Wannier-Mott Excitons in Nanoscale Molecular Ices

The absorption of light to create Wannier-Mott excitons is a fundamental feature dictating the optical and photovoltaic properties of low band gap, high permittivity semiconductors. Such excitons, with an electron-hole separation an order of magnitude greater than lattice dimensions, are largely limited to these semiconductors but here we find evidence of Wannier-Mott exciton formation in solid carbon monoxide (CO) with a band gap of $>8\mathrm{eV}$ and a low electrical permittivity. This is established through the observation that a change of a few degrees K in deposition temperature can shift the electronic absorption spectra of solid CO by several hundred wave numbers, coupled with the recent discovery that deposition of CO leads to the spontaneous formation of electric fields within the film. These so-called spontelectric fields, here approaching $4\times {10}^7\mathrm{V}{\mathrm{m}}^{-1}$, are strongly temperature dependent. We find that a simple electrostatic model reproduces the observed temperature dependent spectral shifts based on the Stark effect on a hole and electron residing several nm apart, identifying the presence of Wannier-Mott excitons. The spontelectric effect in CO simultaneously explains the long-standing enigma of the sensitivity of vacuum ultraviolet spectra to the deposition temperature.

Figure 1

Upper panel: VUV absorption spectra of solid CO in the $A{}^1\mathrm{\Pi }\leftarrow X{}^1\mathrm{\Sigma }$ transition at 14 K. The splitting of lines, most clearly seen in the $v^{\prime }=1$ and 2 vibronic bands may be attributed to the Davydov effect (see text). Lower panel: similar data for solid ${\mathrm{N}}_2$ at 14 K. All spectra were taken with a resolution of 0.1 nm. Red curves show Gaussian fits to spectra used to establish peak absorption wavelengths, the technique used to establish peak shifts shown in Table 1 for spectra taken over the range of temperatures of film deposition shown in Fig. 2, left hand panel.

Figure 2

Left hand panel: VUV absorption spectra of solid CO in the (0,0) band of the $A{}^1\mathrm{\Pi }\leftarrow X{}^1\mathrm{\Sigma }$ transition at a succession of deposition temperatures 14, 20, 21, 22, 23, 24, 25, and 26 K (data taken from Ref. [15]), showing the marked shifts in spectra associated with these deposition temperatures. The broadening of the absorption lines may be attributed to Davydov splitting, components of which are labeled 1 and 2. Right hand panel: similar data for solid ${\mathrm{N}}_2$ at 14, 20, and 24 K, illustrating that spectra of this nonpolar species show that the spectrum remains unchanged over this temperature range. All spectra were taken with a resolution of 0.1 nm and are vertically offset from one another for ease of viewing.

Figure 3

The experimental shift of the peak of the absorption in the (0,0) band of the $\mathrm{A}{}^1\mathrm{\Pi }\leftarrow X{}^1\mathrm{\Sigma }$ transition in solid CO, relative to the peak at 20 K deposition temperature, as a function of deposition temperature at 21, 22, 23, 24, 25, and 26 K (blue squares peak 1, red squares peak 2) versus the results obtained from expression 2 for $\mathrm{\Delta }{\mathcal{E}}_{ij}$, the calculated shift (solid blue and red lines). Peaks 1 and 2 refer to the two Davydov components, which may be identified in Fig. 2, left hand panel. Errors arising in the determination of r, the separation of the hole and electron in the absence of the spontelectric effect, and uncertainties quoted in the spontelectric fields in CO [8], the major sources of error in our estimates, lead to an overall uncertainty in the calculated values of shifts of $\pm 10\%$. The continuous lines in each case were obtained by fitting the variation of the spontelectric field versus temperature of deposition, Table 2, to a quadratic form in this temperature range. An uncertainty in the value of the temperature of $\pm 0.25\mathrm{K}$ has been included. Uncertainty in measured peak shifts are $\pm 4{\mathrm{cm}}^{-1}$.