By introducing a new classification of the growth rate of exponential functions, singular solutions for \(-\Delta u=f(u) \) in 2-dimensions with exponential nonlinearities are constructed. The strategy is to introduce a model nonlinearity ``close" to $f$, which admits an explicit singular solution. Then, one obtains an approximate singular solution, and concludes by a suitable fixed point argument. Our method covers a wide class of nonlinearities in a unified way, e.g., \(f(u) = u^re^{u^q}\ (q>1,r\in \mathbb{R}), f(u) = e^{u^{q}+u^r}\ ({q>1,\ q/2>r>0}) \) or \(f(u) = e^{e^u} \). As a special case, our result contains a pioneering contribution by Ibrahim--Kikuchi--Nakanishi--Wei for \(u(e^{u^2}-1) \). Joint work with Yohei Fujishima (Shizuoka University, Japan), Norisuke Ioku (Tohoku University, Japan) and Bernhard Ruf (Istituto Lombardo, Italy).