Patent Publication Number: US-11024727-B2

Title: Magnetoresistance effect element, magnetic sensor and spin transistor

Description:
This is a Continuation of application Ser. No. 16/356,424 filed Mar. 18, 2019, which in turn claims priority to Japanese Application No. 2018-067658 filed Mar. 30, 2018. The entire disclosures of the prior applications are hereby incorporated by reference herein their entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to a magnetoresistance effect element, a magnetic sensor and a spin transistor. 
     BACKGROUND 
     A magnetoresistance effect element having a ferromagnetic layer as a magnetization free layer, a nonmagnetic spacer layer, and a ferromagnetic layer as a magnetization fixed layer, such as a giant magnetoresistance (GMR) effect element and a tunnel magnetoresistance (TMR) effect element, are known. Such a magnetoresistance effect element is used in a device such as a magnetic sensor, a magnetic head, and a magnetoresistance random access memory (MRAM). 
     Magnetoresistance effect elements currently in practical use have a configuration in which a magnetization free layer, a nonmagnetic spacer layer, and a magnetization fixed layer are stacked in this order. However, in recent years, magnetoresistance effect elements having a configuration in which a magnetization free layer and a magnetization fixed layer are provided on an upper surface of a channel layer composed of a nonmagnetic material have received attention (for example, Patent Document 1 (Japanese Unexamined Patent Application Publication No. 2010-287666) and Patent Document 2 (WO 2015/076187)). In the magnetoresistance effect elements described in Patent Document 1 and Patent Document 2, the magnetization free layer and the magnetization fixed layer are formed on substantially the same plane, spin-polarized electrons injected from the magnetization free layer or the magnetization fixed layer into the channel layer transport or diffuse in the channel layer, and spins accumulate in the channel layer. According to the magnetoresistance effect element having such a configuration, it is expected that a high spatial resolution will be able to be obtained when it is applied to a magnetic sensor such as a magnetic head or the like on the basis of structural differences from a conventional magnetoresistance effect element, and it is also expected that a degree of freedom in a device design can be improved when it is applied to a device. 
     SUMMARY 
     In the magnetoresistance effect element as described above, one of the elements necessary for improving a signal-to-noise ratio (a SN ratio) is to increase a spin diffusion length and a spin lifetime when spin-polarized carriers (electrons or holes) transport or diffuse in the channel layer. From such a viewpoint, in the magnetoresistance effect elements described in the above-mentioned Patent Documents 1 and 2, the channel layer is generally constituted by a semiconductor material having a spin diffusion length and a spin lifetime longer than those of a metallic material. 
     However, even with such a configuration, the SN ratio of the magnetoresistance effect element as described above does not reach a level required for device application. 
     It is desirable to provide a magnetoresistance effect element capable of obtaining a larger SN ratio than a conventional one, and a magnetic sensor and a spin transistor using such a magnetoresistance effect element. 
     A magnetoresistance effect element according to an aspect of the present disclosure includes a semiconductor layer, a first ferromagnetic layer and a second ferromagnetic layer. The first ferromagnetic layer and the second ferromagnetic layer are provided on an upper surface of the semiconductor layer to be spaced apart from each other in a first direction. The semiconductor layer has a first region, a second region and a third region each of which includes a part of the upper surface of the semiconductor layer and a part of a lower surface of the semiconductor layer and contains the same semiconductor material as a base material. The first ferromagnetic layer is provided on the first region, the second ferromagnetic layer is provided on the second region. The third region is sandwiched between the first region and the second region in the first direction. The third region has n-type conductivity. Crystal orientations of the semiconductor material in the first direction are substantially the same in the first region, the second region, and the third region. An interatomic distance of the first region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface is larger than an interatomic distance of the third region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface. 
     Further, a magnetoresistance effect element according to another aspect of the present disclosure includes a semiconductor layer, a first ferromagnetic layer and a second ferromagnetic layer. The first ferromagnetic layer and the second ferromagnetic layer are provided on an upper surface of the semiconductor layer to be spaced apart from each other in a first direction. The semiconductor layer has a first region, a second region and a third region each of which includes a part of the upper surface of the semiconductor layer and a part of a lower surface of the semiconductor layer and contains the same semiconductor material as a base material. The first ferromagnetic layer is provided on the first region, the second ferromagnetic layer is provided on the second region. The third region is sandwiched between the first region and the second region in the first direction. The third region has p-type conductivity. Crystal orientations of the semiconductor material in the first direction are substantially the same in the first region, the second region, and the third region. An interatomic distance of the first region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface is smaller than an interatomic distance of the third region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface. 
     Furthermore, a carrier control type magnetoresistance effect element according to another aspect of the present disclosure includes any one of the above-described magnetoresistance effect elements, an insulating layer provided on the third region, and an electrode provided on the third region with the insulating layer therebetween and provided to be spaced apart from the first ferromagnetic layer and the second ferromagnetic layer. 
     Further, a magnetic sensor according to an aspect of the present disclosure includes any one of the above-described magnetoresistance effect elements. 
     Further, a spin transistor according to an aspect of the present disclosure includes any one of the above-described magnetoresistance effect elements, an insulating layer provided on the third region, and an electrode provided on the third region with the insulating layer therebetween and provided to be spaced apart from the first ferromagnetic layer and the second ferromagnetic layer. The first region and the second region have the same conductivity type as the third region. The electrode serves as a gate electrode. One of the first ferromagnetic layer and the second ferromagnetic layer serves as a source electrode. The other one of the first ferromagnetic layer and the second ferromagnetic layer serves as a drain electrode. 
     Further, a spin transistor according to another aspect of the present disclosure includes a magnetoresistance effect element including a semiconductor layer, and a first ferromagnetic layer and a second ferromagnetic layer provided on an upper surface of the semiconductor layer to be spaced apart from each other in a first direction. The semiconductor layer has a first region, a second region and a third region each of which includes a part of the upper surface of the semiconductor layer and a part of a lower surface of the semiconductor layer and contains the same semiconductor material as a base material. The first ferromagnetic layer is provided on the first region. The second ferromagnetic layer is provided on the second region. The third region is sandwiched between the first region and the second region in the first direction. Crystal orientations of the semiconductor material in the first direction are substantially the same in the first region, the second region, and the third region. An interatomic distance of the first region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface is larger than an interatomic distance of the third region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface. An insulating layer is provided on the third region. An electrode is provided on the third region with the insulating layer therebetween and provided to be spaced apart from the first ferromagnetic layer and the second ferromagnetic layer. The first region and the second region have n-type conductivity. The electrode serves as a gate electrode. One of the first ferromagnetic layer and the second ferromagnetic layer serves as a source electrode. The other one of the first ferromagnetic layer and the second ferromagnetic layer serves as a drain electrode. The third region has p-type conductivity when no voltage is applied to the gate electrode. The gate electrode is configured to be capable of applying a voltage so that an inversion layer having n-type conductivity is formed in at least a part of the upper surface neighboring region of the third region. 
     Further, a spin transistor according to another aspect of the present disclosure includes a magnetoresistance effect element including a semiconductor layer, and a first ferromagnetic layer and a second ferromagnetic layer provided on an upper surface of the semiconductor layer to be spaced apart from each other in a first direction. The semiconductor layer has a first region, a second region and a third region each of which includes a part of the upper surface of the semiconductor layer and a part of a lower surface of the semiconductor layer and contains the same semiconductor material as a base material. The first ferromagnetic layer is provided on the first region. The second ferromagnetic layer is provided on the second region. The third region is sandwiched between the first region and the second region in the first direction. Crystal orientations of the semiconductor material in the first direction are substantially the same in the first region, the second region, and the third region. An interatomic distance of the first region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface is smaller than an interatomic distance of the third region in the crystal orientation of the semiconductor material in the first direction in an upper surface neighboring region including the upper surface. An insulating layer is provided on the third region. An electrode is provided on the third region with the insulating layer therebetween and provided to be spaced apart from the first ferromagnetic layer and the second ferromagnetic layer. The first region and the second region have p-type conductivity. The electrode serves as a gate electrode. One of the first ferromagnetic layer and the second ferromagnetic layer serves as a source electrode. The other one of the first ferromagnetic layer and the second ferromagnetic layer serves as a drain electrode. The third region has n-type conductivity when no voltage is applied to the gate electrode. The gate electrode is configured to be capable of applying a voltage so that an inversion layer having p-type conductivity is formed in at least a part of the upper surface neighboring region of the third region. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view showing a magnetic sensor according to a first embodiment. 
         FIG. 2  is a partially enlarged side view of the magnetic sensor shown in  FIG. 1 . 
         FIG. 3  is a partially enlarged top view of the magnetic sensor shown in  FIG. 1 . 
         FIG. 4  is a partially enlarged side view showing a magnetic sensor according to a second embodiment. 
         FIG. 5  is a partially enlarged top view showing the magnetic sensor according to the second embodiment. 
         FIG. 6  is a perspective view showing a magnetic sensor according to a third embodiment. 
         FIG. 7  is a partially enlarged side view of the magnetic sensor shown in  FIG. 6 . 
         FIG. 8  is a partially enlarged top view of the magnetic sensor shown in  FIG. 6 . 
         FIG. 9  is a partially enlarged side view showing a magnetic sensor according to a fourth embodiment. 
         FIG. 10  is a partially enlarged top view showing the magnetic sensor according to the fourth embodiment. 
         FIG. 11  is a perspective view showing a spin transistor according to a fifth embodiment. 
         FIG. 12  is a cross-sectional view showing a carrier control type magnetoresistance effect element shown in  FIG. 11 . 
         FIG. 13  is a perspective view showing a magnetic sensor according to a sixth embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, modes for carrying out the present disclosure will be described in detail with reference to the accompanying drawings. In each of the drawings, the same reference numerals are used for the same elements when possible. In addition, dimensional ratios in the constituent elements and between the constituent elements in the drawings are respectively arbitrary for ease of viewing of the drawings. 
     First Embodiment 
     With reference to  FIGS. 1 to 3 , a magnetoresistance effect element  1 A and a magnetic sensor  10 A according to a first embodiment will be described.  FIG. 1  is a perspective view showing a magnetic sensor according to the first embodiment.  FIG. 2  is a partially enlarged side view of the magnetic sensor shown in  FIG. 1 .  FIG. 3  is a partially enlarged top view of the magnetic sensor shown in  FIG. 1 . In  FIGS. 1 to 3 , an orthogonal coordinate system is shown. 
     As shown in  FIGS. 1 to 3 , the magnetic sensor  10 A includes the magnetoresistance effect element  1 A and is connected to a current source  20  and a voltage measurement unit  30 . The magnetoresistance effect element  1 A includes a semiconductor layer  2 , a first ferromagnetic layer  3 , a second ferromagnetic layer  4 , a first insulating layer  5 , a second insulating layer  6 , a first protective film  7 , a second protective film  15 , and a third protective film  16 . In  FIG. 2 , illustration other than the semiconductor layer  2  and the first protective film  7  is omitted. In  FIG. 3 , illustration other than the semiconductor layer  2  is omitted. 
