Semiconductor device and method of manufacturing the same

Abstract: A semiconductor device has a substrate composed of a semiconductor which has one of sphalerite and diamond crystal structures. The substrate has a plane orientation inclined at 0.5° to 15° with respect to one of {111} and {110} planes indicated by Miller indices. A first semiconductor layer is formed on the substrate. The first semiconductor layer has a sawtooth-shaped first periodic structure consisting of one of the {111} and {110} planes indicated by the Miller indices and at least one plane indicated by another index. A second semiconductor layer is formed on the first semiconductor layer. The second semiconductor layer has a second periodic structure having a phase shifted from a phase of the first periodic structure. An embodiment of the semiconductor device is a distributed feedback diode laser incorporating a quantum-well or quantum-wire structure.

Description: The present invention relates to a structure of a semiconductor device including a two-dimensional quantum well structure formed on a diffraction grating so as to realize a semiconductor laser having a low threshold current density, a high-speed transistor, and the like, formation of a diffraction grating meeting this object, and a method of manufacturing a semiconductor crystal on the diffraction grating. The present invention is applied to the manufacture of a semiconductor element having high-performance electronic or optical characteristics. Conventionally, extensive studies have been made about a semiconductor structure in which a diffraction grating is formed on a semiconductor substrate, and a layer having a second periodic structure shifted from the phase of the periodic structure of the substrate is grown on the diffraction grating. A diffraction grating is used in various optical circuit elements such as a filter, an optical coupler, a distributed feedback (DFB) laser, a distributed Bragg reflection (DBR) laser, and the like in the field of optical electronics. In particular, a diffraction grating formed for a wavelength control or wavelength variable semiconductor laser represented by the DFB or DBR laser is used as a laser resonator. In addition, the period, shape, and depth of the diffraction grating are important factors for determining laser characteristics (an oscillation threshold, a coupling coefficient, and the like), and to form a high-precision diffraction grating in such a laser with high controllability is an important subject in this technical field. Conventionally, a diffraction grating is formed by a two-step method including formation of a grating-shaped photoresist mask, and etching. However, since the period of a diffraction grating used in the optical electronics field is as fine as 0.1 to 1.0 µm, the conventional photolithography technique cannot be applied to the formation of the photoresist mask. For this reason, a holographic exposure method is normally adopted. This exposure method uses an interference of laser light, and its process will be explained below with reference to Figs. 1A to 1D. As shown in Fig. 1A, a photoresist 1-22 is coated on a substrate 1-21. Two laser beams 1-23 and 1-24 which are sufficiently parallel light beams are radiated on the photoresist layer from two directions (in Fig. 1A, two directions each forming an angle  with respect to the perpendicular) to form interference fringes, thereby periodically exposing the photoresist layer. The exposed photoresist layer is developed and baked, thereby forming a grating-shaped photoresist mask 1-25, as shown in Fig. 1B. Then, etching (wet or dry etching) using the photoresist mask as an etching mask is performed, as shown in Fig. 1C, and thereafter, the etching mask is removed, thereby transferring a periodic structure (diffraction grating) 1-26 to the substrate, as shown in Fig. 1D. In the holographic interference exposure method, if the incident angle of the two laser beams is represented by , and the wavelength of the laser beam is represented by λ, a grating interval Λ (see Fig. 1B) which can be formed is given by Λ = λ/(2sin). As an exposure laser, an Ar laser (λ = 351 nm) or an He-Cd laser (λ = 352 nm) is suitably used. In order to form a mask having Λ ≤ 0.25 µm, the He-Cd laser is used. On the other hand, the oscillation wavelength λ of a DFB or DBR semiconductor laser can be expressed by λ = λ 0 /N eff = 2Λ/m (m = 1, 2,...) (where λ 0 /N eff is the Bragg wavelength in a medium, N eff is the equivalent refractive index of the medium, and Λ is the period of a diffraction grating in this semiconductor laser). m = 1 as an integer means 1st-order diffraction, and m = 2 means 2nd-order diffraction. In such a semiconductor laser, for example, in a short-wavelength laser having a GaAs layer as an active layer, the period Λ of the diffraction grating becomes as small as about 115 nm from the above equation (in the case utilizing 1st-order diffraction) if the oscillation wave length is 0.8 µm. Even when mth-order diffraction is utilized, the period Λ can only be increased to m times of 115 nm. Therefore, in order to decrease the wavelength of an exposure laser beam in the formation of the diffraction grating, the 1st-order diffraction grating cannot be formed in air even when the He-Cd laser having a wavelength λ = 325 nm is used. Thus, as a method of manufacturing a 1st-order diffraction grating (period Λ = 130 nm or less) of a GaAs-based short-wavelength DFB or DBR semiconductor laser, the following three methods are known. As the first method, a sample is dipped in a high-refractive index medium, and interference exposure is performed therein, thereby shortening the period of the diffraction grating by the refractive index of the medium. As the high-refractive index medium, xylene with small light absorption is used. As a similar method, a triangular or rectangular prism may be placed on a photoresist film via a refractive index matching oil, and two exposure light beams may be caused to become incident from the two sides of this prism. As the second method, the period of the diffraction grating obtained by a two beams interference exposure method is halved by another treatment. As illustrated in Fig. 2A, a plurality of grooves (diffraction grating) 2-27a are formed on a substrate 2-27, and an etching mask material (photoresist) 2-28 is formed on the entire surface of the substrate. Thereafter, the etching surface is exposed by exposure and development, as shown in Fig. 2B, and etching is performed, as shown in Fig. 2C, thereby obtaining a diffraction grating having a period half that of the grooves 2-27a, as shown in Fig. 2D. As the third method, as illustrated in Figs. 3A to 3D, a photoresist mask 3-29 is formed on a substrate 3-30 by a two beams interference exposure method, as shown in Fig. 3A, and an SiN x film is grown on the mask by electron cyclotron resonance (ECR)-chemical vapor deposition (CVD), as shown in Fig. 3B. The etching time is adjusted, thereby forming resist and SiN x etching masks 3-29 and 3-32, as shown in Fig. 3C. Etching is performed using these masks, thereby forming a diffraction grating 3-33 having a period half that of the initially formed photoresist mask, as shown in Fig. 3D. The manufacture of a wafer multi-layered structure on a manufactured diffraction grating is a very important technique for the sake of improving the semiconductor technique, and the threshold current density of a laser. A semiconductor device using a superlattice structure has received a lot of attention since it realizes a semiconductor laser having a lower threshold current and a transistor capable of performing a higher-speed operation as compared to conventional ones. As the superlattice structure under examination, a one-dimensional quantum well structure (quantum thin film) is the main stream, and a semiconductor laser utilizing this structure is described in the following reference: Tsang, W.T.: "Extremely Low Threshold (AlGa)As Modified Multi-Quantum Well Heterostructure Laser Grown by Molecular Beam Epitaxy" Appl. Phys. Lett., 39, p786-788 (1981) In contrast to the one-dimensional quantum well structure, if the number of dimensions is increased like a two-dimensional quantum well structure (quantum wire), a three-dimensional quantum well structure (quantum box), and the like, it is presumed that devices having more excellent features can be manufactured. Figs. 4A, 4B, and 4C are perspective views showing the principles of the one-, two-, and three-dimensional quantum well structures, respectively, and Figs. 5A, 5B, and 5C are graphs each showing the relationship between the density of states and energy shown in Figs. 4A, 4B, and 4C, respectively. Although the density of states of the one-, two-, or three-dimensional structure in a bulk crystal state is defined by a parabola, as indicated by a dotted curve in Fig. 5A, the curve of the density of states is changed to a staircase shape, sawtooth shape, and pulse train shape respectively in the one-, two-, and three-dimensional quantum well structures. Since it is presumed that a light absorption or light-emission state sequentially changes with such a change in density of states, a semiconductor laser having an extremely low threshold is expected. Furthermore, in the two-dimensional quantum well structure, it is presumed that the electron mobility is increased due to a simplified scattering mechanism, and such a structure is also important in view of electronic devices. In a quantum wire laser using the two-dimensional quantum well structure or a quantum box laser using the three-dimensional quantum well structure, the following effects are expected from the above-mentioned features: (1) low threshold laser; (2) small temperature