Patent Publication Number: US-2023139139-A1

Title: Quantum-cascade laser element and quantum-cascade laser device

Description:
TECHNICAL FIELD 
     One aspect of the present disclosure relates to a quantum-cascade laser element and a quantum-cascade laser device. 
     BACKGROUND ART 
     A quantum-cascade laser element is known that includes a semiconductor substrate; a semiconductor laminate formed on the semiconductor substrate to include a ridge portion; a current block layer formed over the ridge portion and over the semiconductor substrate; an insulating layer formed on the current block layer; a metal layer formed on a top surface of the ridge portion and on the insulating layer (for example, refer to Patent Literature 1). 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Literature 1: Japanese Unexamined Patent Publication No. 2018-98262 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     In the above-described quantum-cascade laser element, in order to stably output light of a basic mode having a peak of intensity at a central portion of the ridge portion in a width direction, suppressing the oscillation of light of a high-order mode having a peak of intensity on both sides of the central portion is required. In addition, both an improvement in heat dissipation and an improvement in yield rate are required. 
     An object of one aspect of the present disclosure is to provide a quantum-cascade laser element and a quantum-cascade laser device capable of achieving an improvement in heat dissipation, the suppression of the oscillation of a high-order mode, and an improvement in yield rate. 
     Solution to Problem 
     A quantum-cascade laser element according to one aspect of the present disclosure includes: a semiconductor substrate; a semiconductor laminate formed on the semiconductor substrate to include a ridge portion configured to include an active layer having a quantum-cascade structure; an embedding layer including a first portion formed on a side surface of the ridge portion, and a second portion extending from an edge portion of the first portion on a side of the semiconductor substrate along a width direction of the semiconductor substrate; and a metal layer formed at least on a top surface of the ridge portion and on the first portion. In a thickness direction of the semiconductor substrate, a surface of the second portion on a side opposite to the semiconductor substrate is located between a surface of the active layer on a side opposite to the semiconductor substrate and a surface of the active layer on a side of the semiconductor substrate. When viewed in the width direction of the semiconductor substrate, a part of the metal layer on the first portion overlaps the active layer. The metal layer is directly formed on the first portion. 
     The quantum-cascade laser element is provided with the embedding layer including the first portion formed on the side surface of the ridge portion, and the second portion extending from the edge portion of the first portion on a side of the semiconductor substrate along the width direction of the semiconductor substrate. Accordingly, heat generated in the active layer can be effectively dissipated. In addition, the metal layer is formed on the first portion formed on the side surface of the ridge portion. Accordingly, the oscillation of a high-order mode can be suppressed while suppressing a loss in a basic mode. In addition, in the thickness direction of the semiconductor substrate, the surface of the second portion on a side opposite to the semiconductor substrate is located between the surface of the active layer on a side opposite to the semiconductor substrate and the surface of the active layer on a side of the semiconductor substrate, and when viewed in the width direction of the semiconductor substrate, a part of the metal layer on the first portion overlaps the active layer. Accordingly, the oscillation of the high-order mode can be effectively suppressed by locating the metal layer on the first portion beside the active layer while effectively improving heat dissipation by locating the second portion beside the active layer. As a result, both an improvement in heat dissipation and the suppression of the oscillation of the high-order mode can be realized in a well-balanced manner. In addition, the metal layer is directly formed on the first portion. Accordingly, the metal layer can be disposed close to the active layer, and the oscillation of the high-order mode can be effectively suppressed by light absorption of the metal layer. In addition, for example, when another layer is formed between the metal layer and the first portion, a variation in a characteristic of suppressing the oscillation of the high-order mode occurs because of a manufacturing error of the another layer, but since the metal layer is directly formed on the first portion, such a situation can be suppressed, and the yield rate can be improved. Therefore, according to the quantum-cascade laser element, an improvement in heat dissipation, the suppression of the oscillation of the high-order mode, and an improvement in yield rate can be achieved. 
     A thickness of the first portion may be thinner than a thickness of the second portion. In this case, both an improvement in heat dissipation and the suppression of the oscillation of the high-order mode can be realized in a more balanced manner. 
     The metal layer may be formed on the top surface of the ridge portion, on the first portion, and on the second portion, and a dielectric layer may be disposed between the second portion and the metal layer. In this case, bond strength between the metal layer and the embedding layer can be improved. As a result, the peeling or degradation of the metal layer can be suppressed, and the stability of the laser element can be improved. 
     The dielectric layer may be formed such that a part of the second portion is exposed from the dielectric layer, and the metal layer may be in contact with the second portion at the part. In this case, heat dissipation can be further improved. 
