  We perform particle-in-cell simulations of perpendicular nonrelativistic
collisionless shocks to study electron heating and pre-acceleration for
parameters that permit extrapolation to the conditions at young supernova
remnants. Our high-resolution large-scale numerical experiments sample a
representative portion of the shock surface and demonstrate that the efficiency
of electron injection is strongly modulated with the phase of the shock
reformation. For plasmas with low and moderate temperature (plasma beta
$\beta_{\rm p}=5\cdot 10^{-4}$ and $\beta_{\rm p}=0.5$), we explore the
nonlinear shock structure and electron pre-acceleration for various
orientations of the large-scale magnetic field with respect to the simulation
plane while keeping it at $90^\circ$ to the shock normal. Ion reflection off
the shock leads to the formation of magnetic filaments in the shock ramp,
resulting from Weibel-type instabilities, and electrostatic Buneman modes in
the shock foot. In all cases under study, the latter provides first-stage
electron energization through the shock-surfing acceleration (SSA) mechanism.
The subsequent energization strongly depends on the field orientation and
proceeds through adiabatic or second-order Fermi acceleration processes for
configurations with the out-of-plane and in-plane field components,
respectively. For strictly out-of-plane field the fraction of supra-thermal
electrons is much higher than for other configurations, because only in this
case the Buneman modes are fully captured by the 2D simulation grid. Shocks in
plasma with moderate $\beta_{\rm p}$ provide more efficient pre-acceleration.
The relevance of our results to the physics of fully three-dimensional systems
is discussed.