dependency of threshold current; (3) improvement of high-speed modulation due to increase in relaxation vibration resonance frequency; and (4) narrow oscillation spectrum line width. As described above, although increase in the number of dimensions of quantization has various merits, its manufacturing method is still under development. As a manufacturing method under examination, a method shown in Figs. 6A to 6D (disclosed in Japanese Laid-Open Patent Application No. 63-94615) is the main stream. The principle of the manufacturing method will be described below with reference to Figs. 6A to 6D and Fig. 7. Referring to Fig. 6A, a substrate having a (100) plane on its surface is inclined at several degrees toward a (011) direction. The inclined plane is defined by combining a (100) plane 131 and a (011) plane 133. Assume that an AlAs molecule 132 flies onto a crystal face (100). At this time, since the AlAs molecule 132 is unstable on the (100) plane, it is re-evaporated or moves on the (100) plane. When the molecule reaches a step with the (011) plane 133, the AlAs molecule 132 is absorbed by this step, and forms a crystal face. As shown in Fig. 6B, more AlAs molecules 132 are absorbed by this step in turn, and become a crystal. As shown in Fig. 6C, supply of the AlAs molecules 132 is stopped to form an AlAs layer halfway on the (100) plane. Then, when molecules to be supplied are changed to GaAs molecules 134, crystal growth is performed based on the same principle as described above, and GaAs and AlAs regions are formed in the horizontal direction, as shown in Fig. 6D. A film thickness h 135 of each layer corresponds to one atomic layer. When the growth processes shown in Figs. 6C and 6D are repeated, a crystal structure in which GaAs layers 141 and AlAs layers 142 extend in the vertical direction, as shown in Fig. 7, can be obtained. In this manner, when an inclined substrate is used, and the molecular species to be supplied is changed, quantum wires can be manufactured. A crystal growth method will be described in detail below. It is expected that new electronic or optical characteristics different from those of a semiconductor crystal in a bulk state appear in a quantum wire in which electrons and holes as carriers in a semiconductor are confined in a one-dimensional narrow space, or in a two-dimensional superlattice which is constituted by periodically arranging the quantum wires. For example, when the quantum wire is used in an active layer of a semiconductor laser, the threshold current of laser oscillation can be lowered, and a sharp light emission spectrum which is stable against a change in temperature can be obtained. Since the electron mobility in the quantum wire is as high as about 10 7 to 10 8 cm/V·sec, applications to a field effect transistor (FET) having the same high-speed characteristics as those of a high electron mobility transistor (HEMT) and a unique function element are expected. For these reasons, attempts have been made to manufacture the quantum wire and the two-dimensional superlattice. Quantum confinement in the one-dimensional direction can be achieved with a high precision by thin film formation techniques such as an MBE method. In contrast to this, in order to manufacture a quantum wire in which carriers are confined in the two-dimensional directions, certain means for confining a region, corresponding to a well, of an energy band in a barrier region by modulating the energy band in the planar direction in addition to the direction of film thickness is required. Methods proposed and examined as means for manufacturing the quantum wire or the two-dimensional superlattice are classified into the following three types. (Prior Art 1) A method of directly utilizing micropatterning techniques such as lithography, etching, and the like as means for forming an interface for confining a GaAs well region in the planar direction. (Prior Art 2) A GaAs well layer and an AlGaAs barrier layer are grown on a GaAs (001) OFF substrate pre-formed with a three-dimensional pattern using the metal-organic vapor phase epitaxy (MOVPE) method. A method of forming a quantum wire on the bottom surface of a V groove or on a sawtooth-shaped step portion by utilizing a difference between growth rates depending on crystal orientations in this case. (Prior Art 3) If growth conditions are suitably selected upon MBE growth on a GaAs substrate having a surface orientation slightly inclined from a -(001) plane, crystal growth progresses by movement of atomic steps. A method of forming a quantum wire structure by alternately growing GaAs and AlGaAs within a time shorter than a time interval for forming one atomic layer utilizing this fact. The above-mentioned manufacturing methods of the 1st-order diffraction grating (period Λ = 130 nm or less) for a short-wavelength (λ = 0.8 µm) DFB or DBR semiconductor laser suffer from the following problems. In the first method, the light wavefront of an exposure beam is disturbed by scattering or multiple reflections caused by a liquid or its container, or is easily influenced by a vibration of the apparatus and a fluctuation of air, thus impairing the precision of the diffraction grating. In the second method, it is difficult to control the exposure/development conditions after the photoresist film is formed as an etching mask on the entire surface, and a variation occurs in a single plane, thus impairing the precision of the diffraction grating. When wet etching is used in the second etching process, asymmetry of the diffraction grating shape occurs. In the third method, it is difficult to control the etching conditions of the SiN x film on the resist and the SiN x film on the substrate. If dry etching is used in etching, since the etching mask consists of two different materials, i.e., the resist and the SiN x film, these materials have different resistances against an etching gas, resulting in asymmetry of a diffraction grating shape, and low precision of the depth and dimensions. The above-mentioned conventional manufacturing method of the two-dimensional quantum well structure utilizes the periodicity of AlAs or GaAs. However, the AlAs and GaAs layers do not always exhibit constant periodicity, and the widths of the GaAs and AlAs layers often vary, as indicated by 141 and 142 in Fig. 7. In this case, the quantum wires of the manufactured two-dimensional quantum well structure vary, thus considerably impairing the quantum level and density of states. The present invention is to provide a method of manufacturing a laser having two-dimensional quantum wires with high reproducibility without causing the above-mentioned problems. The conventional manufacturing method of the quantum wire suffers some problems. In Prior Art 1, it is difficult to avoid generation of crystal defects caused by micropatterning or the influence of mixing of impurities. Furthermore, it is almost impossible to realize a two-dimensional superlattice in which quantum wires are arranged at a high density by this method. The method of Prior Art 2 is superior to that of Prior Art 1 in that there is almost no fear of generation of crystal defects and mixing of impurities since the quantum wire structure is formed in a single growth process. However, the problem of Prior Art 2 is insufficient confinement of carriers due to a large limitation on the dimensions and shape of the wires which can be manufactured. For this reason, it is difficult to manufacture the two-dimensional superlattice. The method of Prior Art 3 allows a high-density arrangement of quantum wires in principle. However, this technique is essentially easily influenced by a statistic variation or a fluctuation caused in a surface diffusion process of atoms. For this reason, no high-quality two-dimensional superlattice has been manufactured yet. Objects to be attained by the present invention for the purpose of overcoming the conventional problems are the following four items: 1. to avoid generation of crystal defects and mixing of impurities; 2. to allow formation of a wire in a shape and dimensions large enough to obtain a sufficient quantum confinement effect; 3. to form a wire pattern with high reproducibility without being influenced by a fluctuation upon atomic diffusion; and 4. to allow a high-density arrangement of quantum wires with a high degree of freedom. On the other hand, a wavelength-stabilized laser has been enthusiastically studied as a main constituting element of an optical communication device. As a typical structure of this laser, a DFB laser is known. The DFB laser will be described below with reference to Figs. 8A to 8D. Referring to Figs. 8A to 8D, an n-GaAs substrate 340 is used. A 0.5-µm thick Si-doped GaAs layer 341 is stacked on the substrate 340, a 1.5-µm thick Si-doped AlGaAs lower cladding layer 342 is stacked, and then, a 0.2-µm thick GRIN layer 343 is stacked. An undoped GaAs active layer 344 has a thickness of 6 µm. After a 0.2-µm thick upper GRIN layer 345 is stacked on the active layer 344, growth is temporarily stopped (Fig. 8A). After the growth is stopped, a grating 346 is formed on the upper GRIN layer 345 (Fig. 8B). The grating 346 has a pitch of 240 nm, and is formed by an interference exposure method utilizing He-Cd (Figs. 1A to 1D). An upper layer is stacked on the grating 346 formed in this manner. Referring to Fig. 8C, a 0.3-µm thick Be-doped AlGaAs light guide layer 347 is formed on the grating 346, a 1.2-µm thick Be-doped AlGaAs cladding layer 348 is grown on the light guide layer 347, and a 0.5-µm thick Be-doped GaAs capping layer 349 is formed on the cladding layer 348. In order to attain current constriction, a ridge 350 is formed in the formed multi-layered films (Fig. 8D). As a result, a current is concentrated