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Part of PH-03 — Semiconductors & Electronic Devices

Formula Sheet — All Formulas with Dimensional Analysis

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Energy Band Relationships

Eg=hν=hcλE_g = h\nu = \frac{hc}{\lambda}

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

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

Mass Action Law

ne×nh=ni2n_e \times n_h = n_i^2

  • nen_e = electron concentration [m−3m^{-3}]
  • nhn_h = hole concentration [m−3m^{-3}]
  • nin_i = intrinsic carrier concentration [m−3m^{-3}]

Dimensional check: [ne×nh]=m−3×m−3=m−6[n_e \times n_h] = \text{m}^{-3} \times \text{m}^{-3} = \text{m}^{-6} = [ni2][n_i^2] ✓

Rearranged: nh=ni2nen_h = \frac{n_i^2}{n_e} or ne=ni2nhn_e = \frac{n_i^2}{n_h}

LED Wavelength (Band Gap to Color)

λ=hcEg=1.24 eV⋅μmEg (eV)\lambda = \frac{hc}{E_g} = \frac{1.24 \text{ eV·μm}}{E_g \text{ (eV)}}

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

Rectifier Output Frequency

foutHWR=finf_{out}^{HWR} = f_{in}

foutFWR=2×finf_{out}^{FWR} = 2 \times f_{in}

Logic Gate Boolean Expressions

GateBoolean ExpressionDe Morgan Equivalent
ORY=A+BY = A + BY=(A′⋅B′)′Y = (A' \cdot B')'
ANDY=A⋅BY = A \cdot BY=(A′+B′)′Y = (A' + B')'
NOTY=A‾Y = \overline{A}—
NANDY=A⋅B‾Y = \overline{A \cdot B}Y=A′+B′Y = A' + B'
NORY=A+B‾Y = \overline{A + B}Y=A′⋅B′Y = A' \cdot B'

De Morgan's Theorems

A+B‾=A‾⋅B‾\overline{A + B} = \overline{A} \cdot \overline{B}

A⋅B‾=A‾+B‾\overline{A \cdot B} = \overline{A} + \overline{B}

Barrier Potential Values (NEET Data)

MaterialBarrier Potential (V)Knee Voltage (V)
Silicon (Si)~0.7 V~0.7 V
Germanium (Ge)~0.3 V~0.3 V

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