GaNAs/GaAs DiP array design

The GaNAs/GaAs DiP array was fabricated from a multiple quantum well (MQW) sample by a top-down approach employing nanosphere lithography (NSL) and inductively coupled plasma reactive ion etching (ICP-RIE) processes, see Methods section for details. The MQW sample contains seven GaNAs QWs, each with a thickness of 9 nm. The GaAs barrier between the neighboring QWs has a thickness of 20 nm. The N content varies over the range of 1.1–1.32% among the seven GaNAs QWs, see Supplementary Figure 1. Figure 1a shows a scanning electron microscopy (SEM) image of the as-etched DiP array, which exhibits a hexagonal lattice with an inter-pillar distance, a 0 , of ~460 nm as defined by the hexagonal close-packed nanosphere mask. Each NP features a tapered cylindrical shape with smooth side walls and a rather uniform size distribution, manifesting high quality of the nanofabrication. From the magnified SEM image on an individual NP shown in Fig. 1b, the average diameter, d, of the NPs is found to gradually increase from the top, d top = 240 ± 10 nm, to the bottom, d bottom = 360 ± 10 nm, over the height, h, of 370 ± 10 nm. The seven etched dilute nitride GaNAs NDs within each NP are highlighted in red, with the first ND at a distance of 70 nm from the top surface. The periodic modulation of the conduction band (CB) edge along the NP axis is depicted on the left side of Fig. 1b, where the CB energy is lower in the NDs due to incorporation of N41. The energy of the valence band (VB) edge of the NPs, on the other hand, is rather unperturbed42 (not shown here), as the incorporated N states predominantly interact with the CB and the alloy-induced strain in the NDs is relaxed owing to the DiP geometry (see Supplementary Note 1).

Fig. 1 GaNAs/GaAs nanodisk in nanopillar array design. a Scanning electron microscopy (SEM) image of the arrayed GaNAs nanodisk-in-GaAs nanopillars (DiP). b Side-view SEM image of an individual DiP, where the seven GaNAs nanodisks are shown in red color. The energy profile of the conduction band (CB) edge along the nanopillar axis is indicated on the left side. The valence band edge is nearly unperturbed by N alloying or strain, and therefore its profile is approximately flat and not shown here. The scale bars in a and b denote 400 and 100 nm, respectively. c Schematic illustration of the experimental configuration Full size image

Enhanced light absorption and extraction

To investigate the effect of the NP array on the light emission, we measured RT photoluminescence (PL) from the GaNAs/GaAs DiP under unpolarized laser excitation at 800 nm and compare it with the unetched reference MQWs. The results are shown in Fig. 2a. The PL spectra from both DiP and reference MQWs are dominated by two peaks, i.e., the shorter-wavelength one at 870 nm from the GaAs barrier and the broader one at the longer-wavelength of 1000 nm from the GaNAs NDs. Interestingly, the integrated PL intensities from GaNAs and GaAs of the DiP are stronger than that in the planar MQW structure by 1.55 and 3.04 times, respectively, under the same laser power P exc . Given that the etched DiP has a smaller emitting volume than the MQWs and it additionally suffers from enhanced non-radiative surface recombination associated with the unpassivated NP surface, the observed stronger PL from the DiP array clearly demonstrates a better light absorption and/or extraction efficiency than the planar MQWs. This finding is consistent with the PL results from other semiconductors with similar structures43,44. The measured PL intensity, I PL , is affected by multiple factors45,

$$I_{{\mathrm{PL}}} \propto P_{{\mathrm{exc}}}\alpha _{{\mathrm{in}}}V\eta \alpha _{{\mathrm{out}}}\beta,$$ (1)