on the lower portion of the ridge 350, as indicated by arrows 351. In this manner, a light current confinement structure is formed, and a wavelength-stabilized laser is manufactured. However, as can be understood from the above description, this method includes four major processes. In particular, current confinement and light confinement are attained after growth, resulting in complicated processes. As described above, it is difficult for the conventional method to manufacture a semiconductor device having at least one of a current constriction structure and a quantum wire structure such as a laser having two-dimensional quantum wires, a wavelength-stabilized layer, and the like in a small number of processes with high reproducibility. More specifically, it is difficult to manufacture a laser having two-dimensional quantum wires with high reproducibility to have a current constriction effect. Also, a wavelength-stabilized laser requires complicated processes, and for this reason, the yield, in particular, the yield in formation of the ridge 350 (Fig. 8D), is impaired. Further prior art is known from the publication "Direct evidence of lateral bandgap patterning on stepped structures grown on non-planar, vicinal GaAs surfaces by cathodoluminescence investigations", by E. Colas et al., in: Journal of Crystal Growth, Vol. 107, No. 1/4, January 1991, pages 243 to 247. It is an object of the present invention to provide a semiconductor device, which can solve the conventional problems, which can be used in various applications, for example to obtain a quantum wire structure, and can be easily manufactured, and a method of manufacturing the same. This object is achieved by a semiconductor device as set out in claim 1, and a method for manufacturing a semiconductor device as defined in claim 7. Advantageous further developments are as set out in the respective dependent claims. BRIEF DESCRIPTION OF THE DRAWINGS Figs. 1A to 1D are sectional views showing processes in a method of manufacturing a diffraction grating by a conventional holographic interference method; Figs. 2A to 2D are sectional views for explaining processes in a second method of a prior art; Figs. 3A to 3D are sectional views for explaining processes in a third method of a prior art; Figs. 4A to 4C are perspective views showing the principles of one-, two-, and three-dimensional quantum well structures, respectively; Figs. 5A to 5C are graphs showing the relationship between the density of states of electrons and the energy in the quantum well structures shown in Figs. 4A to 4C, respectively; Figs. 6A to 6D are schematic views showing growth processes of a crystal face; Fig. 7 is a perspective view showing a quantum wire structure obtained by growing certain molecular species in the vertical direction in crystals; Figs. 8A to 8D are perspective views for explaining processes in the manufacture of a conventional current constriction structure; Figs. 9A and 9B are sectional views showing a sawtooth pattern formed in the present invention; Figs. 10A and 10B are views respectively showing a new periodic structure formed in the present invention, and modulation of an equivalent refractive index; Fig. 11 is a view showing a long-periodic structure having a plane orientation inclined at 0.5° to 15° on a semiconductor substrate having a plane orientation {111}; Fig. 12 is a view showing a short-periodic structure formed on the long-periodic structure shown in Fig. 11; Fig. 13 is a partially enlarged perspective view of Fig. 12; Fig. 14 is a partially enlarged view of Fig. 13; Fig. 15 is a perspective view showing a multi-layered structure of steps having different growth directions; Fig. 16 is a sectional view showing the first embodiment of a semiconductor device according to the present invention; Figs. 17A and 17B are views showing growth rates of semiconductor layers in Fig. 16 in respective directions; Fig. 18 is a sectional view of a waveguide with a diffraction grating as the second embodiment of a semiconductor device according to the present invention; Fig. 19 is a sectional view showing a two-dimensional quantum well laser as the third embodiment of a semiconductor device according to the present invention; Fig. 20 is a sectional view showing a two-dimensional quantum well laser as the fourth embodiment of a semiconductor device according to the present invention; Fig. 21 is a perspective view showing a field effect transistor having quantum wires as the fifth embodiment of a semiconductor device according to the present invention; Fig. 22 is a sectional view showing a grating formed on the surface of a GaAs substrate, which is inclined at 5° from a (111) plane to have a [110] direction as a rotational axis, by utilizing a laser interference exposure method; Fig. 23 is a sectional view showing a grating formed on the surface of a GaAs substrate, which is inclined at 5° from a (111) plane to have a [110] direction as a rotational axis, by utilizing a laser interference exposure method; Fig. 24 is a view for explaining the principle of the present invention; Fig. 25 is a partially enlarged view of Fig. 24; Fig. 26 is a sectional view for explaining the eighth embodiment of a semiconductor device according to the present invention; Fig. 27 is a sectional view for explaining a current constriction state according to the present invention; Fig. 28 is a cross-sectional view showing the ninth embodiment of a semiconductor device according to the present invention; Fig. 29 is a cross-sectional view showing the 9th embodiment of a semiconductor device according to the present invention. The preferred embodiments of the present invention will be described in detail hereinafter with reference to the accompanying drawings. In the following description, assume that a {111} plane includes equivalent planes such as a (111) plane, a (1*1*1*) plane, a (11*1*) plane, and the like, and a {110} plane includes a (11*0) plane and a (110) plane. Note that symbol 1* is a substitution of a symbol of Miller indices, which symbol is expressed by describing "-" above numeral "1". In the following description, this description method is adopted. An embodiment of a method of manufacturing a semiconductor device according to the present invention comprises the following steps. The method will be described below with reference to Fig. 9A. In the first step, a diffraction grating 52 having a pitch Λ 1 is formed on the surface of a semiconductor substrate 51, which consists of a semiconductor having a sphalerite structure, and has a plane orientation inclined within a range from 0.5° to 15° from a {111} plane, and a semiconductor crystal is grown on the diffraction grating 52 by a solid-state source molecular beam epitaxy (MBE) method, a gas source molecular beam epitaxy (GSMBE) method using molecular beam sources including some gasified sources, a metal-organic molecular beam epitaxy (MOMBE) method using organic metallic compounds as molecular beam sources, or a chemical beam epitaxy (CBE) method using molecular beam sources, all of which are gasified. As a growth condition at this time, a condition for setting a low growth rate on the {111} plane is selected, so that a sawtooth pattern 53 consisting of terrace surfaces defined by the {111} plane and step portions defined by a {110} plane can be formed. A description will be continued with reference to Fig. 9B. A diffraction grating 55 having a pitch Λ 1 is formed on the surface of a semiconductor substrate 54 having a plane orientation which is inclined within a range from 0.5° to 15° from a {110} plane, and a semiconductor crystal is grown on the diffraction grating 55 by the MBE method using solid-state sources, the GSMBE method using molecular beam sources including some gasified sources, the MOMBE method using organic metallic compounds as molecular beam sources, or the CBE method using molecular beam sources, all of which are gasified. As a growth condition at this time, a condition for setting a low growth rate on the {110} plane is selected, so that a sawtooth pattern 56 consisting of terrace surfaces defined by the {110} plane and step portions defined by a {113} or {114} plane can be formed. A pitch Λ 2 of this sawtooth pattern is determined by only the pitch Λ 1 of the grating formed therebelow, and always satisfies Λ 2 = Λ 1 . In the next step, when crystal growth is performed under a condition that the growth rate on the terrace surface is low, and the growth rate on the step surface is high, i.e., under the same growth condition as that of growth on the surface of the first inclination, the growth progresses mainly in the lateral direction while holding the surface pattern or holding at least the periodic structure of the surface without disappearance of steps. When the ratio or types of molecular beams during the growth are changed, a second periodic structure 63 can also be formed, as shown in Fig. 10A. The molecular beams can be changed by opening/closing shutters, bubbles, or the like as in the manufacture of a quantum well. When the modulation time is appropriately selected within a time period shorter than the time required for growing the stepped surfaces over the pitch Λ 2 , the period of the periodic structure can be an integer multiple of the pitch of the diffraction grating. As described above, a second periodic structure having a specific period, i.e., a period 1/N that of a pre-formed first periodic structure, can be formed on a substrate having an inclined region during growth. When a size 65 of the step portion of the periodic structure formed in this manner is set to be 30 nm or less, a quantum effect can be provided. Furthermore, the size of this portion is determined by the pitch of the diffraction grating, and the