## 3 Results and Discussion  
Figure 2 shows the PL spectra for the temperature range 5-25 K. The behavior clearly deviated from the semiconductor-like characteristic described in the introductory section above. The rather small temperature increase considerably impacted both the emission intensities and energy positions of the PL peaks. The PL measurements, which were done within a time span of 10-15 min, show clearly visible noise because we kept the excitation level at the noise threshold (signal/noise \(\geq\) 5) in order to exclude optical fatigue as much as possible and to record the intrinsic emission [11]. Figure 3 reveals that the PL peak intensity \(I\) dropped in proportion to the inverse temperature \(T\), i.e., \(I\) = \(c\)/\(T\), where \(c\) = 851.11 is a constant (goodness of fit 0.997). Excitonic processes frequently cause the inverse temperature dependence of the PL intensity [2]. The PL peak position shifted from 0.78 eV to 0.82 eV, corresponding to a temperature coefficient of 2 meV/K. That energy shift clearly exceeded the bulk band gap shift of 0.5 meV/K [7]. Figure 4 shows the overall temperature dependence of the PL peak. Above 25 K, the energy peak position of the PL peak remained more or less constant until 240-250 K, where it started to increase with the bulk value of 0.5 meV/K. Figure 2: PL (photoluminescence) spectra at cryogenic temperatures. At this point, it is of interest to calculate the band gap energy \(E_{g}(d)\) of free standing QDs of diameter \(d\) = 4.7 nm. For this purpose, we used the expression introduced by [PERSON] et al. [16; 17],  
\[E_{g}(d)=\left[E_{g}^{2}+\frac{2h^{2}E_{g}}{d^{2}m_{e}^{*}}\right]^{1/2}, \tag{1}\]  
where \(E_{g}\) is the band gap of PbS bulk (0.41 eV at 300 K and 0.28 eV at 77 K) [18], \(h\) is [PERSON]'s constant, and \(m_{e}\)*/\(m_{e}\) = 0.085 is the effective mass of the electron. For 4.7 nm, the theoretical band gap is 1.22 eV and 0.99 eV at 300 K and 77 K, respectively, i.e., considerably larger than the PL energy peak positions seen in Figures 2 and 4. For comparison, Figure 5 shows the absorbance peak versus temperature. The dashed line is a linear fit of the data with a slope of 0.16 meV/K. In reasonable agreement with the literature [2], at 300 K, the PL peak of \(\sim\)5 nm particles exhibited a Stokes shift of about 80 meV with respect to the absorbance peak. At 80 K, the absorbance peak  
Figure 4: PL peak position versus temperature. The dashed line is a guide for the eyes. Figure 3: PL intensity versus temperature of the spectra in Figure 2. The dashed line is a fit proportional to 1/_T_. at 0.90 eV in Figure 5 corresponded to a particle size of 5.2 nm, which is within the size tolerance. However, at 300 K the absorbance peak took place at 0.93 eV, corresponding to a particle size of about 6.4 nm. Hence, at cryogenic temperatures the intrinsic features of the QDs rule the absorption, whereas at higher temperatures the band gap of the sample is lowered due to increasing interactions between the QDs. We emphasize here however, that absorption measurements performed on solutions showed the same effect. At room temperature, for solutions with 6.27 mg/mL to 21.95 mg/mL, the absorbance peak stayed constant around 0.93 eV, while for lower concentrations the peak moved gradually towards higher energies and centered around 1.10 eV for 0.78 mg/mL, corresponding again to a particle diameter of 5.2 nm. Hence, in film and solution the increased PbS concentration alters the intrinsic features of the particles. We conclude therefore that the PbS concentration might have a critical cross-over value, which shifts the sample features towards a collective of QDs rather than maintain their separation. The data further stress that the thermal dependence of the PL peak energy is not necessarily linked to the absorption transitions and shows enhanced sensitivity on cryogenic temperature variations. Possibly, the behavior is caused by exciton relaxation processes in combination with carrier trapping, which affects the PL more than the absorption.