patterns in lithography using an ArF excimer laser or EUV (Extreme Ultra-Violet), the defect sizes of transmissive masks (also called optical masks), such as a binary mask and a phase shift mask, and an EUV mask is a mask are also becoming smaller. To find such fine defects, the wavelength of the inspection light source used in defect inspection is approaching the light source wavelength of the exposure light. For example, as a defect inspection apparatus for an optical mask, a mask blank, which is a master thereof, and a substrate, high-sensitivity defect inspection apparatuses with an inspection light source wavelength of 193 nm are becoming popular. As a defect inspection apparatus for an EUV mask, an EUV mask blank, which is a master of an EUV mask, and a substrate, high-sensitivity defect inspection apparatuses with inspection light source wavelengths of 266 nm, 193 nm, and 13.5 nm are becoming popular or have been proposed. The main surface of a substrate used for the conventional transfer mask is managed by surface roughness represented by Rms (root mean square roughness) and Rmax (maximum height) in the fabrication process. Because the detection sensitivity of the high-sensitivity defect inspection apparatus described above is high, however, many false defects are detected in defect inspection of the main surface of the substrate even when the smoothness in compliance with Rms and Rmax becomes higher from the viewpoint of the improvement on the defect quality, raising a problem such that the defect inspection cannot be performed to the end. The false defect mentioned herein refers to a tolerable irregularity (unevenness) on the substrate surface, which does not affect pattern transfer, and which is erroneously determined as a defect in inspection with a high-sensitivity defect inspection apparatus. When a lot of such false defects are detected in defect inspection, critical defects that affect pattern transfer may be buried in many false defects, so that the critical defects cannot be discovered. For example, a defect inspection apparatus having an inspection light source wavelength of 266 nm or 193 nm, which is currently becoming popular, cannot inspect the presence or absence of critical defects, because over 100,000 false defects are detected. Overlooking critical defects in defect inspection would cause failures in the later mass production process of semiconductor devices, leading to wasteful labor and economical loss. DISCLOSURE OF THE INVENTION The present inventors have made intensive studies on such a problem of false defects, and have discovered that management of the bearing curve of the surface roughness and management of the frequency of the bearing depth (%), in addition to the roughness component that has been managed conventionally, can significantly suppress detection of false defects in defect inspection apparatus using a high-sensitivity defect inspection apparatus. The present invention has been made in consideration of the aforementioned problems, and it is an object of the invention to provide a mask blank substrate, a substrate with a multilayer reflective film, a transmissive mask blank, a reflective mask blank, a transmissive mask, a reflective mask, and a method of manufacturing a semiconductor device, which ensure suppression of false defects originating from the surface roughness of a substrate and a film in defect inspection using a high-sensitivity defect inspection apparatus, and facilitate the detection of critical defects such as foreign matters and scratches. To achieve the object, a mask blank substrate for use in lithography according to an exemplary embodiment of the invention is configured that, in a relation between a bearing area (%) and a bearing depth (nm) obtained by measuring, with an atomic force microscope, an area of 1 μm×1 μm in a main surface on a side of the substrate where a transfer pattern is formed, the main surface of the substrate satisfies a relational equation of (BA70−BA30)/(BD70−BD30)≧350 (%/nm), and has a maximum height (Rmax)≦1.2 nm, wherein BA30 is defined as a bearing area of 30%, BA70 is defined as a bearing area of 70%, and BD70 and BD30 are defined to respectively represent bearing depths for the bearing area of 30% and the bearing area of 70%. To achieve the object, a substrate with a multilayer reflective film according to an exemplary embodiment of the invention is configured to comprise a multilayer reflective film having a high refractive index layer and a low refractive index layer alternately laminated on the surface of the aforementioned mask blank substrate of the invention. To achieve the object, a substrate with a multilayer reflective film according to an exemplary embodiment of the invention is a substrate with a multilayer reflective film for use in lithography, the substrate with a multilayer reflective film being configured to comprise a multilayer reflective film having a high refractive index layer and a low refractive index layer alternately laminated on a main surface of a mask blank substrate, wherein a surface of the multilayer reflective film satisfies a relational equation of (BA70−BA30)/(BD70−BD30)≧230 (%/nm), and has a maximum height (Rmax)≦1.5 nm in a relation between a bearing area (%) and a bearing depth (nm) obtained by measuring, with an atomic force microscope, an area of 1 μm×1 μm in the surface of the multilayer reflective film, wherein BA30 is defined as a bearing area of 30%, BA70 is defined as a bearing area of 70%, and BD70 and BD30 are defined to