# Design of High-Power Red VCSEL on a Removable Substrate

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}under pulse current injection at 77 K. To reduce the SEL threshold current, the distribution Bragg reflector (DBR) and oxide confinement layer were employed on the SEL by Deppe in 1994 [17]. This work firstly demonstrated that the oxidation process for controlling the oxide aperture to form a small volume of an optical cavity in SEL is possible. Based on the idea, the first commercial oxide-confined vertical-cavity surface-emitting laser (VCSEL) with an 850 nm emission wavelength was realized in 1997, which can operate over the temperature range from −80 °C to 180 °C [18].

## 2. Design Flow

_{w}, m

^{*}are the thickness of the quantum well, the energy difference between the well and the barrier and the effective mass, respectively. The function int[x] gives the integer part of the result.

_{i}can be derived from [62]:

_{QW}and a

_{barrier}are the lattice constants of the quantum well and the barrier, respectively. With C

_{11}and C

_{12}as elastic stiffness coefficients, a and b as the lattice deformation potentials. The energy change due to strain is the sum of hydrostatic strain H and shear strain S, and the photon energy ${E}_{h\nu}$ is:

_{i}′ and f

_{j}′ are the integrated Fermi functions, ${\u03f5}_{1}$ is the real part of the complex optical dielectric constant, $\overline{n}$ is the real part of refractive index, and ${\rho}_{ij}$ is the reduced density of states. In the case of quantum wells, many sub bands in both the valence band and the conduction band need to be considered, and the gain function is the sum of g

_{ij}over all the sub bands for the allowed transitions. Furthermore, the effect of gain broaden can be take into account via the Landsberg’s model, in which the quantum well form was derived by Zielinski et al. [64,65]. As the number of the quantum well increases, the confinement factor also increases; hence, larger material gain as well as the threshold current [66]. Therefore, it is important to balance between the material gain and threshold current.

_{t}[67]:

_{dip}is the dipole factor; E

_{cj}is the jth conduction sub-band; E

_{kpi}is the ith valence sub-band from the k∙p calculation; the sum is over all possible valence and conduction sub-bands; g

_{0}is a constant defined as

_{b}is the bulk dipole momentum given by:

_{g}

_{0}is the unstrained bandgap; m

_{c}is the effective mass of the conduction band; ${\Delta}_{so}$ is the spin-orbit coupling energy.

_{p}is the thickness of the p-cladding, L

_{n}is the length of the minority electron diffusion, D

_{n}is the minority electron diffusion coefficient, n is the concentration of the minority electron of p-cladding layer edge, and z is the characteristic length of the drift leakage current. Since the characteristic temperature is correlated to the quantum well number and the leakage effect, hence, if the characteristic temperature is not desired, one may return to the gain/loss balance procedure.

_{w}is the number of the quantum wells, a

_{in}is the total internal loss, L is the effective cavity length, R is the reflectivity, B

_{eff}is the effective recombination constant, N

_{t}is the carrier concentration at transparency, and r the radius of the laser. The experience equation of the output optical power can be calculated from [69]:

_{off}is the cutoff temperature, R

_{d}is the series resistance, V

_{0}is the turn-on voltage, ${\lambda}_{c}$ is the thermal conductivity and ${\eta}_{i}$ is the internal quantum efficiency. If the resultant laser performance is not desired, one may return to the beginning of bandgap engineering.

## 3. In AlGaP/InGaP VCSEL Structural Design and Optimization

_{0.45}GaAs/Al

_{0.94}GaAs and five pairs of Al

_{0.45}GaAs/Al

_{0.88}GaAs n type-DBR as bottom mirror. The top mirror is a p-DBR consisting of 37 pairs of Al

_{0.45}GaAs/Al

_{0.88}GaAs. 3 pairs of InGaP/AlGaInP quantum well are sandwiched between bottom and top mirror with a 14 µm oxide aperture. The gain peak wavelength of the QW is aligned with the cavity resonant wavelength at 680 nm at room temperature. The crest of the standing wave occurs in the active region, so that the optical intensity can be effectively concentrated in the center of the active region.

_{n}) corresponding to each eigenvalue can be expressed:

_{n}is corresponding energy, t is the thickness of the quantum well, m is the effective mass of the carrier, and $\hslash $ is the reduced Planck constant, k

_{n}is dimensionless wave vector. The eigenvalue, v

_{n}, depend on potential energy, V, which can be presented:

_{b}is the energy level of the barrier, E

_{w}is the energy level of the quantum well. The indium composition of the well and the aluminum composition of the barrier correspond to E

_{w}and E

_{b}, respectively. If the composition of the QW changes, it will affect v

_{n}[70]. After shifting the term, we can obtain the corresponding energy ${E}_{n}=2{h}^{2}{v}_{n}{}^{2}/m{t}^{2}$. Through the equation, the specific emission wavelength of QW structure can be decided. Moreover, by increasing the indium composition of the well, the potential energy, V, will increase resulting in a red shift wavelength. Therefore, reducing the well thickness to fix the emission wavelength at 680 nm is necessary.