     The semiconductor layer  2  functions as a layer in which spins transport and/or diffuse. The semiconductor layer  2  has a rectangular parallelepiped shape. The semiconductor layer  2  includes an upper surface  2   a  and a lower surface  2   b  facing each other in a Z direction, side surfaces  2   c  and  2   d  facing each other in an X direction, and side surfaces  2   e  and  2   f  facing each other in a Y direction. In the embodiment, the upper surface  2   a , the lower surface  2   b , and the side surfaces  2   c ,  2   d ,  2   e  and  2   f  are substantially flat, but these surfaces may be curved. 
     The semiconductor layer  2  is composed of, for example, a semiconductor material, such as Si, Ge, C (diamond), GaAs or the like having a cubic or pseudo-cubic crystal structure, as a base material. A pseudo-cubic crystal is a crystal structure which is not a cubic crystal (a1=a2=a3 and α=β=γ=90°) due to strain generation. That is, a pseudo-cubic crystal is a crystal structure in which a crystal structure (basic crystal structure) in a state in which strain is not generated is cubic. Crystal orientations of the semiconductor material of the semiconductor layer  2  in the X direction are [110]. Impurities for imparting a conductivity type are added to the semiconductor material (the base material) of the semiconductor layer  2 . In order for the semiconductor layer  2  to have n-type conductivity, an element having a valence electron number larger than that of the semiconductor material (the base material) is added as an impurity. In order for the semiconductor layer  2  to have p-type conductivity, an element having a valence electron number smaller than that of the semiconductor material (the base material) is added as an impurity. When the semiconductor material (the base material) included in the semiconductor layer  2  is Si, impurities for imparting n-type conductivity include P, As, Sb, and so on, and impurities for imparting p-type conductivity include B, Al, Ga, In and so on. The semiconductor layer  2  of the embodiment has n-type conductivity. 
     The semiconductor layer  2  has a first region R 1 , a second region R 2 , and a third region R 3 . Each of the first region R 1 , the second region R 2 , and the third region R 3  includes a part of the upper surface  2   a  and a part of the lower surface  2   b . The first region R 1  includes one end region of each of the upper surface  2   a , the lower surface  2   b , the side surface  2   e  and the side surface  2   f  in the X direction, and the entire side surface  2   c . The second region R 2  includes the other end region of each of the upper surface  2   a , the lower surface  2   b , the side surface  2   e  and the side surface  2   f  in the X direction, and the entire side surface  2   d . The third region R 3  includes a center region of each of the upper surface  2   a , the lower surface  2   b , the side surface  2   e  and the side surface  2   f  in the X direction. The third region R 3  is sandwiched between the first region R 1  and the second region R 2  in the X direction. The first region R 1 , the third region R 3  and the second region R 2  are linearly arranged in this order along the X direction. 
     The first region R 1 , the second region R 2 , and the third region R 3  contain the same semiconductor material as the base material. In the first region R 1 , the second region R 2 , and the third region R 3 , the crystal orientations of this semiconductor material in at least the X direction are substantially the same. That is, the crystal orientation of the semiconductor material in the X-direction in the first region R 1 , the crystal orientation of the semiconductor material in the X-direction in the second region R 2 , and the crystal orientation of the semiconductor material in the X direction in the third region R 3  may be completely coincident with each other or may cross each other at an intersection angle of 5° or less, for example. 
     For example, in the first region R 1 , the second region R 2  and the third region R 3 , it is possible to make the crystal orientations of this semiconductor material in at least the X direction substantially the same by constituting the entire semiconductor layer  2  with a single crystal. When the entire semiconductor layer  2  is composed of a single crystal, the crystal orientations of this semiconductor material in other than the X direction can be the same in the first region R 1 , the second region R 2 , and the third region R 3 . In the embodiment, the first region R 1 , the second region R 2  and the third region R 3  have n-type conductivity. In the first region R 1 , the second region R 2  and the third region R 3 , the crystal orientations of the semiconductor material in the X direction are substantially [110]. That is, the crystal orientations of the semiconductor material in the X direction may completely coincide with the [110] direction, or may cross the [110] direction at an intersection angle of 5° or less (it may be inclined from the [110] direction at the inclination angle of 5° or less). In addition, the upper surface  2   a  is substantially a (001) plane. That is, the upper surface  2   a  may completely coincide with the (001) plane or may cross the (001) plane at an intersection angle of 5° or less (it may be inclined from the (001) plane at an inclination angle of 5° or less). 
     The semiconductor layer  2  has an upper surface neighboring region Rt, a lower surface neighboring region Rb, and a central region Rm. The upper surface neighboring region Rt includes the upper surface  2   a . The upper surface neighboring region Rt is constituted by regions in the vicinities of the upper surface  2   a  in the first region R 1 , the second region R 2  and the third region R 3 . The lower surface neighboring region Rb includes the lower surface  2   b . The lower surface neighboring region Rb is constituted by regions in the vicinities of the lower surface  2   b  in the first region R 1 , the second region R 2  and the third region R 3 . The central region Rm is disposed between the upper surface neighboring region Rt and the lower surface neighboring region Rb in the Z direction. The upper surface neighboring region Rt is, for example, a region within 10 nm or 20 nm from the upper surface  2   a . The lower surface neighboring region Rb is, for example, a region within 10 nm or 20 nm from the lower surface  2   b.    
     The first ferromagnetic layer  3  and the second ferromagnetic layer  4  are provided on the upper surface  2   a  of the semiconductor layer  2  to be spaced apart from each other in the X direction as a first direction. The first ferromagnetic layer  3  is provided on the first region R 1 . The first ferromagnetic layer  3  is provided to cover an upper surface of the first region R 1  (one end region of the upper surface  2   a  in the X direction). The second ferromagnetic layer  4  is provided on the second region R 2 . The second ferromagnetic layer  4  is provided to cover an upper surface of the second region R 2  (the other end region of the upper surface  2   a  in the X direction). A length of the first ferromagnetic layer  3  and the second ferromagnetic layer  4  in the Y direction is the same as a length of the upper surface  2   a  in the Y direction. One of the first ferromagnetic layer  3  and the second ferromagnetic layer  4  serves as a magnetization fixed layer, and the other one of the first ferromagnetic layer  3  and the second ferromagnetic layer  4  serves as a magnetization free layer. In the embodiment, the first ferromagnetic layer  3  serves as a magnetization free layer, and the second ferromagnetic layer  4  serves as a magnetization fixed layer. 
     The first ferromagnetic layer  3  and the second ferromagnetic layer  4  are composed of a ferromagnetic material. For example, a metal or an alloy having at least one element selected from Ni, Fe and Co may be used as the ferromagnetic material of the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . More specifically, a Co—Fe alloy, a Ni—Fe alloy, a Co—B alloy, an Fe—B alloy or a Co—Fe—B alloy may be used. A Heusler alloy such as a Co—Fe—Al alloy, a Co—Fe—Si alloy, a Co—Mn—Si alloy, a Co—Mn—Ge alloy, a Co—Fe—Al—Si alloy, and a Co—Fe—Ga—Ge alloy may be used. A coercive force of the second ferromagnetic layer  4  in a direction in which an external magnetic field is applied is larger than a coercive force of the first ferromagnetic layer  3  in the direction in which an external magnetic field is applied. For example, the coercive force of the second ferromagnetic layer  4  may be larger than the coercive force of the first ferromagnetic layer  3  due to selecting a hard magnetic material for the second ferromagnetic layer  4  and selecting a soft magnetic material for the first ferromagnetic layer  3 . Further, the coercive force of the second ferromagnetic layer  4  may be larger than the coercive force of the first ferromagnetic layer  3  due to exchange-coupling the second ferromagnetic layer  4  to an antiferromagnetic layer. 
     The first insulating layer  5  and the second insulating layer  6  are insulating films which develop a tunnel magnetoresistance effect. The first insulating layer  5  and the second insulating layer  6  are provided on the upper surface  2   a  of the semiconductor layer  2 . The first insulating layer  5  and the second insulating layer  6  are in direct contact with the upper surface  2   a . The first insulating layer  5  is provided between the upper surface  2   a  and the first ferromagnetic layer  3 . That is, the first ferromagnetic layer  3  is provided on the upper surface  2   a  with the first insulating layer  5  interposed therebetween. The second insulating layer  6  is provided between the upper surface  2   a  of the semiconductor layer  2  and the second ferromagnetic layer  4 . That is, the second ferromagnetic layer  4  is provided on the upper surface  2   a  with the second insulating layer  6  interposed therebetween. According to the first insulating layer  5  and the second insulating layer  6 , spin injection efficiency and spin extraction efficiency are improved. 
     Film thicknesses of the first insulating layer  5  and the second insulating layer  6  can be set to 3 nm or less from the viewpoint of suppressing an increase in resistance and making it serve as a tunnel insulating layer. Further, the film thickness of the first insulating layer  5  and the second insulating layer  6  can be set to 0.4 nm or more in consideration of a thickness of one atomic layer. The first insulating layer  5  and the second insulating layer  6  are composed of, for example, magnesium oxide. When the first insulating layer  5  and the second insulating layer  6  are composed of magnesium oxide, the spin injection efficiency and the spin extraction efficiency are particularly improved. 
     The first protective film  7  is provided on the upper surface  2   a  of the semiconductor layer  2  to be sandwiched between the first ferromagnetic layer  3  and the second ferromagnetic layer  4  in the X direction. The first protective film  7  extends in the X direction to connect the first ferromagnetic layer  3  and the second ferromagnetic layer  4  to each other. The first protective film  7  is provided to cover at least an upper surface of the third region R 3  (a central region of the upper surface  2   a  in the X direction). The first protective film  7  is in direct contact with the upper surface of the third region R 3 . A length of the first protective film  7  in the Y direction is the same as a length of the upper surface  2   a  in the Y direction. 
     The second protective film  15  is provided to cover an end portion of the first region R 1  on the side opposite to the third region R 3  side in the X direction. Specifically, the second protective film  15  is provided to cover the side surface  2   c . The second protective film  15  is provided to cover the entire surface of the side surface  2   c . The second protective film  15  is in direct contact with the side surface  2   c.    
     The third protective film  16  is provided to cover an end portion of the second region R 2  on the side opposite to the third region R 3  side in the X direction. Specifically, the third protective film  16  is provided to cover the side surface  2   d . The third protective film  16  is provided to cover the entire surface of the side surface  2   d . The third protective film  16  is in direct contact with the side surface  2   d.    
     The first protective film  7 , the second protective film  15  and the third protective film  16  include, for example, aluminum nitride, silicon nitride, or silicon oxide. The first protective film  7 , the second protective film  15  and the third protective film  16  protect the semiconductor layer  2  from deterioration due to oxidation, for example. The first protective film  7 , the second protective film  15  and the third protective film  16  also serve as strain imparting films which apply strain to the semiconductor layer  2 . The first protective film  7  serves as a strain imparting film which applies strain particularly to the third region R 3 . The second protective film  15  serves as a strain imparting film which applies strain particularly to the first region R 1  and the third region R 3 . The third protective film  16  serves as a strain imparting film which applies strain particularly to the second region R 2  and the third region R 3 . In general, the magnitude and polarity (tensile stress or compressive stress) of internal stress remaining in a film after film deposition are related to a grain boundary density in the film. A force (the compressive stress) for expanding tends to remain as an internal stress in a film having a low grain boundary density, and a force for contracting (the tensile stress) tends to remain as an internal stress in a film having a high grain boundary density. 
