A Menani, L Dehimi, S Dehimi, F Pezzimenti, Modelling and optical response of a compressive-strained AlGaN/GaN quantum well laser diode[J]. J. Semicond., 2020, 41(6): 062301. doi: 10.1088/1674-4926/41/6/062301.

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A. Menani^{
1, }
, L. Dehimi^{
1, 2, }
, S. Dehimi^{
3, }
and F. Pezzimenti^{
4, , }

**Abstract: **The effects of the quantum well (QW) width, carrier density, and aluminium (Al) concentration in the barrier layers on the optical characteristics of a gallium nitride (GaN)-based QW laser diode are investigated by means of a careful modelling analysis in a wide range of temperatures. The device’s optical gain is calculated by using two different band energy models. The first is based on the simple band-to-band model that accounts for carrier transitions between the first levels of the conduction band and valence band, whereas the second assumes the perturbation theory (k.p model) for considering the valence intersubband transitions and the relative absorption losses in the QW. The results reveal that the optical gain increases with increasing the n-type doping density as well as the Al molar fraction of the Al_{x}Ga_{1–x}N layers, which originate the GaN compressive-strained QW. In particular, a significant optical gain on the order of 5000 cm^{–1} is calculated for a QW width of 40 Å at room temperature. In addition, the laser threshold current density is of few tens of A/cm^{2} at low temperatures.

**Key words:**
laser diode, quantum well, optical gain, threshold current, temperature

**Abstract: **The effects of the quantum well (QW) width, carrier density, and aluminium (Al) concentration in the barrier layers on the optical characteristics of a gallium nitride (GaN)-based QW laser diode are investigated by means of a careful modelling analysis in a wide range of temperatures. The device’s optical gain is calculated by using two different band energy models. The first is based on the simple band-to-band model that accounts for carrier transitions between the first levels of the conduction band and valence band, whereas the second assumes the perturbation theory (k.p model) for considering the valence intersubband transitions and the relative absorption losses in the QW. The results reveal that the optical gain increases with increasing the n-type doping density as well as the Al molar fraction of the Al_{x}Ga_{1–x}N layers, which originate the GaN compressive-strained QW. In particular, a significant optical gain on the order of 5000 cm^{–1} is calculated for a QW width of 40 Å at room temperature. In addition, the laser threshold current density is of few tens of A/cm^{2} at low temperatures.

**Key words:**
laser diode, quantum well, optical gain, threshold current, temperature

**References:**

[1] |
Nakamura S, Fasol G. The blue laser diode. Berlin: Springer, 1997 |

[2] |
Zory P S. Quantum well lasers. New York: Academic Press, 1993 |

[3] |
Kieleck C, Eichhorn M, Hirth A, et al. High-efficiency 20–50 kHz mid-infrared orientation-patterned GaAs optical parametric oscillator pumped by a 2 |

[4] |
Liu H C, Dudek R, Shen A, et al. High absorption quantum-well infrared photodetectors. Appl Phys Lett, 2001, 79, 4237 |

[5] |
Bouzid F, Pezzimenti F, Dehimi L, et al. Analytical modeling of dual-junction tandem solar cells based on an InGaP/GaAs heterojunction stacked on a Ge substrate. J Electron Mater, 2019, 48, 4107 |

[6] |
Ustinov V M, Zhukov A E. GaAs-based long-wavelength lasers. Semicond Sci Technol, 2000, 15, R41 |

[7] |
Rogalski A. Infrared detectors: an overview. Infrared Phys Tech, 2002, 43, 187 |

[8] |
Justice J, Bower C, Meitl M, et al. Wafer-scale integration of group III–V lasers on silicon using transfer printing of epitaxial layers. Nat Photonics, 2012, 6, 610 |

[9] |
Bouzid F, Dehimi L, Pezzimenti F, et al. Numerical simulation study of a high efficient AlGaN-based ultraviolet photodetector. Superlattice Microstruct, 2018, 122, 57 |

