A GaAs quantum well structure is given where a thin GaAs layer is embedded betwe

Question

A GaAs quantum well structure is given where a thin GaAs layer is embedded between AlGaAs layers
Assuming the we can treat the electrons in the GaAs conduction band as being trapped in a 1-D potential well in the x direction,

(a) What is the form of the density of states in this in the x-direction?

(b) If we have a quantum well structure as depicted below, what would be the first two energy levels for a quantum well of thickness of 10 nm? The electron mass is

me = 0.07 mo .

(c) What is the hole energy below EV of the sample is mh = 0.5 mo ?

(d) What would be the change in emission wavelength in the quantum well structure from bulk GaAs (1.42 eV)?

Explanation / Answer

The volume, area or length in 3, 2 or 1-dimensional k-spaces are expressed by O_n(k) = c_n * k^n for a n-dimensional k-space with the topologically determined constants c1 = 2,c2 = pi,c3 = 4pi/3 for linear, disk and spherical symmetrical shaped functions in 1, 2 and 3-dimensional Euclidian k-spaces respectively. (b)the first two energy levels for a quantum well of thickness of 10 nm is E_n = 13.6/n^2 eV where n = 1,2,... (c)An exciton is a bound state of an electron and hole which are attracted to each other by the electrostatic Coulomb force. Excitons are the main mechanism for light emission in semiconductors at low temperature (when the characteristic thermal energy kT is less than the exciton binding energy), replacing the free electron-hole recombination at higher temperatures. (d)The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify the elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.

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