respectively represent bearing depths for the bearing area of 30% and the bearing area of 70%. To achieve the object, a transmissive mask blank according to an exemplary embodiment of the invention is configured to comprise a light shielding function film to be a transfer pattern on the main surface of the aforementioned mask blank substrate of the invention. To achieve the object, a reflective mask blank according to an exemplary embodiment of the invention is configured to comprise an absorber film to be a transfer pattern on the multilayer reflective film or the protective film of the aforementioned substrate with a multilayer reflective film of the invention. To achieve the object, a transmissive mask according to an exemplary embodiment of the invention is configured to comprise a light shielding function film pattern provided on the main surface by patterning the light shielding function film of the aforementioned transmissive mask blank of the invention. To achieve the object, a reflective mask according to an exemplary embodiment of the invention is configured to comprise an absorber pattern provided on the multilayer reflective film by patterning the absorber film of the aforementioned reflective mask blank of the invention. To achieve the object, a method of manufacturing a semiconductor device according to an exemplary embodiment of the invention is configured to comprise a step of forming a transfer pattern on a transferred substrate using the aforementioned transmissive mask of the invention by performing a lithography process using an exposure device. To achieve the object, a method of manufacturing a semiconductor device according to an exemplary embodiment of the invention is configured to comprise a step of forming a transfer pattern on a transferred substrate using the aforementioned reflective mask of the invention by performing a lithography process using an exposure device. BRIEF DESCRIPTION OF DRAWINGS FIG. 1(a) is a perspective view illustrating a mask blank substrate 10 according to an exemplary embodiment of the present invention. FIG. 1(b) is a schematic cross-sectional view illustrating the mask blank substrate 10 of the present embodiment. FIG. 2 is a schematic cross-sectional view illustrating an example of the configuration of a substrate with a multilayer reflective film according to an exemplary embodiment of the present invention. FIG. 3 is a schematic cross-sectional view illustrating an example of the configuration of a reflective mask blank according to an exemplary embodiment of the present invention. FIG. 4 is a schematic cross-sectional view illustrating an example of a reflective mask according to an exemplary embodiment of the present invention. FIG. 5 is a schematic cross-sectional view illustrating an example of the configuration of a transmissive mask blank according to an exemplary embodiment of the present invention. FIG. 6 is a schematic cross-sectional view illustrating an example of a transmissive mask according to an exemplary embodiment of the present invention. FIG. 7 is a graph illustrating the results of measuring the bearing curve of the surface roughness of the mask blank substrates according to Examples 1 to 4 of the present invention and Comparative Examples 1 and 2. FIG. 8(a) is a graph illustrating the results of measuring the bearing curve according to the Example 1, and FIG. 8(b) is a graph illustrating a frequency distribution plotting the relation between the bearing depth and the frequency (%) thereof according to the Example 1. FIG. 9(a) is a graph illustrating the results of measuring the bearing curve according to the Comparative Example 1, and FIG. 9(b) is a graph illustrating a frequency distribution plotting the relation between the bearing depth and the frequency (%) thereof according to the Comparative Example 1. FIG. 10(a) is a graph illustrating the results of measuring the bearing curve according to Example 5, and FIG. 10(b) is a graph illustrating a frequency distribution plotting the relation between the bearing depth and the frequency (%) thereof according to the Example 5. DETAILED DESCRIPTION OF THE INVENTION General Description To achieve the above-described object, the present inventions are the following configurations. (First Configuration) A first configuration of the present invention is a mask blank substrate for use in lithography, a main surface of the substrate satisfying a relational equation of (BA70−BA30)/(BD70−BD30)≧350 (%/nm), and having a maximum height (Rmax)≦1.2 nm in a relation between a bearing area (%) and a bearing depth (nm) obtained by measuring, with an atomic force microscope, an area of 1 μm×1 μm in the main surface on the side of the substrate where a transfer pattern is formed, wherein BA30 is defined as a bearing area of 30%, BA70 is defined as a bearing area of 70%, and BD70 and BD30 are defined to respectively represent bearing depths for the bearing area of 30% and the bearing area of 70%. According to the first configuration, the irregularities (surface roughness) forming the main surface become highly aligned surface states while maintaining a very high smoothness, thus reducing a variation in irregularities (surface roughness) that lead to detection of false defects in defect inspection. This makes it possible to suppress detection of false defects in the defect inspection using a high-sensitivity defect inspection apparatus, thereby making the critical defects more noticeable. (Second Configuration) A second configuration of the invention is a