A gallium nitride-based semiconductor laser having a waveguide layer with a graded dielectric constant

Abstract

The embodiment of the specification provides a gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer, which comprises, from bottom to top, a substrate, a lower confinement layer, a lower waveguide layer, an active layer, an upper waveguide layer, an electron blocking layer and an upper confinement layer, wherein the upper waveguide layer is a graded dielectric constant upper waveguide layer, the lower waveguide layer is a graded dielectric constant lower waveguide layer, and at least one of the intensity distribution of indium (In) ions, the concentration distribution of indium (In) atoms, the covalent bond energy distribution, the dielectric constant distribution and the radiative recombination coefficient distribution in the graded dielectric constant upper waveguide layer and the graded dielectric constant lower waveguide layer is distributed as a nonlinear continuous function along the epitaxial growth direction.

Description

Technical Field

[0001] This invention relates to the technical field of semiconductor optoelectronic devices, and in particular to a gallium nitride-based semiconductor laser with a gradient dielectric constant waveguide layer. Background Technology

[0002] Lasers are widely used in laser displays, laser TVs, laser projectors, communications, medical applications, weaponry, guidance, ranging, spectral analysis, cutting, precision welding, and high-density optical storage. Among various types of lasers, all-solid-state semiconductor lasers have become a research hotspot due to their significant advantages such as small size, high efficiency, strong stability, and ease of miniaturization. However, semiconductor lasers differ fundamentally from ordinary light-emitting diodes (LEDs) in their physical mechanisms: lasers rely on stimulated emission of charge carriers and oscillation amplification within a resonant cavity, and their operating current density is typically as high as 2-15 kA / cm². 2 This is more than two orders of magnitude higher than that of LEDs. This extremely high operating intensity leads to severe electron leakage, Auger recombination, and polarization effects in traditional semiconductor lasers, resulting in severe efficiency degradation (Droop effect) and limiting their performance at high power.

[0003] To overcome the aforementioned efficiency degradation and electron matching problems, current methods typically employ optimizing the active region structure or introducing electron blocking layers to improve carrier injection and recombination efficiency. While these techniques improve internal quantum efficiency to some extent, significant drawbacks remain in high-performance applications. With further increases in carrier concentration, fluctuations in high-concentration carriers significantly interfere with the refractive index distribution of the active layer, exacerbating refractive index dispersion and causing the optical field confinement factor to decrease with increasing wavelength, resulting in a substantial reduction in mode gain. Existing waveguide layer designs often fail to completely suppress spatial dissipation of the optical field, leading to leakage of some optical field modes into the substrate, forming standing waves. This not only reduces the suppression efficiency of substrate modes but also directly degrades far-field image (FFP) quality.

[0004] Therefore, it is desirable to provide a gallium nitride-based semiconductor laser with a gradient dielectric constant waveguide layer, which can achieve high-efficiency lasing while precisely controlling the dielectric constant distribution and optical field confinement under complex operating conditions. Summary of the Invention

[0005] This specification provides one or more embodiments of a gallium nitride-based semiconductor laser having a graded dielectric constant waveguide layer. The gallium nitride-based semiconductor laser includes, from bottom to top, a substrate, a lower confinement layer, a lower waveguide layer, an active layer, an upper waveguide layer, an electron blocking layer, and an upper confinement layer. The upper waveguide layer is a graded dielectric constant upper waveguide layer, and the lower waveguide layer is a graded dielectric constant lower waveguide layer. At least one of the following distributions in the graded dielectric constant upper waveguide layer and the graded dielectric constant lower waveguide layer exhibits a nonlinear continuous function distribution along the epitaxial growth direction: indium (In) ion intensity distribution, indium (In) atom concentration distribution, covalent bond energy distribution, dielectric constant distribution, and radiative recombination coefficient distribution. Attached Figure Description

[0006] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein: Figure 1 This is a schematic diagram of a gallium nitride-based semiconductor laser with a gradient dielectric constant waveguide layer, as shown in some embodiments of this specification. Figure 2 This is a SIMS secondary ion mass spectrum of a gallium nitride-based semiconductor laser according to some embodiments of this specification; Figure 3 This is a fitted curve of In ion intensity distribution or In atom concentration distribution and ExpDecay1 in a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification. Figure 4 This is a fitted curve of In ion intensity distribution or In atom concentration distribution and ExpDecay2 of a waveguide layer with a gradient dielectric constant shown in some embodiments of this specification. Figure 5 This is a fitted curve of In ion intensity distribution or In atom concentration distribution and ExpDecay3 in a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification. Figure 6 This is a fitting curve of the In ion intensity distribution or In atom concentration distribution on a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification, and the SGompertz curve. Figure 7 This is a fitting curve of the covalent bond energy distribution and ExpDecay1 of a waveguide layer with a gradient dielectric constant shown in some embodiments of this specification. Figure 8 The graph shows the dielectric constant distribution of the waveguide layer with a gradient dielectric constant and the fitting curve of ExpDecay1 according to some embodiments of this specification. Figure 9This is a fitting curve of the In ion intensity distribution or In atom concentration distribution of the waveguide layer under a gradient dielectric constant, and Slogistic1, according to some embodiments of this specification. Figure 10 This is a graph showing the covalent bond energy distribution of a waveguide layer with a gradient dielectric constant and the Boltzmann fitting curve, according to some embodiments of this specification. Figure 11 The dielectric constant distribution of waveguide layers with graded dielectric constants and the Boltzmann fitting curves are shown in some embodiments of this specification. Figure 12 These are covalent bond energy distribution diagrams of the upper and lower waveguide layers with graded dielectric constants, as shown in some embodiments of this specification. Figure 13 These are dielectric constant distribution diagrams of the upper and lower gradient dielectric constant waveguide layers shown in some embodiments of this specification. Figure 14 This is a fitting curve of the In ion intensity distribution or In atom concentration distribution and Gauss Amp of a waveguide layer with a gradient dielectric constant shown in some embodiments of this specification. Figure 15 This is a fitting curve of In ion intensity distribution or In atom concentration distribution and Invspoly of a waveguide layer with a gradient dielectric constant shown in some embodiments of this specification. Figure 16 This is a fitted curve of the In ion intensity distribution or In atom concentration distribution on a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification, and Hill. Figure 17 The graph shows the distribution of radiative recombination coefficients of waveguide layers with graded dielectric constants and the fitting curve of Gauss Amp, according to some embodiments of this specification. Figure 18 This is a graph showing the distribution of the radiative recombination coefficient of a waveguide layer with a gradient dielectric constant and the fitting curve of Invspoly, based on some embodiments of this specification. Figure 19 This is a fitted curve of the radiative recombination coefficient of the waveguide layer with a graded dielectric constant and Hill, as shown in some embodiments of this specification. Figure 20 This is a fitted curve of the In ion intensity distribution or In atom concentration distribution and BiDoseResp of the waveguide layer under a graded dielectric constant, as shown in some embodiments of this specification. Figure 21 The graph shows the distribution of the radiative recombination coefficient of the waveguide layer with a graded dielectric constant and the fitting curve of BiDoseResp, according to some embodiments of this specification. Figure 22 This is a distribution diagram of the radiative recombination coefficient of the upper and lower waveguide layers with graded dielectric constants, as shown in some embodiments of this specification.

[0007] Figure label: 100: Substrate; 101: Lower confinement layer; 102: Lower waveguide layer; 102a: First lower waveguide layer; 102b: Second lower waveguide layer; 103: Active layer; 104: Upper waveguide layer; 105: Electron blocking layer; 106: Upper confinement layer. Detailed Implementation

[0008] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0009] Figure 1 This is a schematic diagram of a gallium nitride-based semiconductor laser with a gradient dielectric constant waveguide layer, as shown in some embodiments of this specification.

