Intrinsic Carrier Concentration Calculator
Calculate electron and hole concentrations in pure semiconductors at various temperatures
Semiconductor Parameters
Properties at 300K: Eg = 1.12 eV, Nc = 2.82×10¹⁹ cm⁻³, Nv = 1.83×10¹⁹ cm⁻³
Effective Density of States (at 300K)
Effective density of states in conduction band
Effective density of states in valence band
Energy difference between conduction and valence bands
Operating Conditions
Operating temperature of the semiconductor
Units for carrier concentration display
More accurate temperature-dependent formula: Ni = 5.29×10¹⁹ × (T/300)^2.54 × exp(-6726/T)
Calculation Results
Example Calculation
Silicon at 400K
Given: T = 400K, Silicon parameters at 300K
Nc(300K): 2.82×10¹⁹ cm⁻³
Nv(300K): 1.83×10¹⁹ cm⁻³
Eg(300K): 1.12 eV
Step-by-Step Solution
1. Temperature ratio: T/300 = 400/300 = 1.333
2. Nc(400K) = 2.82×10¹⁹ × (1.333)^1.5 = 4.34×10¹⁹ cm⁻³
3. Nv(400K) = 1.83×10¹⁹ × (1.333)^1.5 = 2.82×10¹⁹ cm⁻³
4. Eg(400K) = 1.166 - 4.73×10⁻⁴×400²/(400+636) = 1.083 eV
5. Ni = √(4.34×10¹⁹ × 2.82×10¹⁹) × exp(-1.083/(2×8.617×10⁻⁵×400))
6. Result: Ni = 4.56×10¹² cm⁻³
Common Semiconductors (300K)
Temperature Effects
Physical Constants
Semiconductor Tips
Higher temperature = more carriers
Smaller band gap = higher conductivity
In intrinsic: n = p = ni
Law of mass action: np = ni²
At 0K: semiconductor = insulator
Understanding Intrinsic Semiconductors
What are Intrinsic Semiconductors?
Intrinsic semiconductors are pure semiconductor materials without any significant impurities or defects. Their electrical conductivity depends entirely on temperature, and they behave like insulators at absolute zero (0K) but become conductive as temperature increases due to thermal excitation of electrons across the band gap.
Key Properties
- •Equal Carriers: Number of electrons equals number of holes (n = p = ni)
- •Temperature Dependent: Conductivity increases exponentially with temperature
- •Pure Material: No external doping or impurities
- •Band Gap: Small energy gap (~1 eV) between valence and conduction bands
Carrier Concentration Formula
Primary Formula
Ni = √(Nc × Nv) × exp(-Eg/(2kT))
Ni = intrinsic carrier concentration, Nc/Nv = effective density of states, Eg = band gap energy, k = Boltzmann constant, T = temperature
Temperature Dependencies
Nc(T) = Nc(300K) × (T/300)^(3/2)
Eg(T) = Eg(0) - αT²/(T + β)
Density of states and band gap both vary with temperature
Silicon Empirical (Misiakos-Tsamakis)
Ni = 5.29×10¹⁹ × (T/300)^2.54 × exp(-6726/T)
More accurate empirical formula specifically for silicon
Applications
- •Electronic Devices: Transistors, diodes, integrated circuits
- •Solar Cells: Photovoltaic energy conversion
- •Sensors: Temperature, light, and radiation detectors
- •Research: Fundamental studies of semiconductor physics
vs. Extrinsic Semiconductors
Intrinsic
Pure material, n = p, low conductivity, temperature-dependent only
Extrinsic
Doped material, n ≠ p, high conductivity, depends on doping and temperature