inclination angle of the (111) or (110) plane shown in Figs. 9A and 9B. If the substrate on which the diffraction grating is formed has the same refractive index as that of the first growth layer, the original diffraction grating does not contribute to modulation of an equivalent refractive index. The equivalent refractive index of this waveguide has large lower-order components with respect to the pitch of the original diffraction grating, i.e., large components modulated at a short-wavelength pitch as its feature. In general, the crystal growth rate of a semiconductor varies depending on its crystal face. For example, in this embodiment, the growth rate on the (111) plane is lower than that on the (100) plane, and the growth rate on the (110) plane is lower than that on the (111) plane. For further details, please refer to a reference "Journal of Applied Physics Vol. 64, 3552 (1988)". The following explanation will be given with reference to Fig. 11. In the first step, a first periodic structure having a plane orientation inclined within a range from 0.5° to 15° is formed on a semiconductor substrate which consists of a semiconductor having a sphalerite structure, and a {111} plane orientation. A long period having a pitch 10-5 is formed on this substrate surface. In this case, a periodic structure 10-6 having the pitch 10-5 = 100 µm is formed, so that a flat portion (e.g., 10-3) is not formed. In Fig. 11, a surface 10-1 is inclined at 0.5° to 15° from the {111} or {110} plane. Thereafter, a short-periodic structure is formed on the long-periodic structure. The formation process of the short-periodic structure will be described below with reference to Fig. 12. As a manufacturing method, an interference exposure method is adopted. This manufacturing method will be described later in the middle of the embodiment. Fig. 12 shows a short-periodic structure 11-7 having a pitch of 240 nm formed by the interference exposure method. In this case, the structure 11-7 is formed on a long-periodic structure 11-6. In the next step, a semiconductor crystal is grown on the short-periodic structure by the MBE method using solid-state sources, the GSMBE method using molecular beam sources including some gasified sources, the MOMBE method using organic metallic compounds as molecular beam sources, or the CBE method using molecular beam sources, all of which are gasified. Fig. 13 is an enlarged view of a portion around the structure 11-6 in Fig. 12. A semiconductor film 12-8 is grown on the short-periodic structure formed on the slope portion of the long-periodic structure. As a growth condition at that time, a condition for setting a lower growth rate on the {111} plane than that on the {114} or {113} plane as the slope portion is selected, so that a sawtooth pattern 12-11 consisting of terraces defined by the {111} plane and step portions of the {100} plane can be formed. A semiconductor film 12-9 consisting of a material different from that of the film 12-8 is grown on the sawtooth pattern 12-11 under the same condition. Similarly, a condition setting a low growth rate on the {111} plane is selected. As a result, the semiconductor film 12-9 is concentrated on the step portions. Similarly, a semiconductor film 12-10 consisting of a material different from that of the semiconductor film 12-9 is deposited. At this time, a condition for setting a low growth rate on the {111} plane is also selected. Upon repetition of the above-mentioned processes, regions having different compositions can be partially formed. One important point of this patent is to form planes having different growth rates. Alternatively, a surface inclined within a range from 0.5° to 15° may be similarly formed using a substrate having a {110} plane orientation. In this case, what is important is that a plane having a low growth rate and a plane having a high growth rate are formed, the length of one side of the plane having the high growth rate is easily controlled, and the width of the plane having the low growth rate is longer than that of the plane having the high growth rate. If these conditions are satisfied, a semiconductor region can be easily confined even partially. A method of growing a semiconductor crystal is selected from the MBE method using solid-state sources, the GSMBE method using molecular beam sources including some gasified sources, the MOMBE method using organic metallic compounds as molecular beam sources, and the CBE method using molecular beam sources, all of which are gasified. An example will be described below. Fig. 14 is a partially enlarged view of Fig. 10A. A diffraction grating 13-21 is formed by the interference exposure method. A pitch Λ 1 of the grating is 240 nm. When a film 13-22 is stacked on this grating by an epitaxial method, a width B (13-24) of a step ((100) plane) is determined by the following equation: B = Λ 1 tan/sin' where  is the inclination angle from the {111} or {110} plane, i.e., the above-mentioned value ranging from 0.5° to 15°, and ' is an angle 54.7° defined between the {111} plane and the (100) plane forming the step. When the inclination angle  of the substrate is assumed to be about 5°, the width B (13-24 of the (100) plane forming the step is 26 nm. A crystal is grown on this structure by epitaxial growth. For example, if a GaAs film is grown on a GaAs structure using the MBE method, the growth rate on the (111) plane is faster by three times than the growth rate on the (100) plane. As shown in Fig. 15, a quantum well 14-31 is formed on the step. In this case, a 20-nm thick film 14-32 is stacked on the (100) plane. At this time, a GaAs film 14-33 having a thickness of 6 nm about 1/3 that of the film 14-32 is stacked on the (111) plane. Fig. 15 shows a state wherein the films 14-32 and 14-33 are repetitively stacked. These films can be easily stacked by changing source materials. The crystal growth method will be explained below. A diffraction grating is formed on a semiconductor substrate inclined at 0.5° to 15° from the {111} or {110} plane, and a semiconductor crystal is grown thereon by the MBE or GSMBE method. At this time, the incident direction of molecular beams is not particularly limited. Although the GSMBE method is also called a chemical beam epitaxy (CBE) method or a metal-organic molecular beam epitaxy (MOMBE) method, these methods imply the same scheme. In general, the orientation of a low index face of a crystal has a minimal growth rate. In particular, since the {111} plane (or {110} plane) has a very low growth rate, a sawtooth pattern consisting of terraces of the {111} plane (or {110} plane) and steps having a plane orientation different from the {111} plane (or {110} plane) is formed in the crystal growth. At this time, a height S of a step measured in the vertical direction with respect to the terrace plane, and a period T of the sawtooth pattern measured in the horizontal direction with respect to the terrace plane are respectively expressed as follows using a period P of the grating and an inclination angle a of the substrate: S = P·sin(a) T = P·cos(a) When the direction of at least one molecular beam is inclined within a range from 10° to 80° from the normal direction to the substrate, a region in a shadow of the incident molecular beam is formed from the step portion to the middle of the terrace plane. For this reason, a phenomenon that a new crystal face grows from a step recess portion to form a flat plane is suppressed. On the other hand, since the growth rate on the terrace plane is extremely low, and hence, almost no molecules are absorbed, most of molecules incident on the surface reach the step portion and are absorbed by a crystal, or desorbed into a vacuum phase. Thus, the ratio of molecules crystallized on the terrace plane is very small. As a result, the sawtooth pattern is held on the surface without disappearance of steps, and growth in the lateral direction progresses almost steadily. If we let Vs be the lateral growth rate of the step portion measured in the horizontal direction with respect to the terrace plane, and Vt be the growth rate of the terrace portion in the vertical direction with respect to the terrace plane, the sawtooth pattern on the surface is translated in a direction of an angle b from the horizontal direction of the substrate where b is given by: b = a + tan -1 (Vt/Vs) Since Vt and Vs satisfy Vt << Vs, the angle b has a value closer to the angle a , and the growth progresses in almost the lateral direction. In a process wherein a semiconductor crystal corresponding to a barrier is steadily grown in the lateral direction, as described above, a semiconductor crystal corresponding to a well is grown for a time t, and thereafter, the semiconductor crystal corresponding to the barrier is grown. In this case, the section of the semiconductor crystal corresponding to the well has a structure obtained by coupling rectangular regions having a width L = Vs·t and a height S to have a very small width d = Vt·t . From the above-mentioned equation expressing S, the height S of this rectangle is selected by the period P of the diffraction grating, and the substrate orientation a , and the width L can be precisely controlled by the time t. As a result, a quantum wire having very small dimensions can be manufactured with high precision. When the above-mentioned growth process is repeated at a proper period, a two-dimensional superlattice in which quantum wires are arranged at a high density can be formed. The proper period is expressed by, e.g., T/(N + 1/2) (where N is an integer). In Prior Art 2 described above using the MOVPE method, since a new crystal face is grown from a recess portion of a temporarily formed step, the steps disappear upon progress of the growth, and