JP2000223780A - Semiconductor laser element - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a semiconductor laser element by which a low-noise characteristic due to a self-excited oscillation is obtained in a low-output state, by which a low-noise characteristic due to a multi-longitudinal-mode oscillation by return light is obtained in a high-output state, by which the noise characteristic can be reduced even in the low-output state and the high-output state, and by which the low-noise characteristics can be made compatible. SOLUTION: This semiconductor laser element is constituted in such a way that a first-conductivity clad layer 3, an active layer 5 and a second-conductivity clad layer 4 are laminated on a semiconductor substrate 1 in this order, that a saturable absorption layer with reference to laser oscillation light is provided in the first-conductivity or second-conductivity clad layer, that a current- constricting structure which comprises a stripe-shaped opening is provided in the second-conductivity clad layer 4, that a self-excited oscillation is generated in a low-output state at a light output of 2 to 5 mW, and that a multi- longitudinal-mode oscillation is generated when the return light of a light output is at 0.5 to 20%.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a semiconductor laser device, and more particularly, to a semiconductor laser device used as a light source of a recording / reproducing optical disk device and realizing low noise.

[0002]

2. Description of the Related Art In a recording / reproducing optical disk device, particularly a magneto-optical disk device or a mini disk device, a semiconductor laser element is used as a light source. In general, a method is used in which the optical output from a semiconductor laser element is kept constant and the magnetic field of an optical disk or an optical component is modulated for recording. However, these semiconductor laser devices have a problem that noise (hereinafter referred to as "return light noise") is generated due to return light that re-enters the device due to reflection of an output light on an optical disk or an optical component. There is.

In order to reduce this return light noise, a layer having a saturable absorption effect on laser oscillation light is arranged near an active layer in a semiconductor laser device, and self-excited oscillation for inducing self-oscillation is provided. Type laser is disclosed in JP-A-8-181
No. 60 or JSAP Vol. 66, No. 9, p. 95
1 to p955 (1997). For example,
The laser device proposed in the Journal of Japan Society of Applied Physics
As shown in FIG. 1, n-GaAs substrate 1 has n-GaAs
s buffer layer 2, n-AlGaAs cladding layer 3, active layer 5, p-AlGaAs first cladding layer 6, p-AlG
An aAs saturable absorber layer 18, a p-AlGaAs second cladding layer 9, and an n-AlGaAs current blocking layer 12 are sequentially laminated. The n-AlGaAs current blocking layer 12 has p-A
A stripe-shaped opening 19 reaching the lGaAs second cladding layer 9 is formed, and n-AlGaAs including the opening 19 is formed.
P-AlGaAs third cladding layer 2 on current blocking layer 12
0 and a p-GaAs contact layer 15 are laminated, and a p-type electrode 16 is formed on the p-GaAs contact layer 15 side, and an n-type electrode 17 is formed on the n-GaAs substrate 1 side.

In such a laser device, as shown in FIG. 17, the light output required for recording on an optical disk is 20 mW.
In the high output state from 1 mW to 40 mW, since the laser self-oscillates, the laser noise intensity required for the optical disk device, that is, -125 dB / Hz or less can be satisfied. However, the optical output required for reproducing the optical disc is 3
In the low power state, the noise intensity of the laser is higher than -125 dB / Hz even though the noise due to the return light is required to be reduced even in the low power state of mW. There is a problem that is not realized.

In other words, in order to maintain self-sustained pulsation until a high output state, it is necessary to increase the saturable absorption effect of the laser element. Oscillation occurs in a mode in which spontaneous emission light is mixed. In such a mode, the intensity of the self-excited oscillation is weak, and the quantum noise due to the spontaneous emission light increases, and as a result, the noise intensity increases. Therefore, in the self-pulsation type laser as described above, there is a problem that it is theoretically difficult to achieve both low noise at high output and low noise at low output. The present invention has been made in view of such a problem, and an object of the present invention is to provide a semiconductor laser device that can achieve both low-noise characteristics in a low-output state and a high-output state.

[0006]

According to the present invention, a first conductivity type clad layer, an active layer, and a second conductivity type clad layer are laminated in this order on a semiconductor substrate, and the first conductivity type or the second conductivity type clad layer is laminated on the semiconductor substrate. It has a saturable absorption layer for laser oscillation light in the two-conductivity-type clad layer, and has a current confinement structure having a stripe-shaped opening in the second-conductivity-type clad layer, and has an optical output of 2 mW to 5 mW. In a low output state, self-excited oscillation occurs, and in a high output state with an optical output of 20 mW or more,
Provided is a semiconductor laser device configured to cause multi-longitudinal mode oscillation when the return light of the optical output is 0.5% to 20%.

According to the present invention, there is provided a semiconductor device comprising:
A first conductivity type cladding layer, an active layer and a second conductivity type cladding layer are stacked in this order, and the first conductivity type or the second conductivity type cladding layer has a saturable absorption layer for laser oscillation light in the cladding layer; It has a current confinement structure having a stripe-shaped opening in the cladding layer of the second conductivity type, and self-sustained pulsation occurs in a low output state of an optical output of 2 mW to 5 mW, and in a high output state of an optical output of 20 mW or more. Further, there is provided a semiconductor laser device configured to cause single longitudinal mode oscillation when the return light of the optical output is less than 0.1%.

[0008]

BEST MODE FOR CARRYING OUT THE INVENTION A semiconductor laser device according to the present invention mainly comprises a first conductivity type clad layer, an active layer and a second conductivity type clad layer laminated in this order on a semiconductor substrate. The semiconductor substrate in the present invention is not particularly limited as long as it is a substrate that is usually used for forming a semiconductor laser device. GaAs, AlGaAs, InGa
P, InGaAlP, InGaAs, InP, InGa
A substrate made of a compound semiconductor such as AsP, GaN, InGaN, or Al ₂ O ₃ can be used. Above all,
GaAs, InP and Al ₂ O ₃ substrates are preferred.