mask blank substrate according to the first configuration, wherein the main surface is a surface such that, in the frequency distribution plotting the relation between the bearing depth, measured with the atomic force microscope, and the frequency (%) of the obtained bearing depth, the absolute value of the bearing depth corresponding to the center of a half-value width obtained from an approximation curve obtained by the plotted points or the highest frequency at the plotted points is smaller than the absolute value of the bearing depth corresponding to ½ of a maximum height (Rmax) of the surface roughness of the main surface of the substrate. According to the second configuration, irregularities forming the main surface of the substrate become surface states such that the ratio of concave portions to a reference surface is greater than the ratio of convex portions thereto. When a plurality of thin films are laminated on the main surface, the size of defects on the main surface tend to become smaller, which is preferable from the viewpoint of the defect quality. Particularly, the effect is demonstrated when a multilayer reflective film to be described later is formed on the main surface. (Third Configuration) A third configuration of the invention is a mask blank substrate according to the first configuration or the second configuration, wherein the main surface is subjected to a surface treatment with catalyst-referred etching. According to the third configuration, because the main surface is selectively subjected to a surface treatment from convex portions contacting the surface of the catalyst which is a reference surface by catalyst-referred etching, irregularities (surface roughness) forming the main surface become highly aligned surface states while being kept very smooth, and become such surface states that the ratio of concave portions is greater than the ratio of convex portions with respect to the reference surface. When a plurality of thin films are laminated on the main surface, the size of defects on the main surface tend to become smaller, which is preferable from the viewpoint of the defect quality. Particularly, the effect is demonstrated when a multilayer reflective film to be described later is formed on the main surface. Further, execution of a surface treatment to the main surface by catalyst-referred etching as mentioned above makes it possible to relatively easily form the surface with the surface roughness and the bearing curve characteristics as defined in the first or second configuration. (Fourth Configuration) A fourth configuration of the invention is a mask blank substrate according to any one of the first to third configurations, wherein the mask blank substrate is used in EUV lithography. According to the fourth configuration, the substrate is a mask blank substrate for use in EUV lithography, whereby the surface state of the multilayer reflective film formed on the main surface becomes very smooth, so that the reflectance characteristics to EUV light become better. (Fifth Configuration) A fifth configuration of the invention is a mask blank substrate according to the fourth configuration, wherein a thin film of a material comprising a metal, an alloy, or at least one of oxygen, nitrogen and carbon contained in one of the metal and the alloy, is formed on the main surface of a substrate of a multi-element glass material. Generally, since a mask blank substrate for use in EUV lithography needs the characteristics of low thermal expansion, so that it is preferred to use a multi-element glass material to be described later. The multi-element glass material has a property such that high smoothness is difficult to obtain compared to synthetic quartz glass. Accordingly, a thin film of a material comprising a metal, an alloy, or at least one of oxygen, nitrogen and carbon contained in one of the metal and the alloy is formed on the main surface of the substrate comprising a multi-element glass material. A substrate having the surface state as defined by the first or second configuration is easily obtained by performing a surface treatment to the surface of such a thin film. (Sixth Configuration) A sixth configuration of the invention is a substrate with a multilayer reflective film comprising a multilayer reflective film having a high refractive index layer and a low refractive index layer alternately laminated on the surface of the mask blank substrate according to any one of the first to fifth configurations. According to the sixth configuration, the surface state of the multilayer reflective film formed on the main surface becomes very smooth, so that the reflectance characteristics to EUV light become better. Further, it is possible to sufficiently suppress detection of false defects in the defect inspection of the surface of the multilayer reflective film using a high-sensitivity defect inspection apparatus, and further make the critical defects more noticeable. (Seventh Configuration) A seventh configuration of the invention is a substrate with a multilayer reflective film for use in lithography, the substrate with a multilayer reflective film being configured to comprise a multilayer reflective film having a high refractive index layer and a low refractive index layer alternately laminated on a main surface of a mask blank substrate, wherein a surface of the multilayer reflective film satisfies a relational equation of (BA70−BA30)/(BD70−BD30)≧230 (%/nm), and has a maximum height (Rmax)≦1.5 nm in a relation between a bearing area (%) and a bearing depth (nm) obtained by measuring, with an atomic force microscope, an area of 1 μm×1 μm in the surface of the multilayer reflective film, wherein BA30 is defined as a bearing area of 30%, BA70 is defined as a bearing area of 70%, and BD70 and BD30 are defined to respectively represent bearing depths for the bearing area of 30% and the bearing area of 70%. According to the seventh configuration, the irregularities (surface roughness) forming the surface of the multilayer reflective film become highly aligned surface states while maintaining a very high smoothness, thus reducing a variation in irregularities (surface roughness) that lead to detection of false defects in defect inspection. This makes it possible to suppress detection of false defects in the defect inspection using a high-sensitivity defect inspection apparatus, thereby making the critical defects more noticeable. (Eighth Configuration) An eighth configuration of the invention is a substrate with a multilayer reflective film according to the sixth or seventh configuration, wherein the substrate with a multilayer reflective film has a protective film on the multilayer reflective film. According to the eighth configuration, the substrate with a multilayer reflective film is configured to have the protective film on the multilayer reflective film to suppress damages to the multilayer reflective film at the time of fabricating a transfer mask (EUV mask), so that the reflectance characteristics to EUV light become better. In addition, it is possible to sufficiently suppress detection of false defects in the defect inspection of the surface of the protective film using a high-sensitivity defect inspection apparatus, and further make the critical defects more noticeable. (Ninth Configuration) A ninth configuration of the invention is a transmissive mask blank comprising a light shielding function film to be a transfer pattern on the main surface of the mask blank substrate according to any one of the first to third configurations. According to the ninth configuration, the irregularities (surface roughness) forming the surface of the light shielding function film in the transmissive mask blank become highly aligned surface states while maintaining a very high smoothness, thus reducing a variation in irregularities (surface roughness) that lead to detection of false defects in defect inspection. This makes it possible to suppress detection of false defects in the defect inspection using a high-sensitivity defect inspection apparatus, thereby making the critical defects more noticeable. (Tenth Configuration) A tenth configuration of the invention is a reflective mask blank comprising an absorber film to be a transfer pattern on the multilayer reflective film or the protective film of the substrate with a multilayer reflective film according to the seventh or eighth configuration. According to the tenth configuration, the irregularities (surface roughness) forming the surface of the absorber film in the reflective mask blank become highly aligned surface states while maintaining a very high smoothness, thus reducing a variation in irregularities (surface roughness) that lead to detection of false defects in defect inspection. This makes it possible to suppress detection of false defects in the defect inspection using a high-sensitivity defect inspection apparatus, thereby making the critical defects more noticeable. (Eleventh Configuration) An eleventh configuration of the invention is a transmissive mask comprising a light shielding function film pattern provided on the main surface by patterning the light shielding function film of the transmissive mask blank according to the ninth configuration. (Twelfth Configuration) A twelfth configuration of the invention is a reflective mask comprising an absorber pattern provided on the multilayer reflective film by patterning the absorber film of the reflective mask blank according to the tenth configuration. According to the eleventh and twelfth configurations, it is possible to suppress detection of false defects in the defect inspection on the transmissive mask and the reflective mask using a high-sensitivity defect inspection apparatus, making the critical defects more noticeable. (Thirteenth Configuration) A thirteenth configuration of the invention is a method of manufacturing a semiconductor device, comprising a step of forming a transfer pattern on a transferred substrate using the transmissive mask according to the eleventh configuration by performing a lithography process using an exposure device. (Fourteenth Configuration) A fourteenth configuration of the invention is a method of manufacturing a semiconductor device, comprising a step of forming a transfer pattern on a transferred substrate using the reflective mask according to the twelfth configuration by performing a lithography process using an exposure device. According to the thirteenth and fourteenth configurations, a transmissive mask or a reflective mask from which critical defects such as a foreign matter or scratches is removed can be used in defect inspection using a high-sensitivity defect inspection apparatus, so that a transfer pattern such as a circuit pattern to be transferred onto a resist film formed on a target body such as a semiconductor substrate is free of defects. This makes it possible to manufacture a semiconductor device having a fine and high-precision transfer pattern. Effects of the Invention The mask blank substrate, a substrate with a multilayer