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In this paper, a quantum cascade photodetector based on intersubband transitions in quantum wells with ability of detecting 1.33 μm and 1.55 μm wavelengths in two individual current paths is introduced. Multi quantum wells structures based on III-Nitride materials due to their large band gaps are used. In order to calculate the photodetector parameters, wave functions and energy levels are obtained by solving 1-D Schrodinger–Poisson equation self consistently at 80 ?K. Responsivity values are about 22 mA/W and 18.75 mA/W for detecting of 1.33 μm and 1.55 μm wavelengths, respectively. Detectivity values are calculated as 1.17 × 107 (Jones) and 2.41 × 107 (Jones) at wavelengths of 1.33 μm and 1.55 μm wavelengths, respectively.

Quantum well infrared photodetectors (QWIPs) as thermal imagers using focal plane arrays (FPAs) have been studied extensively [

In this paper, a QCD for detecting of 1.33 μm and 1.55 μm wavelengths in individual current paths based on intersubband transitions in AlGaN/AlN MQWs is designed. Paths are separated by 100 Å AlN In order to calculate photodetector parameters, wave functions and energy levels are obtained by solving 1-D Schrodinger?Poisson equation self consistently at 80˚K. Incident wavelength excite the electrons populated the first energy level of n+ doped QWs, after that they are extracted from first wells by emitting optical phonons emission having energy close to GaN LO-phonon energy (92 meV). Responsivity of paths is about 22 mA/W and 18.75 mA/W for detecting of 1.33 μm and 1.55 μm wavelengths respectively. Detectivity values are calculated as 1.17 × 10^{7} (Jones) and 2.41 × 10^{7} (Jones) at wavelengths of 1.33 μm and 1.55 μm respectively.

A 3D view of the design QCD with ability of detection 1.33 μm and 1.55 μm wavelengths in two separated paths is indicated in

Each path separated by 100 Å AlN. Paths 1 and 2 are designed for detection of 1.33 μm and 1.55 μm wavelengths, respectively. They possess 20 periods Al_{x}Ga_{1−x}N/AlN MQWs, the thickness of barriers and wells listed in ^{11} cm^{−2}. Conduction band edge and wave functions for each path are shown in

Wells | Thickness (Å) | Barriers | Thickness (Å) |
---|---|---|---|

Al_{0.4}Ga_{0.6}N | 20 | AlN | 15 |

Al_{0.7}Ga_{0.3}N | 18 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 10 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 11 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 12 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 13 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 14 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 15 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 16 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 17 | AlN | 16 |

Al_{0.45}Ga_{0.45}N | 19 | AlN | 16 |

Al_{0.4}Ga_{0.6}N | 20 | AlN | 16 |

Wells | Thickness (Å) | Barriers | Thickness (Å) |
---|---|---|---|

Al_{0.5}Ga_{0.5}N | 21 | AlN | 19 |

Al_{0.7}Ga_{0.3}N | 16 | AlN | 20 |

Al_{0.4}Ga_{0.6}N | 9 | AlN | 20 |

Al_{0.4}Ga_{0.6}N | 10 | AlN | 20 |

Al_{0.4}Ga_{0.6}N | 11 | AlN | 20 |

Al_{0.4}Ga_{0.6}N | 12 | AlN | 20 |

Al_{0.4}Ga_{0.6}N | 13 | AlN | 20 |

Al_{0.4}Ga_{0.6}N | 14 | AlN | 20 |

Al_{0.4}Ga_{0.6}N | 15 | AlN | 20 |

Al_{0.5}Ga_{0.5}N | 21 | AlN | 20 |

The wave functions are calculated by solving 1-D Schrodinger-Poisson self consistently at 80 ˚K [^{th} layer for a k layers quantum structures is obtained as Equation (1) [

where, j and k are the number of layers. L_{k}, P_{k}, P_{j}, ε_{j} and ε_{k} are the length of layers, the total polarization and permittivity of j_{th} and k_{th} layer, respectively.

The absorption coefficient is obtained as Equation (2) [

where, E_{i} and E_{f}, are the quantized energy levels for the initial and final states, respectively. M_{fi}, μ, c, L_{eff}, n_{r} and τ_{in} are dipole matrix element between initial and final states, the permeability, the speed of light in free space, the effective spatial extent of electrons in subbands, the refractive index and the intersubband relaxation time respectively. The absorption coefficient at 80˚K for each path is indicated in

Absorption coefficient is linked to dipole matrix element between initial and final states through Equation (2). As illustrated the path for detection of 1.55 μm has small absorption coefficient due to the small overlapping of wave functions between initial and first levels.

