A Zener diode has a contact potential of $1\, V$ in the absence of biasing. It undergoes Zener breakdown for an electric field of $10^{6} \,V / m$ at the depletion region of $p-n$ junction. If the width of the depletion region is $2.5 \,\mu\, m$, what should be the reverse biased potential for the Zener breakdown to occur?