  Using kinetic equation approach we study dynamics of electrons and phonons in
current-carrying superconducting nanostrips after absorption of single photon
of near-infrared or optical range. We find that the larger the ratio
$C_e/C_{ph}|_{T_c}$ ($T_c$ is a critical temperature of superconductor, $C_e$
and $C_{ph}$ are specific heat capacities of electrons and phonons,
respectively) the larger part of photon's energy goes to electrons, they become
stronger heated and, hence, could thermalize faster during initial stage of hot
spot formation. Thermalization time $\tau_{th}$ could be less than one
picoseconds for superconductors with $C_e/C_{ph}|_{T_c}\gg 1$ and small
diffusion coefficient $D\simeq 0.5 cm^2/s$ when thermalization occurs mainly
due to electron-phonon and phonon-electron scattering in relatively small
volume $\sim \xi^2d$ ($\xi$ is a superconducting coherence length, $d<\xi$ is a
thickness of the strip). At larger times due to diffusion of hot electrons
effective temperature inside the hot spot decreases, the size of hot spot
increases, superconducting state becomes unstable and normal domain spreads in
the strip at current larger than so-called detection current. We find
dependence of detection current on the photon's energy, place of its absorption
in the strip, width of the strip, magnetic field and compare it with existing
experiments. Our results demonstrate that materials with $C_e/C_{ph}|_{T_c} \ll
1$ are bad candidates for single photon detectors due to small transfer of
photon's energy to electronic system and large $\tau_{th}$. We also predict
that even several microns wide dirty superconducting bridge is able to detect
single near-infrared or optical photon if its critical current exceeds 70 $\%$
of depairing current and $C_e/C_{ph}|_{T_c} \gtrsim 1$.