[10] |
Dehimi S, Dehimi L, Aissat A. Study and Simulation of a quantum well structure based ZnTe/Zn |

[11] |
Liu H, Wang T, Jiang Q, et al. Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate. Nat Photonics, 2011, 5, 416 |

[12] |
Della Corte F G, De Martino G, Pezzimenti F, et al. Numerical simulation study of a low breakdown voltage 4H-SiC MOSFET for photovoltaic module-level applications. IEEE Trans Electron Devices, 2018, 65, 3352 |

[13] |
De Martino G, Pezzimenti F, Della Corte F G, et al. Design and numerical characterization of a low voltage power MOSFET in 4H-SiC for photovoltaic applications. Proc IEEE International Conference Ph. D. Research in Microelectronics and Electronics – PRIME, 2017 |

[14] |
Yoshida H, Kuwabara M, Yamashita Y, et al. AlGaN-based laser diodes for the short-wavelength ultraviolet region. New J Phys, 2009, 11, 125013 |

[15] |
Bouzid F, Dehimi L, Pezzimenti F. Performance analysis of a Pt/n-GaN Schottky barrier UV detector. J Electron Mater, 2017, 46, 6563 |

[16] |
DenBaars S P, Feezell D, Kelchner K, et al. Development of gallium-nitride-based light-emitting diodes (LEDs) and laser diodes for energy-efficient lighting and displays. Acta Mater, 2013, 61, 945 |

[17] |
Marouf Y, Dehimi L, Pezzimenti F. Simulation study for the current matching optimization in In |

[18] |
Bencherif H, Dehimi L, Pezzimenti F, et al. Improving the efficiency of a-Si: H/c-Si thin heterojunction solar cells by using both antireflection coating engineering and diffraction grating. Optik, 2019, 182, 682 |

[19] |
Zeghdar K, Dehimi L, F Pezzimenti F, et al. Simulation and analysis of the current-voltage-temperature characteristics of Al/Ti/4H-SiC Schottky barrier diodes. Jpn J Appl Phys, 2019, 58, 014002 |

[20] |
Fritah A, Dehimi L, Pezzimenti F, et al. Analysis of |

[21] |
Farrell R M, Haeger D A, Hsu P S, et al. High-power blue-violet AlGaN-cladding-free m-plane InGaN/GaN laser diodes. Appl Phys Lett, 2011, 99, 171113 |

[22] |
Bouzid F, Pezzimenti F, Dehimi L, et al. Numerical simulations of the electrical transport characteristics of a Pt/n-GaN Schottky diode. Jpn J Appl Phys, 2017, 56, 094301 |

[23] |
Bencherif H, L Dehimi L, Pezzimenti F, et al. Analytical model for the light trapping effect on ZnO: Al/c-Si/SiGe/c-Si solar cells with an optimized design. Proc International Conference on Applied Smart Systems – ICASS, 2018 |

[24] |
Marouf Y, Dehimi L, Bouzid F, et al. Theoretical design and performance of In |

[25] |
Monroy E, Guillot F, Leconte S, et al. III-nitride nanostructures for infrared optoelectronics. Acta Phys Pol A, 2006, 110, 295 |

[26] |
Rao S, Pangallo G, Pezzimenti F, et al. High-performance temperature sensor based on 4H-SiC Schottky diodes. IEEE Electron Device Lett, 2015, 36, 720 |

[27] |
De Martino G, Pezzimenti F, Della Corte F G. Interface trap effects in the design of a 4H-SiC MOSFET for low voltage applications. Proc International Semiconductor Conference – CAS, 2018 |

[28] |
Bencherif H, Dehimi L, Pezzimenti F, et al. Temperature and SiO |

[29] |
Megherbi M L, Pezzimenti F, Dehimi L, et al. Analysis of different forward current-voltage behaviours of Al implanted 4H-SiC vertical p–i–n diodes. Solid-State Electron, 2015, 109, 12 |