where α in (α out ) is the in (out)-coupling coefficient which determines the absorption (extraction) efficiency of light. The effective volume of the emitter is denoted by V, which is proportional to the material filling factor, f, i.e., V∝f. Here, f is 1 for the reference MQW sample and 0.38 for the DiP structure that is averaged over seven size-tapered GaNAs NDs. The radiative recombination efficiency (or the internal quantum efficiency) is denoted by η, and β represents the PL collection coefficient, i.e., the fraction of far-field emission that enters the numerical aperture (NA)-defined solid angle of a microscope objective. Based on the reflectivity measurements (see Supplementary Figure 2), we derive α in = 0.94 for the DiP structure and α in = 0.65 for the MQW sample, at the laser wavelength of 800 nm. From the temperature-dependent PL measurements (see Supplementary Figure 3), the GaNAs NDs in the DiP show a quantum efficiency of η = 0.01, which is lower than η = 0.03 of the MQWs due to surface recombination. We note that these values were obtained under unpolarized laser excitation, i.e., under the condition when the SDR effect is inactive. To gain quantitative insight into NP-tailored light output, we performed finite difference time domain (FDTD) calculations using Lumerical’s FDTD software. The PL radiation from the GaNAs NDs is modeled as unpolarized point-dipole emitters at 1000 nm, considering the band-to-band (BB) recombination involving both heavy-holes (HH) and light-holes (LH). The results are displayed in Fig. 2b for a single NP. The DiP array not only provides a vast density of nanostructured surface for efficient subwavelength light diffraction, but also it gives rise to a reduced contrast of effective refractive index with air, n eff , which leads to higher light transmission into free space46,47. More importantly, the shape of the DiP forms a free-standing waveguide which can couple the emission into the cavity mode. Simulations on the emission intensity across the NP cross-section given in Fig. 2c–f show that light is mostly confined at the center of the NPs, indicating a fundamental HE 11 -mode dominated PL output. All these factors can contribute to a higher PL detection efficiency γ, defined by γ = α out β, for the DiP than the planar MQWs. To confirm this, we calculated γ as a function of dipole emitter depth (or ND position) from the top surface for the two sample structures. As shown in the inset of Fig. 2a, γ of the DiP increases with increasing ND depth, reaching a maximum of 2.9% for the deepest ND. Its averaged γ of 2.3% is almost eight times higher than γ = 0.3 % for the MQWs. By applying all these derived parameters into eq. 1, the detected PL intensity from the GaNAs NDs in the DiP is calculated to be 1.4 times stronger than that from the MQWs, which is quite close to the value of 1.55 deduced from the PL results. The good agreement between the experiment and simulations verifies the optimized light management in the DiP structure with a promoted light-matter interaction and mode-profiled PL output. The obtained superior nano-photonic properties identify the GaNAs/GaAs DiP as an ideal emitter to couple with fiber-optics-based quantum networks or in photonic integrated circuits.

Fig. 2 Enhanced light absorption and extraction at room temperature. a Photoluminescence (PL) spectra from the GaNAs nanodisk-in-GaAs nanopillars (DiPs) and the multiple quantum wells (MQWs) structure under unpolarized laser excitation at 800 nm. The inset shows the detection efficiency, γ, of both structures as a function of the dipole-emitter depth, i.e., the nanodisk (ND)/QW position from the top surface. b The side view of the finite difference time domain (FDTD) simulations of the squared electric-field amplitude (proportional to the light intensity) from the GaNAs NDs with distances of 75, 104, 133, 162, 191, 220, and 250 nm from the top surface. The simulation was taken at the middle cross-section of the DiP as marked by the dashed line in f. c–e The top views of the FDTD simulations of the ND light emission intensity with x, y, and z polarization components, respectively, together with that of the total PL intensity (f). The images are obtained in the plane indicated by the dashed line in b Full size image

