Impact of Carrier Momentum (k)-Space Separation on GeSn Infrared Photodetectors

Ge
_1-x
Sn
_x
alloy has emerged as a promising material for complementary metal-oxide semiconductor (CMOS) compatible mid-infrared photodetectors (PDs). In addition to its inherent advantage for being CMOS compatible, the close proximity of its conduction band Γ- (Γ-valley) and L- (L-valley) valleys in energy presents another unique property that can improve the performance of PDs where the efficient direct-gap optical absorption can take place around the Γ-valley while the L-valley plays the role of storing photo-generated carriers for longer lifetime, allowing for more of them being collected as photo-current and therefore enhancing the responsivity and detectivity. The lifetime increase is attributed to the significant percentage of photo-generated electrons residing in the L-valley being separated in momentum (k)-space from the holes near the Γ-point of the Brillouin zone. We shall present a detailed performance analysis of Ge
_1-x
Sn
_x

p-i-n
PDs exploring the momentum (k)-space separation of electrons and holes. We first determine the electron distributions between Γ- and L-valleys for various Sn compositions for small injections of excess carriers, from there we estimate the carrier lifetimes in relation to the carrier collection times under different drift saturation velocities in the Ge
_1-x
Sn
_x
active layer of various thicknesses to evaluate the carrier collection efficiency. We subsequently analyze the optical absorption coefficient and responsivity of the Ge
_1-x
Sn
_x
PDs with different Sn compositions and various active layer thicknesses. The results show that the effect of carrier momentum (k)-space separation is more dominant for lower Sn compositions when the Ge
_1-x
Sn
_x
alloys are indirect with the L-valley sits below the Γ-valley in energy and it persists for higher Sn compositions (up to ∼10%) even when the material becomes direct because photo-generated electrons can still populate the L-valley through the fast inter-valley scattering process owing to its large effective-mass density-of-states. Taking advantage of the strong optical absorption and long carrier lifetime offered by the unique conduction band structure in Ge
_1-x
Sn
_x
, we can optimize the alloy composition and device structure for the Ge
_1-x
Sn
_x
PD designed to operate in specified wavelength range, potentially putting this material system in a position to compete with existing mid-infrared technologies in addition to its economic advantage for being CMOS compatible.