Intraband Exciton Dynamics of n-Doped Silver Selenide Quantum Dots

Abstract

Ag_xSe (x > 2) colloidal quantum dots (CQDs) have recently emerged as a promising environmentally friendly material contender for mid- and long-wave infrared optoelectronics, leveraging their intraband transition (1S_e-1P_e). However, multicarrier interactions in CQDs, particularly Auger recombination, have profound implications on the optoelectronic properties of the materials and their potential in device applications. Understanding the intraband excited-state dynamics in n-doped Ag_xSe is therefore essential for the assessment and successful implementation of this material platform in devices. We, herein, investigate the carrier dynamics of Ag_xSe in both solution and thin-film states using a femtosecond mid-infrared transient absorption spectrometer. Our observations reveal that the multicarrier Auger process depends on the degree of doping in Ag_xSe CQDs and accelerates when the Fermi energy (E_F) level approaches the 1P_e state. The calculated intraband Auger coefficients (C_A) are measured to be on the order of ∼10^–28 cm⁶ s^–1, significantly larger compared to analogous n-doped HgS/Se CQDs.

Colloidal quantum dots (CQDs) have undergone extensive investigation regarding hot electron relaxation and transfer to other heterojunctions, with a primary focus on the dynamics between valence band and conduction band carriers in visible and near-infrared (NIR) QDs.¹⁻⁴ Nonradiative multicarrier interactions, particularly Auger recombination (AR), predominantly govern the relaxation process at high light intensities, thereby limiting the efficiency of optoelectronic devices.^5,6 Although this process has been well studied across the bandgap (i.e., for interband transitions), further research is needed to study carrier kinetics and relaxation from intersubband (or intraband) transitions in n-doped CQDs, where the 1S_e state is already occupied by more than one electron.⁷ In the past, several research groups explored the intraband (1S_e-1P_e) kinetics of CdSe and PbSe QDs, along with the effects of surface ligands.⁸⁻¹¹ Subsequently, Guyot-Sionnest and his team revealed the carrier dynamics of n-HgSe CQDs, unveiling the suppression of the Auger process in intraband excited-state dynamics.¹² They probed the emission frequency of the intraband transition in HgSe CQDs to extract Auger time scales and noted that electronic-to-vibrational energy transfer (EVET) was a limiting factor in carrier extraction. Additionally, Cho and his colleagues conducted an ultrafast study of self-doped HgS colloidal quantum dots.¹³

Most ultrafast-spectroscopy studies have primarily focused on self-doped Hg-chalcogenides and n-doped visible QDs like CdSe, with both having limitations from an environmental perspective and the latter exhibiting limited reach within the mid-infrared window. Recently the discovery of a steady-state intraband transition (1S_e-1P_e) in nontoxic Ag₂Se CQDs has motivated research toward environmentally friendly materials and enabling researchers to fine-tune and leverage higher discrete energy states due to quantum confinement.¹⁴⁻¹⁶ These CQDs offer an appealing choice to replace Hg-based devices, holding promise for utilizing intraband transition in the development of mid-infrared optoelectronics, particularly photodetectors.¹⁷⁻¹⁹ Yet their performance remains well below that of their Hg-based counterparts. We believe that shedding light onto the intraband relaxation pathways is of paramount importance for the further design and optimization of the materials and the devices thereof. Currently, there is no literature addressing these specific aspects. We sought therefore to investigate the intraband carrier dynamics of Ag_xSe CQDs, using a state-of-the-art mid-infrared femtosecond transient absorption spectrophotometer. We evaluate the intraband exciton lifetime and multicarrier interaction in both solution and thin-film states of three different size Ag_xSe on the sub-ps time scale. This investigation is poised to advance the fundamental study of intraband excitons on an ultrafast time scale as well as the infrared device community to enhance the performance of Ag₂Se-based devices by incorporating required modifications in the near future.

