Semiconductor colloidal quantum wells (CQWs), particularly those based on cadmium selenide (CdSe), are emerging as a class of materials with considerable potential in the field of optoelectronics due to their unique optical and electronic properties^[1−3]. These materials exhibit atomic-precision layer thickness, allowing for highly tunable characteristics, such as bandgap^[4], refractive index, and extinction coefficient^{[5, 6]}, which are essential for the design of high-performance optoelectronic devices. The ability to fine-tune these properties through control of the number of monolayers offers new opportunities for integrating CdSe CQWs into advanced applications, including photodetectors^{[7, 8]}, solar cells^[9], lasers^{[10, 11]}, and quantum emitters^{[12, 13]}.

In recent years, two-dimensional (2D) materials have attracted widespread attention due to their modulated electronic structures and unique lattice symmetries. Examples of such materials include perovskites^[14], black phosphorus^[15], and transition metal dichalcogenides^[16], all of which demonstrate highly desirable properties, such as a wide spectral response range, high carrier mobility, optical gain characteristics, and rapid response speeds. However, achieving these properties within a single material system, while maintaining environmental stability, remains a major challenge, hindering their broader application. Semiconductor CQWs, particularly those made from CdSe, offer a solution to this challenge by providing a material system that can be precisely tailored to meet the demands of various optoelectronic applications^[1].

CdSe CQWs, as typical Ⅱ−Ⅵ semiconductors, exhibit tunable bandgaps ranging from approximately 3.5 eV in single-layer CQWs to 1.6 eV in multi-layer configurations. This tunability arises from quantum confinement effects, where the thickness of the CQW strongly influences the electronic and optical properties of the material. The addition of shell layers further enhances these tunable properties, making CQWs a flexible platform for device development^[17−20]. Moreover, CdSe CQWs demonstrate high fluorescence quantum yields, narrow emission spectra, and carrier mobilities reaching up to 100 cm²∙(V·s)^{−1[21, 22]}. These properties make them ideal candidates for applications requiring efficient light absorption and emission, such as in quantum emission devices^{[23, 24]}, solar concentrators^[25], and spintronic technologies^[26].

The synthesis of CdSe CQWs is typically achieved through solution-based methods, with thermal injection being a widely used approach. This method involves the rapid injection of precursors into a high-temperature long-chain ligand solvent, enabling precise control over the thickness and composition of each atomic layer^[27]. The ability to finely tune the number of monolayers and the chemical structure of CdSe CQWs^[28] through this synthesis method significantly enhances their optoelectronic performance, allowing for better device optimization^{[29, 30]}. However, the performance of these devices is strongly dependent on the intrinsic dielectric and optical properties of the CQWs, which include the dielectric function and complex refractive index (n* = n + ik). These parameters govern the interaction between light and matter in the CQWs and display a strong dependence on the number of monolayers.

The refractive index (n) and extinction coefficient (k) are critical material properties that influence the propagation and absorption of light within optoelectronic devices^[31]. In CdSe CQW-based photodetectors, solar cells, and lasers, the complex refractive index directly impacts key performance characteristics such as the absorption spectrum, quantum yield, and lasing threshold. For example, in CQW-based lasers, the refractive index determines the mode gain and loss, which in turn affects the lasing threshold^{[32, 33]}. Similarly, in photodetectors and solar cells, the refractive index influences the absorption depth and efficiency of the device^{[34, 35]}. However, precise knowledge of the complex refractive index is often lacking, which can lead to inaccurate simulations and predictions of device performance.

Various techniques have been employed to determine the dielectric function and complex refractive index of 2D materials, including Kramers−Kronig constrained variational analysis^[36], differential reflection (or transmission) spectroscopy^[37], scattering-type scanning near-field optical microscopy (s-SNOM)^{[38, 39]}, and spectroscopic ellipsometry (SE)^[40−42]. Among these, SE has emerged as a particularly effective method for extracting the optical constants of 2D materials, as it allows for the accurate determination of both the refractive index and extinction coefficient without requiring additional assumptions or functions. SE works by detecting the changes in the polarization state of light before and after interaction with the sample, providing a detailed and reliable analysis of the material's optical properties.