As the material for forming the first conductivity type and second conductivity type cladding layers and the active layer, any material that can be used in the art can be used. Specifically, AlGaAs-based material, InGaAlP-based material, InGa
GaAsP-based materials, InGaN-based materials, and the like can be given.
By appropriately adjusting the composition ratio of these materials for each layer, an active layer and a clad layer constituting a semiconductor laser device having desired characteristics can be obtained. The active layer and the cladding layer may each be composed of a single layer or a plurality of layers in which the composition ratio of these materials is adjusted, or may be composed of a combination of a plurality of layers made of different materials. In particular, the active layer may have a multiple quantum well structure in which layers made of materials having different compositions are stacked, and may have a strained multiple quantum well structure. When the first conductivity type clad layer is composed of a plurality of layers, it is preferable that the plurality of layers are composed of layers having different refractive indices.
It is preferable that, of the plurality of layers constituting the one-conductivity-type cladding layer, a layer adjacent to the active layer has a smaller refractive index than the layers other than this layer. By adjusting the composition of each of the plurality of layers, it is possible to control the light confinement coefficient in the active layer without affecting the optical characteristics.

As a combination of the cladding layer and the active layer of the present invention, specifically, an AlGaAs layer and an AlGaAs
Layer, AlGaInP layer and GaInP / AlGaInP layer (strained multiple quantum well type active layer), AlGaInP layer and Ga
InP layer, AlGaInP layer and GaAs layer, AlGaI
nP layer and GaAlAs layer, GaN layer and InGaN layer, A
Examples include a combination of an lGaN layer and an InGaN layer. Among them, AlGaAs layer and AlGaAs layer, Al
GaInP layer and GaInP / AlGaInP layer, GaN
Layers and InGaN layers are preferred.

The thicknesses of the first conductivity type and second conductivity type cladding layers and the active layer can be appropriately set according to the type of material used, the function of the semiconductor laser device to be obtained, and the like. The thicknesses of the first conductivity type cladding layer, the active layer and the second conductivity type cladding layer are, for example, 0.1 to 5 μm, 0.005
To about 0.5 μm and about 0.1 to 5 μm. Note that the first conductivity type means n-type or p-type, and the second conductivity type means p-type when the first conductivity type is n-type and n-type when the first conductivity type is p-type. By such a combination, various semiconductor laser devices having an oscillation wavelength of about 400 nm to 850 nm can be obtained.

Also, the semiconductor laser device of the present invention has a first
A saturable absorption layer for laser oscillation light is provided in the conductive type or second conductive type cladding layer. Here, the saturable absorption layer is
This is a layer whose absorption coefficient decreases when the carrier concentration increases due to an increase in the absorption of laser oscillation light. Due to the change in the absorption coefficient in the saturable absorption layer, the laser oscillation can be self-oscillated in a pulsed manner to reduce return optical noise.

The saturable absorption layer can be formed using the materials exemplified as the materials constituting the first conductivity type and second conductivity type cladding layers. In this case, the cladding layer may be formed of the same material as that of the first conductivity type or the second conductivity type cladding layer, or may be formed of a different material.
Further, it may be formed on both the first conductivity type and the second conductivity type cladding layers, or may be formed on either one of them. In particular, it is preferable that the same material as the material constituting the first conductivity type or the second conductivity type cladding layer is formed in the second conductivity type cladding layer. The thickness of the saturable absorbing layer can be appropriately adjusted depending on the material used and the like.
About 5 to 40 °. Further, the saturable absorbing layer may be a single layer or a laminated layer. For example,
The saturable absorption layer may be composed of a single layer of an etching stop layer, or a laminated layer of a light guide layer and an etching stop layer. When the saturable absorption layer is formed of a laminated layer of the light guide layer and the etching stop layer, the light guide layer is smaller than the band gap of the second conductivity type cladding layer and larger than the band gap of the etching stop layer. It preferably has a band gap. By defining the band gap of the light guide layer, the confinement of light to the etching stop layer having a saturable absorption effect can be adjusted to obtain a desired low noise characteristic.

Further, when the saturable absorbing layer is provided in the second conductivity type cladding layer, the difference between the laser oscillation wavelength of the active layer and the wavelength corresponding to the band gap of the saturable absorbing layer is- It is preferably from 10 nm to 7 nm. When the wavelength difference is smaller than −10 nm, quantum noise increases at low output. When the wavelength difference is larger than 7 nm, return optical noise increases at low output. Therefore, in order to reduce laser noise at low output, it is preferable that the wavelength difference be within this range.

The semiconductor laser device of the present invention has a current confinement structure having a stripe-shaped opening in the second conductivity type cladding layer. The stripe-shaped opening is preferably formed near the center of the second conductivity type cladding layer, and the width of the opening can be appropriately adjusted by an optical waveguide mechanism. Specifically, the thickness is about 1.2 to 2.8 μm. The current confinement structure in the second conductivity type cladding layer has, for example, a shape in which the second conductivity type cladding layer has a tapered shape, a ridge shape, an inverse tapered shape, a combination shape thereof, or the like from the stripe-shaped opening upward. Preferably, the structure has The width of the top of the current confinement structure is 0.4
It is preferably about 2.0 μm. The current confinement structure is 0.3
And a thickness of about 1.5 μm. Further, the second conductivity type clad layer constituting the current confinement structure may be formed of a single layer or a plurality of layers.

It is preferable that a current blocking layer is disposed around the second conductivity type cladding layer constituting the current confinement portion structure. This current blocking layer is set to a conductivity type different from that of the adjacent cladding layer in order to confine the current in the stripe-shaped opening. The current blocking layer also has a function of confining light in the active layer corresponding to the stripe-shaped opening at the same time. By setting the material of the current blocking layer to be the same as the material of the cladding layer and adjusting the composition ratio, the laser oscillation light is not absorbed and light can be confined by a difference in refractive index. Specifically, when the current blocking layer and the cladding layer are made of a compound semiconductor containing Al, the Al composition ratio of the current blocking layer is set to be larger than the Al composition ratio of the cladding layer, whereby Light confinement by a refractive index difference without light absorption becomes possible. Light confinement due to the refractive index difference is effective in reducing the oscillation threshold current and the operating current because there is no light absorption.

In the case where the current blocking layer is disposed around the second conductivity type clad layer constituting the current confining portion structure,
The difference between the effective refractive index in the direction perpendicular to the second conductivity type cladding layer forming the current constriction portion structure and the effective refractive index in the direction perpendicular to the current blocking layer is 4 × 10 ⁻³ to 8 × 10 ^−3. Is preferred. If the difference in the refractive index is smaller than 4 × 10 ⁻³ , the radiation angle in the direction parallel to the active layer decreases, so that the ellipticity of the emitted light deteriorates. Further, when the refractive index difference is larger than 8 × 10 ⁻³ , noise in a high output state increases.

