Criteria of the electron pumping in electron-hole quantum plasma

The degradation of quantum semiconductor plasma during electron pumping is an important problem since it has several applications in the technological industry. Moreover, the identification of such a problem cannot be accomplished by experiment alone and a further theoretical investigation is required. Owing to the energy gap of semiconductors, electrons should acquire energy in order to move from the valence band to the conduction band. Therefore, to employ the quantum fluid model that includes the exchange-correlation potentials, Bohm potential, and the degenerate pressure, the electron-hole lifetime should be greater than the plasma oscillation time. If the latter condition is not satisfied, the quantum fluid model failed to describe the system and it is convenient to use the density functional theory. As a result of that, we apply the quantum fluid model to GaN where the plasma oscillation has a time of 0.002 ps while the electron-hole lifetime is 1 ps. The modified Kadomtsev-Petviashvili (mKP) equation had been obtained using a new set of stretched coordinates as the Kadomtsev-Petviashvili (KP) equation had been derived in (Afify et al 2019 Chaos Soliton Fract 124, 18–25). Our findings determine whether the quantum fluid model is valid or not in the case of semiconductor plasma. Studying exchange effects in a dynamic context has certain limitations. Thus, we stressed that the more accurate approaches introduced in the literature are hard to apply for nonlinear issues. Further, the applicability of our results is discussed, but not this much. Moreover, the numerical results showed that the electron beam parameters and quantum effects have significant effects on the growth of the solitary waves. (paper)