     An opening that exposes an inner portion of the second portion from the dielectric layer may be formed in the dielectric layer, the inner portion being continuous with the first portion, and the metal layer may be in contact with the inner portion through the opening. In this case, since the metal layer is in contact with the second portion at the inner portion close to the ridge portion, heat dissipation can be even further improved. On the other hand, since the metal layer is firmly bonded to the second portion at an outer portion far from the ridge portion, with the dielectric layer interposed therebetween, the peeling or the like of the metal layer can be effectively suppressed. In addition, there is a possibility that a cleavage streak is formed in the vicinity of an inner edge of the dielectric layer (inner edge of the opening) because of a cleavage process during manufacturing, but since the inner edge of the opening is separated from the ridge portion, the influence of the cleavage streak on a light output characteristic can be suppressed. 
     A width of the opening in the width direction of the semiconductor substrate may be more than or equal to two times a width of the active layer. In this case, a region in which the metal layer is in contact with the second portion can be widened, and heat dissipation can be even further improved. In addition, the influence of the cleavage streak on the light output characteristic can be further suppressed. 
     A width of the opening in the width direction of the semiconductor substrate may be more than or equal to ten times a thickness of the second portion. In this case, the region in which the metal layer is in contact with the second portion can be further widened, and heat dissipation can be even further improved. In addition, the influence of the cleavage streak on the light output characteristic can be even further suppressed. 
     The quantum-cascade laser element according to one aspect of the present disclosure may further include a wire made of metal, that is electrically connected to the metal layer. A connection position between the metal layer and the wire may overlap the dielectric layer when viewed in the thickness direction of the semiconductor substrate. In this case, the occurrence of the peeling or the like of the metal layer caused by a tensile stress that the wire acts on the metal layer can be suppressed. 
     A quantum-cascade laser device according to one aspect of the present disclosure includes: the quantum-cascade laser element; and a drive unit that drives the quantum-cascade laser element. According to the quantum-cascade laser device, an improvement in heat dissipation, the suppression of the oscillation of the high-order mode, and an improvement in yield rate can be achieved. 
     Advantageous Effects of Invention 
     According to one aspect of the present disclosure, it is possible to provide the quantum-cascade laser element and the quantum-cascade laser device capable of achieving an improvement in heat dissipation, the suppression of the oscillation of the high-order mode, and an improvement in yield rate. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a cross-sectional view of a quantum-cascade laser element according to one embodiment. 
         FIG.  2    is a cross-sectional view taken along line II-II of  FIG.  1   . 
         FIGS.  3 ( a ) and  3 ( b )  are views showing a method for manufacturing a quantum-cascade laser element. 
         FIGS.  4 ( a ) and  4 ( b )  are views showing the method for manufacturing a quantum-cascade laser element. 
         FIGS.  5 ( a ) and  5 ( b )  are views showing the method for manufacturing a quantum-cascade laser element. 
         FIGS.  6 ( a ) and  6 ( b )  are views showing the method for manufacturing a quantum-cascade laser element. 
         FIG.  7    is a graph showing an example of an electric field intensity distribution in the quantum-cascade laser element. 
         FIG.  8 ( a )  is a view showing an example of an extension of a basic mode, and  FIG.  8 ( b )  is a view showing an example of an extension of a primary mode. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, one embodiment of the present disclosure will be described in detail with reference to the drawings. In the following description, the same reference signs are used for the same or equivalent elements, and duplicated descriptions will be omitted. 
     [Configuration of Quantum-Cascade Laser Element] 
     As shown in  FIGS.  1  and  2   , a quantum-cascade laser element  1  includes a semiconductor substrate  2 , a semiconductor laminate  3 , an embedding layer  4 , a dielectric layer  5 , a first electrode  6 , and a second electrode  7 . The semiconductor substrate  2  is, for example, an S-doped InP single crystal substrate having a rectangular plate shape. As one example, a length of the semiconductor substrate  2  is approximately 3 mm, a width of the semiconductor substrate  2  is approximately 500 μm, and a thickness of the semiconductor substrate  2  is approximately one hundred and several tens of μm. In the following description, a width direction of the semiconductor substrate  2  is referred to as an X-axis direction, a length direction of the semiconductor substrate  2  is referred to as a Y-axis direction, and a thickness direction of the semiconductor substrate  2  is referred to as a Z-axis direction. A side on which the semiconductor laminate  3  is located with respect to the semiconductor substrate  2  in the Z-axis direction is referred to as a first side S1, and a side on which the semiconductor substrate  2  is located with respect to the semiconductor laminate  3  in the Z-axis direction is referred to as a second side S2. 
