Energy and Band Gap

$E_g = h\nu = \frac{hc}{\lambda}$

$\lambda = \frac{hc}{E_g} \approx \frac{1.24 \text{ eV·μm}}{E_g \text{ [eV]}}$

Mass Action Law

$n_e \times n_h = n_i^2$

$\therefore n_h = \frac{n_i^2}{n_e} \quad \text{and} \quad n_e = \frac{n_i^2}{n_h}$

Rectifier Output Frequency

$f_{out}^{\text{HWR}} = f_{in}$

$f_{out}^{\text{FWR}} = 2 \times f_{in}$

$T_{out}^{\text{FWR}} = \frac{1}{2f_{in}}$

Logic Gate Boolean Expressions

$\text{OR:}\ Y = A + B \qquad \text{AND:}\ Y = A \cdot B \qquad \text{NOT:}\ Y = \overline{A}$

$\text{NAND:}\ Y = \overline{A \cdot B} \qquad \text{NOR:}\ Y = \overline{A + B}$

De Morgan's Theorems

$\overline{A + B} = \overline{A} \cdot \overline{B}$

$\overline{A \cdot B} = \overline{A} + \overline{B}$

LED Wavelength Shortcut (NEET Numerical)

$\lambda\ (\mu m) = \frac{1.24}{E_g\ (eV)}$

Carrier Concentration Numerical Template

$\text{Given: } n_i,\ n_e \quad \Rightarrow \quad n_h = \frac{n_i^2}{n_e}$

Barrier Potential Values

$V_{barrier}(\text{Si}) \approx 0.7\ V \qquad V_{barrier}(\text{Ge}) \approx 0.3\ V$

Band Gap Reference Values

$E_g(\text{Si}) = 1.1\ \text{eV} \quad E_g(\text{Ge}) = 0.67\ \text{eV} \quad E_g(\text{Diamond}) = 5.4\ \text{eV}$