Shock-waves and commutation speed of memristors

Progress of silicon based technology is nearing its physical limit, as minimum feature size of components is reaching a mere 10 nm. The resistive switching behaviour of transition metal oxides and the associated memristor device is emerging as a competitive technology for next generation electronics. Significant progress has already been made in the past decade and devices are beginning to hit the market; however, it has been mainly the result of empirical trial and error. Hence, gaining theoretical insight is of essence. In the present work we report the striking result of a connection between the resistive switching and {\em shock wave} formation, a classic topic of non-linear dynamics. We argue that the profile of oxygen vacancies that migrate during the commutation forms a shock wave that propagates through a highly resistive region of the device. We validate the scenario by means of model simulations and experiments in a manganese-oxide based memristor device. The shock wave scenario brings unprecedented physical insight and enables to rationalize the process of oxygen-vacancy-driven resistive change with direct implications for a key technological aspect -- the commutation speed.