reflective film, the transmissive mask blank, the reflective mask blank, the transmissive mask and the reflective mask according to the invention permit detection of false defects originating from the surface roughness of a substrate and a film to be suppressed in defect inspection using a high-sensitivity defect inspection apparatus, and facilitate the detection of critical defects such as foreign matters and scratches. In the mask blank substrate, the substrate with a multilayer reflective film, the reflective mask blank and the reflective mask for use in EUV lithography, in particular, the multilayer reflective film formed on the main surface of the substrate provides high reflectance while suppressing false defects. According to the above-described method of manufacturing a semiconductor device, a reflective mask or a transmissive mask from which critical defects such as a foreign matter or scratches is removed can be used in defect inspection using a high-sensitivity defect inspection apparatus, so that a transfer pattern such as a circuit pattern to be transferred on a resist film formed on a transferred substrate such as a semiconductor substrate is free of defects. This makes it possible to manufacture a semiconductor device having a fine and high-precision circuit pattern. Description of Illustrated Embodiments [Mask Blank Substrate] A mask blank substrate according to the present invention is described as follows. FIG. 1(a) is a perspective view illustrating a mask blank substrate 10 according to an exemplary embodiment of the present invention. FIG. 1(b) is a schematic cross-sectional view illustrating the mask blank substrate 10 of this embodiment. A mask blank substrate 10 (or simply referred to as substrate 10) is a rectangular plate-like body, and includes two opposite main surfaces 2 and end faces 1. The two opposite main surfaces 2 are an upper surface and a lower surface of the plate-like body, and are formed so as to face each other. At least one of the two opposite main surfaces 2 is the main surface where a transfer pattern is formed. The end faces 1 are side surfaces of the plate-like body, and are adjacent to the outer edges of the opposite main surfaces 2. The end face 1 has a flat end face portion 1d and a curved end face portion 1f. The flat end face portion 1d is a surface connecting the side of one opposite main surface 2 and the side of the other opposite main surface 2, and includes a side surface portion 1a and a chamfered inclined surface portion 1b. The side surface portion 1a is that portion (T side) in the flat end face portion 1d which is substantially perpendicular to the opposing main surfaces 2. The chamfered inclined surface portion 1b is a chamfered portion (C side) between the side surface portion 1a and the opposite main surface 2, and is formed between the side surface portion 1a and the opposite main surface 2. The curved end portions 1f is a portion (R portion) adjacent to the vicinity of a corner portion 10a of the substrate 10 in a plan view of the substrate 10, and includes a side surface portion 1c and a chamfered inclined portion 1e. The plan view of the substrate 10 is, for example, is to see the substrate 10 from a direction perpendicular to the opposite main surface 2. Further, the corner portion 10a of the substrate 10 is, for example, the vicinity of the intersection of the two sides at the outer edge of the opposite main surface 2. The intersection of the two sides may be the intersection of the extensions of the two sides. In this embodiment, the curved end portion 1f is formed into a curved shape by rounding the corner portion 10a of the substrate 10. To achieve the above object, this embodiment is characterized in that at least the main surface on which a transfer pattern is formed, that is, the main surface on that side of a transmissive mask blank 50 where a light shielding function film 51 is formed, or the main surface on that side of a reflective mask blank 30 where a multilayer reflective film 21, a protective film 22, and an absorber film 24 are formed, as described later, has a certain surface roughness and bearing curve characteristics satisfying a certain relational expression. The relation between the surface roughnesses (Rmax, Rms), which are parameters representing the surface states of the main surfaces of the mask blank substrate 10 of this embodiment, and the bearing curve, is described as follows. First, Rms (Root Means Square), which is a representative index of the surface roughness, is the root mean square roughness that is the square root of the mean value of the square of the deviation from an average line to a measurement curve. Rms is expressed by the following equation (1). [ Eq .  