  Given an open set $\Omega\subset\mathbb{R}^3$. We deal with the spectral
study of Dirac operators of the form
$H_{a,\tau}=H+A_{a,\tau}\delta_{\partial\Omega}$, where $H$ is the free Dirac
operator in $\mathbb{R}^3$, $A_{a,\tau}$ is a bounded invertible, self-adjoint
operator in $\mathit{L}^{2}(\partial\Omega)^4$, depending on parameters
$(a,\tau)\in\mathbb{R}\times\mathbb{R}^n$, $n\geqslant1$. We investigate the
self-adjointness and the related spectral properties of $H_{a,\tau}$, such as
the phenomenon of confinement and the Sobolev regularity of the domain in
different situations.
  Our set of techniques, which is based on fundamental solutions and layer
potentials, allows us to tackle the above problems under mild geometric measure
theoretic assumptions on $\Omega$.