Efficient RT spin generation enabled by few defects

Besides the advantage of enhanced light absorption and detection as established above, we shall now demonstrate efficient RT spin generation in the same GaNAs/GaAs DiP via the defect-mediated SDR processes. The Ga i interstitial defects have been shown to be responsible for SDR in GaNAs from the earlier optically detected-magnetic-resonance (ODMR) study27. The principle of the spin generation via SDR is illustrated in Supplementary Figure 4 and described in more detail below, which relies on electron spin polarization of the \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defects with a single bound electron. If a preferential spin orientation of CB electrons is created by circular-polarized (σ+ or σ−) light, even only slightly, SDR will lead to a buildup of spin polarization of both CB and defect electrons during the optical pumping. For example, under σ+ light excitation along the NP axis as shown in Fig. 1c, a spin imbalance is generated for CB electrons with more spin-down than spin-up CB electrons as shown in Supplementary Figure 4, following the optical selection rule of the BB transition (Fig. 3d). This imbalance can be characterized by the ratio n − /n + > 1 between the numbers of the spin-down and spin-up CB electrons, denoted by n − and n + , respectively. Dictated by the Pauli exclusion principle, the capture of a CB electron by the \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defect is allowed only if the CB electron and the electron bound to \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) have opposite spin orientations. As the probability of the spin-up (spin-down) \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defect in capturing a CB electron scales with the number of spin-down (spin-up) CB electrons, the spin-up \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defect should thus have a higher probability by a factor of n − /n + in capturing a spin-down CB electron than the spin-down \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defect in capturing a spin-up CB electron, as illustrated in Supplementary Figure 4a. After the capture, one of the two spin-paired electrons at the \({\mathrm{Ga}}_{\mathrm{i}}^{1 + }\) defect will recombine with a spin-unpolarized VB hole, leaving behind with an equal probability either a spin-up or a spin-down electron at the defect. (Here, the VB hole spins are regarded as unpolarized in the SDR processes due to a stronger spin–orbit interaction and HH-LH coupling that randomize the initially polarized hole spins within picoseconds).48,49. As a result, after one round of the SDR process, more spin-up \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defects are converted to the spin-down \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defect than the other way around, with a factor of n − /n + between their conversion rates. This leads to an imbalance between spin-down and spin-up \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defects, as illustrated in Supplementary Figure 4b, which can be characterized by their ratio N − /N + > 1. With each round of such capture and recombination, more and more spin-up \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defects will be converted to the spin-down \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defects. At the same time, an increasingly larger ratio N − /N + will in turn preferably deplete the spin-up (minority spin) CB electrons, i.e., a spin filtering effect, thereby further increasing the ratio n − /n + and thus the CB electron spin polarization. Eventually this positive feedback process between n − /n + and N − /N + will drive both the \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defect and CB electron spins towards the majority-spin (i.e., spin-down) orientation via the so-called dynamic spin polarization (DSP) process50. As shown in the right panel of Fig. 3a, the resulting spin blockade effect prevents further capture and depletion of CB electrons via the defects, thereby giving rise to a stronger and highly circular-polarized BB emission. During the time when the defect electron spin is preserved, any minority-spin CB electrons generated by either poor optical spin generation by light or due to spin relaxation will immediately be depleted by the SDR processes via the defects as illustrated in Supplementary Figure 4c. This ensures that spin polarization of CB electrons can be maintained at a substantially higher degree than the initial value created by optical pumping without DSP. This is in sharp contrast to the case without SDR and DSP under linear-polarized (σX) laser excitation, see the left panel of Fig. 3a, when both spin-up and spin-down electrons are equally generated in CB, followed by their capture with an equal probability by the spin-unpolarized Ga i defects and recombination with VB holes. No spin polarization of either the defect electrons or CB electrons is expected during the capture and recombination processes, except that this fast non-radiative process equally depletes free carriers of both spin orientations resulting in weak and unpolarized PL emission.