     The grain boundary density in the film can be controlled by film deposition conditions (a film deposition method, a film deposition temperature, a pressure during the film deposition, and so on). For example, in a sputtering method, since a kinetic energy of atoms (molecules) to be deposited is larger than that in an electron beam evaporation method, the atoms (molecules) move on a film surface to fill the grain boundaries during a film deposition process, and as a result, a film having a low grain boundary density tends to be formed. Therefore, in a film formed by a sputtering method, the force for expanding (the compressive stress) tends to remain as an internal stress. On the other hand, in the film formed by the electron beam evaporation method, the force for contracting (the tensile stress) tends to remain as an internal stress. In this way, the magnitudes and polarities of the internal stresses remaining in the first protective film  7 , the second protective film  15  and the third protective film  16  after the film deposition can be controlled by controlling the grain boundary densities in the first protective film  7 , the second protective film  15  and the third protective film  16  by the film deposition conditions. 
     In the embodiment, the first protective film  7  imparts tensile strain to the third region R 3  along the X direction. The second protective film  15  imparts tensile strain particularly to the first region R 1  and the third region R 3  along the X direction. The third protective film  16  imparts tensile strain particularly to the second region R 2  and the third region R 3  along the X direction. 
       FIG. 2  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (110) plane (a (1−10) plane), which is a cross section along an XZ plane, in the semiconductor layer  2 .  FIG. 3  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (001) plane, which is a cross section along an XY plane, in the semiconductor layer  2 . In  FIGS. 2 and 3 , modes of forces F 1  applied from the first protective film  7  (forces due to the internal stress of the first protective film  7 ) to the semiconductor layer  2  are schematically indicated by solid arrows. Modes of forces F 2  applied from the second protective film  15  (forces due to the internal stress of the second protective film  15 ) to the semiconductor layer  2  and forces F 3  applied from the third protective film  16  (forces due to the internal stress of the third protective film  16 ) to the semiconductor layer  2  are schematically indicated by void arrows. These arrows are just images and do not represent exact points of action and magnitudes of the forces. In the embodiment, the first protective film  7  has a compressive stress (a force for expanding) as an internal stress, and the second protective film  15  and the third protective film  16  have tensile stresses (forces for contracting) as internal stresses. As described above, since tensile strain along the X direction is applied to each of the first region R 1 , the second region R 2  and the third region R 3 , the interatomic distances of the first region R 1 , the second region R 2  and the third region R 3  in the crystal orientation of the semiconductor material in the X direction are larger as compared with the interatomic distances of the first region R 1 , the second region R 2  and the third region R 3  in the crystal orientation of the semiconductor material in the X direction when tensile strain along the X direction is not applied. The interatomic distance is a distance between centers of atoms. In  FIGS. 2 and 3 , for ease of understanding, a difference between the interatomic distances is exaggeratedly shown. 
     In particular, as shown in  FIG. 2 , in the third region R 3 , the force F 1  applied from the first protective film  7  decreases from the upper surface  2   a  toward the lower surface  2   b . In the third region R 3 , the force F 2  applied from the second protective film  15  is larger in the upper surface neighboring region Rt and the lower surface neighboring region Rb than in the central region Rm. In the third region R 3 , the force F 3  applied from the third protective film  16  is larger in the upper surface neighboring region Rt and the lower surface neighboring region Rb than in the central region Rm. An amount of change in the force F 2  and the force F 3  according to a position in the Z direction is much smaller than an amount of change in the force F 1  according to the position in the Z direction. Moreover, in the third region R 3 , the force F 2  applied from the second protective film  15  is equal in the upper surface neighboring region Rt and the lower surface neighboring region Rb. In the third region R 3 , the force F 3  applied from the third protective film  16  is equal in the upper surface neighboring region Rt and the lower surface neighboring region Rb. Therefore, an interatomic distance d 3  of the third region R 3  in the crystal orientation of the semiconductor material in the X direction, that is, in the [110] direction, in the upper surface neighboring region Rt is larger than an interatomic distance d 31  of the third region R 3  in the crystal orientation of the semiconductor material in the X direction in the lower surface neighboring region Rb. The force F 3  applied from the third protective film  16  in the first region R 1  and the force F 2  applied from the second protective film  15  in the second region R 2  are not shown because they are small in magnitude. 
     The force F 2  applied from the second protective film  15  becomes smaller as being away from the side surface  2   c . The force F 3  applied from the third protective film  16  becomes smaller as being away from the side surface  2   d . Each of the forces F 1 , F 2  and F 3  is applied to the third region R 3 . In the embodiment, the first protective film  7 , the second protective film  15  and the third protective film  16  are formed so that, in the upper surface neighboring region Rt, the force F 2  applied from the second protective film  15  to the first region R 1  is larger than a sum of the force F 1  applied from the first protective film  7  to the third region R 3  and the force F 2  applied from the second protective film  15  to the third region R 3 , and in the upper surface neighboring region Rt, the force F 3  applied from the third protective film  16  to the second region R 2  is larger than a sum of the force F 1  applied from the first protective film  7  to the third region R 3  and the force F 3  applied from the third protective film  16  to the third region R 3 . Accordingly, in the embodiment, an interatomic distance d 1  of the first region R 1  in the crystal orientation of the semiconductor material in the X direction in the upper surface neighboring region Rt and an interatomic distance d 2  of the second region R 2  in the crystal orientation of the semiconductor material in the X direction in the upper surface neighboring region Rt are larger than the interatomic distance d 3  of the third region R 3  in the crystal orientation of the semiconductor material in the X direction in the upper surface neighboring region Rt. The interatomic distance d 1  and the interatomic distance d 2  are, for example, the same as each other. 
     Particularly, as shown in  FIG. 3 , in the upper surface neighboring region Rt, the third region R 3  has end regions R 3   a  and R 3   b  in a direction orthogonal to the X direction, that is, in the Y direction, and a central region R 3   c  in the Y direction. The end region R 3   a  is disposed on the side surface  2   e  side, and the end region R 3   b  is disposed on the side surface  2   f  side. The force F 1  applied from the first protective film  7  to the semiconductor layer  2  increases from a center of the third region R 3  toward the side surfaces  2   e  and  2   f  in the Y direction. The force F 2  applied from the second protective film  15  to the semiconductor layer  2  and the force F 3  applied from the third protective film  16  to the semiconductor layer  2  also increase from the center of the third region R 3  toward the side surfaces  2   e  and  2   f  in the Y direction. Therefore, an interatomic distance d 3   a  of the end region R 3   a  in the crystal orientation of the semiconductor material in the X direction and an interatomic distance d 3   b  of the end region R 3   b  in the crystal orientation of the semiconductor material in the X direction are larger than an interatomic distance d 3   c  of the central region R 3   c  in the crystal orientation of the semiconductor material in the X direction. The interatomic distance d 3   a  and the interatomic distance d 3   b  are, for example, the same as each other. 
     The current source  20  is a unit which is connected to the first ferromagnetic layer  3  and the second ferromagnetic layer  4  and passes a current between the second ferromagnetic layer  4  and the first ferromagnetic layer  3 . In the embodiment, the current source  20  supplies a constant current flowing through the semiconductor layer  2  from the second ferromagnetic layer  4  toward the first ferromagnetic layer  3 . The voltage measurement unit  30  is a unit which is connected to the first ferromagnetic layer  3  and the second ferromagnetic layer  4  and measures a voltage between the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . 
     In the magnetic sensor  10 A, when a current from the second ferromagnetic layer  4  toward the first ferromagnetic layer  3  is supplied by the current source  20 , electrons having spins (spin-polarized electrons) corresponding to a magnetization direction of the first ferromagnetic layer  3  are injected into the semiconductor layer  2  from the first ferromagnetic layer  3  serving as the magnetization free layer. The injected spin-polarized electrons transport through the third region R 3 , and the spins corresponding to the magnetization direction of the first ferromagnetic layer  3  are accumulated mainly in the second region R 2  in the upper surface neighboring region Rt. The electrical resistance between the second ferromagnetic layer  4  and the second region R 2  changes according to a relative angle between a direction of the spins accumulated in the second region R 2  and the magnetization direction of the second ferromagnetic layer  4  (magnetoresistance effect). A spin output voltage corresponding to the change in the relative angle is generated between the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . Therefore, the magnetization direction of the first ferromagnetic layer  3  can be detected as a direction or magnitude of an external magnetic field by measuring the voltage between the first ferromagnetic layer  3  and the second ferromagnetic layer  4  with the voltage measurement unit  30 . In addition to the spin output voltage, a voltage including a voltage drop due to a resistance of the semiconductor layer  2 , a resistance of the first ferromagnetic layer  3 , a resistance of the second ferromagnetic layer  4 , a resistance between the first ferromagnetic layer  3  and the semiconductor layer  2  and a resistance between the second ferromagnetic layer  4  and the semiconductor layer  2  is measured in the voltage measurement unit  30 . 
     The current source  20  may supply a constant current flowing through the semiconductor layer  2  from the first ferromagnetic layer  3  toward the second ferromagnetic layer  4 . In this case, the spin-polarized electrons corresponding to the magnetization direction of the second ferromagnetic layer  4  are injected into the semiconductor layer  2  from the second ferromagnetic layer  4  serving as the magnetization fixed layer. Therefore, the spins corresponding to the magnetization direction of the second ferromagnetic layer  4  are accumulated mainly in the first region R 1  in the upper surface neighboring region Rt. 
     In the magnetoresistance effect element  1 A, the interatomic distance d 3  is larger than the interatomic distance d 31 . Thus, the inventors of the present disclosure have found that a spin diffusion length and a spin lifetime of the spin-polarized electrons which transport or diffuse in the upper surface neighboring region Rt of the third region R 3  of the semiconductor layer  2  can be increased, as compared with a case in which the interatomic distance d 3  is equal to the interatomic distance d 31 . Accordingly, a spin accumulation effect in the semiconductor layer  2  (mainly in the second region R 2 ) can be increased. Therefore, the magnetoresistance effect generated between the second ferromagnetic layer  4  and the semiconductor layer  2  can be increased. As a result, since an output signal can be increased, a large SN ratio can be obtained. 
     Further, in the magnetoresistance effect element  1 A, since the first protective film  7  serves as the strain imparting film which imparts tensile strain to the third region R 3  along the X direction, the relationship between the interatomic distance d 3  and the interatomic distance d 31  as described above can be easily realized. 
     Further, in the magnetoresistance effect element  1 A, the first protective film  7  is in direct contact with the upper surface of the third region R 3 . Accordingly, since the force F 1  applied from the first protective film  7  to the semiconductor layer  2  increases, the spin diffusion length and the spin lifetime of the spin-polarized electrons in the third region R 3  can be increased. As a result, a larger SN ratio can be obtained. 
     Further, the magnetoresistance effect element  1 A includes the second protective film  15  provided to cover the side surface  2   c  and the third protective film  16  provided to cover the side surface  2   d . The second protective film  15  serves as a strain imparting film which imparts tensile strain particularly to the first region R 1  and the third region R 3  along the X direction. The third protective film  16  serves as a strain imparting film which imparts tensile strain particularly to the second region R 2  and the third region R 3  along the X direction. Thus, the relationship between the interatomic distances d 1 , d 2  and d 3  as described above can be easily realized. 
