Interactive Simulation Lesson

Semiconductor Physics

Explore the fascinating world of semiconductors through interactive simulations. Understand energy bands, crystal structures, doping, P-N junctions, and more — all brought to life with real-time visualizations.

12 Chapters
8 Simulations
∞ Interactions
Start Learning
01

Classification of Solids

Solids are classified into Metals, Semiconductors, and Insulators based on their electrical conductivity (σ) or resistivity (ρ).

Metal (Conductor)

Very low resistivity (or high conductivity). Silver is the best metal conductor.

ρ : 10⁻² – 10⁻⁸ Ωm σ : 10² – 10⁸ Sm⁻¹
Excellent Conductor

Semiconductor

Resistivity / conductivity intermediate to metals and insulators.

ρ : 10⁻⁵ – 10⁶ Ωm σ : 10⁵ – 10⁻⁶ Sm⁻¹
Partial Conductor

Insulator

High resistivity or low conductivity. Examples: Plastic, putty, rubber.

ρ : 10¹¹ – 10¹⁹ Ωm σ : 10⁻¹¹ – 10⁻¹⁹ Sm⁻¹
Non Conductor
02

Energy Bands in Solids

According to Bohr's atomic model, electrons occupy discrete energy levels. In crystals, interatomic interaction causes these levels to split into closely spaced bands.

Why Energy Bands Form

In a crystal, valence electrons are shared by more than one atom due to interatomic interaction. This causes splitting of energy levels. The collection of these closely spaced energy levels is called an Energy Band.

Inside the crystal, each electron has a unique position and no two electrons have exactly the same pattern of surrounding charges — leading to different energy levels.

Valence Band

The band including energy levels of the valence electrons. May be partially or completely filled, but never empty. Does not contribute to electric current.

Conduction Band

The band above the valence band. At room temperature, it is either empty or partially filled. This band contributes to electric current.

Energy Band Gap (Eg)

Minimum energy required to shift electrons from valence to conduction band. It is the gap between the top of valence band and bottom of conduction band.

Eg = hν = hc / λ

⚡ Energy Band Visualizer

Drag the slider to see how band gap changes between conductor, semiconductor, and insulator.

Band Gap: ~1.1 eV (Semiconductor)
03

Comparing Conductor, Insulator & Semiconductor

The key difference lies in the energy band gap — the energy barrier electrons must overcome to conduct electricity.

Property Conductor (Metal) Insulator Semiconductor
Band Gap Eg = 0 (overlapping bands) Eg > 3 eV (very large) Eg < 3 eV (small)
Valence Band Partially filled / overlaps with CB Completely filled Totally filled
Conduction Band Partially filled / overlaps with VB Completely empty Empty (at 0K)
Current Flow Electrons easily jump to CB No electron movement possible Some electrons acquire thermal energy to jump
Conductivity Very high Very low (≈ zero) Moderate (tunable)

Conductor

Eg = 0

Semiconductor

Eg < 3 eV

Insulator

Eg > 3 eV
04

Fermi Energy

The maximum possible energy possessed by free electrons of a material at absolute zero temperature (0 K).

EF

Fermi Energy Level

At absolute zero, all energy states below the Fermi level are completely filled, and all states above it are completely empty. The value of Fermi energy is different for different materials.

  • In metals: EF lies within the conduction band (or overlapping region)
  • In semiconductors: EF lies in the middle of the band gap
  • In insulators: EF lies in the middle of the (large) band gap
05

Intrinsic Semiconductors

Pure semiconductors (Si, Ge) with conductivity due only to intrinsic charge carriers — no impurities added.

What are Intrinsic Semiconductors?

Materials whose conductivity lies between metals and insulators, characterized by a narrow energy gap (<3 eV). At absolute zero, valence band is fully filled and conduction band is empty — behaves like an insulator.

Electron-Hole Pair Generation

When temperature increases, the thermal energy of valence electrons increases. An electron breaks free from its covalent bond, leaving behind a vacancy called a Hole (effective positive charge).

ni = ne = nh

The number of free electrons equals the number of holes in an intrinsic semiconductor.