We synthesized oleylamine (OLM)-capped Ag₂Se CQDs using a colloidal hot injection technique. Here, we varied the reaction time (5, 10, and 15 min) at 120 °C to grow the three different sizes of CQDs. Transmission electron microscopy (TEM) images reveal highly crystalline QDs with calculated average sizes of 5.1 ± 0.7, 5.5 ± 0.6, and 6.2 ± 0.5 nm, denoted as small, medium, and large, respectively (Figure 1A–C). The estimated size heterogeneity in the ensemble sample ranges between 13% and 8%. Qualitative elemental analysis indicates a nonstoichiometric composition of Ag and Se ions in the QDs, which eventually increases with the reaction time (Figure S1). Previous studies have shown that the doping density would increase with the higher atomic percentage of Ag ions in Ag₂Se.^15,20 Due to the nonstoichiometric composition of Ag and Se ions, we designate it as Ag_xSe (where x > 2) instead of Ag₂Se in this study. Additionally, the fast Fourier transform (FFT) analysis of the high-resolution TEM image provides the interplanar distance (d) and corresponding plane (hkl) of 0.242 nm (002), 0.267 nm (211), and 0.246 nm (002) for small, medium, and large CQDs, respectively, consistent with previous findings (Figure 1A–C inset).^15,20,21 Furthermore, X-ray diffraction (XRD) data at room temperature exhibit broad peaks at 36.2° and 44.2°, along with a few small intense peaks. It is noted that the phase of Ag_xSe gradually transforms to tetragonal from a cubic structure with increasing the size of CQDs (Figure S2).^15,21 Previous studies have revealed that the tetragonal structure is a metastable state dependent on factors such as synthesis temperature, surface ligands, atomic vacancies, and crystal defects. We believe that the nonstoichiometric nature creates atomic (Se) vacancies in the QDs, which further stabilize the low surface energy tetragonal phase. Thus, we find an asymmetric tetragonal phase in larger CQDs rather than a symmetric cubic phase.

Figure 1.

(A) TEM images of small (∼5.1 ± 0.7 nm), (B) medium (∼5.5 ± 0.6 nm), and (C) large (∼6.2 ± 0.5 nm) CQDs and their interplanar distance in the inset. (D) Intraband absorption spectra of three different Ag_xSe CQDs (a–c). (E) k·p model of intraband energy as a function of the QD’s radius.

The X-ray photoelectron spectroscopy (XPS) data reveal Ag(3d) peaks at 374.38, 374.27, and 374.24 eV for the 3d_3/2 core states and 368.36, 368.27, and 368.23 eV for the 3d_5/2 core states of small, medium, and large-sized QDs, respectively, along with Se(3d) peaks (Figure S3). It is noteworthy that Ag(0) peaks are not detected, indicating the absence of metallic silver, while Ag(I) states are predominant.¹⁵ The Ag(3d) peaks shift toward lower binding energies with increasing reaction time and QD size (Figure S4). Notably, an increase in the reaction time is expected to raise the doping density of the QDs along with their size.²⁰ To determine the position of the Fermi energy (E_F) level of the three CQDs, we conducted ultraviolet photoelectron spectroscopy (UPS) and fitted the data to estimate energy levels (Figure S5). Remarkably, the E_F of the QDs gradually shifts toward the 1P_e state with the size (Scheme 1). This implies that the carrier density inherently increases with the size of the QDs upon following the current reaction method. This can be the reason that the binding energy peaks of Ag(3d) gradually shift to lower energies as the CQDs become highly n-doped. It is worth noting that these intraband transitions are very sensitive to both the ligand and doping density.

Scheme 1. Estimated Fermi Energy Level (E_F) of Three Different Size Ag_xSe CQDs: (A) 5.1 nm, (B) 5.5 nm, and (C) 6.2 nm.

