Introduction

The growth and characterization of self-assembled quantum dots (QDs), especially those with lattice mismatch, have garnered considerable attention owing to their distinctive physical properties and critical role in determining the luminescence efficiency of electronic and optoelectronic devices1,2,3,4,5,6. Strong carrier confinement in these nanostructures leads to the emergence of a discrete set of energy states separated by several tens of millielectron volts for both electrons and holes. This characteristic makes QDs ideal platforms for investigating carrier dynamics using time-resolved photoluminescence (PL) analysis, a powerful technique for probing recombination, relaxation, and carrier interactions.

In CdZnTe QDs, carrier dynamics are strongly influenced by the ability to control the shape and size distribution of the dots, further enhancing their potential for diverse applications. Recent studies considering low excitation densities have identified distinct relaxation mechanisms underlying carrier dynamics. These mechanisms involve phonon activation, primarily mediated by electron–phonon interactions, which govern the manner in which carriers traverse the energy landscape of QDs. The thermal escape of carriers plays a key role in determining their confinement and subsequent transport behavior. This process, driven by the absorption of multiple longitudinal optical (LO) phonons, is closely associated with carrier trapping at surface defects within QDs7,8. Additionally, Auger processes have been proposed as efficient relaxation pathways; however, their characteristic temperature and density dependencies remain experimentally unverified9,10. The increased efficiency of Auger recombination is commonly attributed to limited electron–electron interaction strength and strict energy and momentum conservation requirements, which restrict the available decay pathways. Phonon contributions are also believed to play a notable role in Auger recombination processes. Despite these insights, a comprehensive theoretical model that adequately captures phonon-assisted mechanisms underlying temperature-dependent Auger recombination in QDs has yet to be established11,12.

In this study, we systematically examine the PL spectra and lifetimes of self-assembled Cd0.6Zn0.4Te QDs under pulsed picosecond excitation as functions of temperature and excitation density. By varying the temperature, we aim to elucidate the mechanisms governing carrier relaxation and recombination. Our findings reveal thermally activated transitions between discrete energy states, with a localization energy of approximately 8 meV at low temperatures. Furthermore, we demonstrate that quantum confinement enhances exciton coupling with both acoustic and LO phonons, even under low excitation conditions where each dot hosts fewer than one electron–hole pair, thereby allowing contributionsfrom Auger processes to be excluded. Herein, we report temperature-dependent rise-time measurements conducted over a range of excitation densities, highlighting the role of multi-phonon absorption involving characteristic LO phonons near 19.2 meV, as well as the contribution of Auger processes at higher excitation densities. Additionally, we determine the temperature-dependent Auger recombination coefficient, Ca(T), and investigate the dynamics of biexciton luminescence. Our results reveal that phonon participation substantially enhances Auger recombination in self-assembled QDs, contributing to a deeper understanding of their optical behavior and potential applications.

Results

Temperature-dependent photoluminescence

Figure 1a presents the PL spectrum of Cd0.6Zn0.4Te QDs at 10 K, along with an atomic force microscopy (AFM) image illustrating their spatial distribution. The PL peak observed at 2.148 eV at 10 K indicates strong quantum confinement, as it is significantly blue-shifted from the CdTe bulk bandgap of 1.54 eV13. AFM analysis reveals that the QDs have a lateral size of approximately 45 ± 5 nm and a height of 7 ± 3 nm, indicating anisotropic confinement. The disparity in the effective masses of electrons and holes (\(m_{e}^{*}\) = 0.135m0 and \(m_{{\text{h}}}^{*}\)  = 1.139m0)14,15 results in differing spatial distributions of their wavefunctions. Holes, having a larger effective mass, are more localized, whereas electrons are more delocalized. This anisotropy modifies the confinement potential and the wavefunction overlap, which, in turn, influence the optical transition strength and the resulting PL intensity.

Fig. 1
figure 1

(a) PL spectrum at 10 K and corresponding AFM image. (b) Temperature-dependent PL spectra of self-assembled CdZnTe QDs. (c) FWHM as a function of temperature at low excitation density (n0 = 0.033 × 1011 cm−2), with best-fit curves shown as discussed in the text. (d) Integrated PL intensity as a function of temperature and the occupation probability of excitonic states.