as a result, the surface becomes flat. Since a terrace is defined by a (001) plane, the growth rate Vt has a value which cannot be ignored. For this reason, a quantum wire structure is formed in only one process of the growth, and it is impossible to arrange quantum wires at a high density. In contrast to this, according to the present invention, since the steps are grown in the lateral direction without disappearing, quantum wires can be continuously arranged. First Embodiment Fig. 16 shows a multi-layered structure of a wafer for a GaAs/AlGaAs-based DFB laser according to the first embodiment of the present invention, which has a 1st-order diffraction grating having a pitch of 125 nm. An Si-doped GaAs substrate 15-11 is a so-called inclined substrate whose substrate surface is inclined at 5° from a (111) A plane in a (100) plane direction. A 0.5-µm thick Si-doped GaAs buffer layer 15-12 is formed on the substrate 15-11, and a 1.5-µm thick Si-doped Al 0.5 Ga 0.5 As cladding layer 15-13 is formed on the layer 15-12. A 200-nm thick Si-doped Al y Ga 1-y As layer 15-14 serves as a light confinement region. The Al content y of the layer 15-14 gradually changes from 0.5, and decreases to 0.3 near an active layer 15-15. A multi-quantum well structure of the active layer consists of five quantum wells constituted by repetitively forming a 10-nm thick undoped Al 0.3 Ga 0.7 As barrier layer and a 6-nm thick undoped GaAs well layer. A 0.3-µm thick Be-doped Al 0.3 Ga 0.7 As layer as an upper light guide layer 15-16 is formed on the active layer 15-15. A resist pattern having a pitch of 250 nm is formed on the surface of the layer 15-16 using a laser interference exposure method, and a 2nd-order diffraction grating 15-17 is formed by dry etching. At this time, the direction of each groove of the grating is perpendicular to a plane defined by the (110) direction, i.e., the normal to the original substrate and the normal to the (111) A plane. After the resist residue and oxides on the surface are removed in an MBE chamber, an Al 0.3 Ga 0.7 As layer 15-18 having the same composition as that of the upper light guide layer, and having an average film thickness of 0.2 µm is grown on the diffraction grating, thus forming periodic steps on the surface. Each step is defined by a terrace plane of the (111) A plane having a width of about 225 nm, and a step plane of a (001) plane having a width of about 38 nm. The period of repetition coincides with the period of 250 nm of the diffraction grating, and the level difference between adjacent steps is about 20 nm. If we let VOO be the GaAs growth rate on a flat substrate, V03 be the Al 0.3 Ga 0.7 As growth rate, Vg00 be the propagation rate of the growth surface on the diffraction grating with respect to GaAs, Vg03 be the propagation rate with respect to Al 0.3 Ga 0.7 As, g00 be the angle defined by the growth direction and the normal to the substrate with respect to GaAs, and g03 be the angle with respect to Al 0.3 Ga 0.7 As (see Figs. 17A and 17B), VOO = 11 nm/min, V03 = 15.7 nm/min, and g00 = g03 = 70.5° in this embodiment. Since Vg00 = V00/cosg00, and Vg03 = V03/cosg03, the propagation rates of the growth surface in a plane parallel to the substrate surface are given by V100 = V00/tang00, and V103 = V03/tang03, thus revealing the propagation rates of the growth surface in the horizontal direction. In this embodiment, V100 = 29.5 nm/min, and V103 = 42.1 nm/min. Using these rates, a periodic structure 15-19 consisting of a Be-doped GaAs layer and a Be-doped Al 0.3 Ga 0.7 As layer is formed by opening/closing a shutter. More specifically, when a GaAs layer is grown for 1 minute and 41 seconds, subsequently, an AlGaAs layer is grown for 1 minute and 47 seconds, a GaAs layer is grown again for 1 minute and 41 seconds, and subsequently, an AlGaAs layer is grown for 1 minute and 47 seconds, the periodic structure of the growth surface progresses by 250 nm in the horizontal direction. During this interval, the growth surface progresses by about 88 nm in the vertical direction. At this time, the repetitive period of the periodic structure in a direction parallel to the substrate surface is 125 nm, and a refractive index modulation structure having a period 1/2 the pitch of the formed diffraction grating can be manufactured. The growth condition is changed, so that the growth rate on the (111) plane is high as well. A 0.2-µm thick Be-doped Al 0.3 Ga 0.7 As layer 15-191 is formed to flatten the growth surface, and a 1.5-µm thick Be-doped Al 0.5 Ga 0.5 As upper cladding layer 15-192 and a 0.3-µm thick Be-doped GaAs capping layer 15-193 are formed on the layer 15-191, thus forming an LD structure. In an optical waveguide with the above-mentioned structure, the equivalent refractive index is modulated by thick GaAs portions arranged in the upper guide layer at 125-nm intervals. Second Embodiment Fig. 18 shows a waveguide with a diffraction grating having a semi-periodic structure according to the second embodiment of the present invention. An Si-doped GaAs substrate 17-71 is an inclined substrate whose substrate surface is inclined at 5° from a (111) A plane in a (100) plane direction. A 1.0-µm thick Si-doped Al 0.5 Ga 0.5 As cladding layer 17-72 is formed on the substrate 17-71. A waveguide layer 17-73 consists of a 200-nm thick undoped Al 0.1 Ga 0.9 As layer. A 0.3-µm thick Be-doped Al 0.3 Ga 0.7 As layer 17-74 as an upper light guide layer is formed on the layer 17-73. A resist pattern having a pitch of 250 nm is formed on the surface of the layer 17-74 using a laser interference exposure method, and a 2nd-order diffraction grating is formed by dry etching. After the resist residue and oxides on the surface are removed in an MBE chamber, an Al 0.3 Ga 0.7 As layer is grown on the diffraction grating by the GSMBE method. After steps are formed-on the surface, a periodic structure 17-75 consisting of a Be-doped Al 0.1 Ga 0.9 As layer and a Be-doped Al 0.3 Ga 0.7 As layer are formed by controlling the supply amounts of source materials using mass-flow controllers. Even when a new facet is formed since the growth surface cannot keep a similar shape, a refractive index modulation structure having a period 1/2 the pitch of the diffraction grating can be manufactured, as shown in Fig. 10B. The growth rate on the (111) plane is set to be large by changing the growth condition, and a 0.2-µm thick Be-doped Al 0.3 Ga 0.7 As layer 17-76 is formed to flatten the growth surface. A 1.5-µm thick Be-doped Al 0.5 Ga 0.5 As upper cladding layer 17-77 and a 0.3-µm Be-doped GaAs capping layer are formed on the layer 17-76. Third Embodiment Fig. 19 shows a two-dimensional quantum well manufactured using the method of the present invention. A substrate 18-41 is an Si-doped GaAs substrate. This substrate has a structure inclined at 2° from the (111) plane in the (110) plane direction. A 1.5-µm thick Si-doped AlGaAs (As composition = 0.5) layer 18-42 is grown on the substrate. Furthermore, an 0.4-µm thick Si-doped AlGaAs (Al composition = 0.1) layer 18-43 is grown on the layer 18-42, and the growth is temporarily stopped. The growth film is taken out from a growth apparatus, and a diffraction grating is formed on the layer 18-43 by interference exposure. The growth film with the diffraction grating formed in this manner is placed in a growth chamber again. In this case, a diffraction grating 18-44 shown in Fig. 19 is formed. In order to provide a buffer effect, a 50-nm thick Si-doped AlGaAs (Al composition = 0.3) layer 18-45 is formed on the diffraction grating. As a result, as has been described above with reference to Figs. 14 and 15, steps defined by the (111) and (100) planes are formed, and the width of the inclined surface (100) is about 10 nm. An undoped GaAs well 18-46 constituting an active layer is grown on the layer 18-45 to have a thickness of about 10 nm on the (100) plane. At this time, the film thickness of the GaAs layer on the (111) plane is 3 nm or less. A 10-nm thick AlGaAs (Al composition = 0.3) barrier layer 18-47 is formed on the well 18-46. Furthermore, a GaAs well 18-48 is formed to have a thickness of 100 nm on the (100) plane. These layers constitute the active layer. A 100-nm thick Be-doped AlGaAs (Al composition = 0.3) light guide layer 18-49 is formed on the active layer. Furthermore, a 1.5-µm Be-doped AlGaAs (Al composition = 0.5) cladding layer is grown on the light guide layer. Finally, a 0.5-µm thick Be-doped GaAs capping layer is grown on the cladding layer, thus completing a laser. The threshold current density of the manufactured two-dimensional quantum well can be improved by about 30% as compared to that of a conventional one-dimensional quantum well. Fourth Embodiment Fig. 20 shows the fourth embodiment of the present invention. The characteristic feature of this embodiment is to arrange a carrier block layer 19-65. Referring to Fig. 20, an Si-doped GaAs substrate 19-61 has a (111) plane, and is inclined at 5° in a (110) plane direction. A 1.5-µm thick Si-doped AlGaAs (Al composition = 50%) layer 19-62 is grown on the substrate. Furthermore, a 200-nm thick Si-doped AlGaAs (Al composition = 10%) light guide layer 19-63 is grown on the layer 19-62, and the growth is temporarily stopped. Then, a diffraction grating having a grating pitch of 250 nm is formed by the interference exposure method described in the third embodiment. The growth film is placed again in a growth chamber, and re-growth is performed. An Si-doped AlGaAs (Al composition = 0.1) light guide layer 19-64 is formed to have a thickness of 100 nm on the (100) plane. Furthermore, a 50-nm thick Si-doped AlGaAs (Al composition = 0.3) carrier block layer 19-65 is formed on the light guide layer 19-64, and subsequently, an active region is