# Homework_Fundamentals of Solid state

```EEE 436 Fall 2022
Homework 1
Problem 1. From the following plots extract
a) Extract 𝑲 and 𝒙𝟏
b) Extract 𝑲 and 𝒏
a) 𝒚 = 𝑲𝒆𝒙/𝒙𝟏
b) 𝒚 = 𝑲𝒙𝒏
Problem 2. Calculate the surface atomic density for the Si (100), (110), and (111) planes.
Give the results in units of [atoms/cm2] as well as units of [atoms/m2]
Problem 3.
a) What is the Miller index notation for a crystalline plane with intercepts of 4a, 2a, and 1a
respectively on the x, y, and z axes (a is the cubic cell side length).
c) What are the Miller indices for a cubic crystal plane that is parallel to the y-axis and with
intercepts of 2a and 3a respectively on the x and z axes.
EEE 436 Fall 2022
Homework 1
Problem 4. Show work to calculate the angle between the following crystal directions:
a) [100] and [111]
b) [111] and [11( 1]
c) [111] and [110]
Problem 5. Referring to the unit cell of the Si lattice shown below (notice the origin of the
coordinates is located at the lower back corner):
a) What are the Miller indices of the plane passing through the points ABC?
b) What are the Miller indices of the plane passing through the points BCD?
c) What are the Miller indices of the direction vector running from the origin of the coordinates
to point D?
Problem 6. Calculate the wavelength (in nanometers) for the 1st three spectral line emissions
in the Hydrogen Balmer series corresponding to transitions from E3→E2, E4→E2, E5→E2
Problem 7. Determine the de Broglie wavelength for an electron with kinetic energy of
a) 1.2 eV
b) 12 eV
c) 120 eV
EEE 436 Fall 2022
Homework 1
Problem 8. An electron is traveling in the negative x direction with kinetic energy of 0.025 eV.
a) Write the equation of a plane wave that describes this particle
b) What is the wave number, wavelength, and angular frequency of the wave that describes
this electron?
Problem 9. Calculate the number of electron states per unit volume for a range of energies
between EC and EC + 0.5 eV (i.e., within 0.5 eV from the bottom of the conduction band) in a
3D semiconductor with parabolic bands (assume m* = m0).
Problem 10. Determine the probability that an energy level 100 meV above the Fermi energy
is occupied by an electron at:
a) Room temperature (T = 300 K)
b) Liquid nitrogen temperature (T = 77 K)
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