Ferroelectric domain switching under low voltage or short pulses is of interest for the development of high-density random access memory (FRAM) devices. Being necessarily very small in size, instability and back switching often occur when the external voltage is removed, which creates serious problems. In this investigation, a general approach to determine the minimum size of ferroelectric domain to avoid back switching was developed, and as an example, a 180^o domain in a ferroelectric thin film covered by the upper and lower electrodes was considered in detail. We note that our approach is generally applicable to many other fields, including phase transformation, nucleation and expansion of dislocation loops in thin films, etc.