Concerted single-nanowire absorption and emission spectroscopy: Explaining the origin of the size-dependent Stokes shift in single cadmium selenide nanowires

Concerted single-nanowire (NW) absorption and emission spectroscopies have been used to measure Stokes shifts in the optical response of individual CdSe NWs. Obtained spectra are free of inhomogeneous broadening inherent to ensemble measurements. They reveal apparent size-dependent NW Stokes shifts with magnitudes on the order of 30 meV. Given that an effective mass model previously used to explain CdSe NW excited state progressions predicts no sizable emission Stokes shift, we have investigated modifications to the theory to rationalize their existence. This has entailed better accounting for the effects of crystal field splitting on NW band edge states. What results are important changes to the spectroscopic assignment of NW band edge transitions that arise from the crossing of hole levels. Furthermore, these modifications simultaneously predict Stokes shifts with size-dependent magnitudes up to 20 meV. However, quantitative agreement with experiment is only achieved by accounting for the role of exciton trap states. Consequently, we conclude that CdSe NW Stokes shifts contain both intrinsic and extrinsic contributions—the latter arising from band edge exciton potential energy fluctuations. At a broader level, these concerted absorption and emission measurements have provided detailed insight into the electronic structure of CdSe NWs, beyond what could be obtained using either single-particle absorption or emission spectroscopies alone.

Figure 1

(a) Low magnification TEM image of an $\langle a\rangle$ ∼ 2.5 nm CdSe NW ensemble. (b) High magnification TEM image of an individual [111] growth direction CdSe NW, exhibiting ZB/W zigzag fringes along its longitudinal axis.

Figure 2

(a) Absorption and emission spectra of three individual CdSe NWs with different radii (open blue circles and solid red lines, respectively). Also shown is the corresponding ensemble absorption (solid blue line) and emission (dashed red line) spectra. Data offset for clarity. (b) Absorption and emission transition energies (symbols) plotted for different NW radii as functions of experimental $1{\Sigma }_{1/2}1{\Sigma }_e$ (α) energies. Solid, dashed, and dotted lines represent predictions of an effective mass model developed for ZB NWs. The model assumes that the dielectric constants of the wire and the surrounding medium are ${\varepsilon }_s=6.1$ and ${\varepsilon }_m=2.0$ respectively.

Figure 3

(a) Plot of size-dependent single-CdSe NW Stokes shifts. (b) Absorption/emission comparison of three wires from the circled points in (a). Data offset for clarity.

Figure 4

(a) Band edge electron $\left(1{\Sigma }_e\right)$ and hole ($1{\Sigma }_{1/2}$ and $1{\Sigma }_{3/2}$) energies. (b) Band edge excitonic energies plotted relative to the $1{\Sigma }_{1/2}1{\Sigma }_e$ energy. (c) ZB and (d) W model predictions for transition energies. The dielectric constants of the wire and the surrounding medium are assumed to be ${\varepsilon }_s=6.1$ and ${\varepsilon }_m=2.0$, respectively.

Figure 5

(a) Plot of size-dependent single-CdSe NW Stokes shifts (open red circles). Superimposed are predicted Stokes shifts, which contain intrinsic and extrinsic $\left(N=1,2,3\right)$ contributions (dashed blue lines). The solid black line represents intrinsic shifts predicted by the W model. (b) Intrawire absorption (open blue circles) and emission (solid red lines) spectra taken from three different positions on a single $a$ ∼ 3.9 nm CdSe NW. The inset shows the associated Stokes shift for each position. Traces offset for clarity.

Figure 6

(a) Low- and (b) high-magnification TEM images of an $\langle a\rangle$ ∼ 3.7 nm NW ensemble.

Figure 7

(a) Low- and (b) high-magnification TEM images of an $\langle a\rangle$ ∼ 5.0 nm NW ensemble.

Figure 8

Squared transition matrix elements for $1{\Sigma }_{3/2}1{\Sigma }_e,2{\Sigma }_{3/2}1{\Sigma }_e$, and $2{\Sigma }_{1/2}1{\Sigma }_e$ using the ZB model. Dielectric constants of the wire and the surrounding medium are assumed to be ${\varepsilon }_s=6.1$ and ${\varepsilon }_m=2.0$, respectively.

Figure 9

Sizing curve correlating NW band edge (α) energy to radius.

Figure 10

Comparison of $|F_z|=\frac{1}{2}$ and $\frac{3}{2}$ hole energies in (a) W and (b) ZB CdSe NWs.

Figure 11

Squared transition matrix elements for $2{\Sigma }_{1/2}1{\Sigma }_e$ and $2{\Sigma }_{3/2}1{\Sigma }_e$ under parallel (||) and perpendicularly $\left(\perp \right)$ polarized excitation. Dielectric constants of the wire and the surrounding medium are assumed to be ${\varepsilon }_s=6.1$ and ${\varepsilon }_m=2.0$, respectively.

Figure 12

Squared transition matrix elements for $1{\Sigma }_{1/2}1{\Sigma }_e$ and $1{\Sigma }_{3/2}1{\Sigma }_e$ under parallel (||) and perpendicularly $\left(\perp \right)$ polarized excitation. Dielectric constants of the wire and the surrounding medium are assumed to be ${\varepsilon }_s=6.1$ and ${\varepsilon }_m=2.0$, respectively.

Figure 13

Trap state probability distribution for $N=1$, 2, 3, 4, and 1/ξ = 18 meV.