Physical model

Fig. 1. Wave functions of the ground electron and hole states in different quantum wells at bias Ub=3.4V.

The LED operation is considered within the 1D drift-diffusion model of carrier transport in the heterostructure that accounts for specific features of the nitride semiconductors - strong piezoeffect, existence of spontaneous electric polarization, low efficiency of acceptor activation, and high threading dislocation density (normally, ~10⁷-10⁹ cm^-2) in the material. Along with bimolecular radiative electron and hole recombination, an original model of non-radiative carrier recombination on threading dislocation cores is incorporated into the SiLENSe code. The latter allows analyzing the interplay between the radiative and non-radiative recombination channels and predicting the internal emission efficiency of the LED structure as a function of threading dislocation density.

The spectrum of light emission from a single- or multiple-quantum-well active region is calculated with account of the complex valence band structure of wurtzite semiconductors by using the 8×8 Kane Hamiltonian. Energies and wave functions of localized carrier states are found from numeric solution of the Schrodinger equation within the effective-mass approximation. Generation of the grid for each QW is totally automatized in the SiLENSe code.

Fig. 2. Electric current versus bias for the MQW LED (comparison with experiment).

The model implemented into the SiLENSe code used the following assumptions:

• Exact account of localized and distributed polarization charges in the LED structure induced by both spontaneous and piezo polarization in nitride semiconductors;
• Fermi statistics is used for electrons and holes covering the cases of both degenerate and non-degenerate semiconductors;
• Partial ionization of donors and acceptors depending on the respective quasi-Fermi level positions is allowed for;
• Strain in the LED structure is calculated assuming coherent growth of all epilayers on an underlying buffer layer, the user can specify partial strain relaxation in some layers;
• Bimolecular radiative electron and hole recombination is considered with neglect of quantum-confined effects on the recombination rate;
• Non-radiative carrier recombination on threading dislocation cores, point defects, and Auger recombination. We have developed an original model of non-radiative recombination on dislocation cores with account of IQE increase due to carrier localization on fluctuations of In composition;
• I-V characteristic of an LED is computed with a given serial resistance that should account for both the lateral current spreading in the LED chip and ohmic contact resistances;

• Fig. 3. Light emission efficiency versus current density. Data on the external emission efficiency are plotted by circles. Effect of dislocation density on the internal emission efficiency is shown.

  Light emission and gain spectra are computed with a post-processing module operating with the band profiles of the LED structure obtained and accounting for (i) the complex structure of the valence band of nitride materials and (ii) the contribution of the confined electronic states;
• Distribution of the electric/magnetic field in TE/TM waveguide modes is computed with account of birefringence of III-nitrides. An original approximation of the frequency-dependent dielectric constant of III-nitride covers the whole spectrum range^*;
• Optical loss because of free carrier absorption is obtained from the known distribution of the electric field intensity in the mode and the carrier concentration^*.