In this study, we investigate the layer-dependent dielectric and optical properties of CdSe CQWs with monolayer numbers ranging from 2 to 7. Using a combination of thermal injection and atomic layer deposition, we successfully synthesized high-quality CdSe CQWs with precise control over their thickness. We utilized spectroscopic ellipsometry to systematically study the evolution of the complex refractive index, dielectric function, and bandgap as a function of monolayer thickness. The optical bandgap of the CdSe CQWs was calculated using absorption spectra and the Tauc formula, revealing a decrease in the bandgap from 3.1 eV at 2 monolayers to 2.0 eV at 7 monolayers, consistent with quantum confinement effects. Additionally, we performed first-principles calculations to further explore the relationship between monolayer thickness and the material's optical properties.

To capture the excitonic behavior in CdSe CQWs, we employed an approach that accounts for exciton localization and asymmetric broadening in the absorption spectra, allowing for an accurate determination of exciton binding energy as a function of layer thickness. This analysis provides valuable insights into the correlation between monolayer number and excitonic properties, which are crucial for optimizing the performance of optoelectronic devices based on CQWs. Our work presents a comprehensive investigation of the layer-dependent dielectric and optical properties of CdSe CQWs, offering a detailed understanding of how monolayer thickness influences key material characteristics. Our findings provide critical guidance for the design and optimization of CQW-based optoelectronic devices, where precise control over material properties is essential for achieving high performance.

High-quality CdSe CQWs with 2 to 7 monolayers (ML) were synthesized using thermal injection and c-ALD methods. Cadmium myristate and selenium were used as precursors, and CQWs ranging from 2 to 5 ML were grown in a three-neck flask by gradually increasing the reaction temperature. After the nucleation and growth of 4 and 5 ML CdSe CQWs, a mixture of cadmium acetate dihydrate (Cd(OAc)₂·2H₂O) in N-methylformamide (NMF) was injected into the reaction medium. The reaction mixture was then heated to 230 °C, promoting lateral growth and increasing the thickness of the initially formed 4 and 5 ML CQWs by steps of 1 ML. The experimental details are provided in the supplementary material.

Fig. 1(a) displays the luminescence images of 2 to 7 ML CdSe CQWs under ultraviolet irradiation, showing a gradual spectral shift from blue to red as the monolayer number increases. The CQWs were spin-coated onto quartz substrates for further characterization. The atomic planes of cadmium and selenium alternate along the CQWs’ short axis, aligned with the (001) direction of the cubic structure, as illustrated in Fig. 1(d). In a cubic zinc blende structure, the six (100) directions are equivalent, but in CdSe CQWs, the (001) direction typically defines the thickness. Surface ligands cause stress and a resulting tetragonal distortion, making the lattice parameters in the thickness direction unequal to those in the in-plane directions.

To investigate the lattice structure, X-ray diffraction (XRD) was used on CQWs with different monolayer numbers, as shown in Fig. 1(e). The XRD patterns revealed characteristic diffraction peaks associated with the zinc blende phase of CdSe, which belongs to the F−43m space group. As the number of monolayers increased, the reaction temperature also rose, but this did not affect the zinc blende phase, indicating the purity and structural integrity of the synthesized samples.

The (111) peaks were smoothed and fitted using a Gaussian function with OMNIC software to calculate the lattice constants. As the monolayer number decreased, the lattice constants deviated further from those of bulk CdSe (JCPDS database #19−0191; space group F−43m; a = 6.077 Å), as presented in Table S1. This deviation is due to the smaller number of single crystal cells and the presence of surface ligands, which induce in-plane lattice expansion and a reduction in the vertical lattice constants. These variations indicate that the lattice parameters are no longer equivalent in all three directions, lifting the degeneracy seen in the zinc blende diffraction pattern.

