Design of a GaN White Light-Emitting Diode Through Envelope Function Analysis

• Published in: IEEE journal of quantum electronics Vol. 46; no. 2; pp. 228 - 237
• Main Authors: Khoshnegar, M., Sodagar, M., Eftekharian, A., Khorasani, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-02-2010; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Charge carrier processes; Electronics; Envelope function analysis; Exact sciences and technology; Function approximation; Gallium nitride; GaN; k cdot p method; Light emitting diodes; Luminescence; optical intensity spectrum; Optical polarization; Optoelectronic devices; Photoluminescence; Piezoelectric polarization; Quantum well devices; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Wave functions; white LED; Quantum well; Envelope function analysis; Binary compound; Stokes shift; Gallium Nitrides; White light; Wave function; Luminescence; Photoluminescence; Theoretical study; Emission spectrum; Light emitting diode; Energy-level transitions; Piezoelectric materials; GaN; optical intensity spectrum; Transfer matrix method; kip method; Hamiltonian; white LED; Heterostructures; Dipole moment; III-V semiconductors; Interband transition
• ISSN: 0018-9197; 1558-1713
• DOI: 10.1109/JQE.2009.2032556

In this paper, we present an envelope function analysis technique for the design of the emission spectra of a white quantum-well light-emitting diode (QWLED). The nanometric heterostructure that we are dealing with is a multiple QW, consisting of periods of three single QWs with various well thicknesses. With the aid of 6 × 6 Luttinger Hamiltonian, we employ the combination of two methods, k·p perturbation and the transfer matrix method, to acquire the electron and hole wave functions numerically. The envelope function approximation was considered to obtain these wave functions for a special basis set. While adjacent valence sub-bands have been determined approximately, the conduction bands are approximated as parabolic. The effect of Stokes shift has also been taken into account. The dipole moment matrix elements for interband atomic transitions are evaluated via the correlation between the electron and hole envelope functions, for both orthogonal polarizations, thus simplifying the calculation of the photoluminescence intensity. Spatial variations in the hole/electron wave functions have been examined with the introduction of piezoelectric and spontaneous polarization internal fields. We theoretically establish the possibility of a highly efficient InGaN red emitter, resulting in a uniform luminescence in red, green, and blue emissions from a white light emitting diode by adjusting the material composition, internal field, and well thickness.