     The semiconductor laminate  3  is formed on a surface  2   a  on the first side S1 of the semiconductor substrate  2 . The semiconductor laminate  3  includes an active layer  31  having a quantum-cascade structure. The semiconductor laminate  3  is configured to oscillate laser light having a predetermined center wavelength (for example, a wavelength in a mid-infrared region which has a center wavelength of any value of 4 to 11 μm). In the present embodiment, the semiconductor laminate  3  is formed by stacking a lower cladding layer  32 , a lower guide layer (not shown), the active layer  31 , an upper guide layer (not shown), an upper cladding layer  33 , and a contact layer (not shown) in order from a semiconductor substrate  2  side. The upper guide layer has a diffraction grating structure functioning as a distributed feedback (DFB) structure. 
     The active layer  31  has, for example, a multiple quantum well structure of InGaAs/InAlAs. Each of the lower cladding layer  32  and the upper cladding layer  33  is, for example, a Si-doped InP layer. Each of the lower guide layer and the upper guide layer is, for example, a Si-doped InGaAs layer. The contact layer is, for example, a Si-doped InGaAs layer. 
     The semiconductor laminate  3  includes a ridge portion  30  extending along the Y-axis direction. The ridge portion  30  is formed of a portion on the first side S1 of the lower cladding layer  32 , the lower guide layer, the active layer  31 , the upper guide layer, the upper cladding layer  33 , and the contact layer. A width of the ridge portion  30  in the X-axis direction is narrower than a width of the semiconductor substrate  2  in the X-axis direction. A length of the ridge portion  30  in the Y-axis direction is equal to a length of the semiconductor substrate  2  in the Y-axis direction. As on example, the length of the ridge portion  30  is approximately 3 mm, the width of the ridge portion  30  is approximately 8 μm, and a thickness of the ridge portion  30  is approximately 8 μm. The ridge portion  30  is located at the center of the semiconductor substrate  2  in the X-axis direction. Each layer forming the semiconductor laminate  3  does not exist on both sides of the ridge portion  30  in the X-axis direction. 
     The ridge portion  30  has a top surface  30   a  and a pair of side surfaces  30   b . The top surface  30   a  is a surface on the first side S1 of the ridge portion  30 . The pair of side surfaces  30   b  are surfaces on both sides of the ridge portion  30  in the X-axis direction. In this example, each of the top surface  30   a  and the side surfaces  30   b  is a flat surface. When viewed in the Y-axis direction, each of the side surfaces  30   b  is inclined with respect to a center line CL of the ridge portion  30  to approach the center line CL as going away from the semiconductor substrate  2  (toward the first side S1). The center line CL is a straight line passing through the center (geometric center) of the ridge portion  30  and being parallel to the Z-axis direction when viewed in the Y-axis direction. The quantum-cascade laser element  1  is configured to be in line symmetry with respect to the center line CL when viewed in the Y-axis direction. 
     The semiconductor laminate  3  has a first end surface  3   a  and a second end surface  3   b  that are both end surfaces of the ridge portion  30  in a light waveguide direction A. The light waveguide direction A is a direction parallel to the Y-axis direction that is an extending direction of the ridge portion  30 . The first end surface  3   a  and the second end surface  3   b  function as light-emitting end surfaces. The first end surface  3   a  and the second end surface  3   b  are located on the same planes as both respective end surfaces of the semiconductor substrate  2  in the Y-axis direction. 
     The embedding layer  4  is a semiconductor layer formed of, for example, a Fe-doped InP layer. The embedding layer  4  includes a pair of first portions  41  and a pair of second portions  42 . The pair of first portions  41  are formed on the pair of respective side surfaces  30   b  of the ridge portion  30 . The pair of second portions  42  extend from edge portions  41   a  on the second side S2 of the pair of respective first portions  41  in the X-axis direction. Each of the second portions  42  is formed on a surface  32   a  of the lower cladding layer  32 . The surface  32   a  is a surface on the first side S1 of a portion of the lower cladding layer  32 , the portion not forming the ridge portion  30 . 
     A surface  42   a  on the first side S1 of each of the second portions  42  is located between a surface  31   a  on the first side S1 of and a surface  31   b  on the second side S2 of the active layer  31  in the Z-axis direction. In other words, when viewed in the X-axis direction, a part on the first side S1 of the second portions  42  overlaps a part on the second side S2 of the active layer  31 . 
     Each of the first portions  41  is formed over the entirety of the corresponding side surface  30   b  of the ridge portion  30  and protrudes from the top surface  30   a  of the ridge portion  30  to the first side S1 in the Z-axis direction. A surface  41   b  of each of the first portions  41  on a side opposite to the ridge portion  30  has a first inclined surface  43  and a second inclined surface  44 . In this example, each of the first inclined surface  43  and the second inclined surface  44  is a flat surface. 