As the crystal size decreases, Scherrer broadening causes the (400) diffraction peak to appear primarily in the plane along the longest dimension of the CQWs [(100) axis or x-direction)], although it may become too weak or broad to be clearly observed. The (220) peak of 4 ML CdSe CQWs was also fitted, as shown in Fig. 1(f). The peaks in the (220), (202), and (022) families showed varying widths and intensities, due to the differing repetition of single crystal cells along these directions. Among these, the (022) peak exhibited the strongest intensity. The analysis of the (220) peak family provides insights into both in-plane and out-of-plane dynamics in the CQWs.

The surface morphology and thickness of the CdSe CQW films were examined using atomic force microscopy (AFM) in non-contact mode. As shown in Fig. 1(b), the films exhibit a specific degree of surface roughness. The RMS roughness values are summarized in Table S2. Knowing the approximate film thickness was crucial for the accurate fitting process during spectroscopic ellipsometry analysis. The thickness was measured by lightly scratching the film with tweezers and analyzing the height difference between the film and the substrate using AFM. The resulting film thicknesses—134, 132, 130, 125, 129, and 127 nm—correspond well with the measurements obtained from spectroscopic ellipsometry (see Table S2).

To investigate the optical properties and layer-dependent bandgap of CdSe CQWs, we measured the absorption and photoluminescence (PL) spectra of CdSe films with varying monolayer numbers, covering an energy range of 1.8 to 3.9 eV (310 to 690 nm), as shown in Fig. 2(a) and Fig. S2. In the absorption spectra, CdSe CQWs exhibit three distinct bleaching features corresponding to heavy-hole (HH), light-hole (LH), and spin−orbit (SO) hole transitions to the first electronic shelf (E1). As we analyzed the series of CdSe CQWs, we observed that the absorption peaks associated with HH excitons shifted from 394 to 607 nm with increasing monolayer numbers. This shift occurs because quantum confinement is primarily restricted to the thickness of the CQWs, as the lateral dimensions are larger than the exciton Bohr radius. Consequently, CQWs have narrower optical characteristics compared to spherical nanocrystals (NCs), which are more isotropic in their quantum confinement. For example, the PL spectrum of 4 ML CdSe CQWs displays a sharp peak at 517 nm with a full width at half maximum (FWHM) of 12 nm (see supplementary material for details). The quantum confinement effect limits the electron energy levels spatially, resulting in a bandgap increase as the monolayer number decreases, which is reflected in the blue shift of the PL spectra.

In layered 2D materials like CdSe CQWs, the absorption spectra combined with the Tauc formula are commonly used to calculate the optical bandgap. The Tauc relation is given by^[40]:${\left(\alpha hv\right)}^{\rho }=C\times \left(hv-E_{\text{g}}\right)\mathrm{,}$where hv is the photon energy, E_g is the optical bandgap, and C is a constant. The parameter ρ represents the nature of the electronic transition and is typically 1/2 for indirect bandgap materials and 2 for direct bandgap materials. Since CdSe is a direct bandgap semiconductor, ρ is set to 2. By plotting (αhv)² against photon energy, the optical bandgap of CdSe CQWs can be estimated from the intercept, as illustrated in Fig. 2(b). The results show that the optical bandgap increases as the number of monolayers decreases, depicted in Fig. 2(c).

To understand the reason behind the increasing bandgap with decreasing monolayer numbers, we calculated the band structure of CdSe CQWs using first-principles density functional theory (DFT). The theoretical simulations for 2, 4, and 7 ML CdSe CQWs are shown in Fig. 2(d)−2(f) (additional simulations for 3, 5, and 6 ML are provided in the supplementary material). The calculated bandgaps are generally smaller than experimental values, which can be attributed to the limitations of DFT in accounting for long-range multibody interactions. Nonetheless, the calculations confirm that CdSe is a direct bandgap semiconductor, with the bandgap increasing as the number of monolayers decreases. The calculated bandgaps for CdSe are 2.8, 2.3, 2.1, 1.9, 1.7, and 1.6 eV for 2, 3, 4, 5, 6, and 7 ML, respectively.

