= Solution
Taking room <temperature> as $300\,\mathrm K$, the <thermal voltage> is $V_T=k_BT/q=0.025852\,\mathrm V$. For the stated <ideal diode>, $n=1$, so
$$
J=10^{-12}\left[\exp\!\left(\frac{0.75}{0.025852}\right)-1\right]
=\boxed{3.98\,\mathrm{A\,cm^{-2}}}.
$$
The $-1$ term is negligible here. A different precise interpretation of room <temperature> changes the result noticeably because of the exponential; the calculation above states its <temperature> explicitly.
For a lower-bandgap material, the <intrinsic carrier concentration> generally rises, increasing the reverse saturation <current density>, approximately through $J_0\propto n_i^2$ with $n_i^2\propto\exp(-E_g/k_BT)$ when other parameters are held comparable. Thus \b[the forward <electric current> at the same <voltage> would normally increase]. If $J_0$ were artificially held fixed at the supplied numerical value, however, the ideal-diode equation would give the same <electric current>: the <band gap> dependence enters through the material parameters rather than as a separate term in that equation.
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