In this paper (arXiv:2305.02281), the spectrum of bound and scattering states of the one dimensional Dirac Hamiltonian describing fermions distorted by a static background built from two Dirac delta potentials is studied. A distinction will be made between mass-spike and electrostatic Dirac delta-potentials. The second quantisation is then performed to promote the relativistic quantum mechanical problem to a relativistic quantum field theory and study the quantum vacuum interaction energy for fermions confined between opaque plates. The work presented here is a continuation of [Guilarte et al 2019 Front. Phys. 7 109].