Fig. 3 Efficient room temperature spin generation enabled by few defects. a Schematic illustration of the defect-driven spin generation via spin-dependent recombination (SDR) under σ+ excitation (the right panel), which shows stronger and co-polarized photoluminescence (PL) than that without the SDR effect under σx excitation (the left panel). The gray horizontal bars represent the defect level. b PL spectra excited by σ+ and σx laser light. c Spectral dependence of the I(σ+)/I(σX) ratio. d Band diagram illustrating the polarized band-to-band transitions involving valence band (VB) heavy-hole (±3/2) and light-hole (±1/2) states. e σ+ and σ− polarized PL spectra under the σ+ excitation. f Spectral dependence of the PL and conduction band (CB) electron spin polarizaion. In converting P PL –P e , the light depolarization factor arising from the finite solid angle of light detection by the microscope objective with the given numerical aperture (NA) has also been taken into account. Since, the PL emission from GaAs is at least partly contributed from the planar GaAs substrate, P e in GaAs could be overestimated by a factor up to 1.5 Full size image

The most crucial condition for the success of the SDR and DSP processes in efficient spin generation is τ sc > τ s > τ nr . Here, a much longer spin lifetime of the defect electron, denoted by τ sc , ensures that the \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defects remain spin polarized during the time when CB electrons undergo spin relaxation. Whenever that happens, the defects will immediately filter out these spin-flipped CB electrons as long as their capture time by the defects (τ nr ) is shorter than the CB electron spin relaxation time τ s . As τ nr is typically in the order of ps, the spin filtering and spin amplification can be accomplished within a very short time. The efficiency of the SDR and DSP processes can also be accelerated by increasing circularly polarized light intensity because it is accompanied by an increasing probability of the \({\mathrm{Ga}}_{\mathrm{i}}^{2 + }\) defects in capturing CB electrons and thus an increasing number of the SDR cycles within the same period of time.

The boost in the PL intensity due to the spin blockade effect can be characterized by the ratio of I(σ+ or σ−)/I(σX), where I(σ+/−/X) represents the PL intensity under right-circular/left-circular/linear-polarized laser excitation, respectively. Figure 3b shows representative PL spectra excited by the 800 nm laser line at P exc of 11.7 mW, where the SDR process in the GaNAs NDs is clearly evident from an apparently stronger emission under σ+ than σX excitation. This can be further corroborated with an unchanged PL signal from GaAs, where no SDR occurs. The corresponding I(σ+)/I(σX) ratio in Fig. 3c clearly exhibits a variation from a value of ~1.06 to ~1.15 with decreasing emission energy. The spectral variation of the I(σ+)/I(σX) ratio suggests the coexistence of SDR processes with different efficiencies. Indeed, our secondary ion mass spectroscopy (SIMS) measurements on the reference MQWs reveal a N fluctuation from [N min ] = 1.1% to [N max ] = 1.32% among the seven QWs (see Supplementary Figure 1), corresponding to a bandgap energy shift from 1.252 to 1.228 eV which is comparable with the spectral width of the broad GaNAs PL. Since a larger N content not only reduces the bandgap energy but also facilitates the formation of Ga i 27,51, and thus SDR efficiency, a higher I(σ+)/I(σX) ratio is expected at the lower emission energy that is in excellent agreement with our experimental finding. The lowest and highest values of the I(σ+)/I(σX) ratio are thus derived from the NDs with [N min ] and [N max ], respectively.

To directly determine spin polarization of CB electrons in the GaNAs NDs, we monitored the circular-polarized PL components under circularly polarized optical pumping (e.g., σ+). The ND emission is strongly co-polarized with the excitation light as shown in Fig. 3e. The derived PL circular polarization degree P PL , defined by P PL = (I+−I−)/(I++I−) where I+/− denotes the σ+/−-polarized PL intensity, is shown in Fig. 3f. It exhibits a spectral variation similar to the I(σ+)/I(σX) ratio, with P PL = 14 and 20% from the NDs with [N min ] and [N max ], respectively. It should be noted that due to the degeneracy of HH and LH VB states in the strain-relaxed NDs, see Supplementary Note 1 and Supplementary Figure 5–6, the detected P PL comprises contributions from both HH and LH subbands of opposite helicity. Based on the well-known 3-to-1 ratio between the oscillator strengths of the BB optical transitions involving the HH and LH states48,52, as illustrated in Fig. 3d, the spin polarization of CB electrons is twice of P PL , i.e., P e = −2P PL . By further taking into account the light depolarization factor arising from the finite solid angle of light detection by the microscope objective with the given NA (see Supplementary Figure 7 and Supplementary Note 2), P e generated in the GaNAs NDs with [N min ] = 1.1% to [N max ] = 1.32% can be determined to be 43 and 60%, respectively. These values are estimated based on the results from Supplementary Figure 7 that 100% electron spin polarization should generate only 33% light circular polarization under our experimental conditions and assuming full LH-HH degeneracy.

