Physics · Unit 5 · 6 hrs
Fundamentals of Solid State Physics
Exam-focused notes for Fundamentals of Solid State Physics (Physics, PHY118): what the TU syllabus asks and how it has actually been tested, with 12 solved past questions from this unit.
What this unit covers
- Crystal structure
- Crystal bonding
- Classical and quantum mechanical free electron model
- Bloch theorem
- Kronig-Penny model
- Tight-binding approximation
- conductors, insulators and semiconductors
- effective mass and holes
conductors, insulators and semiconductors
The energy gaps of some alkali halides are KCl = 7.6 eV, KBr = 6.3 eV, KI = 5.6 eV. Which of these are transparent to visible light? At what wavelength does each become opaque? [5]
- Energy gap of KCl: $Eg = 7.6$ eV - Energy gap of KBr: $Eg = 6.3$ eV - Energy gap of KI: $Eg = 5.6$ eV - Visible light range: $\lambda \approx 4000$ Å to $7000$ Å - Constants: $h = 6.62 \times 10^{-34}$ J·s, $c = 3 \times 10^8$ m/s, $1\text{ eV} = 1.6 \tim...
Full solved answer →The energy gap in silicon is 1.1 eV, whereas in diamond it is 6 eV. What conclusion can you draw about the transparency of the two materials to visible light ($4000 \text{ A}^{\circ} \text{ to } 7000 \text{ A}^{\circ}$)? [5]
Material Band Gap Energy (Eg) -------------------------------- Silicon (Si) 1.1 eV Diamond 6.0 eV Visible light wavelength range: 4000 A° to 7000 A° --- The energy of a photon is given by: $$E = hf = \frac{hc}{\lambda}$$ $$E = \frac{hc}{\lambda} = \frac{6.6...
Full solved answer →effective mass and holes
Discuss effective mass of electrons and holes. [5]
In a crystalline solid (semiconductor), electrons and holes do not move as free particles. They experience the periodic potential of the crystal lattice. To simplify the analysis, we use the concept of effective mass, which accounts for the effect of the la...
Full solved answer →The density of aluminum is $2.70 \text{ g/cm}^3$ and its molecular weight is 26.98 g/mole. (a) Calculate the Fermi energy. (b) If the experimental value of $E_F$ is 12 eV, what is the electron effective mass in aluminum? [Aluminum is trivalent]. [5]
Quantity Value ------ Density, $\rho$ $2.70 \text{ g/cm}^3$ Molar mass, $M$ $26.98 \text{ g/mol}$ Valency, $Z$ 3 (trivalent) Experimental $EF$ $12 \text{ eV}$ $NA$ $6.022\times10^{23}\ \text{mol}^{-1}$ $$n = \frac{\rho NA Z}{M} = \frac{2.70 \times 6.022\tim...
Full solved answer →Discuss effective mass of electrons and holes. [5]
In a crystalline solid (semiconductor), electrons and holes do not move as free particles. They move through a periodic crystal lattice and experience internal forces from the lattice ions in addition to any externally applied force. To simplify the analysi...
Full solved answer →Classical and quantum mechanical free electron model
Describe classical free electron model. [5]
The Classical Free Electron (CFE) model was proposed to explain the electrical and thermal properties of metals. In metals, valence electrons are loosely bound to the nucleus, and when atoms come together to form a solid, these electrons become free to move...
Full solved answer →The density of aluminum is 2.70 g/cm3 and its molecular weight is 26.98 g/mole. a. Calculate the Fermi energy b. If the experimental value of EF is 12 eV, What is the electron effective mass in aluminum? Aluminum is trivalent. [5]
Quantity Value ------ Density $\rho$ $2.70$ g/cm³ Molecular weight $M$ $26.98$ g/mol Valency $Z$ $3$ (trivalent) Experimental $EF$ $12$ eV $NA$ $6.022\times10^{23}$ /mol $\hbar$ $1.055\times10^{-34}$ J·s $me$ $9.11\times10^{-31}$ kg --- Electron density: $$...
Full solved answer →Crystal structure
Sodium has a body-centered cubic structure with a one-atom basis. The density and the atomic weight of sodium are $0.971\text{ g/cm}^3$ and 23 g/mole, respectively. What is the length of the unit cube of the structure? [5]
Quantity Value ------ Structure BCC, one-atom basis Density $\rho$ $0.971\ \text{g/cm}^3$ Atomic weight $M$ $23\ \text{g/mole}$ Avogadro's number $Na$ $6.022\times 10^{23}\ \text{/mole}$ Atoms per unit cell (BCC): $$n = 8\times\tfrac{1}{8} + 1 = 2$$ Density...
Full solved answer →Assuming that atoms in a crystal structure and arranged as close-packed spheres, what is the ratio of the volume of the atoms to the volume available for the simple cubic structure? Assume a one atom basis. [5]
- Structure: simple cubic (SC) - Basis: one atom - Atoms treated as close-packed hard spheres - Required: ratio $\dfrac{\text{volume of atoms}}{\text{volume of unit cell}}$ No numerical values are given (this is a derivation problem); the result is expresse...
Full solved answer →Copper has a face-centered cubic structure with a non-atom basis. The density of copper is $8.96\text{ g/cm}^3$ and its atomic weight is $63.5\text{ g/mole}$. What is the length of the unit cube of the structure? [5]
Quantity Value ------ Structure FCC, one-atom basis Density $\rho$ $8.96\ \text{g/cm}^3$ Atomic weight $M$ $63.5\ \text{g/mole}$ Avogadro number $NA$ $6.022\times10^{23}\ \text{/mole}$ Atoms per cell (FCC) $n$ $4$ Atoms per unit cell (FCC): $$n = 8\times\tf...
Full solved answer →Kronig-Penny model
Give a brief account of Kronig-Penney model. [5]
The Kronig-Penney model is a simplified quantum mechanical model that explains the behaviour of electrons in a periodic potential of a crystalline solid. As noted in the reference context, "this model gives the information of the behaviour of electrons in p...
Full solved answer →Bloch theorem
Explain Bloch theorem. Discuss its use in Kronig-Penney model and hence in band theory. [5]
--- In a crystalline solid, atoms are arranged in a periodic lattice. If the spacing between ions in the x-direction is 'd', then the potential energy of an electron at position x is equal to the potential energy at position x + d: $$V(x) = V(x + d)$$ This ...
Full solved answer →Make Unit 5 stick
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