A new method for calculating electron temperature in subbands of quantum cascade lasers
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摘要: 基于电子动能与温度的关系以及费米黄金定律，对速率方程进行了优化，使其能够计算电子温度，进而实现了更为精准的速率方程求解。与已有的动能平衡法比较，该方法对能带电子温度变化过程进行了详细的描述，故无需采用优化算法求解，所以可以避免因陷入局部最优解而带来的多次计算的收敛值一致性较差的问题。计算结果表明，该方法在选取不同的初始温度时，通过自洽求解，即可解出各能级电子温度，且均可获得一致性较好的收敛值。Abstract: Quantum cascade laser is a newly developed important medium and far infrared laser source. In view of the important parameter of energy band electron temperature in the research and design of quantum cascade lasers, based on the relationship between electron kinetic energy and temperature and Fermi Golden Rule, this paper optimizes the rate equation so that it can calculate the subband electron temperature, thus achieving a more accurate solution of the rate equation. The calculation results show that compared with the existing kinetic energy balance method, this method describes the process of electron temperature change in the energy band in detail, and there is no need to use the optimization algorithm for a solution. When different initial temperatures are selected, the electron temperature of each energy level can be solved by self-consistent solution, and the convergence value with good consistency can be obtained. The results show that the deviation of the convergence value of electron temperature from the mean value is less than 8%, and the deviation of scattering rate is less than 1.6%. This study provides a new method for the design and research of quantum cascade lasers.
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图 1 自洽求解电子数、电子温度程序流程图
Figure 1. Program flow chart of self consistent solution of electron number and electron temperature
图 2 不同偏置电压下各能级电子散射率的计算结果
Figure 2. Calculation result of the scattering rate of each energy level under different bias voltages
图 3 为不同初偏置电压下散射率计算结果相对于均值的相对误差
Figure 3. Relative error of the scattering rate calculation result relative to the mean value under different bias voltage
图 4 各能级电子温度在不同偏置电压下的计算值
Figure 4. (a) Calculation result of the electron temperature of each energy level under different bias voltage
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[1] Faist J, Capasso F, Sivco D L, et al. Short wavelength ( λ~3.4 μm) quantum cascade laser based on strained compensated InGaAs/AlInAs[J]. Applied Physics Letters, 1998, 72(6): 680-682. doi: 10.1063/1.120843 [2] Spitz O, Herdt A, Wu Jiagui, et al. Private communication with quantum cascade laser photonic chaos[J]. Nature Communications, 2021, 12: 3327. doi: 10.1038/s41467-021-23527-9 [3] Rodriguez E, Mottaghizadeh A, Gacemi D, et al. Room-temperature, wide-band, quantum well infrared photodetector for microwave optical links at 4.9 μm wavelength[J]. ACS Photonics, 2018, 5(9): 3689-3694. doi: 10.1021/acsphotonics.8b00704 [4] Irimajiri Y, Morohashi I, Kawakami A. Multifrequency heterodyne detection of molecules using a hot electron bolometer mixer pumped by two phase-locked THz-quantum cascade lasers[J]. IEEE Transactions on Terahertz Science and Technology, 2020, 10(5): 474-479. doi: 10.1109/TTHZ.2020.2990358 [5] Dostál M, Suchánek J, Válek V, et al. Cantilever-enhanced photoacoustic detection and infrared spectroscopy of trace species produced by biomass burning[J]. Energy & Fuels, 2018, 32(10): 10163-10168. [6] Zhang Jianxiong, He Yong, Liang Shanshan, et al. Non-invasive, opsin-free mid-infrared modulation activates cortical neurons and accelerates associative learning[J]. Nature Communications, 2021, 12: 2730. doi: 10.1038/s41467-021-23025-y [7] Liu Xi, Qiao Zhi, Chai Yuming, et al. Nonthermal and reversible control of neuronal signaling and behavior by midinfrared stimulation[J]. Proceedings of the National Academy of Sciences of the United States of America, 2021, 118: e2015685118. [8] Li Z M S, Li Yingying, Ru Guoping. Simulation of quantum cascade lasers[J]. Journal of Applied Physics, 2011, 110: 093109. doi: 10.1063/1.3660207 [9] Jirauschek C, Kubis T. Modeling techniques for quantum cascade lasers[J]. Applied Physics Reviews, 2014, 1: 011307. doi: 10.1063/1.4863665 [10] 孙远昆. 量子级联激光器的数值优化及其光电调制特性研究[D]. 重庆: 重庆大学, 2020: 26-28Sun Yuankun. Numerical optimization and photoelectric modulation characteristics of quantum cascade laser[D]. Chongqing: Chongqing University, 2020: 26-28 [11] Slingerland P, Baird C, Giles R H. Application of multi-subband self-consistent energy balance method to terahertz quantum cascade lasers[J]. Semiconductor Science and Technology, 2012, 27: 065009. doi: 10.1088/0268-1242/27/6/065009 [12] 高星星. 几种粒子群优化算法及其应用研究[D]. 银川: 北方民族大学, 2020: 7-8Gao Xingxing. Several particle swarm optimization algorithms and their applications[D]. Yinchuan: North Minzu University, 2020: 7-8 [13] Peng Chen, Sun Yuankun, Zhu Liguo, et al. Investigation of subband electron temperatures of quantum cascade lasers[J]. IEEE Photonics Journal, 2019, 11: 1500710. [14] Donovan K, Harrison P, Kelsall R W. Self-consistent solutions to the intersubband rate equations in quantum cascade lasers: analysis of a GaAs/Al x Ga1- x As device[J]. Journal of Applied Physics, 2001, 89(6): 3084-3090. doi: 10.1063/1.1341216 [15] Liu Zhijun, Wasserman D, Howard S S, et al. Room-temperature continuous-wave quantum cascade lasers grown by MOCVD without lateral regrowth[J]. IEEE Photonics Technology Letters, 2006, 18(12): 1347-1349. doi: 10.1109/LPT.2006.877006 [16] 祁昶, 石新智, 叶双莉, 等. THz量子级联激光器跃迁速率的数值求解及验证[J]. 光电子·激光, 2013, 24(12):2283-2288 doi: 10.16136/j.joel.2013.12.001Qi Chang, Shi Xinzhi, Ye Shuangli, et al. Numerical calculation and validation of transition rate for terahertz quantum cascade lasers[J]. Journal of Optoelectronics·Laser, 2013, 24(12): 2283-2288 doi: 10.16136/j.joel.2013.12.001 -
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