     Further, in the magnetoresistance effect element  1 A, the second protective film  15  is in direct contact with the side surface  2   c , and the third protective film  16  is in direct contact with the side surface  2   d . Thus, since the force F 2  applied from the second protective film  15  to the semiconductor layer  2  and the force F 3  applied from the third protective film  16  to the semiconductor layer  2  increase, the spin diffusion length and the spin lifetime of the spin-polarized electrons in the semiconductor layer  2  can be increased. As a result, a larger SN ratio can be obtained. 
     Further, in the magnetoresistance effect element  1 A, the semiconductor material of the semiconductor layer  2  has a cubic or pseudo-cubic crystal structure, and in the first region R 1 , the second region R 2 , and the third region R 3 , the crystal orientations of the semiconductor material in the X direction are substantially [110]. Thus, a larger SN ratio can be obtained. 
     Since the magnetic sensor  10 A includes the magnetoresistance effect element  1 A, a large SN ratio can be obtained. 
     Second Embodiment 
     A magnetoresistance effect element  1 B and a magnetic sensor  10 B according to a second embodiment will be described with reference to  FIGS. 4 and 5  focusing on differences from the magnetoresistance effect element  1 A and the magnetic sensor  10 A (refer to  FIG. 1 ) according to the first embodiment.  FIG. 4  is a partially enlarged side view showing the magnetic sensor according to the second embodiment.  FIG. 5  is a partially enlarged top view showing the magnetic sensor according to the second embodiment. In  FIG. 4 , illustration other than the semiconductor layer  2  and the first protective film  7  is omitted. In  FIG. 5 , illustration other than the semiconductor layer  2  is omitted. In  FIGS. 4 and 5 , an orthogonal coordinate system is shown.  FIG. 4  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (110) plane (a (1−10) plane), which is a cross section along an XZ plane, in the semiconductor layer  2 .  FIG. 5  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (001) plane, which is a cross section along an XY plane, in the semiconductor layer  2 . 
     In the magnetoresistance effect element  1 B shown in  FIGS. 4 and 5 , the semiconductor layer  2  has p-type conductivity instead of n-type conductivity. That is, the first region R 1 , the second region R 2  and the third region R 3  have p-type conductivity instead of n-type conductivity. The first protective film  7  imparts compressive strain to the third region R 3  along the X direction. The second protective film  15  imparts compressive strain particularly to the first region R 1  and the third region R 3  along the X direction. The third protective film  16  imparts compressive strain particularly to the second region R 2  and the third region R 3  along the X direction. In  FIGS. 4 and 5 , modes of forces F 4  applied from the first protective film  7  (forces due to the internal stress of the first protective film  7 ) to the semiconductor layer  2  are schematically indicated by solid arrows, and modes of forces F 5  applied from the second protective film  15  (forces due to the internal stress of the second protective film  15 ) to the semiconductor layer  2  and forces F 6  applied from the third protective film  16  (forces due to the internal stress of the third protective film  16 ) to the semiconductor layer  2  are schematically indicated by outline arrows. These arrows are just images and do not represent exact points of action and magnitudes of the forces. In the embodiment, the first protective film  7  has a tensile stress (force for contracting) as the internal stress, and the second protective film  15  and the third protective film  16  have compressive stresses (forces for expanding) as the internal stresses. As described above, since compressive strain along the X direction is applied to each of the first region R 1 , the second region R 2  and the third region R 3 , the interatomic distances of the first region R 1 , the second region R 2  and the third region R 3  in the crystal orientation of the semiconductor material in the X direction are smaller as compared with the interatomic distances of the first region R 1 , the second region R 2  and the third region R 3  in the crystal orientation of the semiconductor material in the X direction when compressive strain along the X direction is not applied. In  FIG. 4  and  FIG. 5 , for ease of understanding, the difference between interatomic distances is exaggeratedly shown. 
     Particularly, as shown in  FIG. 4 , in the third region R 3 , the force F 4  applied from the first protective film  7  decreases from the upper surface  2   a  toward the lower surface  2   b . In the third region R 3 , the force F 5  applied from the second protective film  15  is larger in the upper surface neighboring region Rt and the lower surface neighboring region Rb than in the central region Rm. In the third region R 3 , the force F 6  applied from the third protective film  16  is larger in the upper surface neighboring region Rt and the lower surface neighboring region Rb than in the central region Rm. An amount of change in the force F 5  and the force F 6  according to a position in the Z direction is much smaller than an amount of change in the force F 4  according to the position in the Z direction. Moreover, in the third region R 3 , the force F 5  applied from the second protective film  15  is equal in the upper surface neighboring region Rt and the lower surface neighboring region Rb. In the third region R 3 , the force F 6  applied from the third protective film  16  is equal in the upper surface neighboring region Rt and the lower surface neighboring region Rb. Therefore, the interatomic distance d 3  is smaller than the interatomic distance d 31 . Also, the force F 6  applied from the third protective film  16  in the first region R 1  and the force F 5  applied from the second protective film  15  in the second region R 2  are not shown because they are small in magnitude. 
     The force F 5  applied from the second protective film  15  becomes smaller as being away from the side surface  2   c . The force F 6  applied from the third protective film  16  becomes smaller as being away from the side surface  2   d . Each of the forces F 4 , F 5  and F 6  is applied to the third region R 3 . In the embodiment, the first protective film  7 , the second protective film  15  and the third protective film  16  are formed so that, in the upper surface neighboring region Rt, the force F 5  applied from the second protective film  15  to the first region R 1  is larger than a sum of the force F 4  applied from the first protective film  7  to the third region R 3  and the force F 5  applied from the second protective film  15  to the third region R 3 , and in the upper surface neighboring region Rt, the force F 6  applied from the third protective film  16  to the second region R 2  is larger than a sum of the force F 4  applied from the first protective film  7  to the third region R 3  and the force F 6  applied from the third protective film  16  to the third region R 3 . Accordingly, in the embodiment, the interatomic distance d 1  and the interatomic distance d 2  are smaller than the interatomic distance d 3 . 
     In particular, as shown in  FIG. 5 , the force F 4  applied from the first protective film  7  to the semiconductor layer  2  increases from the center of the third region R 3  toward the side surfaces  2   e  and  2   f  in the Y direction. The force F 5  applied from the second protective film  15  to the semiconductor layer  2  and the force F 6  applied from the third protective film  16  to the semiconductor layer  2  also increase from the center of the third region R 3  toward the side surfaces  2   e  and  2   f  in the Y direction. Thus, the interatomic distance d 3   a  and the interatomic distance d 3   b  are smaller than the interatomic distance d 3   c.    
     In the magnetic sensor  10 B, when a constant current flowing through the semiconductor layer  2  from the first ferromagnetic layer  3  to the second ferromagnetic layer  4  is supplied by the current source  20 , holes having spins (spin-polarized holes) corresponding to the magnetization direction of the first ferromagnetic layer  3  are injected into the semiconductor layer  2  from the first ferromagnetic layer  3  serving as the magnetization free layer. The injected spin-polarized holes transport through the third region R 3 , and the spins corresponding to the magnetization direction of the first ferromagnetic layer  3  are accumulated mainly in the second region R 2  in the upper surface neighboring region Rt. The electrical resistance between the second ferromagnetic layer  4  and the second region R 2  changes according to a relative angle between the direction of the spins accumulated in the second region R 2  and the magnetization direction of the second ferromagnetic layer  4  (magnetoresistance effect). A spin output voltage corresponding to the change in the relative angle is generated between the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . Therefore, the magnetization direction of the first ferromagnetic layer  3  can be detected as a direction or magnitude of an external magnetic field by measuring the voltage between the first ferromagnetic layer  3  and the second ferromagnetic layer  4  with the voltage measurement unit  30 . In addition to the spin output voltage, a voltage including a voltage drop due to a resistance of the semiconductor layer  2 , a resistance of the first ferromagnetic layer  3 , a resistance of the second ferromagnetic layer  4 , a resistance between the first ferromagnetic layer  3  and the semiconductor layer  2  and a resistance between the second ferromagnetic layer  4  and the semiconductor layer  2  is measured in the voltage measurement unit  30 . 
     The current source  20  may supply a constant current flowing through the semiconductor layer  2  from the second ferromagnetic layer toward the first ferromagnetic layer  3 . In this case, the spin-polarized holes corresponding to the magnetization direction of the second ferromagnetic layer  4  are injected into the semiconductor layer  2  from the second ferromagnetic layer  4  serving as the magnetization fixed layer. Therefore, the spins corresponding to the magnetization direction of the second ferromagnetic layer  4  are accumulated mainly in the first region R 1  in the upper surface neighboring region Rt. 
     In the magnetoresistance effect element  1 B, the inventors of the present disclosure have found that, since the interatomic distance d 3  is smaller than the interatomic distance d 31 , a spin diffusion length and a spin lifetime of the spin-polarized holes which transport or diffuse in the upper surface neighboring region Rt of the third region R 3  of the semiconductor layer  2  can be increased, as compared with a case in which the interatomic distance d 3  is equal to the interatomic distance d 31 . Accordingly, a spin accumulation effect in the semiconductor layer  2  (mainly in the second region R 2 ) can be increased. Therefore, the magnetoresistance effect generated between the second ferromagnetic layer  4  and the semiconductor layer  2  can be increased. As a result, since an output signal can be increased, a large SN ratio can be obtained. 
     Further, in the magnetoresistance effect element  1 B, since the first protective film  7  serves as the strain imparting film which imparts compressive strain to the third region R 3  along the X direction, the relationship between the interatomic distance d 3  and the interatomic distance d 31  as described above can be easily realized. 
     Further, in the magnetoresistance effect element  1 B, the first protective film  7  is in direct contact with the upper surface of the third region R 3 . Accordingly, since the force F 4  applied from the first protective film  7  to the semiconductor layer  2  increases, the spin diffusion length and the spin lifetime of the spin-polarized holes in the third region R 3  can be increased. As a result, a larger SN ratio can be obtained. 
     Further, the magnetoresistance effect element  1 B includes the second protective film  15  provided to cover the side surface  2   c  and the third protective film  16  provided to cover the side surface  2   d . The second protective film  15  serves as a strain imparting film which imparts compressive strain particularly to the first region R 1  and the third region R 3  along the X direction. The third protective film  16  serves as a strain imparting film which imparts compressive strain particularly to the second region R 2  and the third region R 3  along the X direction. Thus, the relationship between the interatomic distances d 1 , d 2  and d 3  as described above can be easily realized. 
     Further, in the magnetoresistance effect element  1 B, the second protective film  15  is in direct contact with the side surface  2   c , and the third protective film  16  is in direct contact with the side surface  2   d . Thus, since the force F 5  applied from the second protective film  15  to the semiconductor layer  2  and the force F 6  applied from the third protective film  16  to the semiconductor layer  2  increase, the spin diffusion length and the spin lifetime of the spin-polarized holes in the semiconductor layer  2  can be increased. As a result, a larger SN ratio can be obtained. 
     Since the magnetic sensor  10 B includes the magnetoresistance effect element  1 B, a large SN ratio can be obtained. 
     Third Embodiment 
     A magnetoresistance effect element  1 C and a magnetic sensor  10 C according to a third embodiment will be described with reference to  FIGS. 6 to 8  focusing on differences from the magnetoresistance effect element  1 A and the magnetic sensor  10 A (refer to  FIG. 1 ) according to the first embodiment.  FIG. 6  is a perspective view showing a magnetic sensor according to a third embodiment.  FIG. 7  is a partially enlarged side view of the magnetic sensor shown in  FIG. 6 .  FIG. 8  is a partially enlarged top view of the magnetic sensor shown in  FIG. 6 . In  FIGS. 6 to 8 , an orthogonal coordinate system is shown. 
