In a LED, we can also use ABC model to describe many of its performances. One of them is external quantum efficiency. $($a$)(5$pts$)$ Please write down the basic EQE definition from the lecture note. What is its relation to internal quantum efficiency $({}_{\text{I}\text{O}\text{E}})$ and light extraction efficiency $({}_{\text{e}\text{x}\text{t}})?($b$)(7$pts$)$ Now, if we know that the ${}_{\text{I}\text{Q}\text{E}}$ can be defined as $\frac{B{N}^2}{AN+B{N}^2},$ and ${}_{\text{e}\text{x}\text{t}}$ can be viewed as a constant number $($we can set as $100\%$ for now$).$ N is the carrier concentration. If carrier concentration N is really small, ${}_i($injection efficiency$)=100\%,q$ and V are the elementary charge and active region volume, and the total current is I. Please derive the EQE under this condition$($as a parameter of I, A$,$ B$,$ q$,$ V$).($c$)(3$pts$)$ Now, if N approaches infinity, what will the EQE become?