The responsivity R for each path is obtained as Equation (3) [

where, λ, c, q, h, η, P_{e}, P_{c}, N_{QW} are the incident wavelength, the speed of light in free space, the elementary charge, Planck’s constant, the quantum efficiency, the escape probability of an excited electron in active QW, capture probability into the active QW’s ground state for an electron traveling down the QCD’s cascade and the number of active QW periods of the QCD. Absorption efficiency is expressed as Equation (4) [

where, α and d are the absorption coefficient and thickness of active well in each period, respectively. The responsivity for each path at 80 ˚K is indicated in

In QCDs, resistance of the one period of the structure at zero bias in area of the device defined as R_{0}A, is an important parameter characterized the dark current (current in absence of incident light) [_{0}A only interaction between electrons and LO-phonon is considered and interaction between electrons and acoustical phonons are neglected due to sufficient high differences between the energy levels in the studied structures [_{0}A is obtained as Equation (5) [

Here, G_{ij} is global transition rate between the subband i and subband j and is the sum of the two transition rates for absorption of LO phonons (G_{aij}), and

emission of LO phonons (G_{eij}) [_{0}A as a function of 1000/T is shown in _{0}A) the values in _{0}A for path 1 has lower values than R_{0}A of path 2 due to higher transition rates values as described in the following. Dominant global transition rates between first energy level and other subbands in one period for paths are indicated in

Dominant transition rates values at temperatures of 80 ˚K, 120 ˚K and 240 ˚K for instances for paths 1 and 2 are listed in

As observed in

Global transition rates (m^{−2}·s^{−1}) | T = 80 ˚K | T = 120 ˚K | T = 240 ˚K |
---|---|---|---|

G_{112} | 3.4559 × 10^{23} | 2.3963 × 10^{25} | 1.4414 × 10^{27} |

G_{111} | 1.3865 × 10^{20} | 9.6905 × 10^{21} | 5.9355 × 10^{23} |

G_{110} | 2.1841 × 10^{16} | 1.5361 × 10^{18} | 9.5414 × 10^{19} |

Global transition rates (m^{−2}·s^{−1}) | T = 80 ˚K | T = 120 ˚K | T = 240 ˚K |
---|---|---|---|

G_{110} | 5.9122 × 10^{22} | 4.2822 × 10^{24} | 2.4974 × 10^{26} |

G_{19} | 5.0429 × 10^{18} | 3.5895 × 10^{20} | 2.0865 × 10^{22} |

G_{18} | 1.0339 × 10^{14} | 7.3362 × 10^{15} | 4.2545 × 10^{17} |

(due to having smaller width of the wells) which leads to smaller resistance values. Electron transition capability between two levels is increased by increasing temperature, therefore as shown in

Detectivity for the designed detector is limited by Johnson-noise obtained as Equation 6 [

where, R(λ), R_{0}A are the responsivity spectrum and resistance of device in area of the device, respectively. Detectivity versus incident wavelength for paths at 80 ˚K is shown in

Paths have difference detectiveity values due to having different responsivity and resistivity (at zero bias) values shown in

In this research, a QCD for detecting of 1.33 μm and 1.55 μm wavelengths in individual current paths based on intersubband transitions in AlGaN/AlN MQWs was designed. In order to calculate photodetector parameters, 1-D Schrodinger? Poisson equation self consistently at 80˚K was solved to obtain wave functions and energy levels. Responsivity values about 22 mA/W and 18.75 mA/W for detecting of 1.33 μm and 1.55 μm wavelengths, respectively. Detectivity values are calculated as 1.17 × 10^{7} (Jones) and 2.41 × 10^{7} (Jones) at wavelengths of 1.33 μm and 1.55 μm, respectively.

This work is supported by Photonics and Nanocrystal research Lab. (PNRL), Faculty of Electrical and Computer Engineering of Tabriz University and SP- EPT Labs., ASEPE Company, Industrial Park of Advanced Technologies, Tabriz, Iran.

Khosravi, S. and Rostami, A. (2017) Design of 1.33 μm and 1.55 μm Wavelengths Quantum Cascade Photodetector. Optics and Photonics Jour- nal, 7, 116-126. https://doi.org/10.4236/opj.2017.78B016