     As shown in  FIGS. 6 to 8 , the magnetic sensor  10 C includes the magnetoresistance effect element  1 C and is connected to the current source  20  and the voltage measurement unit  30 . The magnetoresistance effect element  1 C further includes a reference electrode  8 , and a fourth protective film  9  in addition to the semiconductor layer  2 , the first ferromagnetic layer  3 , the second ferromagnetic layer  4 , the first insulating layer  5 , the second insulating layer  6 , the first protective film  7 , the second protective film  15  and the third protective film  16 . In  FIG. 7 , illustration other than the semiconductor layer  2  and the fourth protective film  9  is omitted. In  FIG. 8 , illustration other than the semiconductor layer  2  is omitted. 
     In the magnetoresistance effect element  1 C, the semiconductor layer  2  further includes a fourth region R 4  and a fifth region R 5  in addition to the first region R 1 , the second region R 2  and the third region R 3 . Like the first region R 1 , the second region R 2  and the third region R 3 , each of the fourth region R 4  and the fifth region R 5  includes a part of the upper surface  2   a  and a part of the lower surface  2   b . In the magnetoresistance effect element  1 C, not the second region R 2 , but the fourth region R 4  includes the other end region of each of the upper surface  2   a , the lower surface  2   b , the side surface  2   e  and the side surface  2   f  in the X direction, and the entire side surface  2   d . The first region R 1 , the third region R 3 , the second region R 2 , the fifth region R 5  and the fourth region R 4  are linearly arranged in this order in the X direction. The fifth region R 5  is sandwiched between the second region R 2  and the fourth region R 4  in the X direction as a second direction. The third protective film  16  is provided not to cover the second region R 2  but to cover an end portion of the fourth region R 4  on the side opposite to the fifth region R 5  side in the X direction. The third protective film  16  imparts tensile strain particularly to the fourth region R 4  and the fifth region R 5  in the X direction, instead of the second region R 2  and the third region R 3 . 
     Each of the regions R 1  to R 5  contains the same semiconductor material as the base material. In each of the regions R 1  to R 5 , the crystal orientations of this semiconductor material in at least the X direction are substantially the same. For example, in each of the regions R 1  to R 5 , the crystal orientations of this semiconductor material in at least the X direction can be substantially the same by constituting the entire semiconductor layer  2  with a single crystal. When the entire semiconductor layer  2  is composed of a single crystal, the crystal orientations of the semiconductor material other than the X direction can also be the same in each of the regions R 1  to R 5 . In the embodiment, each of the regions R 1  to R 5  has n-type conductivity. Further, in each of the regions R 1  to R 5 , the crystal orientations of the semiconductor material in the X direction are substantially [110].  FIG. 7  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (110) plane (a (1−10) plane), which is a cross section along an XZ plane, in the semiconductor layer  2 .  FIG. 8  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (001) plane, which is a cross section along an XY plane, in the semiconductor layer  2 . 
     The reference electrode  8  is provided on the upper surface  2   a  of the semiconductor layer  2  to be spaced apart from the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . The reference electrode  8  is in direct contact with the upper surface  2   a  of the semiconductor layer  2 . The reference electrode  8  is provided on the fourth region R 4 . The reference electrode  8  is provided to cover an upper surface of the fourth region R 4  (the other end region of the upper surface  2   a  in the X direction). A length of the reference electrode  8  in the Y direction is the same as a length of the upper surface  2   a  in the Y direction. The reference electrode  8  faces the first ferromagnetic layer  3  in the X direction via the second ferromagnetic layer  4 . 
     The reference electrode  8  is composed of a nonmagnetic material such as aluminum. It is possible to reduce a Schottky barrier caused by junction between the reference electrode  8  and the semiconductor layer  2  using a nonmagnetic material having a work function close to a work function of the semiconductor layer  2  as a material of the reference electrode  8 . Therefore, it is possible to lower resistance of an interface between the reference electrode  8  and the semiconductor layer  2 . 
     The fourth protective film  9  is provided on the upper surface  2   a  of the semiconductor layer  2  to be sandwiched between the second ferromagnetic layer  4  and the reference electrode  8  in the X direction. The fourth protective film  9  extends in the X direction to connect the second ferromagnetic layer  4  and the reference electrode  8  to each other. The fourth protective film  9  is provided to cover an upper surface of the fifth region R 5 . The fourth protective film  9  is in direct contact with the upper surface of the fifth region R 5 . A length of the fourth protective film  9  in the Y direction is the same as a length of the upper surface  2   a  in the Y direction. 
     The fourth protective film  9  is composed of the same material as that of the first protective film  7 , for example. Like the first protective film  7 , the second protective film  15  and the third protective film  16 , the fourth protective film  9  protects the semiconductor layer  2  from deterioration due to oxidation, for example. Like the first protective film  7 , the second protective film  15  and the third protective film  16 , the fourth protective film  9  also serves as a strain-imparting film which imparts strain to the semiconductor layer  2 . The fourth protective film  9  also serves as a strain-imparting film which imparts strain to the fifth region R 5 . In the embodiment, the fourth protective film  9  imparts tensile strain to the fifth region R 5  along the X direction. 
     In  FIGS. 7 and 8 , modes of forces F 7  applied from the fourth protective film  9  (forces due to the internal stress of the fourth protective film  9 ) to the semiconductor layer  2  are schematically indicated by solid arrows, and modes of forces F 3  applied from the third protective film  16  to the semiconductor layer  2  are schematically indicated by void arrows. These arrows are just images and do not represent exact points of action and magnitudes of the forces. In the embodiment, the fourth protective film  9  has the compressive stress (the force for expanding) as the internal stress. As described above, since the tensile strain along the X direction is applied to each of the fourth region R 4  and the fifth region R 5 , the interatomic distances of the fourth region R 4  and the fifth region R 5  in the crystal orientation of the semiconductor material in the X direction are larger as compared with the interatomic distance of the fourth region R 4  and the fifth region R 5  in the crystal orientation of the semiconductor material in the X direction when the tensile strain along the X direction is not applied. In  FIG. 7  and  FIG. 8 , for ease of understanding, the difference between interatomic distances is exaggeratedly shown. 
     In particular, as shown in  FIG. 7 , in the fifth region R 5 , the force F 7  applied from the fourth protective film  9  decreases from the upper surface  2   a  toward the lower surface  2   b . In the fifth region R 5 , the force F 3  applied from the third protective film  16  is larger in the upper surface neighboring region Rt and the lower surface neighboring region Rb than in the central region Rm. An amount of change in the force F 3  according to a position in the Z direction is much smaller than an amount of change in the force F 7  according to the position in the Z direction. Moreover, in the fifth region R 5 , the force F 3  applied from the third protective film  16  is equal in the upper surface neighboring region Rt and the lower surface neighboring region Rb. Therefore, an interatomic distance d 5  of the fifth region R 5  in the crystal orientation of the semiconductor material in the X direction in the upper surface neighboring region Rt is larger than an interatomic distance d 51  of the fifth region R 5  in the crystal orientation of the semiconductor material in the X direction in the lower surface near region Rb. In the fourth region R 4  and the fifth region R 5 , the force F 2  applied from the second protective film  15  is not shown because it is small in magnitude. 
     The force F 3  applied from the third protective film  16  becomes smaller as being away from the side surface  2   d . Each of the forces F 7 , F 2  and F 3  is applied to the fifth region R 5 . In the embodiment, in the upper surface neighboring region Rt, the third protective film  16  and the fourth protective film  9  are formed so that the force F 3  applied from the third protective film  16  to the fourth region R 4  is larger than a sum of the force F 7  applied from the fourth protective film  9  to the fifth region R 5  and the force F 3  applied from the third protective film  16  to the fifth region R 5 . Accordingly, in the embodiment, an interatomic distance d 4  of the fourth region R 4  in the crystal orientation of the semiconductor material in the X direction in the upper surface neighboring region Rt is larger than the interatomic distance d 5 . 
     Particularly, as shown in  FIG. 8 , in the upper surface neighboring region Rt, the fifth region R 5  has end regions R 5   a  and R 5   b  in a direction orthogonal to the X direction, that is, in the Y direction, and a central region R 5   c  in the Y direction. The end region R 5   a  is disposed on the side surface  2   e  side, and the end region R 5   b  is disposed on the side surface  2   f  side. The force F 7  applied from the fourth protective film  9  to the semiconductor layer  2  increases from a center of the fifth region R 5  toward the side surfaces  2   e  and  2   f  in the Y direction. The force F 3  applied from the third protective film  16  to the semiconductor layer  2  also increases from the center of the fifth region R 5  toward the side surfaces  2   e  and  2   f  in the Y direction. Therefore, an interatomic distance d 5   a  of the end region R 5   a  in the crystal orientation of the semiconductor material in the X direction and an interatomic distance d 5   b  of the end region R 5   b  in the crystal orientation of the semiconductor material in the X direction are larger than an interatomic distance d 5   c  of the central region R 5   c  in the crystal orientation of the semiconductor material in the X direction. The interatomic distance d 5   a  and the interatomic distance d 5   b  are, for example, the same as each other. 
     The current source  20  is connected to the first ferromagnetic layer  3  and the second ferromagnetic layer  4  and supplies a constant current flowing through the semiconductor layer  2  from the second ferromagnetic layer  4  toward the first ferromagnetic layer  3 . The voltage measurement unit  30  is connected to the second ferromagnetic layer  4  and the reference electrode  8  and measures a voltage between the second ferromagnetic layer  4  and the reference electrode  8 . The current source  20  may supply a constant current flowing through the semiconductor layer  2  from the first ferromagnetic layer  3  toward the second ferromagnetic layer  4 . In this case, the voltage measurement unit  30  is connected to the first ferromagnetic layer  3  and the reference electrode  8 , and measures the voltage between the first ferromagnetic layer  3  and the reference electrode  8 . 
     In the magnetic sensor  10 C, like the magnetic sensor  10 A (refer to  FIG. 1 ), when a current is supplied by the current source  20 , the spin-polarized electrons are injected into the semiconductor layer  2  from the first ferromagnetic layer  3 . The injected spin-polarized electrons transport through the third region R 3 , and spins corresponding to the magnetization direction of the first ferromagnetic layer  3  are accumulated mainly in the second region R 2  of the upper surface neighboring region Rt. A spin output voltage as a voltage change corresponding to a change in a relative angle between the direction of the spins accumulated in the second region R 2  and the magnetization direction of the second ferromagnetic layer  4  is obtained by measuring a voltage between the second ferromagnetic layer  4  and the reference electrode  8  with the voltage measurement unit  30 . In this case, the obtained spin output voltage is in principle the same as the spin output voltage obtained by the magnetic sensor  10 A. As described above, in addition to the spin output voltage, a voltage including a voltage drop due to a resistance of the semiconductor layer  2 , a resistance of the first ferromagnetic layer  3 , a resistance of the second ferromagnetic layer  4 , a resistance between the first ferromagnetic layer  3  and the semiconductor layer  2  and a resistance between the second ferromagnetic layer  4  and the semiconductor layer  2  is measured in the magnetic sensor  10 A. On the other hand, in the magnetic sensor  10 C, a voltage which does not include a voltage drop due to the resistance of the semiconductor layer  2 , the resistance of the first ferromagnetic layer  3 , and the resistance between the first ferromagnetic layer  3  and the semiconductor layer  2  is measured. Therefore, in the magnetic sensor  10 C, since resistance of a voltage detection path is lower than that in the magnetic sensor  10 A, a high magnetoresistance ratio can be obtained. As a result, a larger SN ratio can be obtained. 
     Also in the magnetoresistance effect element  1 C, the interatomic distance d 3  is larger than the interatomic distance d 31 . Therefore, the same effect as that in the magnetoresistance effect element  1 A can be obtained. 