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As shown in Fig. 1b, the PL peak undergoes a gradual red-shift with increasing temperature, accompanied by spectral broadening and a decrease in intensity. This red-shift is attributed to the temperature-induced narrowing of the bandgap and the thermal population of higher-energy excitonic states. This behavior arises from interactions between carriers and both acoustic and optical phonons, leading to dephasing and reduced carrier localization. Additionally, thermal broadening induced by electron–phonon coupling induces fluctuations in the confinement potential and a consequent spread in energy levels.

Figure 1c presents the temperature-induced broadening of the linewidth, Γ(T), along with several fitting models. The linewidth behavior is modeled using a previously reported expression16: \({\Gamma }\left( {\text{T}} \right) = {\Gamma }_{0} + \sigma T + {\Gamma }_{LO} N_{0} \left( T \right) + \alpha_{i} {\text{exp}}\left( {\frac{{ - E_{i} }}{{k_{B} T}}} \right)\). As indicated, several factors contribute to the linewidth: (i) inhomogeneous broadening (Γ0), which is temperature-independent and originates from variations in QD dimensions, morphology, and spatial arrangement. (ii) Exciton–acoustic phonon coupling (σT), which is represented by the green dashed line and increases linearly with temperature, reflecting the growing influence of acoustic phonons on linewidth broadening. As temperature increases, the interaction between carriers and acoustic phonons intensifies, contributing to linewidth broadening. The exciton–acoustic phonon coupling coefficient, σ, is found to be 35 μeV/K. Notably, given their low energies (on the order of a few millielectron volts), acoustic phonons play a dominant role at low temperatures. The above experimentally extracted value of σ is substantially higher than the theoretical estimate for bulk CdTe (approximately 0.72 μeV), as reported by Rubin et al.16. (iii) Exciton‒optical (LO) phonon coupling \(({\Gamma }_{LO} N_{0} \left( T \right)),\) which is represented by the blue dashed line and accounts for the contribution from LO phonon interactions. This coupling follows the Bose–Einstein distribution, \(N_{o} \left( T \right) = \frac{1}{{\exp \left( {{\raise0.7ex\hbox{${E_{LO} }$} \!\mathord{\left/ {\vphantom {{E_{LO} } {k_{B} T}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${k_{B} T}$}}} \right) - 1}}\), implying that the coupling intensifies with temperature as the LO phonon population rises. The best-fit values are \({\Gamma }_{LO}\) = 22.5 meV and \({\text{E}}_{LO}\) = 19.2 meV. (iv) In addition to phonon-induced broadening, we include a thermally activated term, \(\alpha_{i} \exp \left( {\frac{{ - E_{i} }}{{k_{B} T}}} \right),\) which accounts for the possibility that, at elevated temperatures, carriers gain sufficient thermal energy to escape from confined quantum dot states into higher-lying delocalized states or traps. This escape leads to enhanced non-radiative recombination and additional spectral broadening. The best-fit activation energy, Ei = 8.8 meV, represents the threshold above which such non-radiative channels or delocalized states begin to significantly influence the emission properties. This energy scale indicates that carrier delocalization or trap activation affects the linewidth even at relatively low temperatures. The overall fit aligns well with the experimental data, confirming that inhomogeneous broadening dominates at low temperatures, while at higher temperatures, acoustic and optical phonon interactions, along with thermally activated processes, contribute to the observed linewidth broadening and the degradation of PL efficiency.

