Kinetic plasma instabilities driven by temperature anisotropies are known to play an essential role in collisionless plasma dynamics, scattering the particles and affecting particle heating and energy conversion between the electromagnetic fields and particles (e.g., Gary, 1993). Among these anisotropy-driven instabilities, the whistler anisotropy instability is excited by electron temperature anisotropy T e,‖ /T e,⊥ < 1 while the electron firehose instability (EFI) develops if T e,‖ /T e,⊥ > 1, where T e,‖ and T e,⊥ are the electron temperatures respectively parallel and perpendicular with respect to the background magnetic field. The EFI is believed to constrain the electron temperature anisotropy by inducing heating (cooling) in the perpendicular (parallel) direction with respect to the background magnetic field, thus leading to isotropization.The EFI was described for the first time by Hollweg and Völk (1970) and W. Pilipp and Völk (1971). Then, Gary and Madland (1985) provided the parametric dependencies of the growth rate of the EF modes with the assumption of parallel propagation, that is, the wave vector k is directed parallel to the background magnetic field. One-dimensional Particle-In-Cell (PIC) simulations further investigated the properties of the parallel propagating EF mode (