Electronic Devices (Semiconductor Electronics) - Important Formulas Table

 Electronic Devices (Semiconductor Electronics) - Important Formulas Table

S.No.	Concept / Quantity	Formula	Key Notes
1	Intrinsic Carrier Concentration	$n_i = \sqrt{N_C N_V} \, e^{-E_g / 2kT}$	Depends on temperature
2	Conductivity of Intrinsic Semiconductor	$\sigma_i = n_i e (\mu_e + \mu_h)$	-
3	Conductivity of Extrinsic Semiconductor (n-type)	$\sigma_n \approx N_D e \mu_e$	Majority carriers: electrons
4	Conductivity of Extrinsic Semiconductor (p-type)	$\sigma_p \approx N_A e \mu_h$	Majority carriers: holes
5	Mass Action Law	$n \cdot p = n_i^2$	Valid for both intrinsic & extrinsic
6	Drift Current	$I_d = n e A v_d$	-
7	Diffusion Current	$I_{diff} \propto \frac{dn}{dx}$	Due to concentration gradient
8	Diode Current Equation (Shockley Equation)	$I = I_0 \left( e^{eV / \eta kT} - 1 \right)$	η = 1 (Ge), 2 (Si)
9	Reverse Saturation Current	$I_0$ doubles for every 10°C rise in temperature	Highly temperature dependent
10	Dynamic Resistance of Diode	$r_d = \frac{\eta V_T}{I}$	$V_T = kT/e \approx 26$ mV at 300 K
11	Cut-in Voltage	Si: 0.7 V, Ge: 0.3 V	Forward bias
12	Zener Breakdown Voltage	$V_Z$ (constant in reverse bias)	Used as voltage regulator
13	Half-Wave Rectifier Efficiency	$\eta = 40.6\%$ (maximum)	$\eta = \frac{0.406}{1 + (r_f / R_L)}$
14	Full-Wave Rectifier Efficiency	$\eta = 81.2\%$ (maximum)	-
15	Ripple Factor (Half-Wave)	$r = 1.21$	-
16	Ripple Factor (Full-Wave)	$r = 0.48$	-
17	DC Load Current (Half-Wave)	$I_{dc} = \frac{I_m}{\pi}$	-
18	DC Load Current (Full-Wave)	$I_{dc} = \frac{2I_m}{\pi}$	-
19	Transistor Current Relation	$I_E = I_B + I_C$	Kirchhoff’s Current Law
20	Current Gain (α) in CB Configuration	$\alpha = \frac{I_C}{I_E}$	α < 1
21	Current Gain (β) in CE Configuration	$\beta = \frac{I_C}{I_B} = \frac{\alpha}{1 - \alpha}$	β >> 1
22	Relation between α and β	$\beta = \frac{\alpha}{1 - \alpha}$, $\alpha = \frac{\beta}{1 + \beta}$	-
23	Transconductance (gm)	$g_m = \frac{\Delta I_C}{\Delta V_{BE}}$	-
24	Voltage Gain (CE Amplifier)	$A_v = -\beta \frac{R_C}{r_i}$	Inverted output
25	Power Gain	$A_P = \beta^2 \frac{R_C}{r_i}$	-
26	Input Resistance (CE)	$r_i = \beta \frac{V_T}{I_B}$	-
27	Logic Gate Boolean Expressions	AND: $Y = A \cdot B$ OR: $Y = A + B$ NOT: $Y = \overline{A}$	Universal gates: NAND, NOR
28	NAND as Universal Gate	Can implement all logic functions	Most important
29	LED Emission Wavelength	$\lambda = \frac{hc}{E_g}$	Energy gap determines colour
30	Photodiode Current	$I = I_L + I_0 (e^{eV/\eta kT} - 1)$ (reverse biased)	$I_L$ = light generated current

Important Constants & Relations

• Thermal voltage $V_T = \frac{kT}{e} \approx 26$ mV at room temperature (300 K)
• Energy gap: Si = 1.1 eV, Ge = 0.7 eV, GaAs ≈ 1.43 eV
• Forward resistance of diode ≈ few ohms, Reverse resistance ≈ few MΩ
• $k = 8.62 \times 10^{-5}$ eV/K (Boltzmann constant)

Note: This chapter is very important for both theory (working, characteristics, applications) and numericals (rectifiers, transistor biasing, logic gates) in Class 12 Board Exams, JEE Main, and NEET.