Figure 1d illustrates the peak-integrated PL intensity of the QD emission plotted as a function of \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {k_{B} T}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${k_{B} T}$}}\) on a semi-logarithmic scale, enabling the extraction of the activation energy associated with thermally induced processes at elevated temperatures. At low excitation densities, carrier recombination and relaxation proceed as sequential processes. Under these conditions, e–h pairs may follow various relaxation pathways, including radiative recombination, carrier trapping, Auger nonradiative scattering, and exciton–phonon coupling, before ultimately recombining at the lowest available energy levels17,18. In the present experiments, the excitation density was set to 5 W/cm2 using a photon energy of 3.098 eV and a laser repetition rate of 76 MHz, resulting in a photon fluence of 0.75 × 1011 photons cm−2 per pulse. Given a Cd0.6Zn0.4Te QD density of approximately 2 × 1010 cm−2 and a spot diameter of approximately 100 µm, the average carrier occupancy per dot is given by \(N_{0} = j_{p} \sigma_{0}\), where \(\sigma_{0}\) represents the absorption cross section of thedot19. Under these conditions, \(N_{0}\) is approximately 0.11, indicating a low-excitation regime in which Auger processes can be neglected. Assuming that photon emission primarily competes with carrier–phonon interactions and neglecting trapping and Auger processes, the dominant mechanism responsible for the thermally induced decrease in PL intensity is the thermal escape of heavy holes from the QD structure, governed by quantum confinement effects7,18. Thermal escape is a process in which carriers absorb optical phonons to gain sufficient energy to overcome the potential barrier and transition from confined states within the QD to higher-energy continuum states. As temperature increases, the integrated PL intensity is well described by the Arrhenius equation18:

$$I_{PL} \left( T \right) = \frac{{I_{0} }}{{1 + a\exp \left( {{\raise0.7ex\hbox{${ - E_{local} }$} \!\mathord{\left/ {\vphantom {{ - E_{local} } {k_{B} T}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${k_{B} T}$}}} \right) + b\left( {\exp \left( {{\raise0.7ex\hbox{${E_{LO} }$} \!\mathord{\left/ {\vphantom {{E_{LO} } {k_{B} T}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${k_{B} T}$}}} \right) - 1} \right)^{ - m} }},$$
(1)

where I0 denotes the integrated PL intensity at 0 K; a and b are phenomenological constants that scale the relative contributions of thermal activation and LO phonon-assisted processes, respectively, to the quenching of PL intensity; Elocal denotes the thermal activation energy for low-temperature quenching; m represents the number of LO phonons involved in the thermal escape process; and ELO denotes their energy. The larger activation energy, Eescape (= m × ELO), is associated with the reduction in PL intensity at high temperatures and carries specific physical implications. Figure 1d illustrates the simulation curve to the experimental data, with best-fit parameters Elocal = 8.5 meV, m = 2.3, and ELO = 19.8 meV. Notably, the aforementioned value of Elocal closely matches that of Ei, which was independently extracted from the PL energy and the full width at half maximum (FWHM) analysis of the emission peak. These results indicate that thermally activated transitions occur between two discrete states separated by approximately 8 meV at low temperatures. This behavior may be attributed to the ionization of shallow donor levels and the presence of two quenching stages, potentially involving (i) donor–acceptor recombination19,20, (ii) thermally activated transitions from intrinsic states to higher-energy localized surface states21, or (iii) transitions between intrinsic and defect states22. The fact that PL quenching is primarily attributed to thermal escape rather than defect-mediated nonradiative recombination indicates the high quality of the Cd0.6Zn0.4Te QDs, since defects and dislocations typically introduce nonradiative pathways that degrade luminescence. This process is promoted by multiple LO phonon scattering, where the number of phonons involved (m) depends on the QD size and the statistical distribution of the relevant physical quantities, potentially yielding non-integer or integer values during modeling. Multiplying this phonon number by the carrier energy yields the energy required for thermal escape, corresponding to the energy separation between two low-lying excited states (Eescape = m × ELO), thereby supporting the proposed escape mechanism. Additionally, an analysis of thermal escape provides estimates for the energy separation between adjacent hole states involved in the first three transitions—1S3/2 → 1Se, 2S3/2 → 1Se, and 1P3/2 → 1Pe, which aligns with the value of m × ELO7,18. The occupation probability of excitonic states, \(P_{n} \propto \exp \left( { - \frac{{E_{n} }}{{k_{B} T}}} \right),\) also varies with temperature, as depicted in Fig. 1d. At low temperatures, carriers predominantly occupy the ground state (1S), resulting in efficient radiative recombination. As the temperature increases, these carriers gain thermal energy and begin to populate higher excited states, such as 2S and 1P. The increased occupation of these higher-energy states, which exhibit lower radiative recombination probabilities, results in reduced PL efficiency and broader emission linewidths.