The electronic transitions in the conduction band from the 1S_e state to the 1P_e state has been observed at 2168, 2022, and 1975 cm^–1 for the three sizes of CQDs, respectively (Figure 1D), whereas the bandgap transitions are completely bleached due to doping at the 1S_e state (Figure S6). To realize the bandgap transition of doped Ag_xSe, we have carried out an additional experiment where we dedoped the as-synthesized CQDs by adding 100 μL of 0.1 M 1-dodecanethiol (DDT) ligand solution to the 500 μL of Ag_xSe solution (20 mg/mL) in TCE solvent. We measured the absorbance spectra before and after DDT addition, and it clearly shows the bandgap, which appears in the range of 6000–4500 cm^–1 depending upon the size of CQDs (Figure S7). The size-dependence of the 1S_e-1P_e electronic transition energy (E_intra) has been calculated from the two-band k·p approximation (eq 1) for a QD of radius R, and the details are given in the Supporting Information with the different sizes of QDs for clarity (Figure S8).

1

Notably, the theoretical predictions match well with the experimental results up to a certain size, as depicted in Figure 1E. Beyond this point, deviations begin to appear, which is consistent with previous studies.^12,20 Therefore, the comparatively large n-Ag_xSe consists of both intraband excitonic transitions and localized surface plasmon resonance (LSPR). In the present study, we consider only the intraband transition, avoiding the surface plasmon resonance as an additional characteristic in QDs. The intraband absorption bands were fitted with three sets of Gaussian functions, in contrast to the narrow Lorentzian shape, which was often observed for the LSPR in CQDs (Figure 2A–C).²⁰ Generally, the Gaussian shape absorption spectrum of CQDs arises due to the inhomogeneous size distribution, thermal broadening, discrete energy states, and the splitting of the energy levels.^13,22,23 In the present study, the discrete energy states of the conduction band due to quantum confinement effect and the splitting of degenerate 1P_e level into three nondegenerate states (1Pe₁, 1Pe₂, and 1Pe₃) typically result in the broadening of intraband transitions. The full-width at half-maximum (FWHM) values of the intraband peaks are 636, 634, and 575 cm^–1 for small, medium, and large CQDs, respectively, which are comparable to the previously reported values of self-doped Ag₂Se CQDs (Table S1).^14,20 But, they are quite small compared to the n-doped HgS CQDs (∼1000 cm^–1).¹³ It is noteworthy that spin–orbit coupling and asymmetric shape in HgE (E = S, Se, and Te) CQDs often result in split 1P_e states (1P_1/2 and 1P_3/2).^12,22,24 But here the asymmetric tetragonal crystal phase induces the splitting of the 1P_e orbital into three states. We assign the electronic transition from the 1S_e state to the three nondegenerate 1P_e states as 1S_e-1P_e1, 1S_e-1P_e2, and 1S_e-1P_e3, as depicted in Figure 2A–C. The split energy levels are separated by 30 and 23 meV in ∼5.1 nm QDs, 25 and 30 meV in ∼5.5 nm QDs, and 22 and 27 meV in ∼6.2 nm QDs (Table S1).

Figure 2.

Gaussian-fitted intraband absorption spectra of small (A), medium (B), and large (C) CQDs in solution and their corresponding three nondegenerate 1P_e states (in the inset). Overlap of pump spectra with the intraband absorption spectra where blue lines depict the pump spectra and red dotted lines denote the effective overlap area (D–F).

To assess the intraband kinetics of each size of CQDs, we excited the solution samples in the high-frequency region of the intraband peak where pump wavelength was mostly resonant with 1S_e-1P_e1 and 1S_e-1P_e2 transitions and probed the lower frequency where the 1S_e-1P_e3 transition occurs, as illustrated in Figure 2D–F. We estimate the area of excitation for an individual set of CQDs which effectively overlap with the intraband peaks. Thus, the percentage of overlap of pump spectra with the intraband absorption peaks is 24%, 40%, and 30% for small, medium, and large CQDs, respectively (Figure 2D–F). Considering the homogeneous size distribution of CQDs, we probed at 5000 nm (2000 cm^–1), 5260 nm (1900 cm^–1), and 5650 nm (1770 cm^–1) to monitor the kinetics of the intraband carriers which resonate near the 1S_e-1P_e3 transitions, respectively. A100 μm Teflon spacer was employed in between two CaF₂ windows in the liquid cell to minimize the solvent’s impact during mid-IR transient absorption (TA) measurements.