The observed bandgap variation is driven by interlayer coupling, which increases with monolayer numbers and leads to orbital hybridization. This phenomenon is not unique to CdSe; it has also been observed in other 2D materials such as PdSe₂^[43] and MoS₂^[44], where the bandgap decreases as the number of layers increases. However, CdSe exhibits stronger orbital hybridization due to the higher number of valence electrons in cadmium (12) compared to palladium (10) and molybdenum (6), resulting in a more pronounced change in bandgap with varying monolayer numbers.

To determine the optical constants of CdSe CQWs and systematically examine their variation with different monolayer numbers, we employed SE to analyze CdSe CQW films with thicknesses of CQWs ranging from 2 to 7 ML. Based on AFM measurements, the surface of the CdSe CQW films exhibited similar roughness. To account for this and avoid compromising the SE analysis, we developed a four-phase optical model (air/rough layer/CdSe CQW film/quartz substrate), as shown in Fig. 3(a). The optical constants of the quartz substrate were previously measured using SE and verified against standard reference values.

In the SE analysis, the dispersion model describes the absorption characteristics of the sample by fitting the complex dielectric function. We employed the Tauc−Lorentz oscillator model, which captures the essential features of dispersive excitons. In this model, excitons are not excited at low energies, leading to a zero value for the imaginary part of the dielectric function at those energies. Additionally, phonon coupling between bright and dark excitons causes the absorption peak to adopt an asymmetric shape. Given the strong excitonic effects present in CdSe CQWs, we used a four-oscillator Tauc−Lorentz model to accurately describe the optical properties of CdSe CQWs from 2 to 7 ML. Details of this model are provided in the supplementary material.

Fig. 3(b) and Fig. S3 show the experimental ellipsometry spectra (solid lines) and the best-fit spectra (dots) for the elliptical polarization parameters (Psi and Delta) across the range of CdSe films. The close agreement between the experimental and fitted curves demonstrates the accuracy of the model. Following the fitting procedure, the measured thickness and roughness values for the 2 to 7 ML CdSe films, as detailed in Table S2, closely matched the AFM data. During the fitting process, the mean squared error (MSE) was used to quantify the deviation between the experimental and fitted values, with MSE values for all samples remaining below 2, further validating the accuracy of the SE analysis.

By fitting the SE spectra, we obtained both the real (ε₁) and imaginary (ε₂) parts of the dielectric function for the 2 to 7 ML CdSe CQWs, as shown in Fig. 3(c) and 3(d). Across the examined spectral range, both ε₁ and ε₂ show a clear layer-dependent behavior. The imaginary part, ε₂, is associated with electronic transitions between the valence and conduction bands of CdSe CQWs. As the number of monolayers increases, the peaks of ε₂ shift towards lower energies (redshift), indicating a reduction in the electron transition energy between the valence and conduction bands. This trend aligns with the observed decrease in the bandgap, as measured by the absorption spectra, as the monolayer thickness increases.

The dielectric function and complex refractive index of a material are interrelated, and their relationship is expressed as follows^[45]:

$ϵ=N^2={ϵ}_1-i{ϵ}_2=\left(n^2-k^2\right)-i2nk\mathrm{,}$where ε is the dielectric function of the material, ε₁ and ε₂ are the real and imaginary components of the dielectric function, respectively. N represents the complex refractive index, and n and k correspond to the refractive index and extinction coefficient. By using this relationship, the refractive index and extinction coefficient for the 2 to 7 ML CdSe CQW films were calculated and plotted as functions of energy, as shown in Fig. 4(a) and 4(b). Both parameters show a clear dependence on energy and layer thickness. For the refractive index, it increases with increasing energy, demonstrating normal dispersion. Additionally, as the number of monolayers increases, the refractive index also rises, which can be explained by the higher filling fraction of inorganic components in thicker films. This results in a greater dielectric contribution from atomic and molecular oscillations under photo-excitation.