     When viewed in the light waveguide direction A, the first inclined surface  43  is inclined with respect to the side surface  30   b  of the ridge portion  30  to go away from the side surface  30   b  of the ridge portion  30  as going away from the semiconductor substrate  2 . In this example, when viewed in the light waveguide direction A, the first inclined surface  43  is also inclined with respect to the center line CL of the ridge portion  30  to go away from the center line CL as going away from the semiconductor substrate  2 . The first inclined surface  43  is continuous with the surface  42   a  on the first side S1 of the second portions  42 . When viewed in the X-axis direction, an edge portion of the first inclined surface  43  on a side of the semiconductor substrate  2  overlaps the active layer  31 . 
     The second inclined surface  44  is located on the first side S1 with respect to the first inclined surface  43  and is continuous with the first inclined surface  43 . When viewed in the light waveguide direction A, the second inclined surface  44  is inclined with respect to the center line CL of the ridge portion  30  to approach the center line CL as going away from the semiconductor substrate  2 . In this example, when viewed in the light waveguide direction A, the second inclined surface  44  is also inclined with respect to the side surface  30   b  of the ridge portion  30  to approach the side surface  30   b  as going away from the semiconductor substrate  2 . The second inclined surface  44  protrudes from the top surface  30   a  of the ridge portion  30  to the first side S1 in the Z-axis direction. 
     A thickness T1 of the first portions  41  is thinner than a thickness T2 of the second portions  42 . The thickness T1 of the first portions  41  may be less than or equal to half the thickness T2 of the second portions  42 . The thickness T1 of the first portions  41  is a maximum thickness of the first portions  41  in the X-axis direction. In this example, the thickness of the first portions  41  increases from the second side S2 toward a boundary between the first inclined surface  43  and the second inclined surface  44  and decreases from the boundary toward the first side S1. Namely, the thickness of the first portions  41  is at its maximum at the position of the boundary. Therefore, the thickness T1 of the first portions  41  is a distance between the side surface  30   b  of the ridge portion  30  and the boundary. The thickness T2 of the second portions  42  is a maximum thickness of the second portions  42  in the Z-axis direction. In this example, the thickness of the second portions  42  is uniform throughout the second portions  42 . As one example, the thickness T1 of the first portions  41  is approximately 1 to 2 μm, and the thickness T2 of the second portions  42  is approximately 3.0 μm. 
     The dielectric layer  5  is, for example, an insulating layer formed of a SiN film or a SiO 2  film. The dielectric layer  5  is formed on a surface  47   a  of an outer portion  47  of the second portion  42  such that the top surface  30   a  of the ridge portion  30 , the surface  41   b  of each of the first portions  41 , and a surface  46   a  of an inner portion  46  of each of the second portions  42  are exposed from the dielectric layer  5 . The inner portion  46  is a portion of the second portion  42 , which is continuous with the first portion  41 , and the outer portion  47  is a portion of the second portion  42 , which is located outside the inner portion  46  in the X-axis direction. The surface  46   a  is a surface on the first side S1 of the inner portion  46 , and the surface  47   a  is a surface on the first side S1 of the outer portion  47 . 
     The dielectric layer  5  is formed on the surface  47   a  of the outer portion  47  and is not formed on the surface  46   a  of the inner portion  46  to expose the surface  46   a . In other words, an opening  5   a  that exposes the inner portion  46  from the dielectric layer  5  is formed in the dielectric layer  5 . The opening  5   a  exposes the top surface  30   a  of the ridge portion  30 , the surface  41   b  of each of the first portions  41 , and the surface  46   a  of the inner portion  46  of each of the second portions  42  from the dielectric layer  5 . An outer edge of the dielectric layer  5  reaches an outer edge of the embedding layer  4  in both the X-axis direction and the Y-axis direction. The dielectric layer  5  also functions as an adhesion layer that enhances adhesion between the embedding layer  4  and a metal layer  61  to be described later. 
     A width W1 of the opening  5   a  in the X-axis direction is more than or equal to two times a width W2 of the active layer  31  in the X-axis direction. The width W1 may be more than or equal to five times the width W2. As one example, the width W1 is approximately 50 μm and the width W2 is approximately 9 μm. When the width of the active layer  31  narrows toward the first side S1 as in the present embodiment, the width W2 of the active layer  31  is a width of an end portion on the first side S1. 