stacked on the carrier block layer 19-65. An undoped AlGaAs (Al composition = 0.3) barrier 19-66 is grown to have a thickness of 10 nm on the (100) plane, and an undoped AlGaAs (Al composition = 0.1) well 19-67 is stacked to have a thickness of 60 nm on the (100) plane. Then, a barrier 19-68, a well 19-69, a barrier 19-70, and a well 19-71 are repetitively formed. Furthermore, although a layer 19-72 is also a barrier layer, it is formed to be relatively thick, and the selectivity ratio on the (111) and (100) planes is decreased. As a method of decreasing the selectivity ratio, the substrate temperature is decreased. The barrier layer has a 50-nm thick undoped AlGaAs (Al composition = 0.3) structure. Thereafter, a 100-nm thick light guide layer 19-73 is stacked. The light guide layer has a Be-doped AlGaAs structure, and the Al composition is increased from 0.3 to 0.5. A 1.5-µm thick Be-doped AlGaAs cladding layer 19-74 is stacked on the light guide layer. Finally, a 0.5-µm thick Be-doped AlGaAs layer is stacked, thus completing a laser structure. In this embodiment, the MOCVD method is used in both the primary growth and re-growth processes. In a gas-based growth method, a large selectivity ratio on the (111) and (100) planes can be selected as compared to solid-state source growth as in the MBE method, and a more stable quantum wire can be formed. Fifth Embodiment Fig. 21 is a perspective view showing a field effect transistor using a quantum wire manufactured according to the method of the present invention. A substrate 20-81 comprises an undoped GaAs substrate. In Fig. 21, the (110) plane substrate is inclined at 5° toward a {111} direction. In a layer 20-82, a diffraction grating is formed, and is subjected to re-growth to manufacture a quantum wire. A facet formed with the quantum wire is defined by the (110) and (100) planes. When the MOCVD method as a gas-based growth method is utilized, a selectivity ratio of 1 : 10 or higher can be selected. Contact layers 20-83 correspond to the source, drain, and gate. The field effect transistor includes electrodes 20-86, 20-87, and 20-88. Sixth Embodiment Fig. 22 shows the sixth embodiment of the present invention. A diffraction grating 21-2 is formed, by utilizing the laser inference exposure method, on the surface of a GaAs substrate 21-1, which is inclined at 5° from the (111) plane to have a [110] direction as the rotational axis. This diffraction grating has a stripe direction [110], a period of 0.24 µm, and an amplitude of 0.1 µm. GaAs and AlGaAs crystals are grown on the diffraction grating by the GSMBE method using trimethyl gallium (TMGa), triethyl aluminum (TEAl), and AsH 3 as source gases. An arrow 21-3 indicates the incidence direction of TMGa and TEAl molecular beams, and is inclined at 50° from the normal direction to the substrate. An arrow 21-4 indicates the incidence direction of an AsH 3 molecular beam, and is inclined at 10° from the normal direction to the substrate to the side opposite to the TMGa molecular beam. These incident directions are kept constant during all growth processes. An AlGaAs layer 21-5 is grown on the diffraction grating, and a sawtooth pattern defined by terraces 21-6 and steps 21-7 is formed on the surface of the layer 21-5. The plane orientation of the terrace is (111), and the height of the step is about 21 nm. At this time, the growth rate Vt in a direction perpendicular to the terrace plane is almost negligibly small, and a steady state wherein the growth progresses upon movement of the step in the lateral direction is achieved. 20-nm thick GaAs layers 21-8 and 75-nm thick AlGaAs layers 21-9 are alternatively grown in the lateral direction, and furthermore, an AlGaAs layer 21-10 and a GaAs capping layer 21-11 are grown. As a result, a two-dimensional superlattice 21-12 in which GaAs well regions each having a section of 21 nm × 20 nm are arranged in AlGaAs barriers is formed. Seventh Embodiment Fig. 23 shows the seventh embodiment of the present invention. A diffraction grating 22-14 is formed, using the light interference exposure method, on the surface of a GaAs substrate 22-13, which is inclined at 5° from a (111) plane to have a [110] direction as the rotational axis. This diffraction grating has a stripe direction [110], a period of 0.1 µm, and an amplitude of 0.05 µm. GaAs and AlGaAs crystals are grown on the diffraction grating by the MBE method using Ga, Al, and As as solid-state sources. An arrow 22-15 indicates the incident direction of Ga and Al molecular beams, and is inclined at 50° from the normal direction to the substrate. Similarly, an arrow 22-16 indicates the incident direction of an As molecular beam, and is inclined at 20° from the normal direction to the substrate to the side opposite to the Ga molecular beam. These incident directions are kept constant during all growth processes. An AlGaAs layer 22-17 is grown on the diffraction grating, and a sawtooth pattern defined by terraces 22-18 and steps 22-19 is formed on the surface of the layer 22-17. The plane orientation of the terrace is (111), and the height of the step is 21 nm. At this time, a growth rate Vt in a direction perpendicular to the terrace plane is about 1/10 of a growth rate Vs, in the lateral direction, of the step, and a steady state wherein the growth progresses upon movement of the step in the lateral direction is achieved. Then, 10-nm thick GaAs layers 22-20 and 37-nm thick AlGaAs layers 22-21 are alternatively grown in the lateral direction, and furthermore, an AlGaAs layer 22-22 and a GaAs capping layer 22-23 are grown. As a result, a two-dimensional superlattice 22-12 in which GaAs well regions each having a section of 10 nm × 21 nm are arranged in AlGaAs barriers is formed. When an inclined substrate is utilized, a periodic structure having a period 1/N of that of a periodic structure formed on the inclined substrate can be added. Since the period of the diffraction grating becomes a fraction of the period of the diffraction grating formed by the interference exposure method, the period of the diffraction grating to be formed can be easily controlled by the interference exposure method. Furthermore, a quantum wire can be obtained with high reproducibility. With the above-mentioned embodiments, a quantum wire having a sufficient confinement effect for carriers in a semiconductor, and a two-dimensional superlattice in which such quantum wires are arranged at a high density can be relatively easily manufactured with high reproducibility. An embodiment comprising a current constriction structure in addition to the above-mentioned quantum wire structure will be described below. The principle of formation of a current constriction layer will be described below. A III-V film having an amphoteric impurity is epitaxially grown on a semiconductor substrate having a sphalerite structure (zinc blende structure) such as GaAs, and having a periodic three-dimensional pattern, which commonly has a surface on which a Ga plane is easily formed in at least a portion thereof with a region having a surface orientation inclined within a range from 0° to 20° with respect to a {100} plane, thereby obtaining a semiconductor laser having a current constriction layer without any processes after growth. Note that the {100} plane includes equivalent planes such as a (100) plane, a (010) plane, a (001) plane, and the like. When an Si-doped GaAs or AlGaAs layer is stacked on the portion having such a plane, a region having a different polarity (conductivity type) can be locally formed in the growth film. Si serves as an amphoteric impurity for a III-V compound. When Si is replaced with a Ga site, it changes the polarity to n type; when Si is replaced with an As site, it changes the polarity to p type. In order to allow easy replacement with Ga, the growth surface must be covered with As, and an As dangling bond must be exposed on the surface. This situation can be realized by a plane called a B plane, and can also be obtained by a (511) A plane, a (611) A plane, and the like. In order to replace the As site with Si, a Ga plane must be stably formed on the surface. A plane for realizing this condition includes a (311) A plane, a (211) A plane, a (111) A plane, and the like. A periodic three-dimensional pattern is formed on a semiconductor substrate which has a zinc blende structure such as GaAs, and has, in at least a portion thereof, a region having a surface orientation inclined within a range from 0° to 15° with respect to a {111} or {110} plane, and a III-V film having an amphoteric impurity is epitaxially grown on the three-dimensional pattern and another flat surface, thereby forming a current constriction layer. The {111} plane includes equivalent planes such as a (-111) plane, a (1-11) plane, a (-1-11) plane, and the like, and the {110} plane includes a (-110) plane, a (1-10) plane, and the like. The principle of formation of a quantum wire will be described below. The crystal growth rate of a semiconductor varies depending on the crystal face involved. For example, a (-111) plane has a lower growth rate than that of a (100) plane, and a (-110) plane has a lower growth rate than that of a (111) plane (for further details, refer to an article "Journal of Applied Physics Vol. 64, 3522 (1988)). By utilizing this fact, a quantum wire can be easily manufactured. More details of the principle will be described below with reference to Figs. 24 to 26. In the first step, a grating having a pitch Λ 1 is formed on a substrate 202, which consists of a semiconductor having a zinc blende structure, and has a surface orientation inclined within a range from 0° to 15° from the {111} or {110} plane. An interference exposure method is utilizes as a manufacturing method. The