Further, the semiconductor laser device of the present invention has the above-described configuration, and self-sustained pulsation occurs in a low output state of an optical output of 2 mW to 5 mW, and an optical output of 20 mW.
In the high output state of W or more, the return light of the optical output is 0.5
% To 20%, multi-longitudinal mode oscillation is configured to occur, or self-excited oscillation occurs in a low output state of an optical output of 2 mW to 5 mW, and return light of an optical output in a high output state of an optical output of 20 mW or more. Is less than 0.1%, single longitudinal mode oscillation is configured to occur, or self-sustained pulsation occurs in a low output state of an optical output of 2 mW to 5 mW, and return of an optical output in a high output state of an optical output of 20 mW or more. The multi-longitudinal mode oscillation occurs when the light is 0.5% to 20%, and the single longitudinal mode oscillation occurs when the return light of the optical output is less than 0.1% in a high output state where the optical output is 20 mW or more. ing.
Specifically, one or more of the light confinement coefficient of the active layer, the stripe-shaped opening width, the emission end face reflectance, and the resonator length are adjusted so that the above-mentioned predetermined oscillation occurs.

Here, the return light of the optical output is 0.5% to 2%.
In the case of 0%, when this semiconductor laser device is used in a normal optical information recording / reproducing apparatus, the light reflected on the optical information recording medium becomes 0.5% and the light returning to this semiconductor laser device becomes 0.5%. % To about 20%. Further, the case where the return light of the optical output is less than 0.1% means that even when a laser is emitted from this semiconductor laser element, light hardly returns to the semiconductor laser element.

The light confinement coefficient of the active layer is, for example, as shown in FIG.
As shown in the above, it means the ratio of the amount of light confined in the active layer to the total amount of light confined in each layer near the light emitting end face at the center of the current confinement structure of the semiconductor laser device. Specifically, it can be adjusted in the range of about 0.1 to 0.15. The light confinement coefficient of the active layer can be adjusted by adjusting and changing the thickness of the guide layer of the active layer. In addition, the stripe-shaped opening width means the width of the narrowed second conductivity type cladding layer in the portion where the width changes abruptly in the second conductivity type cladding layer. Specifically, as described above, it can be adjusted in the range of about 1.2 to 2.8 μm.

Further, the output end face reflectivity means the reflectivity at the end face from which the laser light is emitted. In particular,
It can be adjusted in the range of about 8 to 17%. In addition,
The emission end face reflectance can be adjusted to a desired range by the refractive index and the thickness of the insulating film coated on the end face.

The resonator length means the length of the laser resonator. Specifically, it can be adjusted in the range of about 250 to 400 μm. Note that the resonator uses a normal crystal cleavage method, and the length can be adjusted at the time of cleavage.

The semiconductor laser device of the present invention has electrodes formed on the second conductivity type cladding layer and below the substrate. The electrode can be formed of a conductive material usually used as an electrode material. The thickness of the electrode can be appropriately selected depending on the voltage applied to the semiconductor laser element, the material used, and the like. When a current blocking layer is formed around the current constriction structure of the second conductivity type cladding layer, an electrode may be formed on the second conductivity type cladding layer and the current blocking layer. Further, a contact layer may be formed between the second clad layer (and the current blocking layer) and the electrode in order to improve the bonding between the second clad layer and the electrode. Further, in addition to the contact layer, an electrode, a semiconductor substrate, a first conductivity type clad, an active layer, a second conductivity type clad layer, and between the electrodes or in each layer, an etch stop layer, an intermediate layer, a buffer layer, a cap, etc. A layer, a flattening layer, and the like may be formed alone or in combination.

A method for manufacturing a semiconductor laser device according to the present invention will be described. First, a first conductivity type cladding layer, an active layer, a second conductivity type cladding layer, and optionally a saturable absorption layer are laminated on a semiconductor substrate. The method for forming each layer is not particularly limited,
Any of the known methods can be used. For example,
Metal-organic vapor phase epitaxy (MOCVD), molecular beam epitaxy (MBE), liquid phase epitaxy (LPE), and the like.

Next, a part or the whole in the thickness direction of the second conductivity type cladding layer is removed to form a current confinement structure. The removal at this time can be performed by a known method, for example, a photography and etching process. Subsequently, optionally, a current blocking layer is laminated on the second conductivity type cladding layer including the current blocking structure, and etched back by a known method to form a current blocking layer around the current blocking structure, and further optionally. Next, a contact layer and the like are formed on the second conductivity type cladding layer (and the current blocking layer). At this time, the current blocking layer, the contact layer, and the like can be formed by the same method as that for the cladding layer and the like. Subsequently, an electrode is formed on the second conductivity type cladding layer (optionally, a current blocking layer and a contact layer), and optionally, after polishing the semiconductor substrate, an electrode is formed below the semiconductor substrate. The electrode can be formed by, for example, a sputtering method, a vacuum evaporation method, or the like.

Thereafter, it is preferable to optionally form a coating film on the emission end face and the opposite end face. The coating film is made of a material capable of adjusting the reflectance of the emission end face and the opposite end face, for example, Al ₂ O ₃ , SiO ₂ , Si
And the like, and can be formed by a sputtering method or a vacuum evaporation method. Note that the emission end face and the opposite end face are
It is preferable that each is about 8 to 17%. In addition,
The semiconductor laser device of the present invention may be an AlGaAs laser having an oscillation wavelength of 780 nm, an oscillation wavelength of 650 nm or 6 nm.
35 nm band AlGaInP laser, oscillation wavelength 400
It is applicable to an InGaN-based blue laser in the nm band.

Further, it can be used in an optical information recording / reproducing apparatus together with an optical system component for irradiating a laser beam generated from this element to an optical information recording / reproducing medium. The components of the optical system in this case are not particularly limited, and any known components in the art can be used. For example, holograms, diffraction gratings, condenser lenses, objective lenses, etc. Is mentioned. Examples of the optical information recording / reproducing medium include a writable CD, a magneto-optical disk, and a writable DVD. Hereinafter, embodiments of the semiconductor laser device of the present invention will be described with reference to the drawings.

