Fig. 3: Quantification of per-dot excitonic occupancies based on two-band EL spectra.

a The EL spectra of a current-focusing device under pulsed bias (τ_p = 1 μs, f_p = 100 Hz) as a function of j. b The 1S and 1P EL intensities (solid and open circles, respectively; determined from integrated areas) as a function of j inferred from the EL spectra in a. The lines are the calculations conducted using the ‘correlated-injection’ model of ref. ⁷ (Supplementary Note 2) with β = 1.37 × 10⁷C⁻¹ cm² and τ_XX = 1.5 ns (see Supplementary Fig. 15 for calculations conducted for τ_XX = 1.2 ns and 1.9 ns). The ranges of j that correspond to 1 S and 1 P optical gain (pink and green shadings, respectively) are determined based on the condition of achieving population inversion for the 1S and 1P transitions (〈N_th,gain = 1.35 and 3.84, respectively; see Supplementary Note 3). c The ratio of the 1P- and 1S-band EL intensities as a function of j for current focusing LEDs whose emissive layer contains 1 to 4 cg-QD layers. All devices are operated using pulsed bias with τ_p = 1 μs and f_p = 100 Hz. At j of ~1000 A cm⁻², the 1P-to-1S intensity ratio is 1.24, 1.07, 0.75 and 0.37 for devices with the number of the cg-QD layers (m) increasing from 1 to 4. These values correspond to 〈N〉 of 7.8, 7.1, 5.7 and 3.9. In the case of the ideal, 100% EL quantum yield, 〈N〉 should change as 1/m. As a result of nonideal EL performance, the observed drop in 〈N〉 is slower than that predicated by the 1/m dependence.