At low pump fluence (∼20–28 μJ/cm²), the decay profile can be fitted using a single-exponential function, yielding a time constant value of ∼500 and ∼300 ps for 5.1 and 5.5 nm Ag_xSe, respectively (Figure S9). But, we observe two time constant values of 2.5 and ∼191 ps even at low fluence (∼38 μJ/cm²) for 6.2 nm CQDs (discussed later). We assume that the single intraband exciton is generated in 5.1 and 5.5 nm CQDs at low fluence, resulting in a very slow component. It can be attributed to either single-exciton recombination time by transferring the energy to the surface ligand (often called electronic-to-vibrational energy transfer) or the radiative recombination time of a single exciton. Previously, Banin and his co-workers reported long-range energy transfer to the solvent and surface ligand matrix, which competes with the bandgap emission.²⁵ Later, Guyot-Sionnest and his co-workers also revealed the possibility of EVET during the intraband exciton recombination in n-HgSe CQDs.¹² This process is interpreted by the following equation:^12,25

2

where T_EVET, λ, p, σ, ε₀, ε₁, ℏ, and R are the energy transfer time, the wavelength, the transition dipole moment of the intraband transition, the absorption cross-section, the relative permittivity (dielectric constant) of the solvent medium, the relative permittivity of the CQD, the reduced Planck constant, and the outer radius of the CQD, respectively. But, here the kinetic data suggest that there is a minute effect on the EVET process in intraband relaxation kinetics (Figure S10), which corroborates the previous work by Asbury and his co-workers.²⁶ They observed the identical electronic relaxation of higher energy states of the conduction band in PbS QDs despite the significantly different surface chemistries. Thus, EVET is not the only relaxation pathway, pointing to radiative recombination as a potential pathway in accordance with previous reports on intraband emission from similar-sized Ag_xSe CQDs.^15,27

As we systematically increase the pump fluence (up to ∼350–368 μJ/cm²), we observe that the decay profile cannot be accurately fitted by using a single-exponential function. Instead, it is better fitted using a biexponential function, with the triexponential function providing the best-fit results (Figure S9). The kinetic parameters consist of one faster component (τ₁), an intermediate component (τ₂), and a relatively slower component (τ₃). We know that Auger recombination is one of the ultrafast nonradiative relaxation processes of excited carriers, through which the excitation energy is transferred to another carrier and it strongly depends on the number of excitons generated in the QD. It is noted that electron–hole–hole (ehh) process is forbidden in the n-doped CQDs due to the filled valence state. Therefore, the AR occurs only in between the eeh pathway, as sketched in Scheme 2A. Previously, Guyot-Sionnest et al. reported intraband Auger recombination of n-doped HgSe CQDs, which are independent of pump intensity.¹² Lim et al. also reported the faster Auger process of ∼1 ps of n-HgS CQDs, independent of pump fluence.¹³ In the present study, we observe a threshold-like energy density of ∼160–200 μJ/cm², after which the τ₁ time constant does not change significantly with fluence (Figure 3D). This implies that after a certain fluence the relative population of the biexciton state predominates over the single-exciton state, resulting in a rapid multicarrier interaction, and we assume it is nonradiative Auger recombination of biexcitons. The plot of relative amplitude of the faster component (τ₁) as a function of fluence reveals that 6.2 nm CQDs hold a higher amplitude fraction of the decay kinetics (Figure 3E). The multicarrier interaction in 6.2 nm CQDs dominates the decay profile due to the close proximity of the doping level to the 1P_e state. It competes with the other physical processes (e.g., hot carrier cooling, single-exciton recombination). As a consequence, the Auger-heated electron in the higher lying excited state of the conduction band relaxes back to the lowest lying 1P_e state by emitting phonons or by interacting with the surface ligands, which is a common phenomenon for the large bandgap QDs reported elsewhere²⁸⁻³⁰ (Scheme 2B). For small (5.1 nm), medium (5.5 nm), and large (6.2 nm) QDs, the intermediate time scale (τ₂) is approximately 16 ps, 10 ps, and 6 ps, respectively, with a low relative amplitude fraction (0.25–0.1) in the decay profile. This component only arises during the multicarrier interaction at high fluence, and thus the cooling of an Auger-heated electron is assigned to the lowest lying 1P_e state, as illustrated in Scheme 2B. Prior research on n-HgS QDs reported an intermediate component with a range of 5–30 ps, assigned to electron–phonon coupling, which also possessed a lower amplitude fraction (0.1–0.15).¹³ Interestingly, the magnitude of the slow component (τ₃) does not change significantly with the fluence (Figure 3F). It represents the recombination time of the electron in the 1P_e state and the hole in the 1S_e state, which varies significantly with the size of the CQDs.

