Final answer:
To determine the density of states in silicon or GaAs at specific energies, one needs to use the formula related to effective mass and semiconductor band structure. The question does not provide enough information to perform these calculations, and additional data is required.
Step-by-step explanation:
The question implies determining the number of energy states within a certain energy range in silicon and gallium arsenide (GaAs) semiconductors at different temperatures. The challenge is to understand the concept of density of states (DoS) and how it varies with energy and temperature. The density of states is a function that describes the number of states per interval of energy at each energy level available to be occupied by electrons or holes. At T = 300 K and T = 400 K, we would use the DoS formula, which depends on effective mass and energy of the semiconductor material. However, the question as provided does not include enough information or specific parameters to calculate the density of states for silicon and GaAs between given energy levels and at specific temperatures.
To find the density of states at E = 0.80 eV, E = 2.2 eV, and E = 5.0 eV, you would use a formula related to the effective mass of the electrons and the structure of the semiconductor band. However, without the actual formulas or values specific for silicon and GaAs, it is not possible to calculate the exact density of states at these energy levels. Furthermore, the additional information provided in the challenge problems discusses concepts like the free electron gas model and the Fermi factor but is not directly applicable to calculating the density of states without further context.