Embodiment 1 FIG. 1 shows an AlGaAs ridge type laser device according to this embodiment. This laser element has a thickness of 100 μm.
N-GaAs buffer layer 2 (thickness 0.5 μm) n-Al _0.46 Ga _0.54 As first cladding layer 3 (thickness 2 μm)
m) n-Al _0.5 Ga _0.5 As second cladding layer 4 (thickness: 0.
Non-doped multiple quantum well (MQW: Multi Quantum Wel)
l) Active layer 5 p-Al _0.5 Ga _0.5 As first cladding layer 6 (thickness: 0.1 μm)
13 μm) p-Al _0.22 Ga _0.78 As light guide layer 7 (thickness: 100 μm)
Å) and a p-GaAs etching stop layer 8 (thickness 32 Å) are sequentially formed, and the p-GaAs etching stop layer 8 is formed.
Above the p-Al _0.5 Ga _0.5 As second cladding layer 9 (thickness 1.
2 μm) and a p-GaAs cap layer 10 (thickness 0.75 μm), a ridge stripe 11 having a stripe-shaped opening width of 2 μm is formed, and a ridge stripe 11 is formed on the p-GaAs etching stop layer 8 around the ridge stripe 11. , N-A _0.7 Ga _0.3 As first current blocking layer 12 (thickness: 0.
An n-GaAs second current blocking layer 13 (thickness 0.3 μm) and a p-GaAs planarization layer 14 (thickness 1.05 μm) are sequentially formed, and the ridge stripe 11 and the p-type
A p-GaAs contact layer 15 (having a thickness of 40 μm) is formed on the GaAs planarization layer 14, a p-type electrode 16 is formed on the surface of the p-GaAs contact layer 15, and an n-type electrode 17 is formed on the surface of the n-GaAs substrate 1. Further, a coating film (not shown) is formed on the emission end face and the opposite end face.

The MQW active layer 5 has Al _{0.35 at} both ends.
It has a Ga _0.65 As guide layer (thickness: 150 °), between which an Al _0.11 Ga _0.89 As quantum well amount (thickness: 100 °).
5 layers and Al _0.35 Ga _0.65 As quantum barrier layer (50mm thick)
It has a configuration in which four layers are alternately stacked. Hereinafter, a method for manufacturing the laser device of FIG. 1 will be described.

First, an n-GaAs substrate 1 is formed on an n-GaAs substrate 1 by a first metal organic chemical vapor deposition (MOCVD) method.
s buffer layer 2, n-Al _0.46 Ga _0.54 As first cladding layer 3, n-Al _0.5 Ga _0.5 As second cladding layer 4,
Non-doped multiple quantum well active layer 5, p-Al _0.5 Ga
_0.5 As first cladding layer 6, p-Al _0.22 Ga _0.78 As
Light guide layer 7, p-GaAs etching stop layer 8,
p-Al _0.5 Ga _0.5 As second cladding layer 9 and p-G
The aAs cap layer 10 is sequentially formed.

Next, p-Al _0.5 G on the obtained substrate 1
The a _0.5 As second cladding layer 9 and the p-GaAs cap layer 10 are etched by known photolithography and chemical etching to form a ridge stripe 11 having a desired shape. Subsequently, a second MOCVD growth on the substrate 1 on which the ridge stripe 11 was formed
-Al _0.7 Ga _0.3 As first current blocking layer 12, n-Ga
As second current blocking layer 13 and p-GaAs planarization layer 14
Are laminated.

Further, the p-GaAs planarizing layer 14, n-
GaAs second current blocking layer 13 and n-Al _0.7 Ga _0.3
The As first current blocking layer 12 is selectively etched until the surface of the ridge stripe 11 is exposed, and the surfaces of the ridge stripe 11 and the p-GaAs planarization layer 14 are planarized. Thereafter, a p-GaAs contact layer 15 is formed on the surface by third MOCVD growth.

Next, the substrate 1 is polished to a thickness of 10
0 μm, a p-type electrode 16 on the surface of the p-GaAs contact layer 15, an n-type electrode 17 on the surface of the n-GaAs substrate 1,
Form each. Subsequently, the cavity length was set to 3 by the cleavage method.
The thickness was adjusted to 25 μm, a coating film (not shown) having a reflectance of 12% was formed on the emission end face, and a reflectance of 9 was formed on the opposite end face.
A laser element is completed by forming a 0% coating film (not shown).

The laser device thus formed had an oscillation threshold current of 25 mA, a slope efficiency of 0.85 W / A, an operating current of 60 mA at an optical output of 30 mW, and an operating voltage of 1.9 V. In an aging running test at an ambient temperature of 60 ° C. and an optical output of 35 mW, the vehicle ran for 5000 hours or more, and sufficient reliability for practical use was obtained.

In this laser device, the p-GaAs etching stop layer acts as a saturable absorbing layer, so that the layer structure can be simplified, and the saturable absorbing effect of the etching stop layer allows low power output. Self-excited oscillation occurs, and low noise characteristics are obtained.

In this laser device, the light output is 1 mW
From 40 mW to the relative noise intensity due to the return light was measured. The relative noise intensity was measured using an evaluation device corresponding to an optical disk pickup. The distance from the laser to the disk surface was 25 mm, and the center frequency was 7 mm.
20KHz, bandwidth 10KHz, disk surface ± 1μ
m, the return light rate to the laser is 0.5
The measurement was performed by obtaining the maximum noise intensity when changing from% to 20%. The result is shown in FIG. In general,
In a digital disk drive, a standard specification of a laser noise intensity is required to be -125 dB / Hz or less. As shown in FIG.
To 40 mW, the noise intensity was -125 dB / Hz or less, which was a good value sufficiently satisfying the standard specification.

In this laser device, the oscillation spectrum was measured at a light output of 3 mW with no return light (return light rate of less than 0.1%) and with return light. The results are shown in FIGS. 3 (a) and 3 (b). As shown in FIG.
In the case of no return light, the spectrum was modulated by self-excited oscillation, the line width was relatively wide at 1.5 °, and a multi-longitudinal mode was set. As described above, when self-sustained pulsation occurs, the spectrum has an increased line width and a multi-longitudinal mode, so that coherence is reduced and return optical noise can be reduced. As shown in FIG. 3B, even when there is return light, the self-sustained pulsation is not affected, so that an oscillation spectrum similar to that without return light can be obtained.