The integrated PL intensity decreases significantly with increasing temperature, as shown in Fig. 1d. This behavior is well described by an Arrhenius fit, yielding an activation energy of approximately 8.5 meV, which closely corresponds to the energy separation between quantized heavy-hole levels. This agreement supports the interpretation that quantum confinement plays a dominant role, consistent with prior observations in similar CdTe/ZnTe QD systems18. Additionally, the gradual red-shift of the PL peak (Fig. 1b) is consistent with temperature-induced bandgap narrowing and the thermally driven occupation of higher-energy excitonic states. Rather than indicating complete carrier escape or ionization, the observed PL quenching is attributed to phonon-assisted thermal redistribution of holes from the ground state to higher-energy confined or weakly bound states within the quantum dot. These excited states typically exhibit lower radiative efficiency due to reduced oscillator strength or slower relaxation dynamics. The absence of sub-bandgap emission further supports the negligible contribution of trap-assisted recombination.

The strong temperature sensitivity of PL intensity is further amplified by the use of low excitation density (\(\left\langle {\text{N}} \right\rangle\) ≈ 0.1), which limits repopulation of radiative ground states at elevated temperatures. The extracted acoustic phonon coupling coefficient (σ ≈ 35 μeV/K) and LO phonon energy (~ 19.2 meV) both confirm that exciton-phonon interactions, particularly with confined phonons, play a dominant role in both spectral broadening and intensity quenching. These findings underscore the importance of phonon-coupled carrier redistribution in determining optical efficiency in self-assembled CdZnTe QDs.

Excitation power-dependent photoluminescence

Figure 2a presents the PL spectra recorded at excitation densities ranging from 2.5 to 147 W/cm2. The PL intensity exhibits a sublinear dependence on excitation density, with a slope of approximately 0.88 as shown in the log–log plot (Fig. 2b). This sublinear behavior suggests an increasing contribution from nonradiative recombination channels, such as Auger processes, at higher carrier densities. However, complete saturation is not observed within the measured excitation range. Additionally, the band-edge emission near 2.147 eV exhibits a blue shift and spectral broadening with increasing carrier density, attributed to band filling, bandgap renormalization (BGR), and the effects of free carriers due to exciton binding energies23,24,25. Time-resolved PL measurements reveal that, at low excitation densities, the decay follows a relatively long timescale dominated by single-exciton radiative recombination (Fig. 2c). In contrast, at high excitation densities, PL decay accelerates owing to Auger recombination, anon-radiative process in which the recombination energy is transferred to a third carrier, resulting in a reduced PL lifetime. To ensure high signal quality, time-resolved PL measurements were performed at wavelengths corresponding to the peak emission. At low temperatures, the decay dynamics across the PL band are qualitatively similar, with minor variations attributed to spectral inhomogeneity and state filling. These observations support our interpretation of exciton and biexciton recombination dynamics under high-excitation conditions. The initial e–h pair density, n(0), can be estimated using the expression \(n\left( 0 \right) = j\sigma_{0}\), where j denotes the photon fluence per laser pulse (cm−2), and \(\sigma_{0}\) denotes the optical absorption cross section of the QD at the pump wavelength (cm2). The optical absorption cross section of the QDs can be expressed as the product of the bulk absorption coefficient and a local-field correction factor \(\left| {f\left( \omega \right)} \right|^{2}\) as26, \(\sigma_{0} = \alpha_{b} \left( \omega \right)\frac{{n_{1} }}{{n_{2} }}V\left| {f\left( \omega \right)} \right|^{2}\). Here \(, n_{1}\) and \(n_{2}\) denote the real parts of the refractive indices of the QD material and surrounding medium, respectively, and \(\alpha_{b} \left( \omega \right)\) represents the bulk absorption coefficient at angular frequency ω. The local-field correction factor is expressed as \(f\left( \omega \right) = 3m_{2}^{2} /\left( {m_{1}^{2} + 2m_{2}^{2} } \right)\), where m1 and m2 denote the dielectric constants of the surrounding medium and the bulk CdTe material, respectively. At 400 nm, the optical absorption cross section \(\sigma_{0}\) of QDs is calculated to be 3.4 × 10−13 cm2. Under this approximation, the density of states in the QDs is treated as bulk-like, which may result in an overestimation of exciton density at high excitation intensities. Assuming a Poisson distribution for early-time QD occupancy, the pump-power-dependent PL intensity is expressed as a function of photon fluence per laser pulse \(: I_{PL} \sim \left( {1 - e^{{ - j\sigma_{0} }} } \right).\) Fitting this model to the experimental data in Fig. 2b yields an absorption cross section of \(\sigma_{0}\) = 5.35 × 10−13 cm2. These values allow the conversion of measured PL intensity into the corresponding number of generated e–h pairs.