     The width W1 of the opening  5   a  in the X-axis direction may be more than or equal to ten times a thickness T3 of the embedding layer  4  in the Z-axis direction. The thickness T3 of the embedding layer  4  is the thicker of the thickness T1 of the first portions  41  and the thickness T2 of the second portions  42  and is the thickness T2 in this example. Namely, the width W1 of the opening  5   a  may be more than or equal to ten times the thickness T2 of the second portions  42 . As described above, the thickness T2 of the second portions  42  is, for example, approximately 3 μm. 
     The first electrode  6  includes the metal layer  61  and a plating layer  62 . The metal layer  61  is, for example, a Ti/Au layer and functions as a foundation layer for forming the plating layer  62 . The plating layer  62  is formed on the metal layer  61 . The plating layer  62  is, for example, an Au plating layer. A thickness of the first electrode  6  in the Z-axis direction is, for example, 6 μm or more. 
     The metal layer  61  is integrally formed to extend over the top surface  30   a  of the ridge portion  30  and over the first portions  41  and the second portions  42  of the embedding layer  4 . The metal layer  61  is in contact with the top surface  30   a  of the ridge portion  30 . Accordingly, the first electrode  6  is electrically connected to the upper cladding layer  33  via the contact layer. An outer edge of the metal layer  61  is located inside the outer edges of the embedding layer  4  and the dielectric layer  5  in both the X-axis direction and the Y-axis direction. A distance between the outer edge of the metal layer  61  and the outer edge of the dielectric layer  5  (outer edges of the semiconductor substrate  2 , the semiconductor laminate  3 , and the embedding layer  4 ) in the X-axis direction is, for example, approximately 50 μm. 
     The metal layer  61  is directly formed on the first portions  41 . Namely, another layer (for example, the dielectric layer or the insulating layer) is not formed between the metal layer  61  and the first portions  41 . The metal layer  61  is formed over the entirety of the surface  41   b  of each of the first portions  41  and extends over the first inclined surface  43  and over the second inclined surface  44 . When viewed in the X-axis direction, a part of the metal layer  61  on the first inclined surfaces  43  overlaps the active layer  31 . More specifically, an edge portion on the second side S2 of the metal layer  61  on the first inclined surfaces  43  overlaps the active layer  31 . The metal layer  61  is provided to cover a portion of the first portions  41 , the portion protruding from the top surface  30   a  of the ridge portion  30 . 
     The metal layer  61  is in contact with the surface  46   a  of each of the inner portions  46  at the inner portion  46  of each of the second portions  42  through the opening  5   a  formed in the dielectric layer  5 . The metal layer  61  is formed on the second portions  42  at the outer portion  47  of each of the second portions  42  with the dielectric layer  5  interposed therebetween. Namely, the dielectric layer  5  is disposed between the outer portion  47  of each of the second portions  42  and the first electrode  6 . When viewed in the Z-axis direction, an outer edge of the first electrode  6  is located inside the outer edges of the semiconductor substrate  2 , the semiconductor laminate  3 , the embedding layer  4 , and the dielectric layer  5 . 
     A plurality of wires  8  are electrically connected to a surface  62   a  on the first side S1 of the plating layer  62 . Each of the wires  8  is formed, for example, by wire bonding and is electrically connected to the metal layer  61  via the plating layer  62 . A connection position between the metal layer  61  (plating layer  62 ) and each of the wires  8  overlaps the dielectric layer  5  when viewed in the Z-axis direction. The number of the wires  8  is not limited and only one wire  8  may be provided. 
     The second electrode  7  is formed on the surface  2   b  on the second side S2 of the semiconductor substrate  2 . The second electrode  7  is, for example, an AuGe/Au film, an AuGe/Ni/Au film, or an Au film. The second electrode  7  is electrically connected to the lower cladding layer  32  via the semiconductor substrate  2 . 
     In the quantum-cascade laser element  1 , when a bias voltage is applied to the active layer  31  via the first electrode  6  and through the second electrode  7 , light is emitted from the active layer  31 , and light having a predetermined center wavelength of the light is resonated in the distributed feedback structure. Accordingly, the laser light having the predetermined center wavelength is emitted from each of the first end surface  3   a  and the second end surface  3   b . A high reflection film may be formed on one end surface of the first end surface  3   a  and the second end surface  3   b . In this case, the laser light having the predetermined center wavelength is emitted from the other end surface of the first end surface  3   a  and the second end surface  3   b . Alternatively, a low reflection film may be formed on one end surface of the first end surface  3   a  and the second end surface  3   b . In addition, a high reflection film may be formed on the other end surface different from the end surface on which the low reflection film is formed. In both cases, the laser light having the predetermined center wavelength is emitted from one end surface of the first end surface  3   a  and the second end surface  3   b . In the former case, the laser light is emitted from both the first end surface  3   a  and the second end surface  3   b.    
