= Solution
{c}
A <double heterostructure laser> sandwiches a narrow-<band gap> active layer between wider-<band gap> cladding layers. In a <type-I band alignment>, the <conduction band> edge is lower and the <valence band> edge higher in the active layer. <Electrons> therefore see an <energy> well, and <electron holes> also see a well because their excitation <energy> increases when the <valence band> edge decreases. Both carrier populations remain concentrated where <stimulated emission> occurs.
\Image[/past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2021-double-heterostructure.png]
{title=Carrier and optical confinement in a schematic <double heterostructure laser>}
The active layer also normally has the higher <refractive index>, forming an <optical waveguide>. The optical <normal mode> overlaps the injected carriers strongly, and the wider-<band gap> cladding has less interband <absorption> at the emitted <photon energy>. Carrier confinement reduces leakage, while optical confinement reduces the required pump current and hence heating.
Writing $\Gamma$ for the fraction of the optical <normal mode> overlapping the active layer, the threshold condition is $\Gamma g=\alpha_i+\alpha_m$, with internal and mirror losses $\alpha_i,\alpha_m$. A larger overlap and a higher carrier <number density> at a given current both lower the threshold current. The figure shows composition-induced offsets; a working junction also has <band bending> under bias, which is omitted to make the confinement mechanism visible.
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