244 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 37, NO. 2, FEBRUARY 2001 Modeling of GaN Optoelectronic Devices and Strain-Induced Piezoelectric Effects Curt A. Flory and Ghulam Hasnain Abstract—Modeling of nitride-based LEDs and laser diodes re- quires a fast modular tool for numerical simulation and analysis. It is required that the modeling tool reflects the primary physical processes of current injection, quantum well (QW) bound-state dy- namics, QW capture, radiative, and nonradiative transitions. The model must also have the flexibility to incorporate secondary phys- ical effects, such as induced piezoelectric strain fields due to lat- tice mismatch and spontaneous polarization fields. A 1-D model with a phenomenological well-capture process, similar to that de- veloped by Tessler and Eisenstein, has been implemented. The ra- diative processes are calculated from first principles, and the mate- rial band structures are computed using theory. The model also features the incorporation of such effects as thermionic emission at heterojunctions, Shockley–Read–Hall recombination, piezoelec- tric strain fields, and self-consistent calculation of the QW bound states with dynamic device operation. The set of equations under- lying the model is presented, with particular emphasis on the ap- proximations used to achieve the previously stated goals. A sample structure is analyzed, and representative physical parameters are plotted. The model is then used to analyze the effects of incorpora- tion of the strain-induced piezoelectric fields generated by lattice mismatch and the spontaneous polarization fields. It is shown that these built-in fields can accurately account for the blue-shift phe- nomena observed in a number of different GaN LEDs. Index Terms—Piezoelectricity, quantum-well devices, semicon- ductor device modeling, semiconductor lasers, semiconductor light emitting modes. I. INTRODUCTION A. Background T HE DYNAMICS of carrier injection and recombination in quantum-well (QW) optoelectronic heterostructures is a complex nonlinear process that dominates device performance. The QW device has intrinsically different carrier transport and optical interaction processes than a bulk device. In bulk devices, carriers are injected directly into the spatial region where inter- actions with photons occur. As a result, the nonlinearities that occur are predominantly material dependent. However, in a QW device, the optical interaction only occurs in a thin region em- bedded within the larger transport structure. The charge carriers are injected at the ends of the device, and must navigate the full transport structure to arrive at the region of optical inter- actions. This results in nonlinearities which are attributable to device structure, and are thus as diverse as the wide range of ge- ometries used in optoelectronic devices today. For example, it has been observed that QW laser perfor- mance is not completely determined by the structure of the Manuscript received June 27, 2000; revised October 12, 2000. The authors are with Agilent Laboratories, Palo Alto, CA 94303 USA. Publisher Item Identifier S 0018-9197(01)00872-7. QWs [1]–[3]. The geometry of the regions surrounding the wells has been seen to strongly affect the device operation. The complicated process by which the carriers are transported through the barrier and optical confinement regions has signif- icant impact on the overall device characteristics. A number of papers have shown that, even under static conditions, it is necessary to analyze the distribution of carriers throughout the entire device structure [3]–[5]. For example, Hirayama et al. [3] have analyzed the continuity and Poisson equations for a single QW laser to demonstrate significant impact on the efficiency by the current injection process. Also, Barrau et al. [5] emphasized the importance of the electric field distribution along the entire length of a QW device, as they demonstrated that the Coulomb interaction between the electron and hole distributions had a significant impact upon the localization of the electrons in the region of type-II QWs. With the importance of the current injection process estab- lished for QW devices, it is clear that any device-modeling pro- gram that is used to aid in the optimization and design of ex- perimental structures must necessarily include the full carrier transport and well-capture dynamics on some level. B. Model Overview Our goal is to develop a fast modular tool for numerical sim- ulation of nitride-based QW LEDs and laser diodes. As implied by the above discussion, a requirement is that the modeling tool reflect the primary physical processes of current injection, QW capture, QW bound-state dynamics, and radiative and nonradia- tive transitions. It was also determined that the model must have the flexibility to incorporate secondary physical effects, such as induced piezoelectric strain fields due to lattice mismatch of the various layers of the structure. In order to be useful in the iterative analysis and design of experimental devices, it is important for the model to exhibit general trends and tendencies due to the relevant physical pro- cesses dominating device performance. It is not so important to accurately model the (usually) known effects that may modify the absolute magnitude of the calculated parameters, but not materially affect general trends and behaviors. For this reason, our model is restricted to one spatial dimension. While this is a significant approximation, it allows a faster analysis cycle, and simplifies the programmatic incorporation of additional phys- ical effects. The foundation of the model used is the work of Tessler, Eisenstein et al. [4], [6], [7], which incorporates trans- port of carriers using the full continuity equations, and describes QW capture by a simple phenomenological process. The simpli- fied QW capture process allows a weak separation between the 0018–9197/01$10.00 © 2001 IEEE