To evaluate to what extent the SDR effect via the defects have contributed to the spin generation in the DiP, we carried out a detailed study of excitation power-dependent P e and I(σ+)/I(σX) ratio for the NDs with [N min ] and [N max ]. A summary of the results is shown in Fig. 4. For both N compositions, P e increases with increasing P exc owing to accelerated dynamic processes of SDR. This can also be corroborated by a constant P e of ~8% for the GaAs emission, where the SDR effect is absent. From the best fits of a nonlinear coupled rate equation analysis to the power-dependent P e profiles, see Supplementary Note 3 for details, the concentration of the Ga i defects can be estimated to be ~2.6 × 1015 cm−3 and 4.1 × 1015 cm−3 in the NDs with [N min ] and [N max ], respectively. This approximately corresponds to 2 defects in each ND with [N min ] and 3 defects in each ND with [N max ]. It is remarkable that such few defects have led to strong P e up to 60% at RT, demonstrating the extremely high efficiency and robustness of the Ga i -mediated spin generation processes.

Fig. 4 Room temperature spin amplification enabled by few defects. a Power-dependent P e and spin amplification factor \({\mathrm{SAF}} = P_{\mathrm{e}}{\mathrm{/}}P_{\mathrm{e}}^0\) from the GaNAs nanodisks (NDs) with the [N min ] (the open triangles) and [N max ] (the filled circles). The solid symbols are experimental data, and the solid lines are the fitting curves obtained by the rate equation analysis. b For comparison, power-dependent P e from GaAs is also shown by the gray symbols. The vertical bars indicate the experimental error bars which are derived from the statistics of five measurements. The dashed horizontal line marks \(P_{\mathrm{e}}^0\) Full size image

The rate equation analysis also shows that the spin polarization at very low P exc before the optically pumped dynamic spin polarization process of the defect electrons takes place, denoted by \(P_{\mathrm{e}}^0\), is merely 5%. This value reflects the CB electron polarization without the SDR effect. The low \(P_{\mathrm{e}}^0( { = {\textstyle{{P_{\mathrm{e}}^{\mathrm{i}}} \over {1 + \tau /\tau _{\mathrm{s}}}}}} )\) in the GaNAs NDs, much lower than the maximum allowed 50% upon optical pumping of the GaAs barrier, originates from two parts. The first part stems from spin loss of the light emitter itself, by a factor of \({\textstyle{1 \over {1 + \tau /\tau _{\mathrm{s}}}}}\) (about 0.9 in our case), due to CB electron spin relaxation within its lifetime. The second contribution, often the more important one, is related to a low value of \(P_{\mathrm{e}}^{\mathrm{i}}\) (about 5.6% in our case), which reflects significant spin loss during energy relaxation of hot electrons/excitons within the GaAs barriers before spin injection to the GaNAs NDs, spin transport across the GaAs/GaNAs interfaces, and energy relaxation with the NDs after spin injection. In fact, it is such severe spin loss that has prevented GaAs, or any other non-magnetic semiconductor without SDR, from efficient spin generation at RT. When the SDR effect is activated as P exc increases, P e increases and eventually approaches a saturation value of 60% (43%) for the NDs with [N max ] ([N min ]) due to the saturated SDR process. The observed defect-enabled spin gain can be characterized by a spin amplification factor (SAF), i.e., \({\mathrm{SAF}} = P_{\mathrm{e}}{\mathrm{/}}P_{\mathrm{e}}^0\), yielding a maximum SAF of 11 (7.6) for the NDs with [N max ] ([N min ]). These findings further consolidate the effectiveness of the Ga i defects for spin amplification in the GaNAs NDs, which could effectively overcome the severe spin loss in the way no any other approach can.