Fig. 2
figure 2

(a) PL spectra of self-assembled CdZnTe QDs as a function of excitation power density at 10 K. (b) Log–log plot of the PL intensities as functions of carrier density. (c) Time-resolved PL spectra of self-assembled CdZnTe QDs as a function of excitation power density at 10 K.

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Discussion

To describe carrier recombination over a range of excitation intensities, the time-dependent carrier density can be modeled by the following equation27:

$$\frac{dn\left( t \right)}{{dt}} = - An\left( t \right) - Bn\left( t \right)^{2} - Cn\left( t \right)^{3} ,$$
(2)

where n(t) denotes the photogenerated carrier density, and t represents time. The first-, second-, and third-order terms correspond to Shockley–Read–Hall recombination, bimolecular (free carrier) recombination, and Auger recombination, respectively.

Figure 3a displays the contributions of exciton and biexciton emissions, where red symbols represent the experimental data and the fitted curves. The blue and red curves correspond to Voigt functions, V(n, Γ0), which describe the influence of carrier density (n) on exciton emission line shape and broadening. The observed spectral broadening and blue shift in the PL spectra are attributed to the hot-phonon bottleneck effect, wherein hot phonons impede efficient carrier cooling. Consequently, carriers persist in higher energy states, leading to band filling. Such accumulation of hot phonons further contributes to spectral broadening, as carriers are unable to efficiently dissipate excess energy, resulting in a wider spread of emission energies. The oscillator strength of the e–h pair, bound by the Coulomb interaction, is determined based on the probability of transitions from the ground state to excited states through photon absorption or emission. The reduction in exciton oscillator strength can be modeled by the expression28 \(f\left( N \right) = \frac{1}{{(1 + N/N_{C} )}}\), where \(f\left( N \right)\) represents the probability of exciton state occupancy, following Fermi statistics (1 for an occupied state and 0 otherwise), and NC denotes the critical number of e–h pairs at which saturation occurs, evaluated under conditions of selective exciton generation. The oscillator strength decreases to half its value when the system approaches saturation28. As depicted in Fig. 3b, the fitting parameter (N) decreases with increasing carrier density, indicating the onset of saturation and reduced probability of additional state occupancy due to phase-space filling. The average critical number of e–h pairs, \(N_{C}\), is approximately 1.96, corresponding to a carrier density of 3.7 × 1012 cm−2. This value exceeds the carrier density obtained from the bulk Bohr radius, expressed as \(N_{C} \sim {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\pi a_{0}^{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\pi a_{0}^{2} }$}} = 1.2 \times 10^{12}\) cm−2, suggesting that the limited phase space surrounding the bound e–h pair is insufficient to accommodate additional excitons. This behavior indicates that exciton binding is weakened due to renormalization of the exciton wavefunctions under high carrier densities.

Fig. 3
figure 3

(a) Fitting results using the Voigt function for exciton (X) and biexciton (XX) emissions in the PL spectra of CdZnTe QDs at 10 K. Red lines represent biexcitons (XX), blue lines represent excitons (X), and red circles and black curves correspond to the experimental data and fitted curves, respectively. (b) Plot of f(N) and Γ(n) as functions of carrier density, illustrating the reduction in exciton oscillator strength and spectral broadening following laser excitation. (c) Log–log plot of exciton and biexciton peak intensities as functions of excitation density.(d) Modification of the intrinsic bandgap of CdZnTe QDs due to Burstein–Moss shift and BGR. The solid line represents a linear fit to data beyond the onset threshold, indicating band filling by free carriers. Inset: Energy shift as a function of average e–h pair number \(\left\langle {\text{N}} \right\rangle\).