[30] |
Bencherif H, Dehimi L, Pezzimenti F, et al. Multiobjective optimization of design of 4H-SiC power MOSFETs for specific applications. J Electron Mater, 2019, 48, 3871 |

[31] |
Ikeda M, Mizuno T, Takeya M, et al. High-power GaN-based semiconductor lasers. Phys Status Solidi, 2004, 6, 1461 |

[32] |
Pezzimenti F, Bencherif H, Yousfi A, et al. Current–voltage analytical model and multiobjective optimization of design of a short channel gate-all-around-junctionless MOSFET. Solid-State Electron, 2019, 161, 107642 |

[33] |
Asgari A, Dashti S. Optimization of optical gain in Al |

[34] |
Schubert E F, Kim J K. Solid-state light sources getting smart. Science, 2005, 308, 1274 |

[35] |
Ohtoshi T, Yamaguchi K, Nagaoka C, et al. A two dimensional device simulator of semiconductor lasers. Solid-State Electron, 1987, 30, 627 |

[36] |
Chuang S L, Chang C S. k.p method for strained wurtzite semiconductors. Phys Rev B, 1996, 54, 2491 |

[37] |
Chuang S L. Optical gain of strained wurtzite GaN quantum-well lasers. IEEE J Quantum Electron, 1996, 32, 1791 |

[38] |
Silvaco TCAD. Atlas user’s manual device simulation software. California: Silvaco Int., 2016 |

[39] |
Bernardini F, Fiorentini V. Spontaneous versus piezoelectric polarization in III–V Nitrides: Conceptual aspects and practical consequences. Phys Status Solidi B, 1999, 216, 391 |

[40] |
Ambacher O, Majewski J, Miskys C, et al. Pyroelectric properties of Al(In)GaN/GaN heteroand quantum well structures. J Phys Condens Mat, 2002, 14, 3399 |

[41] |
Vurgaftman I, Meyer J R. Nitride semiconductor devices. New York: Wiley, 2007 |

[42] |
Nepal N, Li J, Nakarmi M L, et al. Temperature and compositional dependence of AlGaN the energy band gap of alloys. Appl Phys Lett, 2005, 87, 242104 |

[43] |
Dakhlaoui H. Linear and nonlinear optical absorption coefficients and refractive index changes in GaN/Al |

[44] |
Dehimi S, Dehimi L, Asar T, et al. Modelling of a Cd |

[45] |
Casey H C, Panish M B. Heterostructure lasers. New York: Academic Press, 1978 |

[46] |
Dehimi S, Dehimi L, Asar T, et al. Modeling and simulation of Zn |

[47] |
Dehimi S, Aissat A, Haddad D, et al. Optimization of optical gain in In |

[48] |
Aissat A, Nacer S, Ykhlef F, et al. Modeling of Ga |

[1] |
Nakamura S, Fasol G. The blue laser diode. Berlin: Springer, 1997 |

[2] |
Zory P S. Quantum well lasers. New York: Academic Press, 1993 |

[3] |
Kieleck C, Eichhorn M, Hirth A, et al. High-efficiency 20–50 kHz mid-infrared orientation-patterned GaAs optical parametric oscillator pumped by a 2 |

[4] |
Liu H C, Dudek R, Shen A, et al. High absorption quantum-well infrared photodetectors. Appl Phys Lett, 2001, 79, 4237 |

[5] |
Bouzid F, Pezzimenti F, Dehimi L, et al. Analytical modeling of dual-junction tandem solar cells based on an InGaP/GaAs heterojunction stacked on a Ge substrate. J Electron Mater, 2019, 48, 4107 |

[6] |
Ustinov V M, Zhukov A E. GaAs-based long-wavelength lasers. Semicond Sci Technol, 2000, 15, R41 |