For the extinction coefficient, the transition peaks observed in the ellipsometry analysis correspond to the HH and LH transitions in the absorption spectra, supporting the consistency of the measurement results. As shown in Fig. 4(b), the extinction coefficient is also dependent on the number of monolayers. HH and LH represent the two prominent absorption peaks of CdSe CQW films. Specifically, there is a coupling effect between adjacent layers in the multilayer CdSe CQWs. With increasing monolayer numbers, the interlayer coupling becomes stronger, leading to more complex electron and hole behavior and a corresponding increase in the extinction coefficient across multiple energy bands.

To clarify the relationships between the refractive index, extinction coefficient, and monolayer thickness, we extracted the peak values of these parameters from Fig. 4(a) and 4(b) and plotted them against the number of monolayers, as shown in Fig. 4(c). In thicker CdSe CQWs, a greater amount of material interacts with light, resulting in increased photon absorption and a corresponding rise in the extinction coefficient. However, beyond a certain thickness, the absorption levels off, even as the number of layers continues to increase. Fig. 4(d) presents the refractive index and extinction coefficient normalized by monolayer number. In contrast to the absolute values, thinner CQWs (with fewer monolayers) demonstrate higher normalized refractive indices and extinction coefficients, indicating stronger light−matter interactions per unit volume of material. We attribute this enhanced light−matter interaction in thinner CQWs to greater exciton binding energy, which arises from increased quantum confinement effects and reduced Coulombic screening in these structures.

We calculated the absorption coefficients for the 2 to 7 ML CdSe CQWs using α = 4πk/λ^[46]. Notably, the long-wavelength tail typical of light scattering in stacked CQWs is absent, leaving only the characteristic absorption peaks corresponding to HH and LH excitons [as shown in Fig. 4(e) for 4 ML CdSe CQWs, with spectra for other CQWs provided in the supplementary material]. To fit the absorption spectra for the 2 to 7 ML CdSe CQWs, we used a model that accounts for exciton localization by incorporating asymmetric broadening. The absorption coefficient is decomposed into a sum of exciton lines arising from HH and LH states, as well as transitions from free carriers. The detailed fitting process is described in the supplementary material. As illustrated in Fig. 4(e), the exciton binding energy E_b is the difference between the exciton energy E_x and the energy at which the free carrier transition line reaches half its high-energy limit. In 2D materials, the quantum confinement effect decreases with increasing monolayer thickness, resulting in a reduction in exciton binding energy, as shown in Fig. 4(f). The detailed fitting results are provided in Table S3. Compared with CdSe quantum wells, the exciton binding energies of CdSe quantum dots and CdSe nanorods exhibit significant differences, primarily attributed to their quantum confinement effect and dimensional differences. In quantum dots, the strong confinement in the three spatial dimensions localizes the electron and hole wave functions, thereby enhancing the coulomb interaction. This pronounced quantum confinement effect leads to a maximum exciton binding energy. In contrast, the one-dimensional extension in nanorods and the two-dimensional extension in quantum wells gradually weaken the coulomb interaction between electrons and holes, leading to a reduction in exciton binding energy. In summary, the differences in exciton binding energy among these three low-dimensional CdSe nanostructures are primarily due to the quantum confinement effect and coulomb interaction, and this variation has important significance for the design of optoelectronic devices and optical applications based on exciton properties.

This work provides a detailed investigation of the layer-dependent optical and dielectric properties of CdSe semiconductor colloidal quantum wells, shedding light on how key characteristics like bandgap, refractive index, and extinction coefficient evolve with monolayer thickness. As the monolayer number increases, we observe a pronounced decrease in bandgap, primarily driven by quantum confinement effects, alongside predictable shifts in refractive index and extinction coefficient. Through a rigorous analysis of the absorption spectra, considering exciton localization effects, we achieved a highly accurate representation of excitonic behavior in CdSe CQWs. This research contributes to the fundamental understanding of these materials and paves the way for their integration into a range of high-performance optoelectronic devices. The ability to tailor optical properties through precise control of monolayer thickness offers promising opportunities for applications such as quantum emitters, solar cells, and photodetectors, marking an important step forward in the practical use of 2D semiconductor colloidal quantum wells.