Current in Intrinsic Semiconductors

Free electrons give rise to electron current Ie. Holes move in the direction of the field as positive charge carriers giving hole current Ih.

I = Ie + Ih

💎 Crystal Lattice Simulation

Click on a bond to break it and generate an electron-hole pair. Watch carriers move!

Electrons: 0 | Holes: 0 | Temp: 0K
06

Extrinsic Semiconductors

Semiconductors with impurity atoms added to increase conductivity — the process called Doping.

What is Doping?

The process of adding a desirable impurity to a pure semiconductor to increase its conductivity. The impurity atoms added are called Dopants.

Pentavalent (Donor)

5 valence electrons — donates 1 extra electron

AsSbP
→ N-type Semiconductor

Trivalent (Acceptor)

3 valence electrons — creates a hole

InBAl
→ P-type Semiconductor
Semiconductor
Intrinsic
Pure Si, Ge
ne = nh = ni
Extrinsic
N-type
ne >> nh
P-type
nh >> ne

🧪 Doping Simulator

Toggle between N-type and P-type doping. Watch how carriers change!

Type: N-type | Majority: Electrons | Minority: Holes
07

N-type & P-type Semiconductors

The two types of extrinsic semiconductors — each with different majority charge carriers.

N-type Semiconductor

Obtained by doping tetravalent Si or Ge with pentavalent impurities. The pentavalent impurity donates one extra electron — called a Donor.

Electrons = Majority Carriers
Holes = Minority Carriers
ne >> nh

Very small energy is required (0.01 eV for Ge, 0.05 eV for Si) to free the extra electron from the donor impurity. The donor energy ED lies just below the conduction band.

P-type Semiconductor

Obtained by doping tetravalent Si or Ge with trivalent impurities. The trivalent impurity creates a hole — called an Acceptor.

Holes = Majority Carriers
Electrons = Minority Carriers
nh >> ne

Very small energy is required for an electron to jump into the holes created by acceptor impurity. The acceptor energy EA lies slightly above the valence band (≈ 0.01–0.05 eV).

ne · nh = ni²

The electron and hole concentration in a semiconductor in thermal equilibrium.

🔄 Carrier Concentration Comparison

08

P-N Junction

A single crystal doped such that one half acts as P-type and the other as N-type, forming the foundation of modern electronics.

How is a P-N Junction Formed?

When a P-N junction is formed, the P-side has higher concentration of holes while the N-side has higher concentration of electrons. They begin to diffuse across the junction.

Depletion Layer

As holes diffuse from P→N, they leave behind negative acceptor ions. Electrons diffusing from N→P leave behind positive donor ions. This creates a small region depleted of free charge carriers — the Depletion Layer.

Diffusion & Drift Current

The diffusion of carriers gives rise to Diffusion Current (P→N). The electric field in the depletion region creates Drift Current (N→P). At steady state:

Diffusion Current = Drift Current

Potential Barrier

The potential difference developed across the depletion region is called the Potential Barrier (VB). It opposes further diffusion of majority carriers.

🔗 P-N Junction Simulation

Watch the diffusion process and depletion layer formation in real-time.

Click "Form Junction" to begin the simulation
09

Forward & Reverse Bias

Apply external voltage to a P-N junction and observe how current flows — or doesn't.

Forward Bias

Positive terminal of battery → P-side, Negative terminal → N-side.

  • Applied voltage opposes the barrier voltage
  • Majority carriers flow towards the junction
  • Depletion layer shrinks
  • When V > VB, current flows easily (measured in mA)

Reverse Bias

Positive terminal → N-side, Negative terminal → P-side.

  • Applied voltage supports the barrier voltage
  • Majority carriers move away from junction
  • Depletion layer widens
  • Effective resistance becomes very large, negligible current (μA)

Semiconductor Diode

A P-N junction with metallic contacts at the ends for applying external voltage. It is a two terminal device. The arrow in the diode symbol indicates the conventional direction of current.