     The quantum-cascade laser element  1  can form a quantum-cascade laser device, together with a drive unit that drives the quantum-cascade laser element  1 . The drive unit is electrically connected to the first electrode  6  and to the second electrode  7 . The drive unit is, for example, a pulse drive unit that drives the quantum-cascade laser element  1  such that the quantum-cascade laser element  1  oscillates the laser light in a pulsed manner 
     [Method for Manufacturing Quantum-Cascade Laser Element] 
     A method for manufacturing the quantum-cascade laser element  1  will be described with reference to  FIGS.  3  to  6   . First, as shown in  FIG.  3 ( a ) , a semiconductor wafer  200  having a first major surface  200   a  and a second major surface  200   b  is prepared, and a semiconductor layer  300  is formed on the first major surface  200   a  of the semiconductor wafer  200 . The semiconductor wafer  200  is, for example, an S-doped InP single crystal (100) wafer. The semiconductor wafer  200  includes a plurality of portions, each of which becomes the semiconductor substrate  2 , and is cleaved along a line L in a post-process to be described later. Similarly, the semiconductor layer  300  also includes a plurality of portions, each of which becomes the semiconductor laminate  3 . The semiconductor layer  300  is formed, for example, by epitaxially growing each layer (namely, a layer becoming each of the lower cladding layer  32 , the lower guide layer, the active layer  31 , the upper guide layer, the upper cladding layer  33 , and the contact layer) using MO-CVD. 
     Subsequently, as shown in  FIG.  3 ( b ) , a dielectric film  100  is formed on a portion of the semiconductor layer  300 , the portion becoming the ridge portion  30 , and the semiconductor layer  300  is dry-etched up to the lower cladding layer  32  using the dielectric film  100  as a mask. The dielectric film  100  is formed of, for example, a SiN film or a SiO 2  film. The dielectric film  100  is patterned into a shape shown in  FIG.  3 ( b )  by, for example, photolithography and etching. A width of the dielectric film  100  in the X-axis direction is, for example, approximately 10 μm. 
     Subsequently, as shown in  FIG.  4 ( a ) , the semiconductor layer  300  is wet-etched using the dielectric film  100  as a mask. Accordingly, the ridge portion  30  is formed on the semiconductor layer  300 . 
     Subsequently, as shown in  FIG.  4 ( b ) , an embedding layer  400  is formed on the semiconductor layer  300 . The embedding layer  400  includes a plurality of portions, each of which becomes the embedding layer  4 . The embedding layer  400  is formed, for example, by crystal growth using MO-CVD. Since the dielectric film  100  functions as a mask, the embedding layer  400  is not formed on the dielectric film  100 . 
     Subsequently, as shown in  FIG.  5 ( a ) , the dielectric film  100  is removed by etching, and a dielectric layer  500  is formed on the embedding layer  400 . The dielectric layer  500  includes a plurality of portions, each of which becomes the dielectric layer  5 . The dielectric layer  500  is patterned into a shape shown in  FIG.  5 ( a )  by, for example, photolithography and etching. Accordingly, the opening  5   a  (contact hole) is formed in the dielectric layer  500 . 
     Subsequently, as shown in  FIG.  5 ( b ) , a metal layer  610  is formed over the top surface  30   a  of the ridge portion  30  and over the first portions  41  and the second portions  42  of the embedding layer  4 . Subsequently, as shown in  FIG.  6 ( a ) , a plating layer  620  is formed on the metal layer  610  by plating. The metal layer  610  includes a plurality of portions, each of which becomes the metal layer  61 , and the plating layer  620  includes a plurality of portions, each of which becomes the plating layer  62 . The metal layer  610  is formed, for example, by sputtering or evaporating Ti having a thickness of approximately 50 nm and Au having a thickness of approximately 300 nm in this order. The metal layer  610  on the line L is removed, for example, by etching after the plating layer  620  is formed. The line L is a planned cleavage line that partitions between a plurality of portions that become the quantum-cascade laser elements  1 . 
     Subsequently, as shown in  FIG.  6 ( b ) , the semiconductor wafer  200  is thinned by polishing the second major surface  200   b  of the semiconductor wafer  200 . Subsequently, an electrode layer  700  is formed on the second major surface  200   b  of the semiconductor wafer  200 . The electrode layer  700  includes a plurality of portions, each of which becomes the second electrode  7 . The electrode layer  700  may be subjected to an alloy heat treatment. Subsequently, the semiconductor wafer  200  and the semiconductor layer  300  are cleaved along the line L. Accordingly, a plurality of the quantum-cascade laser elements  1  are obtained. 
