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Use a computer and a commercial software package such as MATLAB, Mathematica, Ma

ID: 1805734 • Letter: U

Question

Use a computer and a commercial software package such as MATLAB, Mathematica, MathCAD, Maple, or Excel spreadsheet in this project. Refer Chapter 2 (Vol 1 of textbooks) for charge neutrality equations for an extrinsic semiconductor. Obtain plots of Fermi energy levels of extrinsic GaAs as a function of temperature in Kelvin for different doping concentrations (Refer figure below). Use the internet and other resources to find the material properties for GaAs. Tellurium is a donor impurity for GaAs. Consider Te donor impurity concentrations at 1018, 10, 1014, and 1012 cm-3 in a GaAs crystal. Generate plots determining the temperature in Kelvin at which the Fermi energy level is equal to the intrinsic Fermi energy level for each doping concentration. Remember that the intrinsic Fermi energy level is also a function of temperature. Zinc is an acceptor doping impurity for GaAs. Consider Zn acceptor impurity concentrations at 1018, 1016, 1014, and 1012 cm-3 in a GaAs crystal. Generate plots determining the temperature at which the Fermi level is equal to the intrinsic Fermi energy level for each doping concentration. Remember that the intrinsic Fermi energy level is also a function of temperature. Note: Make sure to include comments in the program, outputs from the program, and clearly labeled plots !!! Temperature T in Kelvin rightarrow Fermi energy level for GaAs as a function of temperature with impurity concentration as a parameter Ei = EFi = Fermi energy level in intrinsic GaAs; EF = EFn (n-type GaAs) OR EF = EFp (p-type GaAs)

Explanation / Answer

The Fermi level is a hypothetical level of potential energy for an electron inside a crystalline solid. Occupying such a level would give an electron (in the fields of all its neighboring nuclei) a potential energy equal to its chemical potential (average diffusion energy per electron) as they both appear in the Fermi-Dirac distribution function.........................................................