Spin polarization versus internal quantum efficiency

An efficient polarized spin-photon interface must fulfill two stringent requirements: strong electron spin polarization and efficient light emitting. In a most commonly occurring case of a semiconductor without the defect-enabled spin amplification effect, these two requirements favor contradicting conditions. This is because the electron spin polarization \({P}_{\mathrm{e}}^0\) can be described in its simplest form by the equation52

$$P_{\mathrm{e}}^0 = \frac{{P_{\mathrm{e}}^{\mathrm{i}}}}{{1 + \tau /\tau _{\mathrm{s}}}}.$$ (2)

Here, τ denotes the total lifetime of the electrons regardless of their spin orientations, which is contributed from both radiative and non-radiative lifetime (i.e., τ r and τ nr ) following the relationship \({\textstyle{1 \over \tau }} = {\textstyle{1 \over {\tau _{\mathrm{r}}}}} + {\textstyle{1 \over {\tau _{{\mathrm{nr}}}}}}\). (\({\textstyle{1 \over {\tau _{{\mathrm{nr}}}}}} = \gamma _{\mathrm{e}}N_{\mathrm{c}}\), where N c is the defect concentration responsible for the non-radiative recombination and γ e is the trapping coefficient of CB electrons by the defect.) From eq. 2, it is apparent that \(P_{\mathrm{e}}^0\) is restrained over the range of \({\textstyle{{P_{\mathrm{e}}^{\mathrm{i}}} \over {1 + \tau /\tau _{\mathrm{s}}}}} \le P_{\mathrm{e}}^0 \le P_{\mathrm{e}}^{\mathrm{i}}\). Achieving the maximum radiative recombination efficiency η = τ/τ r = 100% is accompanied by the minimum electron spin polarization \(P_{\mathrm{e}}^0 = {\textstyle{{P_{\mathrm{e}}^{\mathrm{i}}} \over {1 + \tau _{\mathrm{r}}/\tau _{\mathrm{s}}}}}\). As τ r is usually found to be comparable or longer than τ s in semiconductor materials and nanostructures, the maximum η is obtained at the expense of severe spin loss. To approach the maximum value of \(P_{\mathrm{e}}^0 \approx P_{\mathrm{e}}^{\mathrm{i}}\), on the other hand, τ needs to be much shorter than τ s . This requires introduction of non-radiative recombination such that τ ≈ τ nr ≪ τ s 53, which simultaneously minimizes η, as η = τ/τ r ≪1 under the same condition. Such an anti-correlation between P e and η can be clearly visualized from the simulations shown by the gray dashed lines in Fig. 5.

Fig. 5 Spin polarization versus internal quantum efficiency. a–d Conduction band electron spin polarization P e . e–h Radiative recombination efficiency of the majority-spin (spin-up) and minority-spin (spin-down), η ± = τ ± /τ r , as well as the total radiative recombination efficiency. They are plotted as a function of τ/τ r , calculated from the rate equation analysis using the following parameters: a, e τ sc = 2τ s , τ r = 10τ sc , \(P_{\mathrm{e}}^0 = 5{\mathrm{\% }}\); b, f τ sc = 2τ s , τ r = τ sc , \(P_{\mathrm{e}}^0 = 5{\mathrm{\% }}\); c, g τ sc = 2τ s , τ r = 0.1τ sc , \(P_{\mathrm{e}}^0 = 5{\mathrm{\% }}\); d,h, τ sc = 2τ s , τ r = 0.1τ sc , \(P_{\mathrm{e}}^0 = 25{\mathrm{\% }}\). τ r is fixed at 3000 ps in all cases, and \({\textstyle{1 \over \tau }} = {\textstyle{1 \over {\tau _{\mathrm{r}}}}} + \gamma _{\mathrm{e}}N_{\mathrm{c}}\). The simulations corresponding to the cases with (without) the defect-mediated SDR are displayed by the colored solid lines (the gray dashed lines). The green and red vertical arrows indicate the enhancements of electron spin polarization and radiative recombination efficiency induced by the few-defect-mediated SDR effect, respectively Full size image