1 ]  Rms = 1 l  ∫ 0 1  Z 2  ( x )   x ( 1 ) In the equation (1), l is a reference length, and Z is the height from the average line to the measurement curve. Rmax, which is likewise a representative index of the surface roughness, is the height of the maximum surface roughness, Rmax is the maximum height of the surface roughness or the difference between the absolute value of the maximum value of the height of the crest of the roughness curve and the absolute value of the maximum value of the depth of the trough of the roughness curve. Rms and Rmax have been used to manage the surface roughness of the mask blank substrate, and are excellent in that the surface roughness can be grasped by a numeral. However, Rms and Rmax are both height information and do not include information about a change in a fine surface shape. By contrast, the bearing curve is a plot of the ratios of sectional areas obtained by cutting irregularities in a measuring area on the main surface of the substrate 10 at a constant-height surface (horizontal plane). The bearing curve can provide visualization and quantification of a variation in the surface roughness of the substrate 10. The bearing curve is generally plotted to have a bearing area (%) on the ordinate and a bearing depth (nm) on the abscissa. A bearing area of 0 (%) represents a maximum point of a reference surface to be measured, and a bearing area of 100 (%) represents a minimum point of the reference surface to be measured. Therefore, the difference between the depth of the bearing area of 0 (%) and the depth of the bearing area of 100 (%) becomes the aforementioned maximum height (Rmax). The “bearing depth” referred to in the invention is equivalent to “bearing height.” In the case of “bearing height,” on the other hand, the bearing area of 0 (%) represents a minimum point of a reference surface to be measured, and the bearing area of 100 (%) represents a maximum point of the reference surface to be measured. Management of the bearing curve for the mask blank substrate 10 according to this embodiment is described as follows. To achieve the aforementioned object, the mask blank substrate 10 according to this embodiment is configured so that a main surface of the substrate satisfies a relational equation of (BA70−BA30)/(BD70−BD30)≧350 (%/nm), and has a maximum height (Rmax)≦1.2 nm in a relation between a bearing area (%) and a bearing depth (nm) obtained by measuring, with an atomic force microscope, an area of 1 μm×1 μm in the main surface on the side of the substrate where a transfer pattern is formed, wherein BA30 is defined as a bearing area of 30%, BA70 is defined as a bearing area of 70%, and BD70 and BD30 are defined to respectively represent bearing depths for the bearing area of 30% and the bearing area of 70%. In other words, (BA70−BA30)/(BD70−BD30) (unit: %/nm) mentioned above represents the inclination of the bearing curve for the bearing areas of 30% to 70%, and setting the inclination to 350 (%/nm) allows the bearing area to reach 100% at a shallower bearing depth (nm). That is, the irregularities (surface roughness) forming the main surface of the substrate 10 become highly aligned surface states while maintaining a very high smoothness, thus reducing a variation in irregularities (surface roughness) that lead to detection of false defects in defect inspection. This makes it possible to suppress detection of false defects in the defect inspection using a high-sensitivity defect inspection apparatus, thereby making the critical defects more noticeable. It is desirable that from the viewpoint of suppressing detection of false defects, the main surface of the substrate 10 should be formed in such a way that the irregularities (surface roughness) forming the main surface become highly aligned surface states, preferably, (BA70−BA30)/(BD70−BD30)≧400 (%/nm), more preferably, (BA70−BA30)/(BD70−BD30)≧450 (%/nm), more preferably (BA70−BA30)/(BD70−BD30)≧500 (%/nm), more preferably, (BA70−BA30)/(BD70−BD30)≧750 (%/nm), more preferably, (BA70−BA30)/(BD70−BD30)≧800 (%/nm), and more preferably, (BA70−BA30)/(BD70−BD30)≧900 (%/nm). In addition, from a similar viewpoint, the surface roughness of the substrate 10 should also have high smoothness, and it is desirable that preferably, maximum height (Rmax)≦1.1 nm, more preferably, maximum height (Rmax)≦1.0 nm, more preferably, maximum height (Rmax)≦0.75 nm, and more preferably, maximum height (Rmax)≦0.5 nm. Further, it is preferable that the surface roughness of the main surface of the substrate 10 should be managed by the root mean square roughness (Rms) in addition to the aforementioned maximum height (Rmax) from the viewpoint of improving the optical characteristics such as the reflectances of the multilayer reflective film, the protective film, absorber film, and light shielding function film which are formed on the main surface of the substrate 10. It is desirable that the surface roughness of the main surface of the substrate 10 should preferably be root mean square roughness (Rms)≦0.12 nm, more preferably, root mean square roughness (Rms)≦0.10 nm, more preferably, root mean square roughness (Rms)≦0.08 nm, and more preferably, root mean square roughness (Rms)≦0.05 nm. It is preferable that the main surface of the substrate 10 is a surface state such that, in the frequency distribution plotting the relation between the bearing depth, measured with the atomic force microscope, and the frequency (%) of the obtained bearing depth, the absolute value of the bearing depth corresponding to the center of a half-value width obtained from an approximation curve obtained by the plotted points or the highest frequency at the plotted points is smaller than the absolute value of the bearing depth corresponding to ½ of a maximum height (Rmax) of the surface roughness of the main surface of the substrate. This surface state is a surface state such that the ratio of concave portions to a reference surface is greater than the ratio of convex portions thereto. Therefore, when a plurality of thin films are laminated on the main surface, the size of defects on the main surface tend to become smaller, which is preferable from the viewpoint of the defect quality. Particularly, the effect is demonstrated when a multilayer reflective film to be described later is formed on the main surface. Further, it