The oscillation spectrum was measured at an optical output of 30 mW without return light and with return light. The results are shown in FIGS. 4 (a) and 4 (b). As shown in FIG. 4A, when there was no return light, the spectrum had a line width of 0.7 ° and a single longitudinal mode. On the other hand, FIG.
As shown in (b), when there is return light, a composite resonator is formed between the laser and the disk surface,
The spectrum was in multi-longitudinal mode with a linewidth of 1.0 ° as the laser gain was modulated. In the multi-longitudinal mode, there is no effect of increasing the line width due to self-pulsation, but as in the case of self-pulsation, the coherence of the laser beam is reduced, so that return optical noise can be reduced. In self-excited oscillation, noise may be generated at a certain frequency under the influence of return light. However, this laser element utilizes multi-longitudinal mode oscillation of the laser due to return light in a high output state. Low noise characteristics more stable than the excitation oscillation can be obtained.

In this laser device, the MQW active layer is composed of five quantum well layers, and the optical confinement coefficient Γact is 0.125. Here, Γact is the ridge stripe 11 of the laser element as shown in FIG.
It is defined by the ratio of the light amount 22 confined in the active layer 5 to the total light amount 21 confined in each layer near the light emitting end face at the center. The active layer is made of MQW
In the case of the active layer, the sum of the light confinement coefficients in all the quantum well layers is defined as Γact. This laser element is MQW
By adjusting the thickness of the guide layer of the active layer, Γac
t can be varied. Therefore, Γact is set to 0.
Relative noise intensity at an optical output of 30 mW when changing from 05 to 0.2, ambient temperature of 60 ° C., optical output of 35 mW
Of the device was measured. The results are shown in FIG.
(B).

As shown in FIG. 6A, it was found that when Δact was 0.1 or more, the specification of noise intensity was −125 dB / Hz or less. Further, as shown in FIG. 6B, when Δact becomes 0.15 or more, the element lifetime becomes 2
It was found that the time was less than 000 hours, and the reliability of the device was deteriorated. From the above, Γact is 0.1 or more, 0.1
It has been found that it is desirable to set it to 5 or less.

This laser device has an n-second cladding layer 4
Is made of Al _0.5 Ga _0.5 As, and the n-first cladding layer 3 is made of Al _0.46 Ga _0.54 As. Since the refractive index decreases as the Al composition ratio increases, the n-second cladding layer 4 has a lower refractive index than the n-first cladding layer 3. Therefore, with such a configuration, it is possible to prevent an increase in the radiation angle with respect to the direction perpendicular to the active layer 5 without reducing the light confinement coefficient in the active layer 5.
In this laser device, the radiation angle with respect to the direction perpendicular to the active layer 5 when the Al composition ratio of the n-first cladding layer was changed was measured. FIG. 7 shows the result. According to FIG. 7, when the Al composition ratio of the n-first cladding layer is 0.5, which is the same as the Al composition ratio of the n-second cladding layer, the vertical radiation angle is 32 degrees, and the vertical radiation angle of the conventional laser device is Since the angle is larger than 28 degrees, there is a problem that the coupling efficiency with the lens is reduced. However, when the Al composition ratio of the n-first cladding layer is set to 0.46 like this laser element, the same vertical emission angle can be obtained as before, and the problem of deterioration of the coupling efficiency between the laser element and the lens is raised. Does not happen.

In this laser device, changes in relative noise intensity and operating voltage at an optical output of 30 mW when the stripe-shaped opening width was changed from 1 μm to 3 μm were measured. The results are shown in FIGS. 8 (a) and 8 (b). FIG.
As shown in (a), the stripe-shaped opening width is 2.8.
If the width is larger than μm, the noise intensity increases and the standard specification of the noise intensity is not satisfied. This indicates that multi-longitudinal mode oscillation hardly occurs at high output when the stripe-shaped opening width is widened. On the other hand, as shown in FIG. 8B, when the opening width of the stripe is narrower than 1.2 μm, there is a problem that the operating voltage at an optical output of 30 mW is higher than 2.2V. From the above, it is desirable that the stripe width is set to be 1.2 μm or more and 2.8 μm or less. When the stripe width is 2.5 μm or less,
Since the noise intensity can be reduced to -130 dB / Hz or less, it is more desirable from the viewpoint of increasing the noise tolerance of the optical disk device.

Further, in this laser device, when the reflectivity of the light emitting end face was changed from 5% to 20%, the change of the relative noise intensity at the light output of 30 mW and 3 mW was measured. The results are shown in FIGS. 9A and 9B. FIG.
As shown in (a), at an optical output of 30 mW, the noise intensity increases as the reflectance increases, and when the reflectance exceeds 17%, the standard specification of the noise intensity is not satisfied. Further, as shown in FIG. 9B, the light output is 3 mW.
In, the noise intensity increases as the reflectance decreases, and when the reflectance is less than 8%, the standard specification of the noise intensity is not satisfied. From the above, the reflectance of the light emitting end face is 8
% Or more and 17% or less. When the light exit end face reflectance is set to 10% or more and 15% or less, the noise intensity becomes -13%.
Since it can be set to 0 dB / Hz or less, it is more desirable from the viewpoint of increasing the noise tolerance of the optical disk device.

Further, in this laser device, when the cavity length was changed from 200 μm to 450 μm, the relative noise intensity at an optical output of 30 mW and the ambient temperature of 60 ° C.
The change in device life at an optical output of 35 mW was measured. The results are shown in FIGS. 10 (a) and (b). As shown in FIG. 10A, the noise intensity tends to increase as the resonator length increases. If the resonator length is longer than 400 μm, the standard specification of the noise intensity will not be satisfied. Also,
As shown in FIG. 10B, as the resonator length becomes shorter, the life tends to be deteriorated. In particular, the cavity length is 250 μm
For smaller sizes, the device lifetime is less than 2000 hours. From the above, the resonator length is 250 μm or more and 400 μm.
m or less is desirable. If the resonator length is 375 μm or less, the noise intensity can be reduced to −130 dB / Hz or less, which is more desirable from the viewpoint of increasing the noise tolerance of the optical disk device.

