Low-frequency hybrid waves are excited by the externally injected electron beam in the presence of a uniform magnetic field B ₀ in a semi-relativistic semiconductor plasma. The properties of the medium are analyzed by employing the quantum hydrodynamic model where quantum characteristics contribute through Fermi degenerate pressure, tunnelling potential, and the exchange-correlation potential. Keeping in view the technological applications of semiconductor systems under extreme conditions, the behaviour of wave instability is analyzed by varying the constituent parameters like number density of plasma species, streaming speed of electron beam and strength of the applied magnetic field.

在半相对论半导体等离子体中，在均匀磁场B ₀存在下，外部注入的电子束会激发低频混合波。通过采用量子流体动力学模型分析介质的特性，其中量子特性通过费米简并压力、隧道势和交换相关势做出贡献。考虑到半导体系统在极端条件下的技术应用，通过改变等离子体种类的数量密度、电子束的流动速度和外加磁场的强度等组成参数来分析波不稳定性的行为。