Vol.:(0123456789) Optical and Quantum Electronics ( 2020) 52:348 https://doi.org/10.1007/s11082-020-02462-x 1 3 Analytical investigation of activation energy for Mg‑doped p‑AlGaN Md. Soyaeb Hasan 1  · Ibrahim Mustafa Mehedi 2,3  · S. M. Faruk Reza 4  · Md Rejvi Kaysir 4  · Md Rafqul Islam 4 Received: 6 October 2019 / Accepted: 2 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract An analytical model has been developed to investigate the activation energy profle in Mg- doped p-Al x Ga 1−x N alloy for the entire range of Al composition. For any Al content, the calculated activation energy quantitatively shows a good agreement with experimental result which has also been confrmed by both Hydrogen atom model and efective Bohr radius model. Through this empirical analysis, a breakthrough is apparent for the hole con- centration and sheet resistivity with particular Al concentration. It is found that the hole concentration is < 10 17  cm −3 while the Al content, x > 30% in p-Al x Ga 1-x N. Moreover, the sheet resistivity is found to be < 1 Ω-cm up to the Al content of 30%. Finally, the tem- perature-induced changing behavior of hole concentration and sheet resistivity have been explored here. These results could be a good insight for fabricating the AlGaN-based real- world devices for future optoelectronics. Keywords p-Al x Ga 1−x N · Mg acceptor · Activation energy · Hole concentration · Sheet resistivity 1 Introduction Since a few years, aluminum gallium nitride (AlGaN) semiconductor alloys are exten- sively being investigated for high efciency light-emitting-diodes and lasers operating in blue to deep-ultra-violet (UV) regime (Jiang et al. 2015). The tunable direct band gap of AlGaN ternary alloy covering the wide spectrum from 3.43 eV to 6.11 eV designates * Ibrahim Mustafa Mehedi imehedi@kau.edu.sa 1 Department of Electrical, Electronic and Communication Engineering, Military Institute of Science & Technology, Dhaka 1216, Bangladesh 2 Department of Electrical and Computer Engineering (ECE), King Abdulaziz University, Jeddah, Saudi Arabia 3 Center Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, Saudi Arabia 4 Department of Electrical and Electronic Engineering, Khulna University of Engineering & Technology, Khulna 9203, Bangladesh