The quatification of the interband transitions in the quantum confined Stark effect*

The potential applications in optical devices such as μ-LED, high-speed modulators, wavelength selective detectors and optically bistable switches have motivated strong interest in the quantum confined Stark effect (QCSE) in the heterostructures. However, the quantification of the QCSE is difficult and complicated which is currently limited to the allowed interband transitions. For the forbidden transitions, the solving process is time-consuming and the crossings of the forbidden transitions may appear when the electric field increases. Thus, a more accurate description of the light emission or absorption properties of quantum wells under the applied electric field is urgently needed. Here, we propose a 3D-plot to study the interband transitions. By the Wentzel–Kramers–Brillouin approximations, we deduce that the average interband transition spacing ΔE below or near the E_g is innert to the electric field strength and the ΔE is inversly proportional to the square of the quantum well's width L by 4πh_bar^2/sqrt(m_em_h) below the E_g and 12πh_bar^2/sqrt(m_em_h) slightly above the E_g . The simulations further validate the 2 scaling laws and the influence of the charge's screening is also studied.