10 pts Semiconductor nanoparticles a What is the color of cr

(10 pts). Semiconductor nanoparticles: a. What is the color of crystalline Si? We know that the bandgap of Si is 1.12 eV. b. What are excitons and exciton Bohr radius? Calculate the exciton Bohr radius in Si. c. When are quantum confinement effects observed in nanocrystallites? Explain and calculate the photon energy in the observation in this picture for nanoparticles with a diameter of 1 nm? Eg = 1.12 eV; m*electron = 1.08; m*hole = 0.57; = 11.7 for Si and Si nano particles; 0 =8.854 x 10-12 (F/m); h=6.626 x 10-34 J.s; melectron= 9.11 x 10-31 kg; c = 3 x 108 m/s; e = 1.6 x 10-19 (C); 1 eV = 1.6 x 10-19 J.

Solution

in the case of quantum size effect the size distribution reflects rather the number density than the volume fractions. For identical density of nanoparticles with two different sizes, in ideally, must be two PL lines at different frequencies with the same intensities. Although the proportion of nanoparticles larger volume will be higher. So, usually a histogram in size is presented, meaning the number density distribution of different nanoparticles. (ii) If there is a high density of nanoparticles in size, it becomes significantly self absorption by nanoparticle with larger size the emission of smaller nanoparticles size. Of course, in this case the nanoparticles with less energy will be over-represented in the photoluminescence spectrum. In this case it is necessary also to carry out the research a time-resolved photoluminescence spectra. Here is an important question regarding the lifetime of the excited state and energy transfer between the particles with close sizes. A similar effect we observed for PbI2 nanoparticles with layered structure. (iii) Of course, the surface of nanoparticles can significantly affect the PL intensity of nanoparticles.

formula which we used to find the particla size from PL spectrum
Delta E = (h^2(3.14)^2)/(2MR^2)
Where M= Effective mass of the electron and hole.
R is the radius of the particle.