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Understanding PN Junction Diodes
Jan 4, 2025
Notes on PN Junction Diode Lecture
Introduction to PN Junction Diode
PN Junction Diode
: Discussed under no applied bias.
Built-in Potential
: Also known as barrier potential.
Depletion Layer Formation
Depletion Layer
: Created due to charge carrier diffusion.
Diffusion
: Process of free charge carriers recombining.
Example:
Hole combines with electron → immobile negative ion.
Electron combines with hole → immobile positive ion.
Charge Neutrality
: Maintained when immobile ions and holes/electrons are present.
Immobile Ions
:
P-side: Layer of negative immobile ions (from hole combining with electrons).
N-side: Layer of positive immobile ions (from electron combining with holes).
Barrier Potential
:
Acts as a barrier, preventing further charge movement.
Positive layer repels holes; negative layer repels electrons.
Expression for Barrier Potential
Formula
:
Barrier potential (V_B) = [ V_B = \frac{kT}{e} \ln \left( \frac{n_a n_d}{n_i^2} \right) ]
Components
:
(k): Boltzmann constant, (1.38066 \times 10^{-23}) J/K.
(T): Absolute temperature in Kelvin.
(e): Charge of an electron, (1.6 \times 10^{-19}) C.
(n_a): Acceptor concentration.
(n_d): Donor concentration.
(n_i): Intrinsic carrier density.
Thermal Voltage (V_T)
Definition
: Equivalent voltage of temperature.
Formula
: ( V_T = \frac{kT}{e} )
Example Calculation
: For room temperature (27°C):
Absolute temperature: 273 + 27 = 300 K.
( V_T = 0.026 ) V (valid for room temperature).
Generalization of Thermal Voltage
For any temperature (T') in °C:
Absolute temperature: (T = 273 + T') K.
Generalized form of (V_T): ( V_T = \frac{(273 + T')}{11600} )
Numerical Problem Example
Given
:
Acceptor concentration (n_a): (10^{16}) cm⁻³
Donor concentration (n_d): (10^{17}) cm⁻³
Intrinsic carrier density (n_i): (1.5 \times 10^{10}) cm⁻³
Calculation of Barrier Potential
:
Use formula: ( V_B = V_T \ln \left( \frac{n_a n_d}{n_i^2} \right) )
Result: ( V_B = 0.757 ) V (for silicon PN junction at room temperature).
Important Values
Barrier potential for silicon: 0.7 V.
Barrier potential for germanium: 0.3 V.
Next Lecture Preview
Discussion on width of depletion region and related numerical problems.
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