A quantum dot infrared photodetector (QDIP) confines electrons in all three dimensions inside a nanocrystal (typically InAs dots in a GaAs barrier). Confinement quantizes the conduction-band energy, approximated for a cubic box of side L as:
E_n = n²h² / (8 m* L²)
ΔE = E_excited − E_ground (intersubband energy)
λ_peak = hc / ΔE
Shrinking the dot (Dot diameter) raises ΔE and blue-shifts λ_peak. An incoming photon (Incident IR wavelength) is absorbed with a probability that peaks when its energy matches ΔE — the "Absorption match" meter is a Lorentzian-shaped overlap between the two.
Because confinement is three-dimensional (not just along the growth axis, as in a quantum-well IR photodetector / QWIP), the dipole matrix element has a component along the growth direction even for light arriving at normal incidence — QDIPs can absorb light straight-on, while QWIPs need a 45° facet or diffraction grating to couple the same polarization. Toggle 45° coupled to compare: the absorbed fraction barely changes for the dot, illustrating that relaxed selection rule.
An excited electron only becomes signal if it escapes the dot before relaxing — by thermionic emission or field-assisted tunneling through the barrier. Bias voltage tilts the conduction band and thins the barrier, raising the escape probability modeled here as a logistic function of bias. That gives the photocurrent:
I_photo ∝ Φ_photon · A(λ) · P_escape(V)
Thermal electrons escape even with no light, producing dark current via thermionic emission over the barrier (Arrhenius law), which bias also assists by lowering the effective barrier E_a:
I_dark ∝ T² · exp[ −(E_a − βV) / (k_B T) ]
Cranking Operating temperature up shows why QDIPs are prized: the same 3D confinement that enables normal-incidence absorption also suppresses phonon-assisted relaxation, letting real devices run warmer than QWIPs before dark current drowns the photosignal — watch Idark overtake Iphoto as T climbs.