[7] |
Rogalski A. Infrared detectors: an overview. Infrared Phys Tech, 2002, 43, 187 |

[8] |
Justice J, Bower C, Meitl M, et al. Wafer-scale integration of group III–V lasers on silicon using transfer printing of epitaxial layers. Nat Photonics, 2012, 6, 610 |

[9] |
Bouzid F, Dehimi L, Pezzimenti F, et al. Numerical simulation study of a high efficient AlGaN-based ultraviolet photodetector. Superlattice Microstruct, 2018, 122, 57 |

[10] |
Dehimi S, Dehimi L, Aissat A. Study and Simulation of a quantum well structure based ZnTe/Zn |

[11] |
Liu H, Wang T, Jiang Q, et al. Long-wavelength InAs/GaAs quantum-dot laser diode monolithically grown on Ge substrate. Nat Photonics, 2011, 5, 416 |

[12] |
Della Corte F G, De Martino G, Pezzimenti F, et al. Numerical simulation study of a low breakdown voltage 4H-SiC MOSFET for photovoltaic module-level applications. IEEE Trans Electron Devices, 2018, 65, 3352 |

[13] |
De Martino G, Pezzimenti F, Della Corte F G, et al. Design and numerical characterization of a low voltage power MOSFET in 4H-SiC for photovoltaic applications. Proc IEEE International Conference Ph. D. Research in Microelectronics and Electronics – PRIME, 2017 |

[14] |
Yoshida H, Kuwabara M, Yamashita Y, et al. AlGaN-based laser diodes for the short-wavelength ultraviolet region. New J Phys, 2009, 11, 125013 |

[15] |
Bouzid F, Dehimi L, Pezzimenti F. Performance analysis of a Pt/n-GaN Schottky barrier UV detector. J Electron Mater, 2017, 46, 6563 |

[16] |
DenBaars S P, Feezell D, Kelchner K, et al. Development of gallium-nitride-based light-emitting diodes (LEDs) and laser diodes for energy-efficient lighting and displays. Acta Mater, 2013, 61, 945 |

[17] |
Marouf Y, Dehimi L, Pezzimenti F. Simulation study for the current matching optimization in In |

[18] |
Bencherif H, Dehimi L, Pezzimenti F, et al. Improving the efficiency of a-Si: H/c-Si thin heterojunction solar cells by using both antireflection coating engineering and diffraction grating. Optik, 2019, 182, 682 |

[19] |
Zeghdar K, Dehimi L, F Pezzimenti F, et al. Simulation and analysis of the current-voltage-temperature characteristics of Al/Ti/4H-SiC Schottky barrier diodes. Jpn J Appl Phys, 2019, 58, 014002 |

[20] |
Fritah A, Dehimi L, Pezzimenti F, et al. Analysis of |

[21] |
Farrell R M, Haeger D A, Hsu P S, et al. High-power blue-violet AlGaN-cladding-free m-plane InGaN/GaN laser diodes. Appl Phys Lett, 2011, 99, 171113 |

[22] |
Bouzid F, Pezzimenti F, Dehimi L, et al. Numerical simulations of the electrical transport characteristics of a Pt/n-GaN Schottky diode. Jpn J Appl Phys, 2017, 56, 094301 |

[23] |
Bencherif H, L Dehimi L, Pezzimenti F, et al. Analytical model for the light trapping effect on ZnO: Al/c-Si/SiGe/c-Si solar cells with an optimized design. Proc International Conference on Applied Smart Systems – ICASS, 2018 |

[24] |
Marouf Y, Dehimi L, Bouzid F, et al. Theoretical design and performance of In |

[25] |
Monroy E, Guillot F, Leconte S, et al. III-nitride nanostructures for infrared optoelectronics. Acta Phys Pol A, 2006, 110, 295 |

[26] |
Rao S, Pangallo G, Pezzimenti F, et al. High-performance temperature sensor based on 4H-SiC Schottky diodes. IEEE Electron Device Lett, 2015, 36, 720 |