[0010] In some embodiments, such as Figure 1 As shown, the gallium nitride-based semiconductor laser 100 includes, from bottom to top, a substrate 101, a lower confinement layer 102, a lower waveguide layer 102a, an active layer 103, an upper waveguide layer 104, an electron blocking layer 105, and an upper confinement layer 106.

[0011] Gallium nitride-based semiconductor lasers are devices that use gallium nitride and gallium nitride alloys as gain media and achieve stimulated emission through electrical injection.

[0012] A substrate is the basic crystalline material that supports the growth of the epitaxial layer of a gallium nitride-based semiconductor laser. An epitaxial layer is the material layer on which epitaxy occurs. Epitaxy is the process of growing a thin crystalline film on a substrate.

[0013] In some embodiments, the substrate may be a GaN single crystal substrate.

[0014] Understandably, when the substrate is a GaN single crystal substrate, the chemical composition and crystal structure are the same as those of the lower confinement layer, resulting in a low dislocation density, and it will not crack or bend due to temperature changes.

[0015] The active layer refers to the material layer in a laser that generates laser light.

[0016] In some embodiments, the active layer can convert electrical energy into light energy.

[0017] In some embodiments, the active layer is an InGaN quantum well (QW) or a GaN quantum well.

[0018] The upper waveguide layer refers to the material layer located above the active layer, which is used to constrain and control the distribution of the optical field.

[0019] In some embodiments, the upper waveguide layer is an InGaN monolayer, a GaN monolayer, or a multilayer stacked structure composed of GaN and InGaN. For example, the upper waveguide layer can be one or more of the following: an InGaN monolayer structure, a GaN monolayer structure, a GaN / InGaN / GaN multilayer stacked structure, or an InGaN / GaN multilayer stacked structure.

[0020] As an example only, the upper waveguide layer can be a single InGaN structure, and the thickness of the upper waveguide layer can be 300~8000 angstroms.

[0021] The lower waveguide layer refers to the material layer located below the active layer, which is used to constrain and control the distribution of the optical field.

[0022] In some embodiments, the lower waveguide layer is a graded dielectric constant lower waveguide layer.

[0023] In some embodiments, the lower waveguide layer is an InGaN monolayer, a GaN monolayer, or a multilayer stacked structure composed of GaN and InGaN.

[0024] For example, the lower waveguide layer can be one or more of the following: InGaN single-layer structure, GaN single-layer structure, GaN / InGaN / GaN multilayer stacked structure, or InGaN / GaN multilayer stacked structure.

[0025] As an example only, the lower waveguide layer can be a combination of GaN / InGaN multilayer stacked structures, and the thickness of the lower waveguide layer can be 300~8000 angstroms.

[0026] In some embodiments, the gradient dielectric constant lower waveguide layer includes a first gradient dielectric constant lower waveguide layer and a second gradient dielectric constant lower waveguide layer. The first gradient dielectric constant lower waveguide layer and the second gradient dielectric constant lower waveguide layer form a radiative recombination coefficient variation angle γ2: 60°≤γ2≤120°. The second gradient dielectric constant lower waveguide layer and the active layer form a radiative recombination coefficient variation angle β2: 0°≤β2≤60°. The gradient dielectric constant upper waveguide layer and the active layer form a radiative recombination coefficient variation angle α2: 15°≤α2≤85°, and 0°≤β2≤α2≤γ2≤120°.

[0027] In some embodiments, the upper waveguide layer is a graded dielectric constant upper waveguide layer, and the lower waveguide layer is a graded dielectric constant lower waveguide layer.

[0028] Gradient dielectric constant upper waveguide layer and graded dielectric constant lower waveguide layer refer to material layers whose dielectric constant changes with the epitaxial growth direction.

[0029] In some embodiments, at least one of the following distributions in the gradient dielectric constant upper waveguide layer and the gradient dielectric constant lower waveguide layer exhibits a nonlinear continuous function distribution along the epitaxial growth direction: indium (In) ion intensity distribution, indium (In) atom concentration distribution, covalent bond energy distribution, dielectric constant distribution, and radiative recombination coefficient distribution.

[0030] In some embodiments, the In ion intensity distribution, In atom concentration distribution, covalent bond energy distribution, and dielectric constant distribution of the waveguide layer with graded dielectric constant satisfy the function distributions of ExpDecay1, ExpDecay2, ExpDecay3, or SGompertz, and the In ion intensity distribution, In atom concentration distribution, covalent bond energy distribution, and dielectric constant distribution of the waveguide layer with graded dielectric constant satisfy the function distribution of Slogistic1.

[0031] In ion intensity distribution is used to describe the relative strength of In ion signals at different times at the same depth.

[0032] Figure 2 This is a SIMS secondary ion mass spectrum of a gallium nitride-based semiconductor laser according to some embodiments of this specification.

[0033] In some embodiments, such as Figure 2 As shown, the In ion intensity distribution can be directly measured by a SIMS testing device.

[0034] In atom concentration distribution is used to describe the specific number of In atoms per unit volume.

[0035] In some embodiments, such as Figure 2 As shown, the In atom concentration distribution can be directly measured using a SIMS testing device.

[0036] ExpDecay1 refers to a single exponential decay function.

[0037] Figure 3 This is a fitted curve of the In ion intensity distribution or In atom concentration distribution and ExpDecay1 of a waveguide layer with a gradient dielectric constant shown in some embodiments of this specification.

[0038] In some embodiments, such as Figure 3 As shown, the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant satisfies the function distribution of ExpDecay1 as follows: In the formula, B is the steady-state value or background value, A is the initial amplitude, C is the offset, and D is the characteristic attenuation constant. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 2 × 10⁻⁶.17 ≤B≤2×10 26 -9×10 26 ≤A≤0, 2≤C≤20000, 10≤D≤10000.

[0039] Steady-state values ​​refer to the limiting values ​​at which physical quantities tend to remain constant as the epitaxial layer thickness increases. These physical quantities may include In ion strength, In atom concentration, covalent bond energy, and dielectric constant, among others.

[0040] Background value refers to the inherent physical quantity of the epitaxial layer material.

[0041] Initial amplitude refers to the maximum extent to which a physical quantity deviates from its background or steady-state value in the initial region of the epitaxial layer.

[0042] Offset refers to the translational distance of the function graph relative to the origin in the direction of epitaxial layer thickness growth.

[0043] The characteristic decay constant is a constant that describes how quickly a physical quantity decreases as the thickness increases.

[0044] Epitaxial layer thickness refers to the dimension between the starting interface and the ending interface of the epitaxial layer along the epitaxial growth direction.

[0045] ExpDecay2 refers to a double exponential decay function.

[0046] Figure 4 This is a fitted curve of the In ion intensity distribution or In atom concentration distribution and ExpDecay2 of the waveguide layer with a gradient dielectric constant shown in some embodiments of this specification.

[0047] In some embodiments, such as Figure 4 As shown, the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant satisfies the function distribution of ExpDecay2 as follows: In the formula, E is the steady-state value or background value, F is the amplitude of the first attenuation term, G is the offset of the first attenuation term, H is the first attenuation constant, J is the amplitude of the second attenuation term, K is the offset of the second attenuation term, and L is the second attenuation constant. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 2 × 10⁻⁶. 17 ≤E≤2×10 26 -9×10 26 ≤F≤0, 80≤G≤80000, 500≤H≤1000000, -9×10 26 ≤J≤0, 80≤K≤80000, 500≤L≤1000000.

