Abstract
<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Polar GaInN and AlGaN quantum wells (QWs) are widely used in light emitting diodes and laser diodes (LDs). However, the widths of such QWs are usually limited to a few nanometers in order to ensure a sufficiently large overlap between the wave functions of the ground electron and the ground hole state. By increasing the QW width we enter the area of ‘dead’ width where, the overlap of the electron and hole wave functions decreases almost to zero and the luminescence efficiency drastically deteriorates. Therefore, it is assumed that wide QWs are not suitable for light emitters and very wide (8-15 nm) QWs are not considered as a promising gain medium for LDs. Hence such QWs are very rarely studied both experimentally and theoretically. In this work the material gain is calculated for Ga<sub>0.8</sub>In<sub>0.2</sub>N/GaN and Al<sub>0.8</sub>Ga<sub>0.2</sub>N/AlN QWs with a width varying in the range of 2-15 nm. We observed that the material gain at fixed carrier concentration for these QWs drops to zero with the increase in the QW width and reaches negative values in the width range of ∼4-8 nm even for high carrier concentrations, but after exceeding a certain width to ∼8-12 nm it begins to increase rapidly and reaches the values greater than those observed for narrow QWs. This phenomenon is related to the screening of the built-in electric field by carriers, which is easier for wide QWs, and the reduction of the distance between the energy levels for electrons and holes. For the latter reason, optical transitions between higher energy states make a very significant contribution to the positive material gain</b> .
Highlights
T HE SPONTANEOUS and piezoelectric polarization in wurtzite III-nitrides is extremely large [1], [2] and Manuscript received April 7, 2021; revised June 17, 2021, July 29, 2021, and September 8, 2021; accepted September 19, 2021
The same three-dimensional carrier concentrations were chosen for this comparison, this concentration can be compared with the current that flows through the quantum wells (QWs) located in the p-n junction, since the laser output power is usually measured as a function of current [16], [17], [24], [26]
The selected carrier concentrations in QW region are quite high and a positive material gain appears at much lower carrier concentrations for thin and wide QWs, but higher carrier concentrations are better to study changes in spectral position of the material gain and its intensity
Summary
T HE SPONTANEOUS and piezoelectric polarization in wurtzite III-nitrides is extremely large [1], [2] and . The polarization phenomena can be beneficial in many semiconductor devices because they enabled interesting physical effects, such as doping-free high electron mobility transistors [3]–[6], polarization-induced doping [7], or enhancement in the tunneling current in devices with tunnel junctions [8]–[10] They are rather not considered favorable in the GaInN and AlGaN quantum wells (QWs) used in light emitting diodes (LEDs) and laser diodes (LDs). Decrease of electron-hole overlap and wide QW are not considered as a promising gain medium for LDs. In the case of GaInN/GaN QWs, the higher the indium content, the larger the built-in electric field related to piezoelectric polarization, and the larger the separation of carrier wave functions. It shows that due to the spontaneous and piezoelectric polarization in III-nitrides, the optimal QW width for applications in LDs is very unintuitive and very different from what is assumed to be optimal for non-polar QWs
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