This optical absorption edge is known as the Urbach edge and is given as follows: (2) where A is a constant of the order of unity, ν is the frequency of the incident beam (ω = 2πν), ν 0 is the constant corresponding to the lowest excitonic frequency, k B is the Boltzmann constant, and T is the absolute temperature. The calculated values of the absorption coefficient for thin films of a-(PbSe)100−x
Compound C molecular weight Cd x nanoparticles are of the order of approximately 105 cm−1, which is consistent with the reported results [43, 44]. The calculated values of absorption coefficient (α) are given in Table 1. It is observed that α shows an overall increasing trend with the increase in the metal (Cd) concentration. It is suggested that bond breaking and bond rearrangement may take place when there is increasing cadmium concentration, which results in the change in local structure of these lead chalcogenide nanoparticles. This includes subtle effects such as shifts in the absorption edge, and more substantial atomic and molecular reconfiguration which is associated with changes in the absorption
coefficient and absorption edge shift. Table 1 Electrical and optical parameters in (PbSe) 100−x Cd x nanoparticle thin films Sample σ dc (Ω−1 cm−1) at 380 K σ 0 (Ω−1 cm−1) ΔE c (eV) ΔE g (eV) α (cm−1) (105) n at 590 nm k at 590 nm (PbSe)95Cd5 3.21 × 10-6 2.69 × 108 0.99 2.41 1.02 1.65 selleck screening library 0.117 (PbSe)90Cd10 1.85 × 10-6 3.61 × 106 0.91 2.19 2.36 1.83 0.632 (PbSe)85Cd15 2.64 × 10-5 8.62 × 106 0.87 2.12 1.94 2.44 0.524
(PbSe)80Cd20 6.69 × 10-5 2.21 × 107 0.85 2.03 3.11 2.73 0.923 In the case of amorphous semiconductors, the fundamental absorption edge follows an exponential law. Above the exponential tail, the Epothilone B (EPO906, Patupilone) absorption coefficient obeys the following equation : (3) where B is a constant, E g is the optical bandgap, and m is a parameter that depends on both the type of Sepantronium manufacturer transition (direct or indirect) and the profile of the electron density in the valence and conduction bands. The values of m can be assumed to be 1/2, 3/2, 2, and 3, depending on the nature of electronic transition responsible for the absorption: m = 1/2 for allowed direct transition, m = 3/2 for forbidden direct transition, m = 2 for allowed indirect transition, and m = 3 for forbidden indirect transition. The present systems of a-(PbSe)100−x Cd x obey the role of direct transition, and the relation between the optical gap, absorption coefficient α, and the energy (hν) of the incident photon is given as follows: (4) The variations of (αhν)2 with photon energy (hν) for a-(PbSe)100−x Cd x nanoparticle films are shown in Figure 5. Using this figure, the intercept on the x-axis gives the value of direct optical bandgap E g, and the calculated values of E g for a-(PbSe)100−x Cd x nanoparticles are given in Table 1.