Scheme 2. Biexciton Generation and Possible Relaxation Schematic Diagram (A–C), A: AR Process Where Rate Constant Denoted as K2, B: Cooling of Hot Electron after AR Event and Rate Constant Denoted as K3, C: Exciton Recombination via Radiative or EVET Process and Rate Constant Denoted as K1; Assignment of Stepwise Rate Constant of the Carrier Relaxation Process for Fitting the Kinetic Model Equations (D).

Figure 3.

(A) Exponential fittings of kinetic data at low fluence and high fluence in solution for ∼5.1 nm CQDs (A), ∼5.5 nm CQDs (B), and ∼6.2 nm CQDs (C), when probing at the lower lying intraband state (1S_e-1P_e3) of their corresponding position as sketched in the top figure. The kinetic data are fitted as acquired from the TAS experiment. No smoothing was done. (D) Faster time constant (τ₁) as a function of fluence. (E) Amplitude fraction of corresponding faster time constant as a function of fluence. (F) Slow time constant (τ₃) as a function of fluence.

We, next, turn our attention to thin-film samples of CQDs, with the objective of investigating the dynamics of intraband excitons, in conditions more relevant to device applications (Figure 4A–C). The samples are deposited on a CaF₂ substrate by spin coating and excited by the mid-IR pump pulses as depicted in Figure S11. The CQDs in the film state are rigid and close to each other compared to the solution phase. Thus, the decay kinetics shows a little different pattern while increasing the pump fluence (Figure S12). Here, the decay curve can be fitted by a two-exponential function instead of a triexponential function. The slow time constant (τ₂) for small, medium, and large QDs varies in the ranges of 177–123 ps, 126–72 ps, and 56–33 ps, respectively, under different fluence levels, although the magnitude is significantly reduced compared to what we observed in solution-phase samples (Figure S13). Energy transfer to the nearest QDs may reduce the time scale of single-exciton recombination in the film state. Figure 4D shows the variation of the faster time constant (τ₁) as a function of fluence, indicating a very small change in the τ₁ component after a certain fluence for larger QDs, while it decreases for small- and medium-sized QDs. We assume that the maximum population is already reached in the highly doped large QD film samples upon excitation, and thus further increases in fluence do not cause a significant change in the biexciton state population. Besides, the corresponding relative amplitude fraction of the τ₁ time constant, which remains near 50% even at low fluence, also indicates a greater possibility of multicarrier interaction in film QDs (Figure 4E).

Figure 4.

Recovery kinetics of thin-film Ag_xSe CQDs: (A) low fluence and high fluence for 5.1 nm QDs, (B) for 5.5 nm QDs, and (C) for 6.2 nm QDs. (D) Variation of faster time scale (τ₁) with fluence. (E) Amplitude fraction of faster time constant as a function of fluence. (F) Decay traces at different fluence are fitted with the kinetic model for 5 nm CQDs where scatter points are experimental results and solids are fitted data at different fluences.

