A student, instead of using the effective mass for Si (1.18∗m(e)), uses the effective mass in Ge (0.22∗m(e)) to calculate density of states in Si. The student of course gets the wrong values.
What is the ratio of the student's answer compared to the right answer?
To determine the ratio of the student's answer compared to the correct answer, we need to compare the calculated density of states in Si using the wrong effective mass for Si to the calculated density of states using the correct effective mass for Si.
The density of states is a physical quantity that represents the number of electronic states in a material at a particular energy. It is typically denoted by the symbol "D" and is often expressed in units of states per unit volume per unit energy.
In semiconductors, the density of states is often calculated using the effective mass approximation, which assumes that the energy-momentum relationship for electrons in the material can be approximated by that of free electrons with an effective mass.
In this case, the student mistakenly used the effective mass for Ge instead of Si to calculate the density of states. Since Si and Ge have different crystal structures and energy-momentum relationships, using the wrong effective mass will result in an incorrect calculation.
To find the ratio of the student's answer compared to the correct answer, we need to compare the values of the calculated density of states using the wrong effective mass to the correct value.
The actual values of the calculated densities of states using the effective mass for Si and Ge will depend on the specific calculations and methods used, such as the energy range, band structure, and other factors. Therefore, without specific numerical values or equations provided, it is not possible to provide an exact ratio.
However, in general, we can expect the ratio of the student's answer to the correct answer to be significantly different. This is because the effective mass is an essential parameter in the calculation of the density of states, and using the wrong value will lead to inaccurate results. The specific ratio will depend on the specific values of the effective masses, the energy range considered, and other factors involved in the calculations.
To obtain the correct values for the density of states in Si, the student should use the appropriate effective mass for Si, which is 1.18*m(e), as mentioned in the question.