manufacturing method will be described later in the middle of the embodiment. Referring to Fig. 24, a periodic structure 207 having a pitch of 240 nm is formed by the interference exposure method. In the second step, semiconductor crystals are grown on the periodic structure 207 by an MBE method using solid-state sources, a GSMBE method using molecular beam sources including some gasified sources, an MOMBE method using organic metallic compounds as molecular beam sources, or a CBE method using molecular beam sources all of which are gasified. Thus, a semiconductor film 208 is grown on the periodic structure 207. As a growth condition at that time, a condition for setting a lower growth speed on a flat plane (e.g., the {111} plane) than that on a plane of a slope portion (e.g., near the {100} plane, for example, a {114} plane, a {113} plane, or the like) is selected, so that a sawtooth pattern 211 consisting of terrace portions 212 each defined by the {111} plane and step portions 213 each defined by the {100} plane can be formed. A semiconductor film 209 consisting of a material different from that of the semiconductor film 208 is grown on the sawtooth pattern under the same condition. At this time, a condition for setting a lower growth rate on the {111} plane 212 is selected. As a result, the semiconductor film 209 is concentrated on the step portions 213, as shown in Fig. 24. Similarly, a semiconductor film 210 different from the semiconductor film 209 is deposited. At this time, a condition for setting a lower growth rate on the {111} plane is selected as well. Upon repetition of these processes, regions 209 and 210 having different compositions can be locally formed. One important point of the present invention is to form planes of different growth rates. What is important is that a plane of a low growth rate and a plane of a high growth rate are formed, the length of one side of the plane of the high growth rate can be easily controlled, and the width of the plane of the low growth rate is larger than that of the plane of the high growth rate. If these conditions are satisfied, the semiconductor regions 209 and 210 can be easily locally confined. A semiconductor crystal growth method includes the MBE method using solid-state sources, the GSMBE method using molecular beam sources including some gasified sources, the MOMBE method using organic metallic compounds as molecular beam sources, and the CBE method using molecular beam sources all of which are gasified. As described above, a semiconductor film having a specific period can be formed on the substrate 202 having an inclined region. When the size of the step portion 213 of the periodic structure formed in this manner is set to be 30 nm or less, a quantum effect can be provided. As shown in Fig. 25 as a partially enlarged view of Fig. 24, a size 224 of the portion 213 is determined by the pitch Λ 1 of the grating 207 and the inclination angle of the (111) plane or (110) plane 212. An example will be described below. The pitch Λ 1 of the grating 207 formed by the interference exposure method is 240 nm. When the film 208 is stacked on the grating by an epitaxial method, the width 224 (B) of the step portion ((100) plane) 213 is determined by the following equation: B = Λ 1 sin/sin' where  is the inclination angle (also the inclination angle of the substrate surface) 222 of the {111} plane, the {110} plane 212 or the like from the substrate surface, which angle ranges from 0° to 15°, as described above. ' is an angle 223 defined between the {111} plane 212 and the (100) plane 213 forming the step portion, and is 54.7°. When the inclination angle 222 is set to be about 5°, the width 224 of the (100) plane 213 forming the step portion is 26 nm. A crystal is grown on the grating by epitaxial growth. For example, when a GaAs film is grown on a GaAs layer using the MBE method, the ratio of the growth rate on the (111) plane 212 to that of the (100) plane 213 is about 1 : 3, and the growth rate on the (100) plane 213 is higher by about three times than that on the (111) plane 212. In this manner, as shown in Figs. 24 and 26, quantum wires are formed at positions corresponding to the step portions 213. By changing the source materials to be supplied, a multi-layered structure can be easily realized, as shown in Fig. 24. In this case, when an Si-doped GaAs or AlGaAs layer is stacked as the layer 208, a region having a different polarity can be locally formed in the growth film 208. This mechanism will be described below with reference to Fig. 26. As described above, Si serves as an amphoteric impurity for a III-V compound. When Si is replaced with a Ga site, it changes the polarity to n type; when Si is replaced with an As site, it changes the polarity to p type. In general, when an Si-doped GaAs layer is grown on a {111} A plane, a p-type GaAs layer can be formed. In contrast to this, when an Si-doped GaAs layer is grown on a {100} plane, an n-type GaAs layer can be formed. By utilizing these characteristics, current constriction is realized. Eighth Embodiment Fig. 28 shows a two-dimensional quantum well (quantum wire) laser comprising a current constriction layer (the resonance direction corresponds to the vertical direction of Fig. 28). Referring to Fig. 28, a substrate 251 is an Si-doped GaAs substrate. The substrate 251 has a plane inclined at 5° from the (111) plane. A 1.5-µm thick Si-doped AlGaAs (Al composition = 0.5) layer 252 is grown on the substrate. Furthermore, a 0.4-µm thick Si-doped AlGaAs (Al composition = 0.1) layer 253 is grown on the layer 252, and growth is temporarily stopped. This wafer is taken out from a growth apparatus, and a grating 260 is formed by the interference exposure method. The exposure is performed in a procedure described previously with reference to Figs. 1A to 1D. Prior to the interference exposure, a three-dimensional pattern having a large period is formed by normal exposure. Thereafter, the interference exposure is performed. As shown in Fig. 1A, a photoresist 1-22 is coated on a growth film 1-21, and two laser beams 1-23 and 1-24, which are collimated to sufficiently parallel beams, are radiated onto the photoresist from the two directions, thereby forming interference fringes. In this manner, the photoresist 1-22 is periodically exposed, and is developed, thereby forming a grating-shaped photoresist mask 1-25, as shown in Fig. 1B. Etching is performed using the photoresist mask 1-25 as an etching mask, as shown in Fig. 1C, and thereafter, the etching mask 1-25 is removed, thereby transferring a periodic structure 1-26 to the growth film 1-21, as shown in Fig. 1D. In a photographic interference exposure method, if we let  be the incident angle of each of the two laser beams 1-23 and 1-24, and λ be the wavelength of each of the laser beams 1-23 and 1-24, a grating pitch Λ to be able to be formed is given by Λ = λ/2sin . As an exposure laser, an Ar laser (λ = 351 nm) or an He-Cd laser (352 nm) is suitable. In order to form a mask satisfying Λ ≤ 250 nm, the He-Cd laser is used, and the desired grating pitch Λ is determined by changing . In this manner, the diffraction grating is formed to have a pitch of 240 nm. The growth film 1-21 with the diffraction grating formed in this manner is placed again in a growth chamber. This diffraction grating is a locally formed diffraction grating or a grating 260, as shown in Fig. 28. In order to provide a buffer effect, a 50-nm thick Si-doped AlGaAs (Al composition = 0.3) layer 261 is formed on the diffraction grating 260. As a result, as has been described above, steps defined by the (111) and (100) planes are formed, and the width of the (100) plane as an inclined plane is about 10 nm. In the Si-doped AlGaAs layer 261, n-type regions are formed on the inclined surface portions of the diffraction grating 260, and p-type regions are formed on upper portions of the diffraction grating 260. An Sn-doped GaAs layer 262 is grown on the Si-doped AlGaAs layer 261 as a current constriction layer. This layer becomes an n-type layer. As a result, an npn junction is formed in a direction parallel to the substrate surface. In this case, the layer 262 grown on the (100) plane has a thickness of about 10 nm. At this time, the film thickness of the GaAs layer 262 on the (111) plane is 3 nm or less. Subsequently, a 10-nm thick AlGaAs (Al composition = 0.3) layer 263 serving as a barrier is formed on the Sn-doped GaAs layer 262. Furthermore, a GaAs layer 264 serving as an active layer is formed to have a thickness of about 10 nm on the (100) plane. A 100-nm thick Be-doped AlGaAs (Al composition = 0.3) layer 265 serving as a light guide layer is formed on the layer 264. Furthermore, a 1.5-µm thick Be-doped AlGaAs (Al composition = 0.5) layer 266 serving as a cladding layer is grown. Finally, a 0.5-µm thick Be-doped GaAs layer 267 serving as a capping layer is grown, thus completing a laser. A current 268 flows a portion where the diffraction grating 260 is formed, the Si-doped AlGaAs layer 261 on which no diffraction grating 260 is formed has p conductivity type, and no current flows therethrough. The manufactured laser exhibits a good current constriction effect. Ninth Embodiment Fig. 29 shows the ninth embodiment in which the present invention is applied to a multi-quantum well laser (the resonance direction corresponds to the vertical direction of Fig. 29). The characteristic feature of this embodiment is to provide a carrier block layer 275. As has been described above, a current flows only through a portion corresponding to each inclined surface portion of a diffraction grating 286, thus constricting the current. The structure of this embodiment will be described below with reference to Fig. 29. Referring to Fig. 29, a