Spike time dependent plasticity (STDP) is a learning rule in biology, where the time-correlation of narrow pre- and post-synaptic spikes (tspike ≈5ms) is tracked across a wide learning window (LW) of time (tLW = ±80ms) by neurotransmitter dynamics at the synapse such that tLW:tspike> 20. In hardware, resistive random access memory (RRAM) (1M)-based synapse shows STDP by the superposition of long preand post-synaptic neural waveforms comparable to the timescale of the learning window. However, this artificially limits the spike rate and needs a complicated peripheral circuit to generate the waveform, which has an area penalty. In this letter, we propose a PrxCa1-xMnO3 (PCMO)-based RRAM (1M) with an impact-ionization (II)based silicon (Si) NIPIN (n-iv-δ p-i-n) selector (1S) diode as a synapse to operate with only short spikes. The NIPIN device transient response is utilized as a clock at the synapse to compute a preand post-spike time correlation, such that the 1M1S synapse requires short pulses instead of long waveforms. We experimentally demonstrate that very short (tspike ~ 80 ns) square pulses are required to generate STDP while the learning window is tLW ≈ ± 1.5 μs, which enables tLW:tspike ≈19. Furthermore, a hardware acceleration of 1000× over biology is shown. The square pulse scheme avoids complex waveforms and related complicated circuits. Thus, the synaptic time-keeping is demonstrated that enables biologically realistic SNN for future brain inspired computing.