Energy Band Relationships

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

• $E_g$ = band gap energy [J or eV]
• $h$ = Planck's constant = $6.626 \times 10^{-34}$ J·s
• $\nu$ = photon frequency [Hz = $s^{-1}$]
• $c$ = speed of light = $3 \times 10^{8}$ m/s
• $\lambda$ = wavelength [m]

Dimensional check: $[h\nu] = \text{J·s} \times \text{s}^{-1} = \text{J}$ ✓

Mass Action Law

$n_e \times n_h = n_i^2$

• $n_e$ = electron concentration [$m^{-3}$]
• $n_h$ = hole concentration [$m^{-3}$]
• $n_i$ = intrinsic carrier concentration [$m^{-3}$]

Dimensional check: $[n_e \times n_h] = \text{m}^{-3} \times \text{m}^{-3} = \text{m}^{-6}$ = $[n_i^2]$ ✓

Rearranged: $n_h = \frac{n_i^2}{n_e}$ or $n_e = \frac{n_i^2}{n_h}$

LED Wavelength (Band Gap to Color)

$\lambda = \frac{hc}{E_g} = \frac{1.24 \text{ eV·μm}}{E_g \text{ (eV)}}$

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

Rectifier Output Frequency

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

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

Logic Gate Boolean Expressions

De Morgan's Theorems

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

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

Barrier Potential Values (NEET Data)