Since the kinetic parameters extracted from monoexponential or multiexponential fittings depend on the pump energy density, it is not possible to directly evaluate the rate constants (K) related with the different carrier relaxation pathways. To determine the state-to-state transition rates, we needed a kinetic model that could fit the experimental data and describe the relaxation processes at play. Our proposed model accounts for both single and biexciton relaxation with varying pump power.

The schematic of the carrier relaxation model is shown in Scheme 2D. The associated ordinary differential equation (ODE) system is summarized in eqs 3–5, where N₀, N₁, and N₂ represent 1S_e, 1P_e, and the higher lying energy state of CQDs, respectively. P(t) denotes the mid-IR Gaussian time profile of the laser pulse for excitation of the sample. K₁, K₂, and K₃ stand for the rate constant of single-exciton recombination either radiatively or through the EVET process, rate of Auger process, and cooling of an Auger-heated electron to the lowest lying excited state of the 1P_e level, respectively (Scheme 2D). This type of ODE system has been previously used to fit carrier and excitonic kinetics in all sorts of epitaxially grown^31,32 and colloidal semiconductors.^33,34 The experimental data are fitted using the model in question by performing a least-squares residual minimization to a numerically solved 3-ODE system for each time trace (12 ODEs for Figure 4F and 9 for Figure S14A) while keeping all the K_i parameters and the laser temporal FWHM as global constants and setting their initial values as (N₀, N₁, N₂) = (1, 0, 0). In this ansatz, the only parameter that varies between the different ODE systems is the amplitude of the laser profile, which directly relates to the pump fluence.

3

4

5

In our analysis, three rate constants (K₁, K₂, and K₃) are sufficient to fit the experimental data. Therefore, we merge both internal conversion (IC) and inter-sublevel transitions (IST) with the K₃ constant. The extracted rate constants are as follows: K₁ ∼ 7.9 × 10^–3 ps^–1, K₂ ∼ 1.5 × 10^–1 ps^–1, K₃ ∼ 1.2 × 10^–1 ps^–1. We validated the kinetic model by fitting it to different batches of small CQDs (Figure S14). Additionally, we found that as the doping density increases, the rate constants become faster than those for small CQDs (Figure S14B). We attribute this to an increased likelihood of electron–electron scattering due to the higher degree of n-doping. For simplicity, we focus on the kinetic model only for small CQDs in this study. Further modifications in the model for high-doped CQDs are essential by including additional parameters to account for LSPR characteristics. However, the Auger coefficient (C_A) is characterized by the equation C_A = V²/8τ_AR, where V is the volume of the QD.¹² The estimated coefficient values in ∼5.1 nm samples are 2.7 × 10^–28 cm⁶ s^–1.

Intraband CQDs raise important questions concerning their low quantum yield and fast multicarrier relaxation pathways. In this work we investigated the intraband carrier dynamics of n-doped Ag_xSe CQDs by employing ultrafast mid-infrared pump–probe spectroscopy and implementing a kinetic model of relaxation. Our observations indicate that the degree of n-doping plays a crucial role in determining the kinetics of intraband carriers. Since the environments of solution-phase QDs and thin-film QDs are different, it is challenging to correlate the kinetics directly, and thus, we can only identify the trends of intraband exciton dynamics in solution and film state samples. The larger Auger coefficient (∼10^–28 cm⁶ s^–1) of intraband biexcitons restricts the potential optoelectronic applications. Consequently, there arise a pressing need to prolong the Auger lifetime by reducing the likelihood of multicarrier interactions. To this end, our work motivates the development of core–shell structure or investigation of alternative surface ligand chemistries for Ag_xSe CQDs.^35,36

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.4c02659.

• Experimental section, characterization methods, TEM images, XRD, UPS, XPS survey absorption spectra, all fitted kinetic data, thin-film absorption of three samples, etc. (PDF)

The authors declare no competing financial interest.