This laser device has a laser oscillation wavelength λ1 at an optical output of 3 mW of 780 nm, and a wavelength λ2 corresponding to the band gap of the p-GaAs etching stop layer having a saturable absorption effect is 782 nm. Therefore,
These differences (Δλ: λ1−λ2) are −2 nm. In this laser device, the wavelength λ2 corresponding to the band gap of the saturable absorption layer can be adjusted by changing the Al composition ratio of the light guide layer. Therefore, the change in relative noise intensity at an optical output of 30 mW and an optical output of 3 mW when Δλ was changed from −15 nm to 10 nm by changing λ2 was measured. The results are shown in FIG.
(A) and (b) show. As shown in FIG.
At an optical output of 30 mW, the noise specification is satisfied only when Δλ is −1.
0 nm or more. Further, as shown in FIG. 11B, when the optical output is 3 mW, Δλ is −10 nm or more and 7 nm.
It is as follows. From the above, the light output is 30 mW and the light output is 3 mW
Δλ which satisfies the standard specification of low noise intensity is -1
0 nm or more and 7 nm or less are desirable. Note that Δλ is 5n
When it is set to m or less, the noise intensity can be made -130 dB / Hz or less, so that it is more desirable from the viewpoint of expanding the noise tolerance of the optical disc device.

In this laser device, when the thickness of the etching stop layer was changed from 10 ° to 50 °, the change of the relative noise intensity at the light output of 30 mW and 3 mW was measured. The results are shown in FIGS. FIG.
As shown in FIG. 2A, when the optical output is 30 mW, the noise intensity tends to increase as the layer thickness increases. 40 layer thickness
When the thickness is larger than Å, the standard specification of the noise intensity is not satisfied. It is considered that when the layer thickness is increased, the amount of light returning to the etching stop layer is increased, and the occurrence of longitudinal multi-mode oscillation of the spectrum tends to be suppressed. In addition, as shown in FIG.
In the case of W, when the layer thickness is smaller than 25 °, the saturable absorption effect is reduced and self-excited oscillation is less likely to occur, so that the noise intensity is higher than the standard specification. As described above, in order to satisfy the standard specifications of the noise intensity at both the light output of 30 mW and the light output of 3 mW, it is desirable to set the etching stop layer thickness to 25 ° or more and 40 ° or less.

In this laser device, the difference (Δn: n1−n1) between the effective refractive index n1 in the direction perpendicular to the active layer inside the ridge stripe and the effective refractive index n2 in the direction perpendicular to the active layer outside the ridge stripe (constituting the current blocking layer). n2)
It becomes 6 × 10 ^-3 . The radiation angle in the direction parallel to the active layer in the high power state is 11 degrees. In this laser device, by changing the thickness of the p-first cladding layer, Δ
n can be varied. Therefore, Δn is 2 × 10
Light output 30m when changed from ^-3 to 10 × 10 ^-3
The change in relative noise intensity at W and the radiation angle in a direction parallel to the active layer were measured. FIGS. 13A and 13B show the results.
Shown in As shown in FIG. 13A, Δn is 8 × 10
^If it is larger than ^-3 , the noise intensity increases and the standard specification is not satisfied. This indicates that as Δn increases, multi-longitudinal mode oscillation hardly occurs at high output.
Further, as shown in FIG. 13B, Δn is 4 × 10 ^−3.
When it becomes smaller, the parallel radiation angle becomes 8 degrees or less, and the ellipticity of the emitted light (= vertical radiation angle / parallel radiation angle) becomes larger than 3.5 for a vertical radiation angle of 28 degrees. In addition, there is a problem that the spot where the laser light is focused by the lens becomes elliptical. From the above, Δn is 4 × 10 ⁻³
As described above, it is desirable that the value be 8 × 10 ⁻³ or less.

Embodiment 2 FIG. 14 shows an AlGaAs laser device according to this embodiment. This laser device has an n-type
On the GaAs substrate 1, an n-GaAs buffer layer 2 (thickness 0.5 μm), an n-Al _0.47 Ga _0.53 As first cladding layer 23 (thickness 2
μm) n-Al _0.5 Ga _0.5 As second cladding layer 4 (thickness: 0.1 μm).
Non-doped multiple quantum well (MQW: Multi Quantum Wel)
l) Active layer 25 p-Al _0.5 Ga _0.5 As first cladding layer 6 (thickness: 0.1 μm)
18 μm) and a p-GaAs etching stop layer 8 (thickness 28 °) are sequentially formed, and the p-GaAs etching stop layer 8 is formed.
Above the p-Al _0.5 Ga _0.5 As second cladding layer 9 (thickness 1.
2 μm) and a p-GaAs cap layer 10 (thickness 0.75 μm), and a ridge stripe 31 having a stripe-shaped opening width of 2.2 μm is formed.
N-Al _0.55 Ga _0.45 As first current blocking layer 32 (thickness 0.6 μm) n-GaAs second current blocking layer 13 (thickness 0.3 μm) And a p-GaAs planarization layer 14 (thickness: 1.05 μm) are sequentially formed.
A p-GaAs contact layer 15 (thickness: 3 μm) is formed on the GaAs planarization layer 14, a p-type electrode 16 is formed on the surface of the p-GaAs contact layer 15, and an n-type electrode 17 is formed on the surface of the n-GaAs substrate 1. Further, a coating film (not shown) is formed on the emission end face and the opposite end face.

The MQW active layer 25 has Al
_{It has a 0.33} Ga _0.67 As guide layer (thickness: 200 Å), between which an Al _0.11 Ga _0.89 As quantum well (thickness: 110) is used.
Å) 4 layers and Al _0.35 Ga _0.65 As quantum barrier layer (thickness: 50)
Iii) It has a configuration in which three layers are alternately stacked. In this laser device, the cavity length was adjusted to 300 μm by a cleavage method, and a coating film (not shown) having a reflectance of 15% on the emission end face and a coating film (not shown) having a reflectance of 75% on the opposite end face. Is formed. The above laser element can be formed by a method substantially similar to that of the first embodiment.

In this laser device, the oscillation threshold current is 30 m
A, a slope efficiency of 0.75 W / A, an operating current of 70 mA at an optical output of 30 mW, and an operating voltage of 1.9 V were obtained. In addition, even in an aging running test at an ambient temperature of 60 ° C. and a light output of 35 mW, the vehicle stably runs for 5000 hours or more, and sufficient reliability for practical use has been obtained. In this laser device, the relative noise intensity due to the return light when the light output was changed from 1 mW to 40 mW was measured. The result is shown in FIG. As shown in FIG. 15, this laser device obtained good values below the standard specification of noise intensity from 2 mW to 40 mW in optical output. This laser device has low noise characteristics due to self-excited oscillation at an optical output of 3 mW, and low noise characteristics due to multi-longitudinal mode oscillation due to return light at an optical output of 30 mW. This laser device is different from the laser device of the first embodiment in that the active layer outside the stripe has the saturable absorption effect. The active layer light confinement coefficient of this laser device is 0.11, Δn
Is 2 × 10 ⁻³ . In this laser element as well, by adjusting the light confinement coefficient of the active layer, the stripe-shaped opening width, the reflectance of the emission end face, and the cavity length, it is possible to achieve both low output and high output and low noise characteristics. .

