Alloying It is possible to engineer both the band gap energy

Alloying: It is possible to engineer both the band gap energy (E_g) and the lattice parameter (a) by controlling the composition of an alloy. For an alloy between two materials A0 and A1: (A0)_1x (A1)_x Vegard\'s law: a(x) = a(0) (1 -x) + a(1) x Bandgap bowing: E_g(x) = E_g(0) (1 - x) + E_g (1) x - b x (1 - x) Consider the system ZnS_1, x Te_x with a bowing parameter b = 2.40 eV. If we want a(x) = a(ZnSe) for an alloy ZnS_1, x Te_x, solve for x. What is E_g at this x? Find the minimum bandgap energy for the ZnS_1, x Te_x system, then find the composition and lattice parameter when E_g is a minimum. Sulfur and tellurium bracket selenium on the periodic table. Is it possible to make an alloy of ZnS_1, x Te_x that has the same properties (a and E_s) as ZnSe? Useful constants: k = 6.626 times 10^34 J s = 4.136 times 10^-15 eV s h =h/(2 pi) k_n = 8.617 times 10^-5 eV/K q = 1.602 times 10^-19 C[1eV/q = 1 V] m_0 = 9.11 times 10^-31 kg

Solution

In solid-state physics, a band gap, also called an energy gap or bandgap, is an energy range in a solid where no electron states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band ininsulators and semiconductors. It is the energy required to promote a valence electron bound to an atom to become a conduction electron, which is free to move within the crystal lattice and serve as a charge carrier to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move in the solid; however, if some electrons transfer from the valence to the conduction band, then current can flow (see carrier generation and recombination). Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances with large band gaps are generallyinsulators, those with smaller band gaps are semiconductors, while conductors either have very small band gaps or none, because the valence and conduction bands overlap.