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 ...
Pulsed light-current characteristics of InGaN/GaN quantum well light-emitting diodes have been measured as a function of temperature, with sublinear behavior observed over the whole temperature range, 130-330 K. A distinctive temperature dependence is also noted where the light output, at a fixed current, initially increases with temperature, before reaching a maximum at 250 K and then decreases with subsequent increases in temperature. On the basis of a drift diffusion model, we can explain the sublinear light-current characteristics and the temperature dependence by the influence of the large acceptor ionization energy in Mg-doped GaN together with a triangular density of states function characteristic of localized states. Without the incorporation of localization effects, we are unable to reproduce the temperature dependence whilst maintaining emission at the observed wavelength. This highlights the importance of localization effects on device performance.
We describe a technique for the measurement of optical gain and loss in semiconductor lasers using a single, multisection device. The method provides a complete description of the gain spectrum in absolute units and over a wide current range. Comparison of the transverse electric and transverse magnetic polarized spectra also provides the quasi-Fermi-level energy separation. Measurements on AlGaInP quantum well laser structures with emission wavelengths close to 670 nm show an internal loss of 10 cm Ϫ1 and peak gain values up to 4000 cm Ϫ1 for current densities up to 4 kA cm Ϫ2 .
The spontaneous emission and optical gain spectra from an InGaAs quantum dot laser have been independently measured under the same operating conditions. Using these spectra a combined probability-distribution function describing the electron occupancy in the conduction and valence bands has been experimentally determined. Comparison of this function with theoretical curves based on Fermi-Dirac statistics shows that for temperatures down to 100 K the carrier occupancy statistics are accurately described by thermal distributions. Measurements at 70 K show a breakdown of thermodynamic equilibrium indicated by non-thermal carrier distributions.
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