[0051]

According to the present invention, a first substrate is provided on a semiconductor substrate.
A conductive type clad layer, an active layer and a second conductive type clad layer are laminated in this order, and the first conductive type or second conductive type clad layer has a saturable absorption layer for laser oscillation light in the second conductive type clad layer; It has a current confinement structure having a stripe-shaped opening in a conductive type cladding layer, and has an optical output of 2 mW to 5 m.
The self-excited oscillation occurs in the low output state of W, and the multi-longitudinal mode oscillation occurs when the return light of the optical output is 0.5% to 20% in the high output state of the optical output of 20 mW or more. In the low output state, low noise characteristics are obtained by self-excited oscillation, and in the high output state, low noise characteristics are obtained by multi-longitudinal mode oscillation with return light. However, noise characteristics can be reduced, and low noise characteristics can be achieved at the same time.

In a high output state with an optical output of 20 mW or more, the optical confinement coefficient of the active layer, the opening width of the stripe, When the output end face reflectance and the resonator length are set, self-sustained pulsation only needs to be generated in the low output state, so that the degree of freedom in designing the element structure can be increased. By adjusting one or more of the optical confinement coefficient of the active layer, the stripe-shaped aperture width, the emission end face reflectance, and the resonator length, a predetermined oscillation is generated in a low output state and a high output state. As a result, it is relatively easy to achieve both low noise characteristics. When the light confinement coefficient of the active layer is 0.1 or more and 0.15 or less,
In a high output state, stable multi-longitudinal mode oscillation due to return light can be caused, sufficient low noise characteristics can be obtained, and deterioration of the laser element life can be suppressed.

When the opening width of the stripe is 1.2 μm or more and 2.8 μm or less, it is possible to reduce noise by stable vertical multi-mode oscillation in a high output state and to increase the operating voltage. Can be suppressed. When the reflectance of the light emitting end face is 8% or more and 17% or less, controllability for achieving both low-noise characteristics in the low-output state and the high-output state can be further improved. Further, when the resonator length is 250 μm or more and 400 μm or less, it is possible to reduce noise in a high output state, and
It is possible to suppress the deterioration of the laser element life.

Further, the first conductivity type cladding layer is composed of a plurality of layers having different refractive indices, and the first conductivity type cladding layer adjacent to the active layer has a higher refractive index than the other layers. In the case of having a small refractive index, even if the light confinement coefficient in the active layer increases, it is possible to suppress an increase in the radiation angle in the direction perpendicular to the active layer. Deterioration of coupling efficiency can be prevented. Further, a saturable absorption layer is provided in the second conductivity type cladding layer, and the difference between the laser oscillation wavelength of the active layer and the wavelength corresponding to the band gap of the saturable absorption layer is −10 nm.
When the distance is from 7 nm to 7 nm, low noise can be achieved by stable self-excited oscillation in a low output state.

Further, the saturable absorption layer comprises a light guide layer and an etching stop layer, and the light guide layer is smaller than the band gap of the second conductivity type cladding layer and is smaller than the band gap of the etching stop layer. In the case of having a large band gap, the etching stop layer used for forming the current confinement structure can be used for the saturable absorption layer, so that the layer structure can be simplified. In addition, by adjusting light confinement to the etching stop layer having a saturable absorption effect, desired low noise characteristics can be obtained. The etching stop layer has a thickness of 2
In the case of a GaAs layer of 5 ° or more and 40 ° or less,
Since the return light to the saturable absorption layer can be reduced, the influence of the return light on the saturable absorption layer can be reduced, so that stable low-noise characteristics can be obtained in the low output state and the high output state.

Further, a current blocking layer is arranged around the second conductivity type cladding layer forming the current constriction portion structure, and the effective refractive index and the vertical direction of the second conductivity type cladding layer forming the current constriction portion structure are perpendicular to the second conductivity type cladding layer. When the difference from the effective refractive index in the direction perpendicular to the current blocking layer is 4 × 10 ⁻³ or more and 8 × 10 ⁻³ or less, low noise characteristics can be obtained in a high output state, and the active layer has Since it is possible to limit the decrease in the radiation angle in the parallel direction, it is possible to suppress the deterioration of the ellipticity of the radiated light, and by using a lens, it is possible to easily focus on a diffraction-limited small spot.
It can be suitably used in an optical disc.

[Brief description of the drawings]

FIG. 1 is a schematic sectional view of a main part for describing an embodiment of a semiconductor laser device of the present invention.

FIG. 2 is a diagram showing a relationship between a relative noise intensity and an optical output of the semiconductor laser device of FIG.

3A and 3B are diagrams showing an oscillation spectrum at (a) no return light and an optical output of 3 mW, and (b) an oscillation spectrum at an optical output of 3 mW in the semiconductor laser device of FIG.

FIGS. 4A and 4B are diagrams showing (a) an oscillation spectrum at an optical output of 30 mW without return light and (b) an oscillation spectrum at an optical output of 30 mW in the semiconductor laser device of FIG.

FIG. 5 is a diagram for explaining a definition of a light confinement coefficient of an active layer.

FIG. 6 shows (a) an optical output 30 in a semiconductor laser device having the same configuration as the semiconductor laser device of the present invention.
It is a figure which shows the relationship between the relative noise intensity in mW, and an optical confinement coefficient, and (b) is a figure which shows the relationship between the element lifetime at 35 mW of optical output, and an optical confinement coefficient.

FIG. 7 is a graph showing the relationship between the vertical radiation angle and the first radiation angle in a semiconductor laser device having the same configuration as the semiconductor laser device in the present invention.
FIG. 4 is a diagram showing a relationship between a conductive type cladding layer and an aluminum composition ratio.

FIG. 8 shows (a) an optical output 30 in a semiconductor laser device having the same configuration as the semiconductor laser device in the present invention.
It is a figure which shows the relationship between relative noise intensity in mW, and the stripe-shaped aperture width, and (b) is a figure which shows the relationship between the operating voltage at the optical output of 30 mW, and a stripe-shaped aperture width.

