ity). Thus, there's a threshold frequency $\nu_0 = \frac{\Phi}{h}$. * **Instantaneous Emission:** Since the interaction is one-to-one, if a photon has enough energy, the electron is ejected immediately. * **Kinetic Energy:** The kinetic energy depends directly on the photon's frequency ($h\nu$) and the material's work function ($\Phi$). Increasing light intensity only means more photons are striking the surface, leading to more emitted electrons, but not higher kinetic energy for each individual electron. **Implications:** The photoelectric effect provided strong evidence for the particle nature of light (wave-particle duality) and solidified the concept of energy quantization, which was foundational for the development of quantum mechanics. #### 1.4 Essential Diagrams

*Figure 1.1: Bohr Model of the Hydrogen Atom, showing quantized energy levels and electron orbits.*

*Figure 1.2: Comparison of continuous, emission, and absorption spectra. Note how absorption lines match emission lines.*

*Figure 1.3: Schematic of the Photoelectric Effect. Incident photons strike a metal surface, ejecting electrons if their energy exceeds the work function.* ### Day 2: Atomic Structure to Crystal Formation #### 2.1 Silicon Crystal Structure (Diamond Lattice) Silicon (Si) is the most widely used semiconductor material, and its crystal structure is fundamental to its electronic properties. Silicon atoms arrange themselves in a highly ordered, repeating pattern known as a **crystal lattice**. Specifically, silicon crystallizes in the **diamond cubic structure**. **Key Features of the Diamond Lattice:** * **Unit Cell:** The smallest repeating unit that, when stacked together, forms the entire crystal. The diamond cubic unit cell is a face-centered cubic (FCC) lattice with two atoms per lattice point. * **FCC Basis:** Imagine an FCC structure. In addition to atoms at the corners and face centers, there are four more atoms located within the unit cell. These additional atoms are displaced by $\frac{1}{4}$ of the unit cell diagonal from the FCC lattice points. * **Coordination Number 4:** Each silicon atom is covalently bonded to four nearest neighbor silicon atoms. These bonds are arranged tetrahedrally. * **Tetrahedral Bonding:** The four bonds from a central silicon atom point towards the vertices of a regular tetrahedron. The angle between any two bonds is $109.5^\circ$. * **Open Structure:** Compared to simple cubic or FCC structures, the diamond lattice is relatively open, meaning there is significant empty space within the unit cell. This is due to the directional nature of the covalent bonds. * **Strong Bonds:** The covalent bonds are strong, making silicon a hard material with a high melting point. **Visualizing the Diamond Lattice:** It can be thought of as two interpenetrating FCC lattices, one displaced from the other by a vector $(\frac{a}{4}, \frac{a}{4}, \frac{a}{4})$ where 'a' is the lattice constant (edge length of the unit cell).

*Figure 2.1: Diamond cubic unit cell. Note the tetrahedral bonding of each atom.* #### 2.2 Covalent Bonding in Group IV Elements Silicon belongs to Gro