is preferable that the main surface of the substrate 10 should be a surface treated by catalyst-referred etching. CAtalyst-Referred etching (hereinafter also referred to as CARE) is a surface treatment method selectively removing fine convex portions present on the main surface to smooth the main surface by active species generated from the molecules of the treatment liquid which are adsorbed to the catalyst, by making the main surface of the substrate 10 and the catalyst to move closer or come in contact with each other while a treatment fluid that do not exhibit solubility in a normal state is interposed between the main surface of the substrate 10 and the catalyst. According to the fourth configuration, because the main surface of the substrate 10 is selectively subjected to a surface treatment from convex portions contacting the surface of the catalyst which is a reference surface by catalyst-referred etching, irregularities (surface roughness) forming the main surface become highly aligned surface states while being kept very smooth, and become such surface states that the ratio of concave portions is greater than the ratio of convex portions with respect to the reference surface. When a plurality of thin films are laminated on the main surface, the size of defects on the main surface tend to become smaller, which is preferable from the viewpoint of the defect quality. Particularly, the effect is demonstrated when a multilayer reflective film to be described later is formed on the main surface. Further, execution of a surface treatment to the main surface by catalyst-referred etching as mentioned above makes it possible to relatively easily form the surface with the surface roughness and the bearing curve characteristics as defined in the first or second configuration. When the material for the substrate 10 is a glass material, at least one material selected from the group of platinum, gold, a transition metal, and an alloy comprising at least one thereof may be available as the catalyst. Further, at least one solution selected from the group of functional water such as pure water, ozone water or hydrogen water, a low-concentration alkaline aqueous solution, and a low-concentration acidic aqueous solution may be available as the treatment solution. With the surface roughness of the main surface of the substrate and the bearing curve characteristics being set in the above-described ranges as described above, it is possible to significantly suppress detection of false defects in defect inspection with a high-sensitivity defect inspection apparatus using inspection light having a wavelength region of 150 nm to 365 nm or a high-sensitivity defect inspection apparatus using inspection light (EUV light) having a wavelength region of 0.2 nm to 100 nm, for example, the mask substrate/blank defect inspection apparatus “MAGICS M7360” for EUV exposure of Lasertec Corp. (inspection light source wavelength: 266 nm), the reticle, the optical mask/blank and the EUV mask/blank defect inspection apparatus “Teron 600 series” of KLA-Tencor Corp. (inspection light source wavelength: 193 nm) and in a defect inspection apparatus using EUV light for an inspection light source (inspection light source wavelength: 13.5 nm). It is noted that the inspection light source wavelength is not limited to 266 nm, 193 nm, and 13.5 nm. 532 nm, 488 nm, 364 nm, and 257 nm may be used as the inspection light source wavelength. The mask blank substrates to be subjected to defect inspection using a high-sensitivity defect inspection apparatus with the inspection light source wavelength include a transmissive mask blank substrate, and a reflective mask blank substrate. It is preferable that the main surface of the mask blank substrate 10 according to this embodiment on which a transfer pattern is formed should be treated to have a high flatness at least from the viewpoint of obtaining the pattern transfer accuracy and position precision. For an EUV reflective mask blank substrate, it is preferable that the flatness of an area of 132 mm×132 mm or an area of 142 mm×142 mm of the main surface of the substrate 10 on which a transfer pattern is formed should be not more than 0.1 μm, particularly preferably, not more than 0.05 μm. Further, the main surface opposite to the main surface of the substrate 10 on which a transfer pattern is formed is a surface that is electrostatically chucked when the substrate 10 is set in the exposure apparatus, the flatness of an area of 142 mm×142 mm is not more than 1 μm, particularly preferably, not more than 0.5 μm. For the mask blank substrate 10 to be used for a transmissive mask blank for exposure by an ArF excimer laser, the flatness of an area of 132 mm×132 mm or an area of 142 mm×142 mm of the main surface of the substrate 10 on which a transfer pattern is formed should be not more than 0.3 μm, particularly preferably, not more than 0.2 μm. Any material transparent to the exposure wavelength is available as a material for a transmissive mask blank substrate for exposure by an ArF excimer laser. In general, synthetic quartz glass is used. Other available materials may be aluminosilicate glass, soda-lime glass, borosilicate glass, and non-alkali glass. Any material having a low thermal expansion property is available as a material for a reflective mask blank substrate for EUV exposure. For example, a SiO2—TiO2 glass (2-element based (SiO2—TiO2) and 3-element based (SiO2—TiO2—SnO2 or the like)), e.g., what is called multi-element glass such as SiO2—Al2O2—Li2O