Theory and design of In${}_x$Ga${}_{1-x}$As${}_{1-y}$Bi${}_y$ mid-infrared semiconductor lasers: type-I quantum wells for emission beyond 3 $\mu$m on InP substrates

We present a theoretical analysis and optimisation of the properties and performance of mid-infrared semiconductor lasers based on the dilute bismide alloy In${}_x$Ga${}_{1-x}$As${}_{1-y}$Bi${}_y$, grown on conventional (001) InP substrates. The ability to independently vary the epitaxial strain and emission wavelength in this quaternary alloy provides significant scope for band structure engineering. Our calculations demonstrate that structures based on compressively strained In${}_x$Ga${}_{1-x}$As${}_{1-y}$Bi${}_y$ quantum wells (QWs) can readily achieve emission wavelengths in the 3 – 5 $\mu$m range, and that these QWs have large type-I band offsets. As such, these structures have the potential to overcome a number of limitations commonly associated with this application-rich but technologically challenging wavelength range. By considering structures having (i) fixed QW thickness and variable strain, and (ii) fixed strain and variable QW thickness, we quantify key trends in the properties and performance as functions of the alloy composition, structural properties, and emission wavelength, and on this basis identify routes towards the realisation of optimised devices for practical applications. Our analysis suggests that simple laser structures – incorporating In${}_x$Ga${}_{1-x}$As${}_{1-y}$Bi${}_y$ QWs and unstrained ternary In${}_{0.53}$Ga${}_{0.47}$As barriers – which are compatible with established epitaxial growth, provide a route to realising InP-based mid-infrared diode lasers.