_{j}− f

_{i}) smaller. Therefore, when the thickness is reduced to a certain thickness, the QW will have a gain extreme value [20].

#### 3.1. Leakage Effect

#### 3.2. Temperature Dependence of Optical Gain and Resonance Mode Gain

#### 3.3. Threshold Current

## 4. Temperature Characteristics of InAlGaP/InGaP VCSEL with Substrates Removal

_{net}and the junction temperature (T

_{j}):

_{a}and R

_{th}is the environment temperature and thermal resistance of the laser, respectively, and ${P}_{net}={P}_{total}-{P}_{optical}$. Figure 8 shows the results of laser thermal resistance calculation for different substrate thicknesses. When the thickness of VCSEL substrate decreases from 500 to 250 µm, the junction temperature decreases from 427 to 376 K. The thermal resistance decreases from 3936 to 2361 K/W. The result of the change of thermal resistance and thickness is a linear function. We analyze this function using the basic Equation (27) of linear thermal resistance:

_{0}is the intercept of the thickness of the linear function when the substrate is 0, L is the thickness of the substrate, k is the thermal conductivity of GaAs, and A is the equivalent cross-sectional area of the substrate. When the thermal conductivity of GaAS is 46, the equivalent cross-sectional area can be deduced from the slope to be 61 × 61 µm

^{2}. The calculation of the equivalent area is consistent with the simulation condition. It is confirmed that when the substrate thickness is far away from the heat source, the thermal resistance and substrate thickness are a linear relationship. However, when the substrate thickness is less than 100 µm, the linear relationship between thermal resistance and the substrate gradually deteriorates. The thermal resistance of VCSEL is 587 K/W for a substrate thickness of 0 µm. The difference compared to the intercept R

_{0}is 360 K/W. This difference can be explained by the distribution of the isothermal curve. As the thickness of the substrate gets closer to the VCSEL heat source, the isothermal surface is no longer parallel to the substrate cross-section. The linear thermal resistance cannot describe the lateral temperature variation, which makes the simulation results gradually deviate away from the linear function. The simulation results show that the thermal resistance can decrease from 2361 to 587 K/W resulting in a 24% difference in resistance when the VCSEL substrate thickness is significantly thinned. This result is also confirmed by the VCSEL substrate removal process in other wavelength ranges [73,74]. Furthermore, non-linear thermal resistance variations can be confirmed from the analysis of different electronic devices [72,75,76]. Therefore, the substrate thinning process is a feasible method to further improve the maximum power and operating current of red VCSELs. Figure 7b shows that the operating current increases from 12.8 to 18 mA when the thickness of the VCSEL substrate decreases from 500 to 100 µm. The operating range is improved by 40.6% to achieve a higher power red laser. Substrate-removed VCSELs exhibit superior device performance in both high-speed VCSELs or high-power arrays. In general, substrates with a minimum thickness of 10 µm are feasible and proven [77,78,79,80].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Layer | Material | Group | Repeat | Start x | Finish x | Thickness (µm) | Dopant | Type |
---|---|---|---|---|---|---|---|---|