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The broadening of the PL peak is also influenced by increased excitation density. The combined effects of free carrier interactions and phase-space filling contribute to this broadening. The excitonic contribution to spectral broadening can be modeled by the expression \(\Delta {\Gamma } = {\Gamma }\left( n \right)xf\left( N \right) - {\Gamma }\left( 0 \right).\) The FWHM increases with rising ⟨N⟩, primarily due to exciton–exciton interactions, enhanced dephasing, and BGR at elevated carrier densities. To gain deeper insight into the photoexcitation dynamics of excitons and biexcitons, we analyzed their emission energies and integrated intensities as functions of excitation power. As illustrated in Fig. 3c, the integrated intensity of the exciton increases linearly with \(\left\langle {\text{N}} \right\rangle\), the average number of e–h pairs. In contrast, the biexciton intensity increases sublinearly when \(\left\langle {\text{N}} \right\rangle\) remains below the average critical number of e–h pairs. At higher excitation densities, biexciton generation becomes more pronounced, demonstrating an approximately quadratic dependence of PL intensity on \(\left\langle {\text{N}} \right\rangle\). Multiple excitons in QDs increase the probability of non-radiative recombination processes such as Auger recombination, thereby reducing radiative efficiency. At high excitation densities, exciton–exciton interactions lead to exciton bleaching, where radiative recombination of excitons is suppressed owing to increased collisions and saturation of available recombination channels. This results in a further decrease in oscillator strength and PL intensity.

The changes in oscillator strength are accompanied by BGR, as depicted in Fig. 3d. BGR arises from enhanced carrier–carrier interactions and Coulomb screening, which lower the effective bandgap and produce a redshift in the emission spectrum29. Coulomb screening also weakens e–h binding, contributing to the reduction in excitonic oscillator strength. The BGR effect associated with free-carrier screening can be described by the empirical relation30 \(\Delta E_{BGR} = - k.n^{1/3}\), where n denotes the carrier density, and k represents the BGR coefficient that accounts for exchange contributions from electron–electron interactions. BGR effects observed under high-intensity excitation have been recently recognized as key parameters for optimizing QD-based lasing applications.

At high excitation intensities, the characteristic PL intensity at which abrupt increases occur shifts to higher excitation intensities, while the corresponding PL decay time becomes shorter. These trends are attributed to Auger recombination, which primarily affects multi-exciton states. The energy level spacing in the valence band is narrower than the energy of longitudinal optical (LO) phonons. Consequently, excess recombination energy cannot be dissipated via phonon emission and is instead transferred to a third carrier, re-exciting it to a higher energy state. Assuming the carrier density n is equal to the hole density under high excitation, the Auger recombination rate can be described as \(n/\tau_{a} = C_{a} N^{3}\), where τa and Ca denote the Auger lifetime and Auger nonradiative recombination coefficient, respectively10,31. This relation implies that the Auger lifetime scales with \(1/N\)2. the measured PL decay intensity is proportional to n(t), we use the absorption cross section \(\sigma_{0}\) = 5.35 × 10−13 cm2 to convert the measured PL intensity data into corresponding e–h pair numbers. Figure 4a illustrates the average number of e–h pairs per QD, \(\left\langle {\text{N}} \right\rangle\), as a function of time after excitation. Notably, the luminescence intensity shifts over time without normalization, allowing direct observation of \(\left\langle {\text{N}} \right\rangle\) decay. When \(\left\langle {\text{N}} \right\rangle\) ≤ 1, each Cd0.6Zn0.4Te QD is unlikely to host more than one exciton, and the recombination dynamics remain independent of the pump fluence. As the carrier density increases \((1 < N < N_{c} )\), the oscillator strength f(N) decreases due to phase-space filling and Coulomb screening, which reduce exciton binding energy. This reduction in (N) may be associated with enhanced Auger recombination, as both effects are driven by elevated carrier densities. When \(\left\langle {\text{N}} \right\rangle\) exceeds NC, biexcitonic Auger recombination becomes the dominant mechanism. In this regime, the recombination rate depends on the average number of e–h pairs per dot, typically ranging from 2.9 to 7.8. For a biexciton, two charge triplet configurations are possible, each offering an independent recombination pathway. The total recombination rate thus reflects the contributions of both channels. To analyze population dynamics, we fitted the time-resolved PL spectra in Fig. 2b using a biexponential function of the form32,

$$N\left( t \right) = A*exp\left( { - t/\tau_{a} } \right) + \left( {1 - A} \right)*exp\left[ { - \left( {t/\tau_{d} } \right)^{\beta } } \right].$$
(3)
Fig. 4
figure 4