[0048] The amplitude of the first decay term refers to the maximum change in the physical quantity of the first exponentially decaying term relative to the steady-state value or background value.

[0049] The offset of the first decay term refers to the horizontal shift of the first exponential decay term relative to the origin in the direction of epitaxial layer thickness.

[0050] The first decay constant refers to the characteristic constant of the first exponential decay term that changes with the increase of epitaxial layer thickness.

[0051] The amplitude of the second decay term refers to the maximum change in the physical quantity of the second exponential decay term relative to the steady-state value or background value.

[0052] The offset of the second attenuation term refers to the horizontal shift of the second exponential attenuation term relative to the origin in the direction of epitaxial layer thickness.

[0053] The second decay constant is a characteristic constant that refers to the second exponential decay term, which varies with the increase of epitaxial layer thickness.

[0054] ExpDecay3 refers to a triple-exponential decay function.

[0055] Figure 5 This is a fitted curve of the In ion intensity distribution or In atom concentration distribution on a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification, and ExpDecay3.

[0056] In some embodiments, such as Figure 5 As shown, the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant satisfies the function distribution of ExpDecay3 as follows: In the formula, M is the steady-state value or background value, N is the amplitude of the first attenuation term, P is the offset of the first attenuation term, Q is the first attenuation constant, R is the amplitude of the second attenuation term, S is the offset of the second attenuation term, T is the second attenuation constant, U is the amplitude of the third attenuation term, V is the offset of the third attenuation term, and W is the third attenuation constant. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 3 × 10⁻⁶. 17 ≤M≤3×10 26 -8×10 26 ≤N≤0, 0.8≤P≤8000, 0.2≤Q≤2000, -8×10 26 ≤R≤0, 0.8≤S≤8000, 0.2≤T≤2000, -8×10 26 ≤U≤0, 0.8≤V≤8000, 0.2≤W≤2000.

[0057] The amplitude of the third decay term refers to the maximum change in the physical quantity of the third exponential decay term relative to the steady-state value or background value.

[0058] The offset of the third decay term refers to the horizontal shift of the third exponential decay term relative to the origin of the coordinate system in the direction of epitaxial layer thickness.

[0059] The third decay constant refers to the characteristic constant of the third exponential decay term as the thickness of the epitaxial layer increases.

[0060] SGompertz refers to the Gompertz logic function.

[0061] Figure 6 This is a fitting curve of the In ion intensity distribution or In atom concentration distribution on a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification, and SGompertz.

[0062] In some embodiments, such as Figure 6 As shown, the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant satisfies the function distribution of SGompertz: In the formula, a is the saturation value, k is the growth rate constant, and b is the inflection point position parameter. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 6 × 10⁻⁶. 15 ≤a≤6×10 25 , 0.8≤k≤800, 0.008≤b≤800.

[0063] The saturation value refers to the maximum value that a physical quantity can reach as the thickness of the epitaxial layer increases.

[0064] The growth rate constant is a parameter that describes how quickly a physical quantity increases with the thickness of the epitaxial layer.

[0065] The inflection point location parameter refers to the coordinates of the point on the SGompertz fitted curve where the growth rate reaches its maximum value. For example, the inflection point location parameter can be the coordinates of the point on the SGompertz fitted curve where the second derivative of the fitted curve is zero.

[0066] Slogistic1 refers to the symmetric S-shaped growth function.

[0067] Figure 9 This is a fitting curve of the In ion intensity distribution or In atom concentration distribution of the waveguide layer under a gradient dielectric constant, as shown in some embodiments of this specification, and Slogistic1.

[0068] In some embodiments, such as Figure 9As shown, the In ion intensity distribution or In atom concentration distribution of the waveguide layer under a graded dielectric constant satisfies the function distribution of Slogistic1: In the formula, p is the saturation value, q is the growth rate constant, and r is the inflection point position parameter. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 2 × 10⁻⁶. 15 ≤p≤2×10 25 -20000≤q≤0, 0.001≤r≤100.

[0069] In some embodiments of this specification, the lower waveguide layer adopts a Slogistic1 symmetric logic distribution, and the upper waveguide layer adopts an ExpDecay or SGompertz distribution. This ensures a smooth and stable transition of components from the initial interface to the steady state, avoiding early lattice deformation in the lower structure. This combination of "asymmetric gradients" can precisely control the barrier height on both sides of the quantum well. While ensuring efficient carrier injection, it optimizes the near-field mode through asymmetric refractive index distribution, reducing mode leakage.

[0070] Covalent bond energy distribution refers to the distribution of energy between adjacent atoms through covalent bonds across different epitaxial layer thicknesses. The covalent bond energy distribution of waveguide layers with graded dielectric constants can be referenced... Figure 12 As shown.

[0071] Figure 7 This is a fitting curve of the covalent bond energy distribution and ExpDecay1 of a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification.

[0072] In some embodiments, such as Figure 7 As shown, the covalent bond energy distribution of the waveguide layer with graded dielectric constant satisfies the function distribution of ExpDecay1 as follows: In the formula, c is the steady-state value or background value, d is the initial amplitude, f is the offset, and g is the characteristic attenuation constant. The dependent variable is the covalent bond energy of the waveguide layer with a graded dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: -4000≤c≤0, 0.02≤d≤2000, 15≤f≤15000, 15≤g≤15000.

[0073] The characteristic decay constant is a parameter that describes how the energy of a covalent bond changes with the independent variable.

[0074] The covalent bond energy distribution of waveguide layers with graded dielectric constants can be referenced. Figure 12 As shown.

[0075] The Boltzmann function is an alternative sigmoid function to the Slogistic1 function.

[0076] Figure 10 This is a graph showing the covalent bond energy distribution of a waveguide layer with a gradient dielectric constant and the Boltzmann fitting curve, according to some embodiments of this specification.

[0077] In some embodiments, such as Figure 10 As shown, the covalent bond energy distribution of the waveguide layer under graded dielectric constant satisfies the Boltzmann function distribution as follows: In the formula, For high steady-state values, Here, t represents the low steady-state value, t is the midpoint parameter of the transition, and u is the transition rate parameter. The dependent variable is the covalent bond energy of the waveguide layer with a graded dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: 0.02 ≤ ≤2000, 0.02≤ ≤2000, 0.01≤t≤1000, 8×10 -8 ≤u≤800.

[0078] A high steady-state value refers to a constant plateau value where the covalent bond energy reaches a relatively high level in the fitted curve. A constant plateau is a segment of the fitted curve where it no longer rises or falls.

[0079] The low steady-state value refers to the constant plateau value of the covalent bond energy on the lower side of the fitted curve.

[0080] The transition midpoint parameter refers to the epitaxial layer thickness coordinate value at the midpoint between the low steady-state value and the high steady-state value.

[0081] The transition rate parameter is a parameter that describes the degree of drastic switching of covalent bond energy between low and high steady-state values.

[0082] In some embodiments, the gradient dielectric constant lower waveguide layer includes a first gradient dielectric constant lower waveguide layer and a second gradient dielectric constant lower waveguide layer. The first and second gradient dielectric constant lower waveguide layers form a covalent bond energy variation trend angle γ1: 60°≤γ1≤120°. The second gradient dielectric constant lower waveguide layer and the active layer form a covalent bond energy variation trend angle β1: 0°≤β1≤60°. The gradient dielectric constant upper waveguide layer and the active layer form a covalent bond energy variation trend angle α1: 15°≤α1≤85°, and 0°≤β1≤α1≤γ1≤120°.

