The saturation current density of a P-N junction germanium diode is 250mA/m2  at 300 K. Find the voltage ( in  V ) that would have to be applied across the junction to cause a forward current density  105A/m2 to flow. ( K=1.38×10−23 J/K)

The current in the junction diode is given by I=IS(eeVηKT−1)      For  Ge     η=1Dividing by cross-section area, we get J=JS(eeVKT−1)      →(1) Put JS=250mA/m2   =250×10−3A/m2 J=105A/m2,    T=300 KAfter solving (1) ,  JJs +1 = eeVKT⇒lnJJs +1 =eVKT ⇒V = KTe lnJJs +1⇒V = 1.38×10−23×3001.6×10-19 ln105250×10−3 +1⇒V = 258.75×10-4 ×12.899=0.33 V