We consider the process of tunneling ionization of atoms at moderate intensities. The question that interests us in particular is the long debated question of whether the finite speed of light precludes tunneling to happen instantaneously. The usual paradigm employed in the experiments to quantify the notion of the tunneling time is based on the so-called attoclock technique. In the attoclock, the target atom is ionized with an elliptically polarized laser pulse and the photo-electron momentum distribution (PMD) is detected in the plane of the polarization. The angular peak of the PMD is offset from the direction dictated by the vector potential at the instant of tunneling and this angular offset provides information about the  tunnelling delay. Using this technique, vanishing tunneling delays have been observed experimentally and predicted theoretically in the calculations employing the nonrelativistic time dependent Schrodinger equation (TDSE). We address the question  of tunneling delay using relativistic approach. We choose a case of the weakly relativistic spinless particle and solve the TDSE with the leading order kinematic correction in the attoclock setup. For the particles with spin the relativistic kinematic effects are closely intertwined with other relativistic effects such as the spin-orbit interaction. By examining the case of the spinless particle, we concentrate on the effects of the relativistic kinematics only. The relativistic kinematics  is a direct consequence of the finiteness  of the speed of light. By examining the case of the spinless particle we can, therefore, study the effect of the finite value of the speed of light on the tunneling delay. We find that the relativistic kinematic effects make the tunneling time finite.\

Dr Igor Ivanov worked within the Research School of Physics of the ANU from 2004 until 2014. At the end of 2014 Dr Ivanov moved to South Korea where he worked at the Centre for the Relativistic Laser Science of the Institute for Basic Science. In 2024 Dr Ivanov returned to Australia and is currently a departmental visitor in Fundamental and Theoretical Physics.