This seemingly fundamental obstacle in simultaneously achieving both strong P e and high η can be effectively overcome by the defect-mediated SDR effect presented in this work. The key to the success here is a strong spin polarization degree of the defect electrons such that the non-radiative recombination times of the spin-up and spin-down CB electrons, namely, \(\tau _{{\mathrm{nr}}}^ \pm = {\textstyle{1 \over {\gamma _{\mathrm{e}}N_ \mp }}}\), becomes markedly different. Here, N ± represents the concentration of the Ga i defects in the paramagnetic charge state occupied by a single electron with the subscript ‘±’ denoting the spin-up and spin-down orientation of electrons. In the extreme case when the defect electrons are completely spin polarized, say N + ≈ N c and N − ≈ 0, non-radiative recombination of the CB electrons with the majority-spin (i.e., spin-up) diminishes since \(\tau _{{\mathrm{nr}}}^ + = {\textstyle{1 \over {\gamma _{\mathrm{e}}N_ - }}} \to \infty\) yielding η + →100%. This is in sharp contrast to the CB electrons with the minority-spin (i.e., spin-down) that suffer strong non-radiative recombination in the same way as the case without the SDR effect described above, because \(\tau _{{\mathrm{nr}}}^ - = {\textstyle{1 \over {\gamma _{\mathrm{e}}N_ + }}}\). This strong deviation in non-radiative recombination via the defects between the majority-spin and minority-spin CB electrons in turn drives CB electrons toward amplified spin polarization (\(P_{\mathrm{e}} > P_{\mathrm{e}}^{\mathrm{i}}\)) well exceeding the maximum limit of \(P_{\mathrm{e}}^0 \approx P_{\mathrm{e}}^{\mathrm{i}}\) imposed in the absence of the SDR effect. For a quantitative analysis, we performed detailed simulations of P e and η ± = τ ± /τ r as a function of τ/τ r with the aid of the coupled rate equations given in Supplementary Note 3. The results are shown in Fig. 5, which demonstrate that, over the regime when the SDR is highly active, both P e and η (for the desired spins) can be significantly enhanced by orders of magnitude from that without the SDR effect. We should note that, as the minority-spin CB electrons are depleted by the defect-mediated non-radiative recombination processes, the total quantum efficiency η total , including PL yield from both majority-spin and minority-spin CB electrons, should lie between the quantum efficiency values of the two. The η total values calculated based on the rate equations are shown as a function of τ/τ r in Fig. 5, together with the values of the majority-spin and minority-spin quantum efficiency. The simulations confirm the significant enhancement of not only the majority-spin quantum efficiency but also total PL quantum yield by activating the SDR effect. The upper bound of η total achievable by the defect-mediated SDR effect is determined by the number of minority-spin CB electrons needed to be depleted via the non-radiative processes. Theoretically, it can approach 50% when \(P_{\mathrm{e}}^{\mathrm{i}}\) is close to zero and 100% in the other extreme case of \(P_{\mathrm{e}}^{\mathrm{i}}\) close to 100%.

It is clear from the simulations shown in Fig. 5 that the exact extent of the enhancement in both P e and η by the SDR effect critically depends on the defect concentration (thus τ), CB electron spin relaxation time τ s and the initial spin polarization \(P_{\mathrm{e}}^{\mathrm{i}}\). This provides a guideline for further improvements by increasing the SDR defect concentration and by suppressing CB electron spin relaxation through, e.g., quantum confinement. The simulations also show the potential of our approach to simultaneously fulfill both requirements for strong electron spin polarization with P e approaching 100% and high radiative recombination efficiency in the studied DiP structure. Future effort is also required to improve polarized spin-light conversion by removing the HH-LH degeneracy–the source of partial cancellation (by 1/2) in emitting light polarization, through strain engineering and/or quantum confinement such that the BB transition at RT only involves the HH states.