based crystallized glass is available. In addition, a substrate of silicon or metal in addition to a glass substrate may be used. Examples of the metal substrate include an Invar alloy (Fe—Ni-based alloy). As described above, because the mask blank substrate for EUV exposure needs low thermal expansion characteristics, is required in the substrate, a multi-element glass material is used; however, this material undesirably has a difficulty in obtaining high smoothness as compared with synthetic silica glass. To solve this problem, a thin film made of a metal, an alloy or a material containing at least one of oxygen, nitrogen, carbon contained in either the metal or the alloy is formed on a substrate made of a multi-element glass material. Then, the surface of such a thin film is subjected to mirror polishing and a surface treatment, making it possible to relatively easily form a surface with the surface roughness and the bearing curve characteristics in the aforementioned ranges. As the material for the thin film, for example, Ta (tantalum), an alloy containing Ta or a Ta compound containing at least one of oxygen, nitrogen, carbon contained in either the metal or the alloy is preferable. As the Ta compound, for example, TaB, TaN, TaO, TaON, TaCON, TaBN, TaBO, TaBON, TaBCON, TaHf, TaHfO, TaHfN, TaHfON, TaHfCON, TaSi, TaSiO, TaSiN, TaSiON, TaSiCON and the like may be used. Of these Ta compounds, TaN, TaON, TaCON, TaBN, TaBON, TaBCON, TaHfN, TaHfON, TaHfCON, TaSiN, TaSiON, and TaSiCON containing nitrogen (N) are more preferable. It is desirable that in view of the high smoothness of the surface of the thin film, the thin film should have an amorphous structure. The crystal structure of the thin film can be measured by X-ray diffractometer (XRD). The processing method for obtaining the surface roughness and bearing curve characteristics as specified above is not particularly limited in the invention. The invention is characterized in that the bearing curve and the frequency of the bearing depth at the surface roughness of the mask blank substrate are managed, and such a surface roughness may be achieved by, for example, processing methods illustrated in Examples 1 to 3 to be described later. [Substrate with a Multilayer Reflective Film] The substrate with a multilayer reflective film 20 according to an exemplary embodiment of the invention is described as follows. FIG. 2 is a schematic diagram illustrating a substrate with a multilayer reflective film 20 according to this embodiment. The substrate with a multilayer reflective film 20 according to the embodiment is configured to have the multilayer reflective film 21 provided on the main surface of the above-described mask blank substrate 10 where a transfer pattern is formed. This multilayer reflective film 21 provides a reflective mask for EUV lithography with the capability of reflecting EUV light, and has a structure of a multilayer reflective film having elements of different reflectances laminated periodically. The material for the multilayer reflective film 21 is not particularly limited as long as it reflects EUV light; the reflective multilayer film 21 generally has a reflectance of 65% alone, and has an upper reflectance limit of 73%. In general, such a multilayer reflective film 21 may have thin films made of a material with a high refractive index (high refractive index layers) and thin films made of a material with a low refractive index (low refractive index layers) alternately laminated by about 40 to 60 periods. For example, it is preferable that the multilayer reflective film 21 for EUV light with a wavelength of 13 nm to 14 nm is a Mo/Si periodic multilayer film having Si films and Mo films alternately laminated by about 40 periods. As other multilayer reflective films for use in the region of EUV light, a Ru/Si periodic multilayer film, a Mo/Be periodic multilayer film, a Mo compound/Si compound periodic multilayer film, a Si/Nb periodic multilayer film, a Si/Mo/Ru periodic multilayer film, a Si/Mo/Ru/Mo periodic multilayer film, and a Si/Ru/Mo/Ru periodic multilayer film are available. The methods of forming the multilayer reflective film 21 are known in the art; for example, the multilayer reflective film 21 may be formed by depositing individual layers by magnetron sputtering, ion beam sputtering or the like. For the aforementioned Mo/Si periodic multilayer film, for example, the multilayer reflective film 21 is formed by ion beam sputtering to deposit a film with a thickness of about several nanometers on the substrate 10 using a Si target first, then deposit a Mo film with a thickness of about several nanometers using a Mo target, as one period, and then laminate those two films by 40 to 60 periods. To protect the multilayer reflective film 21 from dry etching or wet cleaning in the process of manufacturing a reflective mask for EUV lithography, the protective film 22 (see FIG. 3) may be formed on the multilayer reflective film 1 formed as described above. The structure with the multilayer reflective film 21 and the protective film 22 on the mask blank substrate 10 may be included in the substrate with a multilayer reflective film according to invention. As the material for the protective film 22, for example, materials such as Ru, Ru—(Nb, Zr, Y, B, Ti, La, Mo), Si—(Ru, Rh, Cr, B), Si, Zr, Nb, La and B can be used. Of the materials, if those containing ruthenium (Ru) applied, reflectance characteristics of the multilayer reflective film
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