FIG. 9 shows (a) an optical output 30 in a semiconductor laser device having the same configuration as the semiconductor laser device in the present invention.
FIG. 9 is a diagram showing a relationship between relative noise intensity in mW and end face reflectance;
(B) is a diagram showing the relationship between the relative noise intensity at an optical output of 3 mW and the end face reflectance.

FIG. 10 shows (a) optical output 3 in a semiconductor laser device having the same configuration as the semiconductor laser device in the present invention.
The figure which shows the relationship between the relative noise intensity at 0 mW, and a resonator length,
(B) is a diagram showing the relationship between the device life at a light output of 30 mW and the cavity length.

FIG. 11 shows (a) light output 3 in a semiconductor laser device having the same configuration as the semiconductor laser device in the present invention.
The figure which shows the relationship between relative noise intensity at 0 mW, and (DELTA) (lambda),
(B) is a diagram showing the relationship between the relative noise intensity at a light output of 3 mW and Δλ.

FIG. 12 shows (a) optical output 3 in a semiconductor laser device having the same configuration as the semiconductor laser device in the present invention.
It is a figure which shows the relationship between the relative noise intensity at 0 mW, and the film thickness of an etching stop layer, and (b) The figure which shows the relationship between the relative noise intensity at the light output of 3 mW, and the film thickness of an etching stop layer.

FIG. 13 shows (a) optical output 3 in a semiconductor laser device having the same configuration as the semiconductor laser device of the present invention.
The figure which shows the relationship between relative noise intensity at 0 mW, and (DELTA) n,
(B) is a diagram showing the relationship between the relative noise intensity at a light output of 3 mW and Δn.

FIG. 14 is a schematic sectional view of a main part for describing another embodiment of the semiconductor laser device of the present invention.

FIG. 15 is a diagram showing a relationship between a relative noise intensity and an optical output of the semiconductor laser device of FIG. 14;

FIG. 16 is a schematic sectional view of a main part of a conventional semiconductor laser device.

FIG. 17 is a diagram showing a relationship between a relative noise intensity and an optical output of the semiconductor laser device of FIG. 16;

[Explanation of symbols]

 Reference Signs List 1 substrate 2 buffer layer 3, 23 n-first cladding layer 4 n-second cladding layer 5, 25 active layer 6 p-first cladding layer 7 p-light guide layer 8 p-etching stop layer 9 p-second Clad layer 10 p-cap layer 11, 31 ridge stripe 12, 32 n-first current blocking layer 13 n-second current blocking layer 14 p-planarization layer 15 p-contact layer 16 p-type electrode 17 n-type electrode 21 Light intensity distribution perpendicular to active layer 22 Light intensity distribution in active layer

Claims (14)

[Claims] 1. A first conductive type clad layer, an active layer and a second conductive type clad layer are laminated in this order on a semiconductor substrate, and laser oscillation light is provided in the first conductive type or second conductive type clad layer. And a current confinement structure having a stripe-shaped opening in the cladding layer of the second conductivity type. Self-excited oscillation occurs in a low power state of 2 mW to 5 mW in optical output, And a multi-longitudinal mode oscillation when the return light of the optical output is 0.5% to 20% in a high output state of an optical output of 20 mW or more. 2. A cladding layer of a first conductivity type, an active layer and a cladding layer of a second conductivity type are laminated on a semiconductor substrate in this order, and laser oscillation light is provided in the cladding layer of the first or second conductivity type. And a current confinement structure having a stripe-shaped opening in the cladding layer of the second conductivity type. Self-excited oscillation occurs in a low power state of 2 mW to 5 mW in optical output, In addition, in a high output state of an optical output of 20 mW or more, a single longitudinal mode oscillation occurs when the return light of the optical output is less than 0.1%. 3. The semiconductor according to claim 2, further comprising a multi-longitudinal mode oscillation when the return light of the optical output is 0.5% to 20% in a high output state of an optical output of 20 mW or more. Laser element. 4. One or two of an optical confinement coefficient of an active layer, a stripe-shaped opening width, an output end face reflectivity, and a resonator length so that a predetermined oscillation occurs in a low output state and a high output state.
The semiconductor laser device according to claim 1, wherein at least one is adjusted. 5. The semiconductor laser device according to claim 4, wherein the light confinement coefficient of the active layer is 0.1 or more and 0.15 or less. 6. The semiconductor laser device according to claim 4, wherein a stripe-shaped opening width is 1.2 μm or more and 2.8 μm or less. 7. A light emitting end face having a reflectivity of 8% or more and 17% or more.
%. The semiconductor laser device according to any one of claims 4 to 6, wherein 8. A resonator having a length of 250 μm or more and 400 μm or more.
The semiconductor laser device according to claim 4, wherein m is equal to or less than m. 9. The first conductivity type clad layer is composed of a plurality of layers having different refractive indices, and the first conductivity type clad layer adjacent to the active layer has a higher refractive index than the other layers. The semiconductor laser device according to claim 5, which has a small refractive index. 10. A saturable absorbing layer is provided in the second conductivity type cladding layer, and a difference between a laser oscillation wavelength of the active layer and a wavelength corresponding to a band gap of the saturable absorbing layer is -1.
The semiconductor laser device according to any one of claims 4 to 9, wherein the thickness is from 0 nm to 7 nm. 11. The saturable absorption layer includes a light guide layer and an etching stop layer, wherein the light guide layer is smaller than a band gap of the second conductivity type cladding layer and is smaller than a band gap of the etching stop layer. The semiconductor laser device according to claim 10 having a large band gap. 12. An etching stop layer having a thickness of 25 °
The semiconductor laser device according to claim 11, comprising a GaAs layer having a thickness of 40 ° or less. 13. A saturable absorbing layer having a thickness of 25 ° or more,
11. The semiconductor laser device according to claim 10, comprising an etching stop layer made of a GaAs layer of 0 [deg.] Or less. 14. A current blocking layer is disposed around a second conductivity type cladding layer forming a current constriction portion structure, and has an effective refractive index and a vertical refractive index perpendicular to the second conductivity type cladding layer forming the current constriction portion structure. 11. The semiconductor laser device according to claim 10, wherein a difference from an effective refractive index in a direction perpendicular to the current blocking layer is 4 × 10 ⁻³ or more and 8 × 10 ⁻³ or less.