P N

🔋 Bias Simulator

Drag the voltage slider to apply forward or reverse bias. Watch the depletion layer and current change!

Voltage: 0V | No bias applied | Current: 0 mA
10

I-V Characteristics of P-N Junction

The graphical relation between voltage applied across a P-N junction and current flowing through it — the I-V Characteristics of a junction diode.

Forward Biased Characteristics

  • At start, when applied voltage is low, current through the diode is almost zero — the potential barrier opposes the voltage
  • Till applied voltage exceeds the potential barrier, current increases very slowly (OA portion)
  • With further increase, current increases very rapidly (AB portion) — the diode behaves like a conductor
  • The forward voltage beyond which current starts increasing rapidly is called Knee Voltage or Threshold Voltage
Vknee = 0.3V (Ge) | 0.7V (Si)

If the line AB is extended back, it cuts the voltage axis at the potential barrier voltage.

Reverse Biased Characteristics

  • Applied voltage supports the flow of minority charge carriers across the junction
  • A very small current flows due to minority carriers (measured in μA)
  • Reverse current remains almost constant over a long range of reverse bias
  • At Breakdown Voltage, reverse current increases very rapidly (CD portion)

Avalanche Breakdown

When reverse bias equals breakdown voltage, the junction current increases very rapidly. This is called Avalanche Breakdown. The junction may get damaged due to excessive heating if this current exceeds the rated value.

📈 I-V Curve Simulation

Drag the voltage slider to trace the I-V characteristic curve in real-time.

Voltage: 0V | Current: 0 mA | No bias
11

Diode as a Rectifier

The process of converting alternating current (AC) into direct current (DC) is called Rectification. The device used is called a Rectifier.

Principle: A junction diode allows current to pass only when it is forward biased.
Half-Wave Rectifier

How it Works

  • AC source is supplied to the primary of a transformer
  • Secondary supplies alternating voltage across terminals A and B
  • When A is +ve and B is -ve (positive half cycle): diode is forward biased → current flows through load RL
  • When A is -ve (negative half cycle): diode is reverse biased → no current flows, no voltage across RL
  • This cycle repeats for +ve and -ve half alternately

This process is called Half Wave Rectification.

Full-Wave Rectifier

How it Works

  • Uses a Centre-Tap Transformer with two diodes (D1 and D2)
  • When A is +ve and B is -ve: D1 is forward biased → conducts. D2 is reverse biased → doesn't conduct
  • When B is +ve and A is -ve: D2 is forward biased → conducts. D1 is reverse biased → doesn't conduct
  • Output voltage across RL is obtained in both half cycles

This process is called Full Wave Rectification.

12

Complete Formula Reference

All key formulas from Semiconductor Physics — at a glance.

Energy Band Gap

Eg = hν = hc / λ

Minimum energy to shift electron from VB to CB

Intrinsic Carrier Concentration

ni = ne = nh

In pure semiconductor, free electrons = holes

Total Current (Intrinsic)

I = Ie + Ih

Electron current + Hole current

Mass Action Law

ne · nh = ni²

Product of electron & hole concentration = constant

N-type Carrier Relation

ne >> nh

Electrons are majority carriers in N-type

P-type Carrier Relation

nh >> ne

Holes are majority carriers in P-type

Steady State P-N Junction

Idiffusion = Idrift

At equilibrium, diffusion current = drift current

Knee / Threshold Voltage

Vknee (Ge) = 0.3V  |  Vknee (Si) = 0.7V

Forward voltage where current rises rapidly

Donor Energy Level

ED ≈ 0.01 eV (Ge) | 0.05 eV (Si)

ED lies just below conduction band

Acceptor Energy Level

EA ≈ 0.01 – 0.05 eV above VB

EA lies slightly above valence band

Reverse Bias Barrier

Vbarrier = VB + Vapplied

Barrier increases in reverse bias

Resistivity Ranges

Metal: 10⁻²–10⁻⁸ Ωm
Semi: 10⁻⁵–10⁶ Ωm
Insulator: 10¹¹–10¹⁹ Ωm

Classification by resistivity