Consider a very small (on the order of nanometers) semiconducting material, aka a quantum dot. Because...

 

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Consider a very small (on the order of nanometers) semiconducting material, aka a quantum dot. Because of the small size of the dot, energy bands narrow to discrete energy levels like atomic energy levels rather than being semiconductor's energy bands. The exciton is confined to the quantum dot in a manner analogous to a particle in a box. In fact, the energy of the quantum dot is given by the following equation: E = Eelectron Ehole + Egap where the energy of the hole and the electron are the same as the particle in the box. The term Eg is present because the particles are not in an empty box; they are in a semiconductor so they have a zero-point energy. a) Estimate the Q.D. energy by using the particle in a box problem in 1D. Assume a box with length L. (Neglect Eg) b) Estimate the Q.D. energy by using the uncertainity principle for a dot with radius R. (Neglect Eg) c) Why the color of the emitted light is depending on size? Plot the fisrt two energy levels and wave functions for red and blue Q.D.'s. (Hint: Wavelength of Blue: 475 nm while of Red: 650 nm. ) Consider a very small (on the order of nanometers) semiconducting material, aka a quantum dot. Because of the small size of the dot, energy bands narrow to discrete energy levels like atomic energy levels rather than being semiconductor's energy bands. The exciton is confined to the quantum dot in a manner analogous to a particle in a box. In fact, the energy of the quantum dot is given by the following equation: E = Eelectron Ehole + Egap where the energy of the hole and the electron are the same as the particle in the box. The term Eg is present because the particles are not in an empty box; they are in a semiconductor so they have a zero-point energy. a) Estimate the Q.D. energy by using the particle in a box problem in 1D. Assume a box with length L. (Neglect Eg) b) Estimate the Q.D. energy by using the uncertainity principle for a dot with radius R. (Neglect Eg) c) Why the color of the emitted light is depending on size? Plot the fisrt two energy levels and wave functions for red and blue Q.D.'s. (Hint: Wavelength of Blue: 475 nm while of Red: 650 nm. )