(a) Average number of excitons per QD, n(t), as a function of time after excitation. PL intensities are plotted without normalization, resulting in overlapping decay curves. (b) Auger decay time (red circles) and Auger coefficient (blue circles) extracted at different excitation intensities. (c) PL decay time of CdZnTe QDs as a function of temperature at an excitation intensity of 30 W/cm2. (d) Auger coefficient as a function of temperature at 30 W/cm2 excitation intensity. The solid line represents the theoretical fit based on the temperature dependence of LO phonon-assisted Auger recombination.

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In the above equation, the first term represents the Auger recombination process, with τₐ denoting the Auger lifetime. This component dominates the decay dynamics at short time scales. The second term captures the longer-time-scale behavior, with τd and β treated as fixed parameters derived from a stretched exponential fitting procedure applied under low-excitation conditions 32. Figure 4b presents the extracted τa values as a function of the average number of e–h pairs, \(\left\langle {\text{N}} \right\rangle\), at 10 K. Both quantities decrease with increasing \(\left\langle {\text{N}} \right\rangle\), indicating that Auger recombination becomes more efficient at higher carrier densities. The shorter τₐ at larger \(\left\langle {\text{N}} \right\rangle\) corresponds to faster nonradiative decay, driven by increased exciton–exciton interactions. The reduction in Ca eflect the saturation of available recombination channels or phase-space filling effects that influence Auger dynamics under high excitation density. Beyond this saturation point, Auger recombination becomes the dominant mechanism, as it does not rely on the availability of states for photon emission.

Figure 4c presents the temperature dependence of the decay time under an excitation power of 30 W/cm2 (\(\left\langle {\text{N}} \right\rangle\) = 1.61 e–h pairs), with experimental data fitted using a curve. The PL decay time initially increases with temperature up to approximately 40 K, then decreases at higher temperatures. This nonmonotonic behavior reflects the competing influences of radiative and nonradiative processes. At very low temperatures, fast nonradiative channels such as shallow trapping or phonon-assisted processes can dominate, resulting in shorter lifetimes As the temperature rises, phonon scattering becomes less effective in facilitating these rapid decay pathways, or carriers may thermally escape from shallow traps, leading to longer decay times. Beyond ~ 40 K, the increasing phonon population enhances nonradiative recombination, particularly phonon-assisted Auger processes, causing the decay time to decrease. Similar temperature-dependent trends have been reported in both colloidal and epitaxial QDs, including CdSe/ZnS and CdTe systems7,8. Moreover, phonons assist in momentum conservation, thereby facilitating Auger recombination. As temperature increases, the rising phonon population further promotes phonon-assisted Auger processes. The temperature dependence of the Auger recombination coefficient can be modeled as follows32,33:

$$C_{a} \left( T \right) \propto \frac{{k_{B} T}}{{E_{th}^{3/2} }}\frac{1}{{\exp \left( {E_{LO} /k_{B} T} \right) - 1}}\left( {\frac{{\exp \left( { - E_{th} /k_{B} T} \right)}}{{\left( {E_{th} - E_{LO} } \right)^{2} }} + \frac{1}{{\left( {E_{th} + E_{LO} } \right)^{2} }}} \right)$$
(4)

where Ca(T) depends on the phonon energy (ELO), Boltzmann constant (kB), and Auger threshold energy (Eth). As illustrated in Fig. 4d, the Auger coefficient C(T) increases exponentially with temperature, suggesting that phonons facilitate energy transfer between carriers. Moreover, BGR at elevated temperatures leads to a narrowing of the bandgap and increased overlap between electron and hole wavefunctions, which further enhances Auger recombination. The best-fit values obtained are Eth = 44.5 meV and ELO = 19.2 meV, indicating that Auger recombination remains relatively limited at moderate carrier densities. However, the temperature-driven increase in Ca(T) negatively impacts device efficiency, thermal stability, and optical gain, highlighting the need for effective thermal management in high-power, high-efficiency devices to mitigate performance losses.