     Further, in the magnetoresistance effect element  1 C, the interatomic distance d 5  is larger than the interatomic distance d 51 . Therefore, an electrical resistance value in the vicinity of the upper surface of the fifth region R 5  of the semiconductor layer  2  in the X direction can be reduced as compared with a case in which the interatomic distance d 5  is equal to the interatomic distance d 51 . Since the fifth region R 5  is a voltage detection path, output noise can be reduced. As a result, it is possible to obtain a larger SN ratio than the conventional one. 
     Since the magnetic sensor  10 C includes the magnetoresistance effect element  1 C, a large SN ratio can be obtained. 
     Fourth Embodiment 
     A magnetoresistance effect element  1 D and a magnetic sensor  10 D according to a fourth embodiment will be described with reference to  FIGS. 9 and 10  focusing on differences from the magnetoresistance effect element  1 C and the magnetic sensor  10 C (refer to  FIG. 6 ) according to the third embodiment.  FIG. 9  is a partially enlarged side view showing the magnetic sensor according to the fourth embodiment.  FIG. 10  is a partially enlarged top view showing the magnetic sensor according to the fourth embodiment. In  FIG. 9 , illustration other than the semiconductor layer  2  and the fourth protective film  9  is omitted. In  FIG. 10 , illustration other than the semiconductor layer  2  is omitted. In  FIGS. 9 and 10 , an orthogonal coordinate system is shown.  FIG. 9  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (110) plane (a (1−10) plane), which is a cross section along an XZ plane, in the semiconductor layer  2 .  FIG. 10  enlargedly and schematically shows a form of atom arrangement at a plurality of portions of a (001) plane, which is a cross section along an XY plane, in the semiconductor layer  2 . 
     In the magnetoresistance effect element  1 D shown in  FIGS. 9 and 10 , as in the magnetoresistance effect element  1 B shown in  FIGS. 4 and 5 , the semiconductor layer  2  has p-type conductivity instead of n-type conductivity. That is, in addition to the first region R 1 , the second region R 2  and the third region R 3 , the fourth region R 4  and the fifth region R 5  have p-type conductivity instead of n-type conductivity. Further, as in the magnetoresistance effect element  1 B, the first protective film  7  imparts the compressive strain to the third region R 3  along the X direction. The third protective film  16  imparts the compressive strain particularly to the fourth region R 4  and the fifth region R 5  along the X direction. The force F 4  applied from the first protective film  7  (the force due to the internal stress of the first protective film  7 ) to the semiconductor layer  2  decreases from the upper surface  2   a  toward the lower surface  2   b . Therefore, the interatomic distance d 3  is smaller than the interatomic distance d 31 . The force applied from the first protective film  7  to the semiconductor layer  2  increases from the center of the third region R 3  in the Y direction toward the side surfaces  2   e  and  2   f . Thus, the interatomic distance d 3   a  and the interatomic distance d 3   b  are smaller than the interatomic distance d 3   c  of the central region R 3   c . In  FIG. 9  and  FIG. 10 , for ease of understanding, the difference between the interatomic distances is exaggeratedly shown. 
     The fourth protective film  9  imparts the compressive strain to the fifth region R 5  along the X direction. In  FIGS. 9 and 10 , modes of forces F 8  applied from the fourth protective film  9  to the semiconductor layer  2  are schematically indicated by solid arrows, and modes of the forces F 6  applied from the third protective film  16  to the semiconductor layer  2  are schematically indicated by void arrows. These arrows are just images and do not represent an exact points of action and magnitudes of the force. In the embodiment, the first protective film  7  and the fourth protective film  9  have the tensile stress (the force for contracting) as the internal stress, and the second protective film  15  and the third protective film  16  have the compressive stresses (the forces for expanding) as the internal stresses. As described above, since the compressive strain along the X direction is applied to each of the fourth region R 4  and the fifth region R 5 , the interatomic distances of the fourth region R 4  and the fifth region R 5  in the crystal orientation of the semiconductor material in the X direction are smaller as compared with the interatomic distances of the fourth region R 4  and the fifth region R 5  in the crystal orientation of the semiconductor material in the X direction when the compressive strain along the X direction is not applied. 
     In particular, as shown in  FIG. 9 , in the fifth region R 5 , the force F 8  applied from the fourth protective film  9  decreases from the upper surface  2   a  toward the lower surface  2   b . In the fifth region R 5 , the force F 6  applied from the third protective film  16  is larger in the upper surface neighboring region Rt and the lower surface neighboring region Rb than in the central region Rm. An amount of change in the force F 6  according to a position in the Z direction is much smaller than an amount of change in the force F 8  according to the position in the Z direction. Moreover, in the fifth region R 5 , the force F 6  applied from the third protective film  16  is equal in the upper surface neighboring region Rt and the lower surface neighboring region Rb. Therefore, the interatomic distance d 5  is smaller than the interatomic distance d 51 . In the fourth region R 4  and the fifth region R 5 , the force F 5  applied from the second protective film  15  is not shown because it is small in magnitude. 
     The force F 6  applied from the third protective film  16  becomes smaller as being away from the side surface  2   d . Each of the forces F 5 , F 6  and F 8  is applied to the fifth region R 5 . In the embodiment, in the upper surface neighboring region Rt, the third protective film  16  and the fourth protective film  9  are formed so that the force F 6  applied from the third protective film  16  to the fourth region R 4  is larger than a sum of the force F 8  applied from the fourth protective film  9  to the fifth region R 5  and the force F 6  applied from the third protective film  16  to the fifth region R 5 . Accordingly, in the embodiment, an interatomic distance d 4  is smaller than the interatomic distance d 5 . 
     In particular, as shown in  FIG. 10 , the force F 8  applied from the fourth protective film  9  to the semiconductor layer  2  increases from the center of the fifth region R 5  toward the side surfaces  2   e  and  2   f  in the Y direction. The force F 6  applied from the third protective film  16  to the semiconductor layer  2  also increases from the center of the fifth region R 5  toward the side surfaces  2   e  and  2   f  in the Y direction. Therefore, the interatomic distance d 5   a  and the interatomic distance d 5   b  are smaller than the interatomic distance d 5   c.    
     In the magnetic sensor  10 D, as in the magnetic sensor  10 B according to the second embodiment (refer to  FIG. 4 ), when a current is supplied by the current source  20 , the spin-polarized holes are injected from the first ferromagnetic layer  3  into the semiconductor layer  2 . The injected spin-polarized holes transport through the third region R 3 , and the spins corresponding to the magnetization direction of the first ferromagnetic layer  3  are accumulated mainly in the second region R 2  in the upper surface neighboring region Rt. A spin output voltage as a voltage change corresponding to a change in a relative angle between the direction of the spins accumulated in the second region R 2  and the magnetization direction of the second ferromagnetic layer  4  is obtained by measuring a voltage between the second ferromagnetic layer  4  and the reference electrode  8  with the voltage measurement unit  30 . In this case, the obtained spin output voltage is in principle the same as the spin output voltage obtained by the magnetic sensor  10 B. As described above, in addition to the spin output voltage, a voltage including a voltage drop due to the resistance of the semiconductor layer  2 , the resistance of the first ferromagnetic layer  3 , the resistance of the second ferromagnetic layer  4 , the resistance between the first ferromagnetic layer  3  and the semiconductor layer  2 , and the resistance between the second ferromagnetic layer  4  and the semiconductor layer  2  is measured in the magnetic sensor  10 B. On the other hand, in the magnetic sensor  10 D, a voltage which does not include a voltage drop due to the resistance of the semiconductor layer  2 , the resistance of the first ferromagnetic layer  3 , and the resistance between the first ferromagnetic layer  3  and the semiconductor layer  2  is measured. Therefore, in the magnetic sensor  10 D, since the resistance of the voltage detection path is lower than that in the magnetic sensor  10 B, a high magnetoresistance ratio can be obtained. As a result, a larger SN ratio can be obtained. 
     Also in the magnetoresistance effect element  1 D, the interatomic distance d 3  is smaller than the interatomic distance d 31 . Therefore, the same effect as that in the magnetoresistance effect element  1 B can be obtained. 
     Further, in the magnetoresistance effect element  1 D, the interatomic distance d 5  is smaller than the interatomic distance d 51 . Therefore, an electrical resistance value of the upper surface neighboring region Rt of the fifth region R 5  of the semiconductor layer  2  in the X direction can be reduced as compared with the case in which the interatomic distance d 5  is equal to the interatomic distance d 51 . Since the fifth region R 5  is a voltage detection path, the output noise can be reduced. As a result, it is possible to obtain a larger SN ratio than the conventional one. 
     Since the magnetic sensor  10 D includes the magnetoresistance effect element  1 D, a large SN ratio can be obtained. 
     Fifth Embodiment 
     A magnetoresistance effect element  1 E and a spin transistor  50  according to a fifth embodiment will be described with reference to  FIGS. 11 and 12 .  FIG. 11  is a perspective view showing the spin transistor according to the fifth embodiment.  FIG. 12  is a cross-sectional view showing a carrier control type magnetoresistance effect element shown in  FIG. 11 . In  FIGS. 11 to 12 , an orthogonal coordinate system is shown. As shown in  FIGS. 11 to 12 , the spin transistor  50  includes a magnetoresistance effect element  1 E, a third insulating layer  11 , and a gate electrode  12 , and is connected to a power supply  41  and a power supply  42 . The magnetoresistance effect element  1 E, the third insulating layer  11  and the gate electrode  12  constitute a carrier control type magnetoresistance effect element  51 E. The magnetoresistance effect element  1 E includes the semiconductor layer  2 , the first ferromagnetic layer  3 , the second ferromagnetic layer  4 , the first insulating layer  5 , the second insulating layer  6 , the second protective film  15 , and the third protective film  16 . The semiconductor layer  2  has the first region R 1 , the second region R 2 , and the third region R 3 , as in the case of the magnetoresistance effect element  1 A (refer to  FIG. 1 ). 
     The third insulating layer  11  is provided on the third region R 3 . The third insulating layer  11  is in direct contact with the upper surface of the third region R 3 . The third insulating layer  11  is provided between the first ferromagnetic layer  3  and the second ferromagnetic layer  4  to be spaced apart from the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . A length of the third insulating layer  11  in the Y direction is the same as a length of the upper surface  2   a  in the Y direction. For example, the third insulating layer  11  has an oxide insulator such as a silicon oxide, a hafnium oxide, a zirconium oxide, an aluminum oxide, a lanthanum oxide, an yttrium oxide or a magnesium oxide, or a nitride insulator such as an aluminum nitride or a silicon nitride. The third insulating layer  11  also serves as a strain imparting film which imparts strain to the third region R 3 . The third insulating layer  11  imparts strain to the third region R 3  along the X direction. The gate electrode  12  is provided on the third region R 3  with the third insulating layer  11  interposed therebetween. The gate electrode  12  is provided to be spaced apart from the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . For example, a metal, an alloy or a conductive nitride having an element such as Pt, W, Ta, Ti, Al or the like can be used as an electrode material constituting the gate electrode  12 . Also, polycrystalline silicon, silicide, germanide or the like can be used. The gate electrode  12  is configured to be capable of applying a voltage such that an inversion layer  17  is formed in at least a part of the upper surface neighboring region Rt of the third region R 3 . 
     In the magnetoresistance effect element  1 E, doping of an impurity to the semiconductor layer  2  is selectively performed. Therefore, there is a difference in carrier concentration in the semiconductor layer  2 . Specifically, the carrier concentration in the first region R 1  and the second region R 2  is higher than the carrier concentration in the third region R 3 . That is, the first region R 1  and the second region R 2  are heavily doped regions, and the third region R 3  is a lightly doped region. The first region R 1  and the second region R 2  have the same conductivity type. 
