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 ...

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Standard rate equation models of island formation in the InAs/GaAs(001) system have been reassessed in terms of new experimental evidence from real time in-situ reflectance anisotropy spectroscopy (RAS) measurements. These measurements have revealed the behaviour and role of the wetting layer in the modified Stranski-Krastanov growth mode during molecular beam epitaxial growth showing that it can continue to significantly increase in thickness following the onset of islanding. The presence of two dimensional (2D) islands, which act as precursors to three dimensional (3D) islands (the quantum dots) in conventional models, does in principle allow an extension of the "wetting layer". However, it has been found necessary to extend the standard model to include extra terms that allow material to be incorporated into (and detach from) the wetting layer and which cannot convert to 3D islands. With this improved model, it is found possible to achieve agreement with the RAS measurements.

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D e p m n e " t o / P h r s i c s a~A s t~"~~~, CordiffUniversily. P.O. Box 913. Cardiff CF24 3YB. Woles, U. K. Tel. +44 (0)2920 874458 Fax. +M (OJ2920 840567 emil: smowronpml?&& Weng W. Chow Semiconductor Material and Devices Depmnent, Sondin Nnrionnl Lnbomton'es, Albuquerque. NM 87185-OM))Abstract:. We have measured piezoelectric fields in p-i-n LED structures using the quantum confined 'Stark effect and photocurrent absorption. The results agree with calculations of the absorption where material parameters are interpolated from the binaries. >The piezoelectric field in InGaN quantum wells plays an important role in the operation of nitride bas@ LEDs and lasers, affecting the emission wavelength, the gain spectrum and spontaneous recombination current. Values of the piezoelectric field strength reported in the literature vary by more than a factor of two even for the same nominal indium content and it is therefore uncertain which value of piezoelectric constant should be used when modelling, or understanding the performance of, these structures. In this work we have measured the piezoelectric field strength for a number of p-i-n structures and hence determined the piezoelectric constant. We have measured the amplitude and energy of the peak of the photocurrent absorption spectrum as a function of the externally applied reverse bias.The reverse bias acts to.oppose the piezoelectric field reducing the effect of the piezoelectrically induced quantum confined Stark effect until at a critical value of bias the quantum well is square. At this bias the overlap of.elecmn g d hole wavefunctions (and hence the amplitude of the absorption) and the lowest electron to heavy hole transition energy are maximised (see figure 1). At higher bias the well is skewed in the opposite sense and the amplitude and energy of the absorption peak decrease.We.have measured absorption'specga as a function of the reverse bias and an example of the raw data is plotted in figure 2. The peak amplitude of the photocurrent absorption and the energy of the peak of the lowest transition energy are plotted in figure 3 as a function of the externally applied reverse bias. All the data shown are for a sample consisting of 5 Ino.lsG%.ssN quantum wells, each 3nm wide with 7nm wide Ina.03G%.p7N baniers as described in reference 1. Both the amplitude and transition energy have a maximum at the same value of external voltage of 8M.5 V. The piezoelectric field is derived from this voltage using the expression [2]:where V is the externally applied bias, V,, is the built in voltage, N is the number of wells, L, is the well width, 4, is the width of the undoped active region and dd is the depletion width. To correctly determine the depletion width of a p-i-n structure we make use of an analytic approximation we have derived that includes the effect of the field in the intrinsic region.-We confirm that this is a good approximation over the full range of reverse bias we employ using the software package SimwinTM. Using this approximation we determine the piezoel...