33 | GaAs | 1 | N/A | 0.0150 | 2 × 10^{20} | p | ||

32 | Al_{x}GaAs | 1 | 0.45 | 0.0230 | 1 × 10^{20} | p | ||

31 | Al_{x}GaAs | 1 | 0.88 | 0.45 | 0.0100 | 2 × 10^{18} | p | |

30 | Al_{x}GaAs | 4 | 37 | 0.88 | 0.0464 | 3 × 10^{18} | p | |

29 | Al_{x}GaAs | 4 | 37 | 0.45 | 0.88 | 0.0100 | 3 × 10^{18} | p |

28 | Al_{x}GaAs | 4 | 37 | 0.45 | 0.0431 | 3 × 10^{18} | p | |

27 | Al_{x}GaAs | 4 | 37 | 0.88 | 0.45 | 0.0100 | 3 × 10^{18} | p |

26 | Al_{x}GaAs | 1 | 0.88 | 0.0431 | 3 × 10^{18} | p | ||

25 | Al_{x}GaAs | 1 | 0.45 | 0.88 | 0.0100 | 2 × 10^{18} | p | |

24 | Al_{x}GaAs | 1 | 0.45 | 0.0280 | 3 × 10^{18} | p | ||

23 | Al_{x}GaAs | 1 | 0.88 | 0.45 | 0.0100 | 2 × 10^{18} | p | |

22 | Al_{x}GaAs | 1 | 0.985 | 0.0250 | 3 × 10^{18} | p | ||

21 | Al_{x}GaAs | 1 | 0.90 | 0.0460 | 3 × 10^{18} | p | ||

20 | Al_{x}Ga_{1−x}InP | 1 | 0.70 | 0.0200 | 1 × 10^{18} | p | ||

19 | Al_{x}Ga_{1−x}InP | 1 | 0.50 | 0.70 | 0.0320 | 1 × 10^{18} | p | |

18 | Al_{x}Ga_{1−x}InP | 1 | 0.50 | 0.0235 | N/A | Undoped | ||

17 | InGaP | 1 | N/A | 0.0054 | N/A | Undoped | ||

16 | Al_{x}Ga_{1−x}InP | 3 | 2 | 0.50 | 0.0080 | N/A | Undoped | |

15 | InGaP | 3 | 2 | N/A | 0.0054 | N/A | Undoped | |

14 | Al_{x}Ga_{1−x}InP | 1 | 0.50 | 0.0235 | N/A | Undoped | ||

13 | Al_{x}Ga_{1−x}InP | 1 | 0.70 | 0.50 | 0.0500 | 1 × 10^{18} | n | |

12 | Al_{x}Ga_{1−x}InP | 1 | 0.70 | 0.0200 | 1 × 10^{18} | n | ||

11 | Al_{x}GaAs | 1 | 0.88 | 0.0464 | 2 × 10^{18} | n | ||

10 | Al_{x}GaAs | 1 | 0.45 | 0.88 | 0.0100 | 2 × 10^{18} | n | |

9 | Al_{x}GaAs | 2 | 5 | 0.45 | 0.0413 | 2 × 10^{18} | n | |

8 | Al_{x}GaAs | 2 | 5 | 0.88 | 0.45 | 0.0100 | 2 × 10^{18} | n |

7 | Al_{x}GaAs | 2 | 5 | 0.88 | 0.0464 | 2 × 10^{18} | n | |

6 | Al_{x}GaAs | 2 | 5 | 0.45 | 0.88 | 0.0100 | 2 × 10^{18} | n |

5 | Al_{x}GaAs | 1 | 50 | 0.45 | 0.0413 | 2 × 10^{18} | n | |

4 | Al_{x}GaAs | 1 | 50 | 0.94 | 0.45 | 0.0100 | 2 × 10^{18} | n |

3 | Al_{x}GaAs | 1 | 50 | 0.94 | 0.0464 | 2 × 10^{18} | n | |

2 | Al_{x}GaAs | 1 | 50 | 0.45 | 0.94 | 0.0100 | 2 × 10^{18} | n |

1 | GaAs | 1 | N/A | 100 | 3 × 10^{18} | n |

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**Figure 2.**The relationship between the thickness of the well and the indium composition of the well under different barrier aluminum compositions.

**Figure 3.**The relationship between the indium composition of well and its maximum material gain value under different barrier aluminum composition.

**Figure 4.**(

**a**) Normalized current density distribution under different aluminum compositions, (

**b**) conduction band diagram of active layer for different barrier aluminum compositions, and (

**c**) input current density and percentage of leakage current under different aluminum compositions and temperature.

**Figure 5.**Relationship between (

**a**) gain spectrum and resonance mode gain at different temperatures and (

**b**) temperature versus cavity mode gain, under different barrier aluminum compositions.

**Figure 6.**(

**a**) Temperature versus threshold current and (

**b**) current versus spontaneous and excited radiation rates at 25 °C, under different barrier aluminum compositions.

**Figure 7.**(

**a**) Temperature distribution profile at 12 mA, (

**b**) current-voltage relationship, (

**c**) photoelectric characteristic curve for different substrate thicknesses, and (

**d**) junction temperature–current relationship.

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**MDPI and ACS Style**

Peng, C.-Y.; Huang, W.-T.; Lu, Z.-K.; Chen, S.-C.; Kuo, H.-C.
Design of High-Power Red VCSEL on a Removable Substrate. *Photonics* **2022**, *9*, 763.
https://doi.org/10.3390/photonics9100763

**AMA Style**

Peng C-Y, Huang W-T, Lu Z-K, Chen S-C, Kuo H-C.
Design of High-Power Red VCSEL on a Removable Substrate. *Photonics*. 2022; 9(10):763.
https://doi.org/10.3390/photonics9100763

**Chicago/Turabian Style**

Peng, Chun-Yen, Wei-Ta Huang, Zhi-Kuang Lu, Shih-Chen Chen, and Hao-Chung Kuo.
2022. "Design of High-Power Red VCSEL on a Removable Substrate" *Photonics* 9, no. 10: 763.
https://doi.org/10.3390/photonics9100763