[27] |
De Martino G, Pezzimenti F, Della Corte F G. Interface trap effects in the design of a 4H-SiC MOSFET for low voltage applications. Proc International Semiconductor Conference – CAS, 2018 |

[28] |
Bencherif H, Dehimi L, Pezzimenti F, et al. Temperature and SiO |

[29] |
Megherbi M L, Pezzimenti F, Dehimi L, et al. Analysis of different forward current-voltage behaviours of Al implanted 4H-SiC vertical p–i–n diodes. Solid-State Electron, 2015, 109, 12 |

[30] |
Bencherif H, Dehimi L, Pezzimenti F, et al. Multiobjective optimization of design of 4H-SiC power MOSFETs for specific applications. J Electron Mater, 2019, 48, 3871 |

[31] |
Ikeda M, Mizuno T, Takeya M, et al. High-power GaN-based semiconductor lasers. Phys Status Solidi, 2004, 6, 1461 |

[32] |
Pezzimenti F, Bencherif H, Yousfi A, et al. Current–voltage analytical model and multiobjective optimization of design of a short channel gate-all-around-junctionless MOSFET. Solid-State Electron, 2019, 161, 107642 |

[33] |
Asgari A, Dashti S. Optimization of optical gain in Al |

[34] |
Schubert E F, Kim J K. Solid-state light sources getting smart. Science, 2005, 308, 1274 |

[35] |
Ohtoshi T, Yamaguchi K, Nagaoka C, et al. A two dimensional device simulator of semiconductor lasers. Solid-State Electron, 1987, 30, 627 |

[36] |
Chuang S L, Chang C S. k.p method for strained wurtzite semiconductors. Phys Rev B, 1996, 54, 2491 |

[37] |
Chuang S L. Optical gain of strained wurtzite GaN quantum-well lasers. IEEE J Quantum Electron, 1996, 32, 1791 |

[38] |
Silvaco TCAD. Atlas user’s manual device simulation software. California: Silvaco Int., 2016 |

[39] |
Bernardini F, Fiorentini V. Spontaneous versus piezoelectric polarization in III–V Nitrides: Conceptual aspects and practical consequences. Phys Status Solidi B, 1999, 216, 391 |

[40] |
Ambacher O, Majewski J, Miskys C, et al. Pyroelectric properties of Al(In)GaN/GaN heteroand quantum well structures. J Phys Condens Mat, 2002, 14, 3399 |

[41] |
Vurgaftman I, Meyer J R. Nitride semiconductor devices. New York: Wiley, 2007 |

[42] |
Nepal N, Li J, Nakarmi M L, et al. Temperature and compositional dependence of AlGaN the energy band gap of alloys. Appl Phys Lett, 2005, 87, 242104 |

[43] |
Dakhlaoui H. Linear and nonlinear optical absorption coefficients and refractive index changes in GaN/Al |

[44] |
Dehimi S, Dehimi L, Asar T, et al. Modelling of a Cd |

[45] |
Casey H C, Panish M B. Heterostructure lasers. New York: Academic Press, 1978 |

[46] |
Dehimi S, Dehimi L, Asar T, et al. Modeling and simulation of Zn |

[47] |
Dehimi S, Aissat A, Haddad D, et al. Optimization of optical gain in In |

[48] |
Aissat A, Nacer S, Ykhlef F, et al. Modeling of Ga |

A Menani, L Dehimi, S Dehimi, F Pezzimenti, Modelling and optical response of a compressive-strained AlGaN/GaN quantum well laser diode[J]. J. Semicond., 2020, 41(6): 062301. doi: 10.1088/1674-4926/41/6/062301.

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Manuscript received: 19 September 2019 Manuscript revised: 05 December 2019 Online: Accepted Manuscript: 20 January 2020 Uncorrected proof: 12 May 2020 Published: 01 June 2020

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