[0083] Understandably, by constructing an asymmetric gradient trend angle from the inside out, the smooth injection of charge carriers is prioritized at the active layer interface to reduce the turn-on voltage. At the same time, the asymmetric slope of the upper and lower waveguide layers is used to shift the center of the optical field towards the low-loss region. Finally, the high-slope inflection point inside the waveguide is combined to coordinate the strong confinement of the optical field and the effective release of the heterojunction stress.

[0084] In some embodiments of this specification, microscopic quantitative management of the stress distribution within the epitaxial layer is achieved by functionalizing the covalent bond energy distribution. The application of ExpDecay and SGompertz functions in the upper waveguide layer results in a gradual bond energy release with time- or thickness-dependent characteristics, preventing explosive stress concentration at the interface. The lower waveguide layer employs the Boltzmann function, which utilizes its classic bistable switching characteristics to establish an extremely stable energy transition plateau between the substrate and the active region. This design significantly improves the surface flatness of the epitaxial wafer, providing an excellent interface environment for subsequent high-strength, high-quality quantum well growth.

[0085] Dielectric constant distribution refers to the distribution of dielectric constant across different epitaxial layer thicknesses.

[0086] The dielectric constant distribution of the waveguide layer with graded dielectric constant can be found in [reference]. Figure 13 As shown.

[0087] Figure 8 This is a graph showing the dielectric constant distribution of a waveguide layer with a gradient dielectric constant and the fitting curve of ExpDecay1, based on some embodiments of this specification.

[0088] In some embodiments, such as Figure 8 As shown, the dielectric constant distribution of the waveguide layer with graded dielectric constant satisfies the function distribution of ExpDecay1 as follows: In the formula, h is the steady-state value or background value, j is the initial amplitude, m is the offset, and n is the characteristic attenuation constant. The dependent variable is the dielectric constant of the waveguide layer with a gradient dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: 2≤h≤20000, -8000≤j≤0, 15≤m≤15000, and 15≤n≤15000.

[0089] The dielectric constant distribution of waveguide layers with graded dielectric constants can be found in [reference needed]. Figure 13 As shown.

[0090] Figure 11 This is a graph showing the dielectric constant distribution of a waveguide layer with a gradient dielectric constant, and the Boltzmann fitting curve, according to some embodiments of this specification.

[0091] In some embodiments, such as Figure 11 As shown, the dielectric constant distribution of the waveguide layer under graded dielectric constants satisfies the Boltzmann function distribution as follows: In the formula, For high steady-state values, Here, w represents the low steady-state value, w is the midpoint transition parameter, and i is the transition rate parameter. The dependent variable is the dielectric constant of the waveguide layer with a graded dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: 0.09 ≤ ≤9000, 0.08≤ ≤8000, 0.01≤w≤1000, 8×10 -8 ≤i≤800.

[0092] In some embodiments, the gradient dielectric constant lower waveguide layer includes a first gradient dielectric constant lower waveguide layer and a second gradient dielectric constant lower waveguide layer. The first and second gradient dielectric constant lower waveguide layers form a dielectric constant variation trend angle ρ1: 60°≤ρ1≤120°. The second gradient dielectric constant lower waveguide layer 102b forms a covalent bond energy variation trend angle σ1 with the active layer: 0°≤σ1≤60°. The gradient dielectric constant upper waveguide layer forms a covalent bond energy variation trend angle θ1 with the active layer: 15°≤θ1≤85°, and 0°≤σ1≤θ1≤ρ1≤120°.

[0093] In some embodiments of this specification, the functional constraint of the dielectric constant distribution directly optimizes the optical waveguide characteristics of the laser. Employing different nonlinear functions for the upper and lower waveguide layers not only eliminates interface scattering losses during photon propagation but also achieves controlled optical field shifting by controlling the transition parameters of functions such as Boltzmann, effectively avoiding severe optical absorption problems. This significantly improves the laser's slope efficiency and reduces the threshold current density.

[0094] In some embodiments, the In ion intensity distribution, In atom concentration distribution, and radiative recombination coefficient distribution of the waveguide layer with graded dielectric constant satisfy the functional distributions of GaussAmp, InvsPoly, or Hill, and the In ion intensity distribution, In atom concentration distribution, and radiative recombination coefficient distribution of the waveguide layer with graded dielectric constant satisfy the functional distribution of BiDoseResp.

[0095] GaussAmp refers to the Gaussian amplitude function.

[0096] Figure 14This is a fitting curve of the In ion intensity distribution or In atom concentration distribution and Gauss Amp of a waveguide layer with a gradient dielectric constant shown in some embodiments of this specification.

[0097] In some embodiments, such as Figure 14 As shown, the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant satisfies the Gauss-Amp function distribution as follows: In the formula, Baseline value, Peak amplitude: the maximum height of the Gaussian peak. The peak center location: the center of symmetry of the Gaussian peak. To broaden the parameters: control the width of the Gaussian peak. The larger the peak, the wider it is. The smaller the peak, the sharper the peak. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: -3 × 10⁻⁶ 25 ≤ ≤0, 8×10 15 ≤ ≤8×10 26 0.022≤ ≤2000, 0.007≤ ≤7000.

[0098] The baseline value refers to the basic reference value of physical quantities in the epitaxial layer region when they are not modulated by a function.

[0099] InvsPoly refers to the inverse polynomial function.

[0100] As an example only, the In ion intensity distribution or In atom concentration distribution in a waveguide layer with a graded dielectric constant satisfies the Gauss-Amp function distribution as follows: .

[0101] Figure 15 This is a fitted curve of In ion intensity distribution or In atom concentration distribution on a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification, and Invspoly.

[0102] In some embodiments, such as Figure 15 As shown, the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant satisfies the InvsPoly function distribution as follows: In the formula, Baseline value, Peak amplitude: the maximum height of the peak. Peak center location: the center of symmetry of the curve. Peak width parameter: controls the overall width of the peak. The larger the peak, the wider it is. The smaller the peak, the narrower it is. , , For polynomial coefficients: the peak shape is adjusted by quadratic, quartic, and sixth-degree terms respectively. The steepness of the dominant peak: The larger the peak, the steeper its sides; , "Tail decay" of the dominant peak: , The larger the peak value, the slower the peak tail decays. = =0, the function degenerates into an inverse quadratic function. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where -1 × 10⁻⁶. 25 ≤ ≤0, 6×10 15 ≤ ≤6×10 26 0.001≤ ≤1000, 0.006≤ ≤6000, 0.002≤ ≤2000, -20≤ ≤20, 0.009≤ ≤9000.

[0103] As an example only, the In ion intensity distribution or In atom concentration distribution in a waveguide layer with a graded dielectric constant satisfies the InvsPoly function distribution as follows: .

[0104] Hill refers to the Hill function.

[0105] Figure 16 This is a fitted curve of the In ion intensity distribution or In atom concentration distribution on a waveguide layer with a gradient dielectric constant, as shown in some embodiments of this specification, and Hill.

[0106] In some embodiments, such as Figure 16 As shown, the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant satisfies Hill's functional distribution as follows: In the formula, This is the saturated response value. Synergy coefficient: This coefficient modulates the "steepness" and synergy of the response curve. It is the half-saturation constant. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 4 × 10⁻⁶. 15 ≤ ≤4×10 25 , 0≤ ≤1500, 0.0008≤ ≤800.

