Determination of the piezoelectric field in InGaN quantum wells

Abstract

In many studies, the value of the experimentally determined internal piezoelectric field has been reported to be significantly smaller than theoretical values. We believe this is due to an inappropriate approximation for the electric field within the depletion region, which is used in the analysis of experimental data, and we propose an alternative method. Using this alternative, we have measured the strength of the internal field of InGaN p-i-n structures, using reverse bias photocurrent absorption spectroscopy and by fitting the bias dependent peak energy using microscopic theory based on the screened Hartree-Fock approximation. The results agree with those using material constants interpolated from binary values. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1896446͔The internal field in GaN based quantum wells plays an important role in the operation of nitride-based light emitting diodes and lasers, affecting the emission wavelength, 1 the oscillator strength, 2 and the recombination lifetime, 3 hence an accurate value of the internal field is essential in understanding the properties of these devices. The internal field skews and breaks the symmetry of the well, causing spatial separation of the electron and hole wave functions and hence reduces the electron-hole overlap function. Reported values of the internal field 4,5 for the same nominal indium content vary by more than a factor of two, which is far greater than the expected error due to unintended variations in the indium content. Also there are large reported differences between theoretical and experimental results. 6 The majority of approaches to determine the internal field, have relied upon counteracting the quantum-confined Stark effect with an externally applied reverse bias and measuring properties of the quantum well as a function of this applied reverse bias. The reverse bias acts to oppose the internal field reducing the effect of the induced quantum confined Stark effect. At low bias, the well is skewed due to the internal field. At a critical bias, the contributions from the applied bias and the internal field are equal and opposite. In this case, the overlap of electron and hole wave functions and the ground state electron to heavy hole transition energy are maximized.The value of the externally applied bias to achieve flat band ͑"square-up" the quantum well͒ can then be used to obtain the internal field. The net internal field E in the well ͑E = 0 when the well is square͒ is related to the applied bias V using: 4where E int , L w , N, 0 , d d , and d u are the internal field, the quantum well width, the number of quantum wells, the built-in potential and the depletion and intrinsic widths, respectively. The width of the intrinsic region d u is given by the sum of the multiple well and barrier widths. The internal field E int , is the sum of the fields due to the piezoelectric effect and the spontaneous polarization. The first term of Eq. ͑1͒ is the background field written as the total voltage drop divided by the distance, over ...

High quantum efficiency of semipolar GaInN/GaN quantum wells

“…1 and 2 yield the piezoelectric fields. The polar quantum well containing about 10 % indium has its flatband voltage at −22 V. This corresponds to a piezoelectric field of −1.9 MV/cm, being in accordance with previously published values [9,10]. A negative field like here is pointing from the surface to the substrate.…”

Electronic Properties of InGaN/GaN Vertical‐Cavity Lasers

“…However, experimental investigations of InGaN quantum wells often result in weaker built-in fields than predicted, ranging from 20% [33] to 80% [34] of the theoretical value, with typical results near 50% [35]. This broad variation has been attributed to partial compensation of the polarization field by fixed defect and interface charges [36] or to inappropriate analysis of measured data [37]. On the other hand, the theoretical polarization formulas may deviate from reality, especially for InGaN, as only AlGaN measurements have been used for validation [31].…”

Effects of built-in polarization on InGaN-GaN vertical-cavity surface-emitting lasers

“…This broad variation has been attributed to partial compensation of the built-in polarization by fixed defect and interface charges [14] or to inappropriate analysis of measured data [15]. On the other hand, the theoretical polarization model may deviate from reality, especially for InGaN, as only AlGaN measurements have been used for validation [1].…”