     Functions and Effects 
     The quantum-cascade laser element  1  is provided with the embedding layer  4  including the first portions  41  formed on the side surfaces  30   b  of the ridge portion  30 , and the second portions  42  extending from the edge portions  41   a  on the second side S2 of the first portions  41  along the X-axis direction (width direction of the semiconductor substrate  2 ). Accordingly, heat generated in the active layer  31  can be effectively dissipated. In addition, the metal layer  61  is formed on the first portions  41  formed on the side surfaces  30   b  of the ridge portion  30 . Accordingly, the oscillation of a high-order mode can be suppressed while suppressing a loss in a basic mode. In addition, the surface  42   a  on the first side S1 (side opposite to the semiconductor substrate  2 ) of each of the second portions  42  is located between the surface  31   a  on the first side S1 of and the surface  31   b  on the second side S2 (semiconductor substrate  2  side) of the active layer  31  in the Z-axis direction (thickness direction of the semiconductor substrate  2 ), and when viewed in the X-axis direction, a part of the metal layer  61  on the first portions  41  overlaps the active layer  31 . Accordingly, the oscillation of the high-order mode can be effectively suppressed by locating the metal layer  61  on the first portions  41  beside the active layer  31  while effectively improving heat dissipation by locating the second portions  42  beside the active layer  31 . As a result, both an improvement in heat dissipation and the suppression of the oscillation of the high-order mode can be realized in a well-balanced manner. In addition, the metal layer  61  is directly formed on the first portions  41 . Accordingly, the metal layer  61  can be disposed close to the active layer  31 , and the oscillation of the high-order mode can be effectively suppressed by light absorption of the metal layer  61 . In addition, for example, when another layer (for example, the dielectric layer or the insulating layer) is formed between the metal layer  61  and the first portions  41 , a variation in the characteristic of suppressing the oscillation of the high-order mode occurs because of a manufacturing error of the another layer, which is a concern. For example, because of an alignment error, the thickness of the another layer differs between one side and the other side of the ridge portion  30  in the X-axis direction, and it is concerned that a refractive index structure differs. In this regard, in the quantum-cascade laser element  1 , since the metal layer  61  is directly formed on the first portions  41 , such a situation can be suppressed, and the yield rate can be improved. Therefore, according to the quantum-cascade laser element  1 , an improvement in heat dissipation, the suppression of the oscillation of the high-order mode, and an improvement in yield rate can be achieved. As a result, a high-quality and stable beam quality can be realized. 
     Here, an effect of suppressing the oscillation of a high-order transverse mode will be further described with reference to  FIGS.  7  and  8   .  FIG.  7    shows an electric field intensity distribution in the width direction of the semiconductor substrate  2  with the center of the ridge portion  30  set as an origin of an X axis. An intensity distribution of a basic mode M0 is shown by a solid line, and an intensity distribution of a primary mode M1 is shown by an alternate long and two short dashed line. As shown in  FIG.  7   , light of the basic mode M0 has a peak of intensity in the vicinity of the center of the ridge portion  30 , and light of the primary mode M1 has a peak of intensity on both sides of the center of the ridge portion  30 . 
       FIG.  8 ( a )  is a view showing an extension of the basic mode M0 when viewed in the light waveguide direction A, and  FIG.  8 ( b )  is a view showing an extension of the primary mode M1 when viewed in the light waveguide direction A. As shown in  FIGS.  8 ( a ) and  8 ( b ) , each of the basic mode M0 and the primary mode M1 has a substantially elliptical extension of which a major axis is along the Z-axis direction. As described above, since the metal layer  61  that tends to absorb light is formed on the first portions  41 , the oscillation of the light of the primary mode M1 can be suppressed while suppressing loss of the light of the basic mode M0 (while confining the light of the basic mode M0 in the ridge portion  30 ). 
     The thickness T1 of the first portions  41  is thinner than the thickness T2 of the second portions  42 . Accordingly, both an improvement in heat dissipation and the suppression of the oscillation of the high-order mode can be realized in a more balanced manner. 
     The metal layer  61  is formed on the top surface  30   a  of the ridge portion  30 , on the first portions  41 , and on the second portions  42 , and the dielectric layer  5  is disposed between the second portions  42  and the metal layer  61 . Accordingly, bond strength between the metal layer  61  and the embedding layer  4  can be improved. As a result, the peeling or degradation of the metal layer  61  can be suppressed, and the stability of the laser element can be improved. 
     The dielectric layer  5  is formed such that a part of the second portions  42  is exposed from the dielectric layer  5 , and the metal layer  61  is in contact with the second portions  42  at the part. Accordingly, heat dissipation can be further improved. Incidentally, generally, a thermal conductivity of a SiN or SiO 2  dielectric is lower than a thermal conductivity of a semiconductor or metal. 