     In the case in which the first region R 1  and the second region R 2  have the n-type conductivity and the third region R 3  has the n-type conductivity, the carrier control type magnetoresistance effect element  51 E constitutes an NNN type spin MOSFET. In the case in which the first region R 1  and the second region R 2  have the n-type conductivity and the conductivity type of the third region R 3  when a voltage is not applied to the gate electrode  12  is p-type, the carrier control type magnetoresistance effect element  51 E constitutes an NPN type spin MOSFET. In the case in which the first region R 1  and the second region R 2  have the p-type conductivity and the conductivity type of the third region R 3  when the voltage is not applied to the gate electrode  12  is the n-type, the carrier control type magnetoresistance effect element  51 E constitutes a PNP type spin MOSFET. In the case in which the first region R 1  and the second region R 2  have the p-type conductivity and the third region R 3  has the p-type conductivity, the carrier control type magnetoresistance effect element  51 E constitutes a PPP type spin MOSFET. 
     One of the first ferromagnetic layer  3  and the second ferromagnetic layer  4  serves as a source electrode, and the other one of the first ferromagnetic layer  3  and the second ferromagnetic layer  4  serves as a drain electrode. In the embodiment, the first ferromagnetic layer  3  serves as a source electrode, and the second ferromagnetic layer  4  serves as a drain electrode. The power supply  41  is connected to the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . The power supply  42  is connected to the ground and the gate electrode  12 . The first ferromagnetic layer  3  is connected to the ground. 
     In the carrier control type magnetoresistance effect element  51 E, it is possible to control the conductivity type and the carrier density of the third region R 3  by applying a voltage to the gate electrode  12  by the power supply  42 . 
     In the case in which the carrier control type magnetoresistance effect element  51 E constitutes the NNN type spin MOSFET, when a positive voltage is applied to the second ferromagnetic layer  4  by the power supply  41 , even without applying a voltage to the gate electrode  12 , the spin-polarized electrons are injected from the first ferromagnetic layer  3  into the semiconductor layer  2  and flow through the third region R 3  toward the second ferromagnetic layer  4 . When a positive voltage is applied to the gate electrode  12  by the power supply  42 , the carrier density in the vicinity of the upper surface of the third region R 3  increases, and thus the spin-polarized electrons easily flow. When a negative voltage is applied to the gate electrode  12  by the power supply  42 , the carrier density in the vicinity of the upper surface of the third region R 3  decreases, and thus the spin-polarized electrons hardly flow 
     In the case in which the carrier control type magnetoresistance effect element  51 E constitutes the NPN type spin MOSFET, when a positive voltage is applied to the gate electrode  12  by the power supply  42 , the inversion layer  17  having the n-type conductivity is formed in the third region R 3  of the upper surface neighboring region Rt. Therefore, when a positive voltage is applied to the second ferromagnetic layer  4  by the power supply  41 , the spin-polarized electrons are injected from the first ferromagnetic layer  3  into the semiconductor layer  2  and transport or diffuse through the third region R 3  toward the second ferromagnetic layer  4 . On the other hand, in a state in which no voltage is applied to the gate electrode  12  or a state in which a negative voltage is applied, a high-resistance depletion layer is formed at an interface between the first region R 1  and the second region R 2  and the third region R 3 , and thus even when a voltage is applied to the second ferromagnetic layer  4  by the power supply  41 , the spin-polarized electrons hardly flow. 
     In the case in which the carrier control type magnetoresistance effect element  51 E constitutes the PNP type spin MOSFET, when a negative voltage is applied to the gate electrode  12  by the power supply  42 , the inversion layer  17  having the p-type conductivity is formed in the third region R 3  of the upper surface neighboring region Rt. Therefore, when a negative voltage is applied to the second ferromagnetic layer  4  by the power supply  41 , the spin-polarized holes are injected from the first ferromagnetic layer  3  into the semiconductor layer  2  and transport or diffuse through the third region R 3  toward the second ferromagnetic layer  4 . On the other hand, in a state in which no voltage is applied to the gate electrode  12  or a positive voltage is applied, the high-resistance depletion layer is formed at the interface between the first region R 1  and the second region R 2  and the third region R 3 , and thus even when a voltage is applied to the second ferromagnetic layer  4  by the power supply  41 , the spin-polarized holes hardly flow. 
     In the case in which the carrier control type magnetoresistance effect element  51 E constitutes the PPP type spin MOSFET, when a negative voltage is applied to the second ferromagnetic layer  4  by the power supply  41 , even without applying a voltage to the gate electrode  12 , the spin-polarized holes are injected from the first ferromagnetic layer  3  into the semiconductor layer  2  and flows through the third region R 3  toward the second ferromagnetic layer  4 . When a negative voltage is applied to the gate electrode  12  by the power supply  42 , the carrier density in the vicinity of the upper surface of the third region R 3  increases, and thus the spin-polarized holes easily flow. When a positive voltage is applied to the gate electrode  12  by the power supply  42 , the carrier density in the vicinity of the upper surface of the third region R 3  decreases, and thus the spin-polarized holes hardly flow. 
     When the carrier control type magnetoresistance effect element  51 E constitutes the NNN type and NPN type spin MOSFETs, a region in which the spins transport and/or diffuse has the n-type conductivity. In this case, the second protective film  15 , the third protective film  16  and the third insulating layer  11  impart the tensile strain to the third region R 3 , and the interatomic distances d 1 , d 2 , d 3 , d 31 , d 3   a , d 3   b  and d 3   c  have the same relationship as that in the magnetoresistance effect element  1 A (refer to  FIG. 1 ). Therefore, in the carrier control type magnetoresistance effect element  51 E (the magnetoresistance effect element  1 E), the same effect as in the case of the magnetoresistance effect element  1 A can be obtained. 
     When the carrier control type magnetoresistance effect element  51 E constitutes the PNP type and PPP type spin MOSFETs, a region in which the spins transport and/or diffuse has the p-type conductivity. In this case, the second protective film  15 , the third protective film  16  and the third insulating layer  11  impart the compressive strain to the third region R 3 , and the interatomic distances d 1 , d 2 , d 3 , d 31 , d 3   a , d 3   b  and d 3   c  have the same relationship as that in the magnetoresistance effect element  1 B (refer to  FIG. 4 ). Therefore, in the carrier control type magnetoresistance effect element  51 E (the magnetoresistance effect element  1 E), the same effect as in the case of the magnetoresistance effect element  1 B can be obtained. 
     When the first region R 1  and the second region R 2  have the same conductivity type as that of the third region R 3 , that is, when the carrier control type magnetoresistance effect element  51 E constitutes the NNN type or PPP type spin MOSFET, a normally-on type (depletion type) spin transistor  50  in which a spin-polarized current flows without applying a voltage to the gate electrode  12  can be realized. When the first region R 1  and the second region R 2  have conductivity types different from that of the third region R 3 , that is, when the carrier control type magnetoresistance effect element  51 E constitutes the NPN type or PNP type spin MOSFET, a normally-off type (enhancement type) spin transistor  50  in which a spin-polarized current does not flow unless a voltage is applied to the gate electrode  12  can be realized. 
     Sixth Embodiment 
     The magnetoresistance effect element  1 F and the magnetic sensor  10 F according to a sixth embodiment will be described with reference to  FIG. 13 .  FIG. 13  is a perspective view showing a magnetic sensor according to a sixth embodiment. In  FIG. 13 , an orthogonal coordinate system is shown. As shown in  FIG. 13 , the magnetic sensor  10 F includes the magnetoresistance effect element  1 F and is connected to the current source  20 , the voltage measurement unit  30 , and a power supply  43 . The magnetoresistance effect element  1 F has the same configuration as that of the magnetoresistance effect element  1 E (refer to  FIG. 11 ). The third insulating layer  11  and the gate electrode  12  have the same configurations as the third insulating layer  11  and the gate electrode  12  (refer to  FIG. 11 ) according to the fifth embodiment. The magnetoresistance effect element  1 F, the third insulating layer  11  and the gate electrode  12  constitute a carrier control type magnetoresistance effect element  51 F. The carrier control type magnetoresistance effect element  51 F has the same configuration as the carrier control type magnetoresistance effect element  51 E (refer to  FIG. 11 ). The current source  20  supplies a constant current flowing through the semiconductor layer  2  from the second ferromagnetic layer  4  toward the first ferromagnetic layer  3 . The voltage measurement unit  30  is connected to the first ferromagnetic layer  3  and the second ferromagnetic layer  4  and measures a voltage between the first ferromagnetic layer  3  and the second ferromagnetic layer  4 . The power supply  43  is connected to the ground and the gate electrode  12 . The first ferromagnetic layer  3  is connected to the ground. 
     According to the carrier control type magnetoresistance effect element  51 F, like the carrier control type magnetoresistance effect element  51 E (refer to  FIG. 11 ), it is possible to control the conductivity type and the carrier density of the third region R 3  by applying an electric field to the gate electrode  12  by the power supply  43 . 
     Since the magnetic sensor  10 F includes the carrier control type magnetoresistance effect element  51 F, a large SN ratio can be obtained. Also, in the magnetic sensor  10 F, the conductivity type and the carrier density of the third region R 3  can be controlled. Therefore, for example, in the upper surface neighboring region Rt, a spin accumulation effect in the semiconductor layer  2  can be increased by applying a voltage to the gate electrode  12  so that the carrier density in the third region R 3  increases. Thus, the magnetoresistance effect can be increased. As a result, since the output signal can be increased, a large SN ratio can be obtained. 
     The present disclosure is not limited to the above-described embodiments. 
     In the magnetoresistance effect elements  1 A,  1 B,  1 C and  1 D, the first protective film  7  serves as the strain imparting film depending on the film deposition conditions of the first protective film  7 , but the first protective film  7  may serve as a strain imparting film using a difference between a thermal expansion coefficient of the first protective film  7  and a thermal expansion coefficient of the semiconductor layer  2 . For example, a material having a thermal expansion coefficient higher than the thermal expansion coefficient of the semiconductor layer  2  is used as a material of the first protective film  7 , and the first protective film  7  is formed on the third region R 3  at a high temperature. In this case, when the temperature is lowered from a high temperature to a normal temperature, a contraction amount of the first protective film  7  is larger than a contraction amount of the semiconductor layer  2 . As a result, the tensile stress (the force for contracting) remains in the first protective film  7 . Further, for example, a material having a thermal expansion coefficient smaller than the thermal expansion coefficient of the semiconductor layer  2  is used as the material of the first protective film  7 , and the first protective film  7  is formed on the third region R 3  at a high temperature. In this case, the contraction amount of the first protective film  7  is smaller than the contraction amount of the semiconductor layer  2  when the temperature is lowered from a high temperature to a normal temperature. As a result, the compressive stress (the force for expanding) remains in the first protective film  7 . 
     Further, for example, a material having a thermal expansion coefficient larger than the thermal expansion coefficient of the semiconductor layer  2  is used as the material of the first protective film  7 , and the first protective film  7  is formed on the third region R 3  at a low temperature equal to or less than room temperature. In this case, when the temperature is raised from the low temperature, an expansion amount of the first protective film  7  is larger than an expansion amount of the semiconductor layer  2 . As a result, the compressive stress (the force for expanding) remains in the first protective film  7 . Further, for example, a material having a thermal expansion coefficient smaller than the thermal expansion coefficient of the semiconductor layer  2  is used as a material of the first protective film  7 , and the first protective film  7  is formed on the third region R 3  at the low temperature equal to or less than the room temperature. In this case, when the temperature is raised from the low temperature, the expansion amount of the first protective film  7  is smaller than the expansion amount of the semiconductor layer  2 . As a result, the tensile stress (the force for contracting) remains in the first protective film  7 . Strain can be imparted to the third region R 3  using the force provided from the first protective film  7  (the force due to the internal stress of the first protective film  7 ) as described above. 
     Specific examples of combinations of materials of the semiconductor layer  2  and the first protective film  7  are shown in Tables 1 and 2. Table 1 shows a case in which the first protective film  7  has the compressive stress as the internal stress. Table 2 shows a case in which the first protective film  7  has the tensile stress as the internal stress. 
     