The above results emphasize the critical influence of carrier dynamics on the PL properties and Auger recombination processes of Cd0.6Zn0.4Te QDs across a range of temperatures and excitation densities. Strong quantum confinement effects at low temperatures are reflected in the PL spectra, which exhibit an emission peak at 2.148 eV. The differing effective masses of electrons and holes result in anisotropic confinement, altering wavefunction distributions and influencing optical transition strengths. With increasing temperature, the PL emission broadens and weakens due to enhanced phonon interactions, which promote carrier dephasing and reduce localization. This thermal broadening underscores the interplay between excitons and phonons, with exciton–acoustic phonon coupling playing a notable role in linewidth expansion. At high excitation densities, Auger recombination dominates the relaxation process. Both the Auger decay time (τₐ) and the Auger coefficient (Ca) decrease with increasing \(\left\langle {\text{N}} \right\rangle\), indicating enhanced nonradiative energy transfer among carriers. This leads to faster PL decay and reduced radiative efficiency, driven by stronger exciton–exciton interactions and the saturation of recombination channels. This behavior reflects the saturation of radiative recombination pathways as available states become filled, thereby enhancing the contribution of non-radiative processes. The results demonstrate that increased phonon populations at elevated temperatures enhance Auger recombination. The exponential increase in the Auger coefficient with temperature highlights the importance of effective thermal management to minimize performance degradation in devices. A thorough understanding of these carrier dynamics is essential for optimizing the performance of semiconductor devices, especially those incorporating QDs, as they balance the advantages of quantum confinement with the detrimental effects of Auger recombination and thermal interactions.

In summary, this study advances the understanding of carrier dynamics in CdZnTe QDs by elucidating the mechanisms governing carrier relaxation and recombination. The results reveal that quantum confinement in these QDs strongly affects exciton–phonon interactions, leading to distinct energy relaxation pathways. Thermally activated transitions and Auger recombination highlight the critical role of phonon-mediated processes in determining the optical efficiency of QDs. Variations in temperature and excitation density reveal a complex interplay among these processes, offering valuable insights for designing high-performance optoelectronic devices. These findings underscore the importance of thermal management and carrier density optimization to improve device efficiency, particularly in CdZnTe-QD-based applications. Future studies should aim to develop theoretical models that integrate these findings to deepen the understanding of carrier dynamics in semiconductor nanostructures.

Methods

Sample structure

The study sample was grown on a GaAs(100) substrate using molecular beam epitaxy. The substrate was first degreased in warm trichloroethylene, then cleaned with acetone and methanol, and finally rinsed thoroughly with deionized water. After chemical cleaning, the GaAs substrate was mounted onto a molybdenum susceptor. A 900-nm-thick ZnTe buffer layer was grown at 320 °C, followed by the deposition of 3.0 monolayers of Cd0.6Zn0.4Te at the same temperature, leading to the formation of QDs. The Cd0.6Zn0.4Te QDs were subsequently capped with a 100-nm-thick ZnTe layer grown at 320 °C. The source temperatures for Cd, Zn, and Te during the growth of the Cd0.6Zn0.4Te layer were 220, 280, and 300 °C, respectively. Cd mole fractions in the CdxZn1−xTe QDs were determined based on those obtained for CdxZn1−xTe thin films grown under the same conditions on ZnTe buffer layers through X-ray diffraction measurements considering straineffects.

Measurement techniques

Time-resolved PL decay curves were recorded using the time-correlated single photon counting (TCSPC) method. Excitation was provided by 400 nm frequency-doubled femtosecond pulses produced by a 76 MHz mode-locked Ti:sapphire laser system. The sample temperature was varied between 10 and 100 K using an He closed-cycle refrigerator Displex system. The PL signal was dispersed using a 15 cm monochromator and detected by a multichannel plate photomultiplier tube. A commercial TCSPC module (PicoHarp, PicoQuant GmbH) was used to record the PL decay curves. The FWHM of the total instrument response function was less than 130 ps.