# Investigation of Magnetic Circular Dichroism Spectra of Semiconductor Quantum Rods and Quantum Dot-in-Rods

^{1}

^{2}

^{*}

## Abstract

**:**

**A**and

**B**terms, which characterize the splitting and mixing of states. Effective values of

**A**and

**B**terms were determined for each transition. A relatively high value of the

**B**term is noted, which is most likely associated with the anisotropy of quantum rods.

## 1. Introduction

**A**-term); (2) the effect of mixing of the zero-field states in the presence of magnetic field (

**B**-term); (3) the difference in the populations of sublevels of an initially degenerate ground state (

**C**-term). The

**A**term appears in the MCD spectrum as a feature with the distinctive first derivative band shape. The

**A**term without an admixture of the

**B**and

**C**terms and without overlapping with other transitions gives the position of the zero-field transition as the point of MCD spectrum intersection with the abscissa axis. The

**A**term occurs in systems with a symmetry axis of the third or higher order. In a system with lower symmetry, only the

**B**terms are present. The

**C**term is observed only in systems with a degenerate ground state. The

**C**term is normally negligible at room temperature [15].

**A**-term shape. In contrast, MCD spectra of AgInS

_{2}/ZnS quantum dots include both

**A**and

**B**terms due to the anisotropy of the AgInS

_{2}crystal lattice. MCD spectra of anisotropic CdSe nanoplates also demonstrate both

**A**and

**B**terms [17]. Moreover, the authors demonstrated that the combination of MCD and traditional absorption spectroscopy helps to specify the position of the poorly resolved electron transitions in spectra of nanostructures [17,18], but there are only a very limited number of publications on the investigation of quantum-size exciton transitions by the MCD method, and studies of anisotropic QRs or DiRs by this method have not been previously reported.

**A**and

**B**terms were determined for all absorption bands observed in the spectra.

## 2. Materials and Methods

#### 2.1. Measurement Procedure

#### 2.2. MCD Spectra Analysis Technique

**A**,

**B**,

**C**(at room temperature, $\frac{{C}_{0}}{kT}$ is usually negligible); $f\left(E\right)$—normalized absorption curve in the region of the investigated transition ${\int}_{0}^{\infty}f\left(E\right)dE=1$; $k$—Boltzmann constant; $T$—temperature; ${\beta}_{B}$—Bohr magneton; $H$—magnetic field strength; $\gamma $—constant proportional to the oscillator strength; $c$—sample concentration; $z$—optical path.

^{2}.

_{1}/D

_{0}and B

_{0}/D

_{0}. To determine these parameters from the experimental spectra, we used formulas [18] obtained from Equations (1) and (2) under the assumption that the absorption spectrum is described by a Gaussian curve:

^{−1}, ${D}_{m}$ is the absorbance peak value in absorbance units, $\Delta {D}_{m}$ is the value at the maximum (or minimum) of the MCD transition also in absorbance units, $\left(Dif\right)$ is the difference between the maximum (minimum) on the long-wavelength slope of the MCD transition and in the minimum (maximum) on the short-wavelength decline of this transition; $H$—magnetic field strength in Tesla, ${\beta}_{B}$ = 0.4671 cm

^{−1}/T.

#### 2.3. Description of the Fitting Procedure

**B**term and the second one represents the

**A**term, the spectrum is approximated as a sum of these expressions over all transitions. The parameter $b$ depends on band FWHM: $b=4ln2/{\mathsf{\Gamma}}^{2}$; the parameters $a$ and $c$ are proportional to the band amplitudes; $\lambda $—is wavelength; ${\lambda}_{0}$—is the center of the band. Band centers were fixed at the same wavelength as transitions in absorbance spectra. The $a$, $b$, $c$ parameters were fitted in PeakFit software incorporated in the program «Origin 8» (OriginLab Corp.).

_{1}/D

_{0}and B

_{0}/D

_{0}calculation by Equations (3) and (4). It must be emphasized that in this approach, each band in the absorption spectrum is associated with only one transition in the MCD spectrum. In fact, each observed MCD transition consists of a group of closely spaced electronic transitions [16]. Therefore, calculated

**A**and

**B**terms can be considered only as some effective, summed values.

## 3. Results

^{2}) was 1.096. Figure 2 demonstrates the results of MCD spectra fitting. Asymmetry of almost all fitted bands indicates the contribution of both the

**A**and

**B**terms to each transition. However, it should be noted that the 2nd band is Gaussian, which indicates the predominant contribution of the

**B**term. The transition positions and corresponding numerical values of A

_{1}/D

_{0}and B

_{0}/D

_{0}in the QRs MCD spectra are presented in Table 1.

^{2}was 1.056. As in the case with QRs, asymmetry of the 2nd and the 3rd fitted bands indicates the contribution of both the

**A**and

**B**terms. The band related to the CdSe quantum dot contained in DiRs with a center at a wavelength of 577 nm has the shape of a Gaussian derivative, which indicates the presence of the

**A**term without a noticeable contribution of the

**B**term. The shortest wavelength band under consideration has a predominant contribution of the

**B**term. The numerical values of the parameters

**A**and

**B**in the MCD spectra of DiRs are presented in Table 1. Table 1 shows the appearance of negative signs B

_{0}/D

_{0}. The signs of numerical values, according to the calculations, can be both positive and negative. They determine the sign of dichroism in a given transition induced in the positive direction of an external magnetic field.