[0107] As an example only, the In ion intensity distribution or In atom concentration distribution in a waveguide layer with a graded dielectric constant satisfies Hill's functional distribution as follows: .

[0108] The saturation response value refers to the maximum limit value of the fitted curve as the thickness of the epitaxial layer increases.

[0109] The synergy coefficient is a parameter that describes the nonlinear steepness and sensitivity of the fitted curve.

[0110] The half-saturation constant refers to the coordinate value of the epitaxial layer thickness corresponding to the fitted curve when the physical quantity reaches half of the saturation response value.

[0111] BiDoseResp refers to the Biphasic Dose Response Function.

[0112] Figure 20 This is a fitted curve of the In ion intensity distribution or In atom concentration distribution and BiDoseResp of the waveguide layer under a gradient dielectric constant, as shown in some embodiments of this specification.

[0113] In some embodiments, such as Figure 20 As shown, the In ion intensity distribution or In atom concentration distribution of the waveguide layer under graded dielectric constant satisfies the function distribution of BiDoseResp as follows: In the formula, Baseline background value, The maximum response amplitude of branch 1, For branch 1, the weighting coefficient is... The half-effect dose of the branch circuit, For the slope factor of branch 1: control the steepness of the S-curve of branch 1. The maximum response amplitude of branch 2, The half-effect dose of branch 2, For the slope factor of branch 2 response: control the steepness of the curve of branch 2. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: -3 × 10⁻⁶ 25 ≤ ≤0, 0.00001≤ ≤1000, -1000≤ ≤0, 2×10 15 ≤ ≤2×10 25 2×10 15 ≤ ≤2×10 25 0.0009≤ ≤9000, -50000≤ ≤0, 0≤ ≤80000.

[0114] As an example only, the In ion intensity distribution or In atom concentration distribution in the waveguide layer under a graded dielectric constant satisfies the function distribution of BiDoseResp as follows: .

[0115] In some embodiments of this specification, higher-order composite functions such as GaussAmp, InvsPoly, and Hill are introduced to constrain the In ion intensity distribution and In atom concentration distribution, representing a higher level of simulation and control over complex interface behavior. Compared to the basic sigmoid curve, the synergistic coefficient of the Hill function can simulate the rapid saturation "abrupt" growth, while GaussAmp can accurately describe local component pulses. The lower waveguide layer employs the BiDoseResp biphase function, simultaneously performing the dual functions of "interface protection" and "body constraint" within the same layer, greatly expanding the design freedom of the device when dealing with complex bandgap engineering.

[0116] The radiative recombination coefficient distribution is a parameter characterizing the ability of electrons to generate photons through stimulated or spontaneous emission in the active layer, upper waveguide layer, or lower waveguide layer. The radiative recombination coefficient distribution of a graded dielectric constant upper waveguide layer can be found in [reference needed]. Figure 22 As shown.

[0117] Figure 17 The graph shows the distribution of the radiative recombination coefficient of a waveguide layer with a gradient dielectric constant and the fitting curve of Gauss Amp, based on some embodiments of this specification.

[0118] In some embodiments, such as Figure 17 As shown, the radiative recombination coefficient distribution of the waveguide layer with graded dielectric constant satisfies the Gauss-Amp function distribution as follows: In the formula, Baseline value, Peak amplitude: the maximum height of the Gaussian peak. The peak center location: the center of symmetry of the Gaussian peak. For broadening parameters: control the width of the Gaussian peak. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where: 4 × 10⁻⁶. -20 ≤ ≤4×10 -5 2×10 -20 ≤ ≤2×10 -10 0.002≤ ≤2000, 0.006≤ ≤6000.

[0119] As an example only, the distribution of the radiative recombination coefficient of a waveguide layer with a graded dielectric constant satisfies the Gauss-Amp function distribution as follows: .

[0120] Figure 18 This is a graph showing the distribution of the radiative recombination coefficient of a waveguide layer with a gradient dielectric constant and the fitting curve of Invspoly, based on some embodiments of this specification.

[0121] In some embodiments, such as Figure 18 As shown, the radiative recombination coefficient distribution of the waveguide layer with graded dielectric constant satisfies the InvsPoly function distribution as follows: In the formula, The baseline value is R, where R is the peak amplitude: the maximum height of the peak. Peak center location: the center of symmetry of the curve. Peak width parameter: controls the overall width of the peak. The larger the peak, the wider it is. The smaller the peak, the narrower it is. , , For polynomial coefficients: the peak shape is adjusted by quadratic, quartic, and sixth-degree terms respectively. The steepness of the dominant peak: The larger the peak, the steeper its sides; , "Tail decay" of the dominant peak: , The larger the peak size, the slower the peak tail decays (broad-tailed peak); = =0, the function degenerates into an inverse quadratic function. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where: 4 × 10⁻⁶. -20 ≤ ≤4×10 -5 1×10 -22 ≤ ≤1×10 -2 0.0001≤ ≤1000, 0.0005≤ ≤5000, 0.002≤ ≤2000, -20≤ ≤20, 0.009≤ ≤9000.

[0122] As an example only, the distribution of the radiative recombination coefficient of a waveguide layer with a graded dielectric constant satisfies the InvsPoly function distribution as follows: .

[0123] Figure 19 This is a fitted curve of the radiative recombination coefficient of the waveguide layer with a gradient dielectric constant and Hill, as shown in some embodiments of this specification.

[0124] In some embodiments, such as Figure 19 As shown, the radiative recombination coefficient distribution of the waveguide layer with graded dielectric constant satisfies Hill's functional distribution: In the formula, This is the saturated response value. Synergy coefficient: This coefficient modulates the "steepness" and synergy of the response curve. It is the half-saturation constant. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where 8 × 10⁻⁶. -20 ≤ ≤8×10 -2 0.000008≤ ≤800, 1×10 4 ≤ ≤1×10 24 .

[0125] As an example only, the radiative recombination coefficient distribution of a waveguide layer with a graded dielectric constant satisfies Hill's functional distribution as follows: .

[0126] The distribution of the radiative recombination coefficient of waveguide layers with graded permittivity can be found in [reference needed]. Figure 22 As shown.

[0127] Figure 21 This is a graph showing the distribution of the radiative recombination coefficient of a waveguide layer with a graded dielectric constant and the fitting curve of BiDoseResp, based on some embodiments of this specification.

[0128] In some embodiments, such as Figure 21 As shown, the radiative recombination coefficient distribution of the waveguide layer under graded dielectric constant satisfies the function distribution of BiDoseResp as follows: In the formula, Baseline background value, The maximum response amplitude of branch 1, For branch 1, the weighting coefficient is... The half-effect dose of the branch circuit, For the slope factor of branch 1: control the steepness of the S-curve of branch 1. This represents the maximum response amplitude of branch 2. The half-effect dose of branch 2, For the slope factor of branch 2 response: control the steepness of the curve of branch 2. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where: -4 × 10⁻⁴ 25 ≤ ≤0, 9×10 -23 ≤ ≤9×10 -3 0.0009≤ ≤900, 0.0002≤ ≤200, -50000≤ ≤0, 9×10 -23 ≤ ≤9×10 -3 -2×10 19 ≤ ≤0, 0≤ ≤80000.

[0129] As an example only, the radiative recombination coefficient distribution of a waveguide layer with graded dielectric constant satisfies the function distribution of BiDoseResp as follows: .