substrate 271 is an Si-doped GaAs substrate. The substrate 271 has a plane inclined at 10° from the (111) plane. A 1.5-nm thick Si-doped AlGaAs (Al composition = 0.5) 272 is grown on the substrate 271. Furthermore, a 200-nm thick Si-doped AlGaAs (Al composition = 0.1) layer 273 serving as a light guide layer is grown on the layer 272, and growth is temporarily stopped. As described in the eighth embodiment, a three-dimensional pattern (i.e. convex and concave) structure having a large period of 200 mm is formed by a normal exposure method, and a diffraction grating 286 having a pitch of 250 nm is formed by a grating formation method based on the interference exposure method. The wafer is placed again in a growth apparatus, and re-growth is performed. An Sn-doped AlGaAs (n-type, Al composition = 0.1) layer 274 as a light guide layer is formed to have a thickness of 100 nm on the (100) plane. Furthermore, a 50-nm thick Si-doped AlGaAs (Al composition = 0.3) layer 275 as a carrier block layer is formed on the layer 274. As a result, a current channel is formed on inclined surface portions, as has been described above. Subsequently, an active region is stacked on the layer 275. An Sn-doped AlGaAs (Al composition = 0.3) layer 276 as a barrier layer is grown to have a thickness of 10 nm on the (100) plane. Upon combination of these layers 274, 275, and 276, an npn junction is formed, thus blocking a current. An undoped AlGaAs (Al composition = 0.1) layer 277 as a well layer is stacked to have a thickness of 60 nm on the (100) plane. The above-mentioned processes are repeated to form a layer 278 (barrier layer), a layer 279 (well layer), a layer 280 (barrier layer), and a layer 281 (well layer). Although a layer 282 is a barrier layer, it is formed to be relatively thick, and the selectivity ratio of the growth rates on the (111) and (100) planes is decreased. As a method of decreasing the selectivity ratio, the substrate temperature is decreased. The layer 282 comprises an undoped AlGaAs (Al composition = 0.3, thickness = 50 nm) layer. Thereafter, a 100-nm thick light guide layer 283 is stacked. The layer 283 comprises a Be-doped AlGaAs layer, and the Al composition is decreased from 0.3 to 0.5. A 1.5-nm thick Be-doped AlGaAs layer 284 as a cladding layer is stacked on the layer 283. Finally, a 0.5-nm thick Be-doped GaAs layer 285 is tacked, thus completing a laser structure. In this embodiment, the MOCVD method is used in both the primary growth and re-growth processes. In a gas-based growth method, a large selectivity ratio on the (111) and (100) planes can be selected as compared to solid-state source growth as in the MBE method, and a more stable quantum wire can be formed. A current is confined in the diffraction grating portion 286. In the eighth and ninth embodiments, the current constriction layer structure is simultaneously formed. However, in place of the current constriction layer structure, another conventional current constriction structure may be manufactured, and a quantum wire structure alone may be formed. In each of the embodiments of the semiconductor devices comprising the current constriction structure, any other means capable of simultaneously forming a p-n junction in the lateral direction by growing a film can be easily applied to these embodiments. For example, the same effect can be obtained by doping Se and Zn on a processed substrate. As a growth method, an MOCVD method, MBE method, CBE method, halide-based VPE method, chloride-based VBE method, and the like are available. As a compound material, III-V group compound semiconductors such as InGaAsP, InAlAs, InAlGaP, and the like may also be used. As described above, when a proper substrate such as an inclined substrate is used, a quantum wire can be manufactured with high reproducibility, and a current constriction effect can be realized as well. When an amphoteric impurity is utilized, a current constriction layer structure can be easily manufactured by growing a film on a three-dimensional structure such as a grating. When a three-dimensional structure having planes which absorb a dopant in different ways is used, a current constriction layer structure can be easily realized. Therefore, the yield can be improved as compared to the prior art.

Claims: A semiconductor device comprising: a substrate (15-11; 17-71; 18-41; 19-61; 20-81; 21-1; 22-13; 251; 271) which consists of a semiconductor having one of sphalerite and diamond crystal structures, and has, in at least a portion thereof, a plane orientation inclined at 0,5° to 15° with respect to one of {111} and {110} planes indicated by Miller indices; a diffraction grating (15-17; 18-44; 20-82; 21-2; 22-14; 260; 286) which is formed on the surface of said substrate; a first semiconductor layer (15-18; 18-45; 19-64; 21-5; 22-17; 261; 274) which is formed on said diffraction grating, and has a sawtooth-shaped first periodic structure consisting of terraces of one of the {111} and {110} planes and steps having a plane orientation different from the {111} and {110} planes correspondingly; and a second semiconductor layer (15-19; 17-75; 18-46 to 18-48; 19-65, 19-66; 21-12; 22-24; 262; 275) which is formed on said first semiconductor layer, and has a second periodic structure having a phase shifted from a phase of said first periodic structure. A device according to claim 1, wherein the size of the step of the periodic structures of the first and second semiconductor layers is 30nm or less so as to provide a quantum wire structure. A device according to claim 1, wherein said first semiconductor layer consists of a semiconductor doped with an amphoteric impurity, and has an n-type region formed on an inclined surface portion of said diffraction grating, and has a p-type region formed on the remaining portion of said diffraction grating. A device according to claim 1, wherein said second semiconductor layer comprises an active layer having a quantum wire structure. A device according to claim 1, wherein said second periodic structure of said second semiconductor layer constitutes a diffraction grating. A semiconductor device according to claim 1, wherein the refractive index of said first semiconductor layer is same as the refractive index of said substrate. A method of manufacturing a semiconductor device, comprising the steps of: preparing a substrate (15-11; 17-71; 18-41; 19-61; 20-81; 21-1; 22-13; 251; 271) which consists of a semiconductor having one of sphalerite and diamond crystal structures, and has, in at least a portion thereof, a plane orientation inclined at 0,5° to 15° with respect to one of {111} and {110} planes indicated by Miller indices; forming a diffraction grating (15-17; 18-44; 20-82; 21-2; 22-14; 260; 286) on the surface of said substrate; forming, on said diffraction grating, a first semiconductor layer (15-18; 18-45; 19-64; 21-5; 22-17; 261; 274) under a condition for setting a low growth rate on the {111} and {110} plane correspondingly so that a sawtooth-shaped first periodic structure is formed, consisting of terraces of one of the {111} and {110} planes and steps having a plane orientation different from the {111} and {110} planes correspondingly; and forming, on said first semiconductor layer, a second semiconductor layer (15-19; 17-75; 18-46 to 18-48; 19-65, 19-66; 21-12; 22-24; 262; 275) which has a second periodic structure having a phase shifted from a phase of said first periodic structure; wherein the growth of said second semiconductor layer is performed under a condition that the growth rate on the terrace surface is low and the growth rate on the step surface is high so as to hold the periodic structure of said first semiconductor layer without disappearance of steps. A method according to claim 7, wherein the size of the step of the periodic structures of the first and second semiconductor layers is 30nm or less so as to provide a quantum wire structure. A method according to claim 7, wherein said first semiconductor layer consists of a semiconductor doped with an amphoteric impurity, and has an n-type region formed on an inclined surface portion of said diffraction grating, and has a p-type region formed on the remaining portion of said diffraction grating. A method according to claim 7, wherein said second semiconductor layer is formed by a crystal growth method which has different growth rates depending on plane orientations. A method according to claim 10, wherein said second semiconductor layer is formed by one crystal growth method selected from the group consisting of solid-state source molecular beam epitaxy, gas source molecular beam epitaxy, metal-organic beam epitaxy, and metal-organic chemical vapor epitaxy. A method of manufacturing a semiconductor device according to claim 7, wherein the step of forming said second semiconductor layer is done by use of one of solid-state source molecular beam epitaxy and gas source molecular beam epitaxy and wherein a direction of a central line of a molecular beam of at least one molecular type forms an angle of 10° to 80° with a normal to a plane orientation of said substrate. A method according to claim 12, wherein an energy band modulation structure is formed in a direction parallel to the plane orientation by changing types of the molecules of the molecular beams in the middle of the step of forming said second semiconductor layer.

Inventors: MIYAZAWA SEIICHI, MIZUTANI NATSUHIKO, OHTSUKA MITSURU, MIYAZAWA, SEIICHI, MIZUTANI, NATSUHIKO, OHTSUKA, MITSURU, MIYAZAWA, SEIICHI, C/O CANON KABUSHIKI KAISHA, MIZUTANI, NATSUHIKO, C/O CANON KABUSHIKI KAISHA, Ohtsuka, Mitsuru, c/o Canon Kabushiki Kaisha
Applicants: CANON KK, CANON KABUSHIKI KAISHA
Application year: 1993
Main classification: H01S3
IPC codes: H01L29, H01S5, H01L33