_{1}/D

_{0}and B

_{0}/D

_{0}for both QRs and DiRs (see Table 1) by the order of values are very similar to the corresponding parameters for CdSe nanoplates (where A

_{1}/D

_{0}~0.01–0.20 and B

_{0}/D

_{0}~0.0001–0.001 1/cm

^{−1}) [17]. QRs and DiRs, as well as nanoplates, demonstrate the relatively high values of the

**B**term compared with CdSe QDs [16], where the contribution of the term

**B**is negligible. The existing

**B**term in elongated rods and planar nanoplatelets can be associated with the shape anisotropy of these nanostructures.

**B**term is also observed in a magnitude comparable to the

**B**terms in anisotropic particles, while in the CdSe QD contained in DiR only the

**A**term is observed. According to the results in Table 1 the term

**A**is present in almost all transitions, which means that all these transitions are degenerate, except perhaps the second and fourth transitions in the QRs.

**A**in each transition or in each group of transitions of close energy [17]. Changing of nanocrystal shape from zero-dimensional (0D) QDs to one-dimensional nanorods (1D) removes triple degeneracy of transition. The nanorods retain the 2-fold degeneracy (xy-polarization, perpendicular to the QR’s long axis) and have non-degenerate transitions (z-polarization, along the long axis). Contribution of the

**B**term can relate to both the xy transition (it can also contain the contribution of the

**A**term) and the z transition (it cannot contain the contribution of the

**A**term). It is impossible to distinguish between these two cases at this stage.

## 4. Conclusions

**A**and

**B**, characterizing the splitting and mixing of states for the absorption bands observed in the spectra have been determined. The numerical values have been found to be A

_{1}/D

_{0}~10

^{−2}–0.8 and B

_{0}/D

_{0}~10

^{−6}–10

^{−3}1/cm

^{−1}. We believe that this research will be useful for further understanding of the electronic and optical properties of anisotropic semiconducting nanostructures.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Magnetic circular dichroism (MCD) spectra and absorption spectra at a field strength of ±1.5 T: (

**a**) CdSe/ZnS QRs: the red curve shows the MCD spectrum at a field strength of −1.5 T, the black curve shows the MCD spectrum at a field strength of +1.5 T; (

**b**) CdSe/CdS DiRs: the red curve is the MCD spectrum at a field strength of −1.5 T, the black curve is the MCD spectrum at a field strength of +1.5 T.

**Figure 2.**Fitting of MCD (top) and absorption spectrum (bottom) of QRs CdSe/ZnS. On the MCD spectrum the orange curve is the 1st band, the green curve is the 2nd band, the blue curve is the 3rd band, the violet curve is the 4th band, the dotted line is the QR CdSe/ZnS MCD spectrum at the field strength of −1.5 T, the orange curve is an approximation.

**Figure 3.**MCD spectrum fitting and absorption spectrum (bottom) of DiRs CdSe/CdS. On the MCD spectrum: the orange curve is the 1st band, the green curve is the 2nd band, the blue curve is the 3rd band, the violet curve is the 4th band, the dashed line is the spectrum of the MCD DiRs CdSe/CdS at a field strength of −1.5 T, the orange curve is an approximation.

Transition | Transition Energy, eV | Peak Center, nm | A_{1}/D_{0} | B_{0}/D_{0}, 1/cm^{−1} |
---|---|---|---|---|

CdSe/ZnS QRs | ||||

1 | 2.00 | 617 | 0.143 | 0.0004 |

2 | 2.15 | 576 | 0.005 | 0.0004 |

3 | 2.47 | 502 | 0.765 | −6.3 × 10^{−5} |

4 | 2.74 | 452 | 0.093 | 0.0029 |

CdSe/CdS DiRs | ||||

1 | 2.15 | 577 | 0.031 | <6 × 10^{−6} |

2 | 2.66 | 465 | 0.110 | −0.0003 |

3 | 2.93 | 422 | 0.452 | 0.0007 |

4 | 3.31 | 374 | 0.116 | 0.0018 |

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**MDPI and ACS Style**

Safin, F.; Maslov, V.; Gromova, Y.; Korsakov, I.; Kolesova, E.; Dubavik, A.; Cherevkov, S.; Gun’ko, Y.K.
Investigation of Magnetic Circular Dichroism Spectra of Semiconductor Quantum Rods and Quantum Dot-in-Rods. *Nanomaterials* **2020**, *10*, 1059.
https://doi.org/10.3390/nano10061059

**AMA Style**

Safin F, Maslov V, Gromova Y, Korsakov I, Kolesova E, Dubavik A, Cherevkov S, Gun’ko YK.
Investigation of Magnetic Circular Dichroism Spectra of Semiconductor Quantum Rods and Quantum Dot-in-Rods. *Nanomaterials*. 2020; 10(6):1059.
https://doi.org/10.3390/nano10061059

**Chicago/Turabian Style**

Safin, Farrukh, Vladimir Maslov, Yulia Gromova, Ivan Korsakov, Ekaterina Kolesova, Aliaksei Dubavik, Sergei Cherevkov, and Yurii K. Gun’ko.
2020. "Investigation of Magnetic Circular Dichroism Spectra of Semiconductor Quantum Rods and Quantum Dot-in-Rods" *Nanomaterials* 10, no. 6: 1059.
https://doi.org/10.3390/nano10061059