[0130] In some embodiments, the gradient dielectric constant lower waveguide layer includes a first gradient dielectric constant lower waveguide layer and a second gradient dielectric constant lower waveguide layer. The first gradient dielectric constant lower waveguide layer and the second gradient dielectric constant lower waveguide layer form a radiative recombination coefficient variation angle γ2: 60°≤γ2≤120°. The second gradient dielectric constant lower waveguide layer and the active layer form a radiative recombination coefficient variation angle β2: 0°≤β2≤60°. The gradient dielectric constant upper waveguide layer and the active layer form a radiative recombination coefficient variation angle α2: 15°≤α2≤85°, and 0°≤β2≤α2≤γ2≤120°.

[0131] In some embodiments of this specification, by controlling the spatial distribution of the radiative recombination coefficient using functions such as GussAmp, the point of highest luminous efficiency can be precisely located in the region with the highest carrier injection density. The application of the BiDoseResp function in the lower waveguide layer achieves secondary blocking of hole overflow through a double-step distribution. This deep electro-optical synchronization optimization design effectively suppresses the Droop effect, enabling the laser to maintain linearly increasing optical output even under high current.

[0132] An electron blocking layer is a thin layer of high-bandgap material located between the active layer and the upper waveguide layer.

[0133] In some embodiments, the electron blocking layer can block electrons within the active region.

[0134] In some embodiments, the electron blocking layer is any one or any combination of AlGaN, GaN, InGaN, AlInGaN, or AlN.

[0135] As an example only, the electron blocking layer can be AlGaN with a thickness of 5 to 800 angstroms.

[0136] The upper limit layer refers to the material layer located above the active layer, with a refractive index lower than that of the upper waveguide layer and the active layer.

[0137] In some embodiments, the upper confinement layer can confine the light field to the active layer, preventing light leakage from the top of the gallium nitride-based semiconductor laser.

[0138] In some embodiments, the upper confinement layer is any one or any combination of AlGaN, AlN, GaN, AlInN, or AlInGaN.

[0139] As an example only, the upper confinement layer can be a combination of AlGaN / AlGaN with a thickness of 500~9000 angstroms.

[0140] The lower confinement layer refers to a material layer located below the active layer, with a refractive index lower than that of the lower waveguide layer and the active layer.

[0141] In some embodiments, the lower confinement layer can confine the light field to the active layer, preventing light leakage from the bottom of the gallium nitride-based semiconductor laser.

[0142] In some embodiments, the lower confining layer is any one or any combination of AlGaN, GaN, AlN, InGaN, AlInGaN, or AlInN.

[0143] As an example only, the lower confinement layer can be an AlGaN / AlGaN combination with a thickness of 5000~50000 angstroms.

[0144] It is understandable that by designing the fitting curves of the In ion intensity distribution or In atom concentration distribution in the waveguide layer with a graded dielectric constant to satisfy any one of the distributions ExpDecay1, ExpDecay2, ExpDecay3, and SGompertz, and by making the fitting curves of the covalent bond energy distribution satisfy any one of the distributions ExpDecay1, ExpDecay2, ExpDecay3, and SGompertz, the bond energy distribution, defect formation energy distribution, and probability distribution of bond breakage-induced defects and dislocations in the laser waveguide layer can be controlled. This, in turn, controls the fitting curves of the dielectric constant (including relative dielectric constant and static relative dielectric constant) to satisfy any one of the distributions ExpDecay1, ExpDecay2, ExpDecay3, and SGompertz. Simultaneously, the In ion intensity distribution in the waveguide layer under a graded dielectric constant can also be designed. Alternatively, the fitting curve of the In atom concentration distribution satisfies the Slogistic 1 function distribution, making the fitting curve of the covalent bond energy distribution of the waveguide layer under the graded dielectric constant satisfy the Boltzmann function distribution. This allows for the modulation of the dielectric constant fitting curve to satisfy the Boltzmann function distribution, thereby controlling the optical field confinement factor of the laser waveguide layer. This controls the laser's transverse (in-substrate plane) and longitudinal (substrate normal) optical fields, such as the horizontal optical field confinement of the ridge waveguide and the vertical optical field confinement of the quantum well and cladding. This achieves optical field confinement, enhances optical field confinement, reduces optical field mode leakage loss, and improves far-field beam quality. Simultaneously, it modulates the junction capacitance between the waveguide layer and the active layer, modulating the laser's modulation rate and dynamic response, reducing the defect-induced decrease in dielectric constant of the active layer and waveguide layer, suppressing current accumulation and congestion in the active layer and waveguide layer, and reducing device aging and optical decay. Based on the above gallium nitride-based semiconductor laser design, the differences between gallium nitride-based semiconductor lasers and traditional lasers can be shown in Table 1 below through experimental comparison. Table 1 It should be noted that nitride semiconductor lasers have the following problems: Internal optical absorption losses include impurity absorption loss, carrier absorption loss, waveguide sidewall scattering loss, and quantum well absorption loss. High impurity absorption loss in the optical waveguide, inherent carbon impurities in p-type semiconductors can compensate for acceptor loss and disrupt p-type structure, and the low ionization rate of p-type doping (below 10%) results in a large amount of unionized Mg acceptor impurities (above 90%) generating a self-compensation effect and increasing internal optical losses, leading to decreased laser slope efficiency and increased threshold current. Lattice mismatch and large strain in the active layer induce a strong piezoelectric polarization effect, producing a strong QCSE (quantum confinement) Stark effect, causing band tilt in the quantum well, increasing the valence band step difference, suppressing hole injection, making hole transport in the quantum well more difficult, resulting in non-uniform carrier injection, and reducing the probability of electron-hole wavefunction overlap. This leads to non-uniform laser gain, decreased radiative recombination efficiency, and limits the improvement of laser electro-lasing gain.

[0145] This specification designs a SIMS test fitting curve for the In ion intensity distribution or In atom concentration distribution of the upper waveguide layer with a graded dielectric constant to satisfy any one of the Gauss Amp, InvsPoly, or Hill function distributions. This ensures that the fitting curve for the radiative recombination coefficient distribution of the laser epitaxial waveguide layer satisfies any one of the Gauss Amp, InvsPoly, or Hill function distributions. This achieves efficient matching of spatially modulated carrier distribution, quantum recombination, and optical field in the gallium nitride laser epitaxial layer, thereby guiding electrons and holes to converge into the quantum well, reducing the probability of carriers escaping to the upper and lower confinement layers, suppressing electron and hole leakage, reducing non-radiative recombination such as Auger recombination and defect recombination in the upper and lower waveguide layers, and improving carrier injection efficiency. Simultaneously, a graded dielectric constant is designed... The SIMS test fitting curves of the In ion intensity distribution or In atom concentration distribution in the lower waveguide layer satisfy the BiDoseResp function distribution. This ensures that the fitting curve of the radiative recombination coefficient distribution in the waveguide layer with a graded dielectric constant also satisfies the BiDoseResp function distribution. By controlling quantum recombination and matching the optical field, the optical field mode center coincides with the active region, reducing mode field penetration into the high-loss upper and lower confinement layers, lowering the optical absorption loss of the electron blocking layer and upper confinement layer, and improving the laser's optical power and slope efficiency. Through the design of the radiative recombination coefficient distribution in the upper and lower waveguide layers, carrier, quantum recombination, and optical field are efficiently localized, improving laser gain. This efficiently localizes carriers and the optical field in the active layer (quantum well), while suppressing non-radiative recombination and absorption loss in the waveguide region, further improving threshold current, slope efficiency, and reliability. Based on the above gallium nitride-based semiconductor laser design, the differences between gallium nitride-based semiconductor lasers and traditional lasers can be shown in Table 2 below. Table 2 The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A gallium nitride-based semiconductor laser with a gradient dielectric constant waveguide layer, characterized in that, The gallium nitride-based semiconductor laser comprises, from bottom to top, a substrate, a lower confinement layer, a lower waveguide layer, an active layer, an upper waveguide layer, an electron blocking layer, and an upper confinement layer. The upper waveguide layer is a graded dielectric constant upper waveguide layer, and the lower waveguide layer is a graded dielectric constant lower waveguide layer. At least one of the following distributions in the graded dielectric constant upper and lower waveguide layers—the indium (In) ion intensity distribution, the indium (In) atom concentration distribution, the covalent bond energy distribution, the dielectric constant distribution, and the radiative recombination coefficient distribution—exhibits a nonlinear continuous function distribution along the epitaxial growth direction.

2. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 1, characterized in that, The In ion intensity distribution, In atom concentration distribution, covalent bond energy distribution, and dielectric constant distribution of the waveguide layer with the graded dielectric constant satisfy a function distribution of ExpDecay1, ExpDecay2, ExpDecay3, or SGompertz; the In ion intensity distribution, In atom concentration distribution, covalent bond energy distribution, and dielectric constant distribution of the waveguide layer with the graded dielectric constant satisfy a function distribution of Slogistic1.

3. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 2, characterized in that, The In ion intensity distribution or In atom concentration distribution of the waveguide layer with the graded dielectric constant satisfies the function distribution of ExpDecay1 as follows: In the formula, B is the steady-state value or background value, A is the initial amplitude, C is the offset, and D is the characteristic attenuation constant. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 2 × 10⁻⁶. 17 ≤B≤2×10 26 -9×10 26 ≤A≤0, 2≤C≤20000, 10≤D≤10000; The In ion intensity distribution or In atom concentration distribution of the waveguide layer with the graded dielectric constant satisfies the function distribution of ExpDecay2 as follows: In the formula, E is the steady-state value or background value, F is the amplitude of the first attenuation term, G is the offset of the first attenuation term, H is the first attenuation constant, J is the amplitude of the second attenuation term, K is the offset of the second attenuation term, and L is the second attenuation constant. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 2 × 10⁻⁶. 17 ≤E≤2×10 26 -9×10 26 ≤F≤0, 80≤G≤80000, 500≤H≤1000000, -9×10 26 ≤J≤0, 80≤K≤80000, 500≤L≤1000000; The In ion intensity distribution or In atom concentration distribution of the waveguide layer with the graded dielectric constant satisfies the function distribution of ExpDecay3 as follows: In the formula, M is the steady-state value or background value, N is the amplitude of the first attenuation term, P is the offset of the first attenuation term, Q is the first attenuation constant, R is the amplitude of the second attenuation term, S is the offset of the second attenuation term, T is the second attenuation constant, U is the amplitude of the third attenuation term, V is the offset of the third attenuation term, and W is the third attenuation constant. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 3 × 10⁻⁶. 17 ≤M≤3×10 26 -8×10 26 ≤N≤0, 0.8≤P≤8000, 0.2≤Q≤2000, -8×10 26 ≤R≤0, 0.8≤S≤8000, 0.2≤T≤2000, -8×10 26 ≤U≤0, 0.8≤V≤8000, 0.2≤W≤2000; The In ion intensity distribution or In atom concentration distribution of the waveguide layer with the graded dielectric constant satisfies the function distribution of the SGompertz equation: In the formula, a is the saturation value, k is the growth rate constant, and b is the inflection point position parameter. The dependent variable is the In ion intensity distribution or In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 6 × 10⁻⁶. 15 ≤a≤6×10 25 , 0.8≤k≤800, 0.008≤b≤800; The In ion intensity distribution or In atom concentration distribution of the waveguide layer under the graded dielectric constant satisfies the Slogistic 1 function distribution as follows: In the formula, p is the saturation value, q is the growth rate constant, r is the inflection point position parameter, y5 is the dependent variable: In ion strength, or In atom concentration distribution, and x is the independent variable: epitaxial layer thickness, where: 2 × 10 15 ≤p≤2×10 25 -20000≤q≤0, 0.001≤r≤100; The covalent bond energy distribution of the waveguide layer with the graded dielectric constant satisfies the function distribution of ExpDecay1 as follows: In the formula, c is the steady-state value or background value, d is the initial amplitude, f is the offset, and g is the characteristic attenuation constant. The dependent variable is the covalent bond energy of the waveguide layer with a graded dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: -4000≤c≤0, 0.02≤d≤2000, 15≤f≤15000, 15≤g≤15000; The covalent bond energy distribution of the waveguide layer under the graded dielectric constant satisfies the Boltzmann function distribution as follows: In the formula, For high steady-state values, Here, t represents the low steady-state value, t is the midpoint parameter of the transition, and u is the transition rate parameter. The dependent variable is the covalent bond energy of the waveguide layer with a graded dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: 0.02 ≤ ≤2000, 0.02≤ ≤2000, 0.01≤t≤1000, 8×10 -8 ≤u≤800; The dielectric constant distribution of the waveguide layer with the graded dielectric constant satisfies the functional distribution of ExpDecay1 as follows: In the formula, h is the steady-state value or background value, j is the initial amplitude, m is the offset, and n is the characteristic attenuation constant. The dependent variable is the dielectric constant of the waveguide layer with a graded dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: 2≤h≤20000, -8000≤j≤0, 15≤m≤15000, 15≤n≤15000; The dielectric constant distribution of the waveguide layer with the graded dielectric constant satisfies the Boltzmann function distribution as follows: In the formula, For high steady-state values, Here, w represents the low steady-state value, w is the midpoint transition parameter, and i is the transition rate parameter. The dependent variable is the dielectric constant of the waveguide layer with a graded dielectric constant, and the independent variable is the thickness of the epitaxial layer, where: 0.09 ≤ ≤9000, 0.08≤ ≤8000, 0.01≤w≤1000, 8×10 -8 ≤i≤800.

4. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 1, characterized in that, The graded dielectric constant lower waveguide layer includes a first graded dielectric constant lower waveguide layer and a second graded dielectric constant lower waveguide layer. The angle γ1 between the covalent bond energy variation trends of the first graded dielectric constant waveguide layer and the second graded dielectric constant waveguide layer is: 60°≤γ1≤120°. The angle β1 between the covalent bond energy variation trend of the waveguide layer and the active layer under the second graded dielectric constant is: 0°≤β1≤60°. The angle α1 between the covalent bond energy variation trend of the waveguide layer and the active layer with the gradient dielectric constant is 15°≤α1≤85°, and 0°≤β1≤α1≤γ1≤120°.

5. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 1, characterized in that, The graded dielectric constant lower waveguide layer includes a first graded dielectric constant lower waveguide layer and a second graded dielectric constant lower waveguide layer. The angle ρ1 between the dielectric constant variation trends of the first graded dielectric constant lower waveguide layer and the second graded dielectric constant lower waveguide layer is: 60°≤ρ1≤120°. The second graded dielectric constant waveguide layer and the active layer form an angle σ1 with the dielectric constant variation trend: 0°≤σ1≤60°. The gradient dielectric constant upper waveguide layer and the active layer form an angle θ1 between their dielectric constants: 15°≤θ1≤85°, and 0°≤σ1≤θ1≤ρ1≤120°.

6. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 1, characterized in that, The In ion intensity distribution, In atom concentration distribution, and radiative recombination coefficient distribution of the waveguide layer with the graded dielectric constant satisfy the functional distributions of GaussAmp, InvsPoly, or Hill; the In ion intensity distribution, In atom concentration distribution, and radiative recombination coefficient distribution of the waveguide layer with the graded dielectric constant satisfy the functional distribution of BiDoseResp.

7. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 6, characterized in that, The In ion intensity distribution or In atom concentration distribution of the waveguide layer with the graded dielectric constant satisfies the GaussAmp function distribution as follows: In the formula, Baseline value, Peak amplitude: the maximum height of the Gaussian peak. The peak center location: the center of symmetry of the Gaussian peak. To broaden the parameters: control the width of the Gaussian peak. The larger the peak, the wider it is. The smaller the peak, the sharper the peak. The dependent variable is the In ion intensity distribution or the In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: -3 × 10⁻⁶. 25 ≤ ≤0, 8×10 15 ≤ ≤8×10 26 0.022≤ ≤2000, 0.007≤ ≤7000; The In ion intensity distribution or In atom concentration distribution of the waveguide layer under the graded dielectric constant satisfies the function distribution of BiDoseResp as follows: In the formula, Baseline background value, This represents the maximum response amplitude of branch 1. For branch 1, the weighting coefficient is... The half-effect dose of the branch circuit, For the slope factor of branch 1: control the steepness of the S-curve of branch 1. This represents the maximum response amplitude of branch 2. The half-effect dose of branch 2, For the slope factor of branch 2 response: control the steepness of the curve of branch 2. The dependent variable is the In ion intensity distribution or the In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: -3 × 10⁻⁶. 25 ≤ ≤0, 0.00001≤ ≤1000, -1000≤ ≤0, 2×10 15 ≤ ≤2×10 25 2×10 15 ≤ ≤2×10 25 0.0009≤ ≤9000, -50000≤ ≤0, 0≤ ≤80000; The In ion intensity distribution or In atom concentration distribution of the waveguide layer with the graded dielectric constant satisfies the InvsPoly function distribution as follows: In the formula, Baseline value, Peak amplitude: the maximum height of the peak. Peak center location: the center of symmetry of the curve. Peak width parameter: controls the overall width of the peak. The larger the peak, the wider it is. The smaller the peak, the narrower it is. , , For polynomial coefficients: the peak shape is adjusted by quadratic, quartic, and sixth-degree terms respectively. The "steepness" of the dominant peak: The larger the peak, the steeper its sides; , "Tail decay" of the dominant peak: , The larger the peak value, the slower the peak tail decays. = =0, the function degenerates into an inverse quadratic function. The dependent variable is the In ion intensity distribution or the In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: -1×10 25 ≤ ≤0, 6×10 15 ≤ ≤6×10 26 0.001≤ ≤1000, 0.006≤ ≤6000, 0.002≤ ≤2000, -20≤ ≤20, 0.009≤ ≤9000; The In ion intensity distribution or In atom concentration distribution of the waveguide layer with the graded dielectric constant satisfies the functional distribution of Hill as follows: In the formula, This is the saturated response value. Synergy coefficient: This coefficient modulates the "steepness" and synergy of the response curve. It is the half-saturation constant. The dependent variable is the In ion intensity distribution or the In atom concentration distribution, and the independent variable is the epitaxial layer thickness, where: 4 × 10⁻⁶. 15 ≤ ≤4×10 25 , 0≤ ≤1500, 0.0008≤ ≤800; The radiative recombination coefficient distribution of the waveguide layer with the graded dielectric constant satisfies the Gauss Amp function distribution as follows: In the formula, Baseline value, Peak amplitude: the maximum height of the Gaussian peak. The peak center location: the center of symmetry of the Gaussian peak. For broadening parameters: control the width of the Gaussian peak. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where: 4 × 10⁻⁶. -20 ≤ ≤4×10 -5 2×10 -20 ≤ ≤2×10 -10 0.002≤ ≤2000, 0.006≤ ≤6000; The radiative recombination coefficient distribution of the waveguide layer with the graded dielectric constant satisfies the functional distribution of BiDoseResp as follows: In the formula, Baseline background value, This represents the maximum response amplitude of branch 1. For branch 1, the weighting coefficient is... The half-effect dose of the branch circuit, For the slope factor of branch 1: control the steepness of the S-curve of branch 1. This represents the maximum response amplitude of branch 2. The half-effect dose of branch 2, For the slope factor of branch 2 response: control the steepness of the curve of branch 2. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where: -4 × 10⁻⁴ 25 ≤ ≤0, 9×10 -23 ≤ ≤9×10 -3 0.0009≤ ≤900, 0.0002≤ ≤200, -50000≤ ≤0, 9×10 -23 ≤ ≤9×10 -3 -2×10 19 ≤ ≤0, 0≤ ≤80000; The radiative recombination coefficient distribution of the waveguide layer with the graded dielectric constant satisfies the functional distribution of InvsPoly as follows: In the formula, The baseline value is R, where R is the peak amplitude: the maximum height of the peak. Peak center location: the center of symmetry of the curve. Peak width parameter: controls the overall width of the peak. The larger the peak, the wider it is. The smaller the peak, the narrower it is. , , For polynomial coefficients: the peak shape is adjusted by quadratic, quartic, and sixth-degree terms respectively. The "steepness" of the dominant peak: The larger the peak, the steeper its sides; , "Tail decay" of the dominant peak: , The larger the peak size, the slower the peak tail decays (broad-tailed peak); = =0, the function degenerates into an inverse quadratic function. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where: 4 × 10⁻⁶. -20 ≤ ≤4×10 -5 1×10 -22 ≤ ≤1×10 -2 0.0001≤ ≤1000, 0.0005≤ ≤5000, 0.002≤ ≤2000, -20≤ ≤20, 0.009≤ ≤9000; The radiative recombination coefficient distribution of the waveguide layer with the graded dielectric constant satisfies the functional distribution of Hill as follows: In the formula, This is the saturated response value. Synergy coefficient: This coefficient modulates the "steepness" and synergy of the response curve. It is the half-saturation constant. The dependent variable is the radiation recombination coefficient, and the independent variable is the epitaxial layer thickness, where 8 × 10⁻⁶. -20 ≤ ≤8×10 -2 0.000008≤ ≤800, 1×10 4 ≤ ≤1×10 24 .

8. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 1, characterized in that, The graded dielectric constant lower waveguide layer includes a first graded dielectric constant lower waveguide layer and a second graded dielectric constant lower waveguide layer. The angle γ2 between the radiative recombination coefficients of the first graded dielectric constant waveguide layer and the second graded dielectric constant waveguide layer is: 60°≤γ2≤120°. The angle β2 between the waveguide layer and the active layer under the second graded dielectric constant is: 0°≤β2≤60°. The angle α2 between the waveguide layer and the active layer with the gradient dielectric constant forms the trend of the radiative recombination coefficient: 15°≤α2≤85°, and 0°≤β2≤α2≤γ2≤120°.

9. A gallium nitride-based semiconductor laser with a graded dielectric constant waveguide layer as described in claim 1, characterized in that, The substrate is a GaN single-crystal substrate; the lower waveguide layer is an InGaN single layer, a GaN single layer, or a multilayer stacked structure composed of GaN and InGaN; the active layer is an InGaN or GaN quantum well; the upper waveguide layer is an InGaN single layer or a multilayer stacked structure composed of GaN and InGaN; the electron blocking layer is any one or any combination of AlGaN, GaN, InGaN, AlInGaN, or AlN; the upper confinement layer is any one or any combination of AlGaN, AlN, GaN, AlInN, or AlInGaN; and the lower confinement layer is any one or any combination of AlGaN, GaN, AlN, InGaN, AlInGaN, or AlInN.

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