       
         
           
               
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                   
                 Protective film having compressive stress as internal stress 
               
            
           
           
               
               
               
            
               
                 Semicon- 
                 Film deposition at higher 
                 Film deposition at lower 
               
               
                 ductor 
                 temperature than room 
                 temperature than room 
               
               
                 layer 
                 temperature 
                 temperature 
               
               
                   
               
               
                 Silicon 
                 Silicon oxide 
                 Zirconium oxide, magnesium 
               
               
                   
                   
                 oxide, aluminum oxide, 
               
               
                   
                   
                 yttrium oxide, hafnium oxide, 
               
               
                   
                   
                 aluminum nitride, silicon 
               
               
                   
                   
                 nitride 
               
               
                 Germanium 
                 Silicon oxide, silicon nitride, 
                 Zirconium oxide, magnesium 
               
               
                   
                 aluminum nitride, hafnium 
                 oxide, aluminum oxide, 
               
               
                   
                 oxide 
                 yttrium oxide 
               
               
                 Carbon  
                 Silicon oxide 
                 Zirconium oxide, magnesium 
               
               
                 (diamond) 
                   
                 oxide, aluminum oxide, 
               
               
                   
                   
                 yttrium oxide, hafnium oxide, 
               
               
                   
                   
                 aluminum nitride, silicon 
               
               
                   
                   
                 nitride 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                   
                 Protective film having tensile stress as internal stress 
               
            
           
           
               
               
               
            
               
                 Semicon- 
                 Film deposition at higher 
                 Film deposition at lower 
               
               
                 ductor 
                 temperature than room 
                 temperature than room 
               
               
                 layer 
                 temperature 
                 temperature 
               
               
                   
               
               
                 Silicon 
                 Zirconium oxide, magnesium 
                 Silicon oxide 
               
               
                   
                 oxide, aluminum oxide, 
                   
               
               
                   
                 yttrium oxide, hafnium oxide, 
                   
               
               
                   
                 aluminum nitride, silicon 
                   
               
               
                   
                 nitride 
                   
               
               
                 Germanium 
                 Zirconium oxide, magnesium 
                 Silicon oxide, silicon nitride, 
               
               
                   
                 oxide, aluminum oxide, 
                 aluminum nitride, hafnium 
               
               
                   
                 yttrium oxide 
                 oxide 
               
               
                 Carbon  
                 Zirconium oxide, magnesium 
                 Silicon oxide 
               
               
                 (diamond) 
                 oxide, aluminum oxide, 
                   
               
               
                   
                 yttrium oxide, hafnium oxide, 
                   
               
               
                   
                 aluminum nitride, silicon 
                   
               
               
                   
                 nitride 
               
               
                   
               
            
           
         
       
     
     In the magnetoresistance effect elements  1 A,  1 B,  1 C,  1 D,  1 E and  1 F, the second protective film  15  and the third protective film  16  may serve as the strain imparting film using the difference between the thermal expansion coefficient of the second protective film  15  and the third protective film  16  and the thermal expansion coefficient of the semiconductor layer  2 . Specific examples of combinations of the materials of the semiconductor layer  2 , the second protective film  15  and the third protective film  16  can be the same as the specific examples of the combinations of the materials of the semiconductor layer  2  and the first protective film  7  shown in Tables 1 and 2. 
     In the magnetoresistance effect elements  1 C and  1 D, the fourth protective film  9  may serve as the strain imparting film using the difference between the thermal expansion coefficient of the fourth protective film  9  and the thermal expansion coefficient of the semiconductor layer  2 . Specific examples of combinations of the materials of the semiconductor layer  2  and the fourth protective film  9  can be the same as the specific examples of the combinations of the materials of the semiconductor layer  2  and the first protective film  7  shown in Tables 1 and 2. In the carrier control type magnetoresistance effect elements  51 E and  51 F, the third insulating layer  11  may serve as the strain imparting film using the difference between the thermal expansion coefficient of the third insulating layer  11  and the thermal expansion coefficient of the semiconductor layer  2 . Specific examples of combinations of the materials of the semiconductor layer  2  and the third insulating layer  11  can be the same as the specific examples of the combinations of the materials of the semiconductor layer  2  and the first protective film  7  shown in Tables 1 and 2. 
     The magnetoresistance effect elements  1 A,  1 B,  1 C and  1 D have the first protective film  7  which imparts the strain to the third region R 3 , but the first protective film  7  may not be provided as long as the strain introduced into the third region R 3  by the first protective film  7  or the like remains and the relationship between the above-described interatomic distances is maintained. The magnetoresistance effect elements  1 A,  1 B,  1 C,  1 D,  1 E and  1 F have the second protective film  15  and the third protective film  16  which impart the strain to the third region R 3  or the like, but the second protective film  15  and the third protective film  16  may not be provided as long as the strain introduced into the third region R 3  or the like by the second protective film  15  and the third protective film  16  or the like remains and the relationship between the above-described interatomic distances is maintained. The magnetoresistance effect elements  1 C and  1 D have the fourth protective film  9  which imparts the strain to the fifth region R 5 , but the fourth protective film  9  may not be provided as long as the strain introduced into the fifth region R 5  by the fourth protective film  9  or the like remains and the relationship between the above-described interatomic distances is maintained. 
     In the carrier control type magnetoresistance effect elements  51 E and  51 F, the third insulating layer  11  imparts the strain to the third region R 3  along the X direction, but the third insulating layer  11  may not serve as the strain imparting film. For example, before the formation of the third insulating layer  11 , a strain imparting film which is not the third insulating layer  11  may be formed on the third region R 3  and then may introduce the strain into the third region R 3 . In this case, the third insulating layer  11  can be formed in a state in which the film is removed and the strain remains in the third region R 3 . Further, for example, the carrier control type magnetoresistance effect elements  51 E and  51 F may include a protective film provided to cover the upper surface of the gate electrode  12 , and the protective film may serve as the strain imparting film. 
     In the magnetoresistance effect elements  1 C and  1 D, the fifth region R 5  is sandwiched between the second region R 2  and the fourth region R 4  in the X direction, and the first region R 1 , the third region R 3 , the second region R 2 , the fifth region R 5  and the fourth region R 4  are linearly arranged in this order in the X direction (that is, the first direction and the second direction coincide with each other), but the present disclosure is not limited thereto. The first direction and the second direction may be different from each other, and for example, the fifth region R 5  may be sandwiched between the second region R 2  and the fourth region R 4  in a direction intersecting the X direction, and the direction in which the first region R 1 , the third region R 3  and the second region R 2  are arranged and the direction in which the second region R 2 , the fifth region R 5  and the fourth region R 4  are arranged may intersect each other. In this case, the magnetoresistance effect elements  1 C and  1 D have a bent shape as a whole. The magnetoresistance effect elements  1 C and  1 D may have a curved shape as a whole. 
     The magnetoresistance effect elements  1 A,  1 B,  1 C,  1 D,  1 E and  1 F may not have the first insulating layer  5  and the second insulating layer  6 . 
     In the magnetoresistance effect elements  1 C and  1 D, like the magnetoresistance effect element  1 F, the third insulating layer  11  and the gate electrode  12  may be provided on the third region R 3  instead of the first protective film  7 . In this case, the magnetic sensors  10 C and  10 D may be connected to the power supply  43  which applies a voltage to the gate electrode  12 , as in the magnetic sensor  10 F. Thus, it is possible to control the conductivity type and the carrier density of the third region R 3 . 
     In the magnetic sensors  10 A,  10 B,  10 C,  10 D and  10 F, a voltage source may be used instead of the current source  20 , and a current measurement unit may be used instead of the voltage measurement unit  30 , and a change in the resistance due to the magnetoresistance effect may be measured by a change in current value.