     The opening  5   a  that exposes the inner portions  46  of the second portions  42  from the dielectric layer  5  is formed in the dielectric layer  5 , the inner portions  46  being continuous with the first portions  41 , and the metal layer  61  is in contact with the inner portions  46  through the opening  5   a . Accordingly, since the metal layer  61  is in contact with the second portions  42  at the inner portions  46  close to the ridge portion  30 , heat dissipation can be even further improved. On the other hand, since the metal layer  61  is firmly bonded to the second portions  42  at the outer portions  47  far from the ridge portion  30 , with the dielectric layer  5  interposed therebetween, the peeling or the like of the metal layer  61  can be effectively suppressed. In addition, there is a possibility that a cleavage streak is formed in the vicinity of an inner edge of the dielectric layer  5  (inner edge of the opening  5   a ) because of a cleavage process during manufacturing, but since the inner edge of the opening  5   a  is separated from the ridge portion  30 , the influence of the cleavage streak on a light output characteristic can be suppressed. For example, the cleavage streak can be formed in the embedding layer  4  and reach the lower cladding layer  32  and the semiconductor substrate  2 . 
     The width W1 of the opening  5   a  in the X-axis direction is more than or equal to two times the width W2 of the active layer  31 . Accordingly, a region in which the metal layer  61  is in contact with the second portions  42  can be widened, and heat dissipation can be even further improved. In addition, the influence of the cleavage streak on the light output characteristic can be further suppressed. 
     The width W1 of the opening  5   a  in the X-axis direction is more than or equal to ten times the thickness T3 of the second portions  42 . Accordingly, the region in which the metal layer  61  is in contact with the second portions  42  can be further widened, and heat dissipation can be even further improved. In addition, the influence of the cleavage streak on the light output characteristic can be even further suppressed. 
     The wires  8  made of metal are electrically connected to the metal layer  61 , and the connection position between the metal layer  61  and each of the wires  8  overlaps the dielectric layer  5  when viewed in the Z-axis direction. Accordingly, the occurrence of the peeling or the like of the metal layer  61  caused by a tensile stress that the wires  8  act on the metal layer  61  can be suppressed. 
     Modification Examples 
     The present disclosure is not limited to the above-described embodiment. The material and the shape of each configuration are not limited to the material and the shape described above, and various materials and shapes can be adopted. Another known quantum-cascade structure is applicable to the active layer  31 . Another known stack structure is applicable to the semiconductor laminate  3 . As one example, in the semiconductor laminate  3 , the upper guide layer may not have a diffraction grating structure functioning as a distributed feedback structure. 
     The outer edge of the metal layer  61  in the Y-axis direction may reach the outer edges of the embedding layer  4  and the dielectric layer  5 . In this case, heat dissipation on the first end surface  3   a  and on the second end surface  3   b  can be improved. Each of the side surfaces  30   b  of the ridge portion  30  may extend parallel to the center line CL. The metal layer  61  (first electrode  6 ) may be formed only on the top surface  30   a  of the ridge portion  30  and on the first portions  41  and may not formed on the second portions  42 . The metal layer  61  may be configured to include a plurality of portions separated from each other. For example, the metal layer  61  on the first portions  41  may be provided separately from the metal layer  61  on the second portions  42 . 
     The plating layer  62  may not be provided, and only the metal layer  61  may form the first electrode  6 . In this case, the wires  8  may be connected to a surface on the first side S1 of the metal layer  61 . In the embodiment, the inner portions  46  of the second portions  42  are exposed from the dielectric layer  5 , and the metal layer  61  is in contact with the inner portions  46 , but a part of the second portions  42  may be exposed from the dielectric layer  5 , and the metal layer  61  may be in contact with the second portions  42  at the part. In the embodiment, the surface  62   a  of the plating layer  62  is located on the second side S2 with respect to the top surface  30   a  of the ridge portion  30 , but the surface  62   a  may be located on the first side S1 with respect to the top surface  30   a . The plating layer  62  may be formed by plating such that the surface  62   a  is located on the first side S1 with respect to the top surface  30   a , and then the surface  62   a  may be flattened by polishing. 
     REFERENCE SIGNS LIST 
       1 : quantum-cascade laser element,  2 : semiconductor substrate,  3 : semiconductor laminate,  4 : embedding layer,  5 : dielectric layer,  5   a : opening,  8 : wire,  30 : ridge portion,  30   a : top surface,  30   b : side surface,  31 : active layer,  31   a ,  31   b : surface,  41 : first portion,  41   a : edge portion,  42 : second portion,  42   a : surface,  46 : inner portion,  61 : metal layer.