IGCSE, Edexcel, IB and AP Science Courses | Dr Dabour Hub Academy

Overview

🌳 Concept tree

Lesson 1→Intrinsic and Doped Semiconductors, the p-n Junction and Transistors

├── Conductors, insulators and semiconductors

├── The silicon crystal

├── Free electrons and holes

├── Motion of holes

├── Conduction in a semiconductor compared with a metal

├── Sensitivity of semiconductors

├── Worked examples (Lesson 1)

├── Why dope?

├── n-type semiconductor (donor impurities)

├── p-type semiconductor (acceptor impurities)

├── The law of mass action

├── Summary comparison

├── Worked examples (Lesson 2)

├── Formation of the junction

├── Biasing the junction

├── The diode as a switch and as a rectifier

├── Electronic tuning (the varactor)

├── Worked examples (Lesson 3)

├── Structure

├── Operation (n-p-n, common base)

├── Current ratios

├── The transistor as an amplifier

├── The transistor as a switch (and inverter)

└── Worked examples (Lesson 4)

Lesson 1: Intrinsic and Doped Semiconductors, the p-n Junction and Transistors · 1 / 26

Conductors, insulators and semiconductors

From the point of view of electrical conductivity there are three kinds of solid:

Comparison aspect	Main idea	Keywords
Conductors	(metals) conduct electricity and heat easily	metalselectricityheateasily
Insulators	(wood plastics glass) do not conduct electricity or heat	woodplasticsglassconduct
Semiconductors	(silicon germanium) lie in between. At absolute zero a semiconductor acts as an insulator its conductivity increases as the temperature rises. (In a metal in contrast the resistance increases with temperature.)	silicongermaniumbetweenabsolute

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The silicon crystal

Silicon is one of the most common elements on Earth it is found in sand (SiO₂) and in the rocks of the Earth’s crust.
A crystal is a regular arrangement of atoms in a solid.
In a pure silicon crystal:

Each silicon atom (atomic number 14) has four electrons in its outer shell (it is tetravalent).
Each atom shares one electron with each of its four neighbours, so every atom has eight electrons in its outer shell on a sharing basis (a complete shell). The pair of shared electrons forms a covalent bond.
There are two kinds of electrons in the crystal:

Inner electrons, tightly bound to their parent atoms.

Valence electronsin the outer shell; they form the covalent bonds and have more freedom than the inner ones.

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Free electrons and holes

At very low temperature (near 0 K), all bonds are intact no free electrons exist (unlike a metal), so the crystal is an insulator.
When the temperature rises, thermal energy may break some bonds. A valence electron is freed and can move through the crystal. It leaves behind a vacancy in the broken bond, called a hole.
Since the atom was neutral, the absence of an electron means a net positive charge at the vacancy: the hole behaves like a positive charge. We do not call the atom an ion, because it quickly takes an electron from another bond to refill its own vacancy; the hole then moves to somewhere else.
Breaking a bond needs a minimum energy, which may be thermal or optical (a photon of enough energy, e.g. light falling on the crystal, can also produce an electron-hole pair).
The reverse process, when a free electron falls into a hole and mends a bond, is recombination, in which energy is released (as heat or light).

In a pure semiconductor the number of free electrons (n) always equals the number of holes (p): n = p = nᵢ (the intrinsic concentration).
At every temperature a dynamic equilibrium (thermal equilibrium) is reached: the number of bonds broken per second equals the number of bonds mended per second, so n and p remain constant (though not the same individual electrons and holes).
Only a small percentage of the bonds are broken at room temperature.
Raising the temperature (or illuminating the crystal) raises nᵢ.

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Motion of holes

Electrons and holes move randomly in the crystal.
A hole appears to move because an electron from a neighbouring bond jumps into the vacancy, leaving a new vacancy behind it.
The motion of a hole in one direction is thus equivalent to the motion of bound electrons in the opposite direction.
Under an electric field the free electrons drift toward the positive terminal and the holes toward the negative terminal; both contribute to the current in the same direction.
The free electrons are in fact still confined they are free to move in the whole crystal but cannot leave it.

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Conduction in a semiconductor compared with a metal

Comparison aspect	Metal	Pure semiconductor
Charge carriers	free electrons only	free electrons and holes
Number of free electrons	very large and nearly constant independent of temperature	small, increases quickly with temperature
Effect of rising temperature	resistivity increases (the ions vibrate and obstruct the electrons)	resistivity decreases (more carriers)
At absolute zero	conducts	insulator

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Sensitivity of semiconductors

Semiconductors are very sensitive to environmental conditions: light, heat, pressure, radiation, humidity and chemical pollution.
This makes them useful as sensors or measuring devices for these quantities (light meters, temperature sensors, pressure sensors, radiation detectors).
The electronic components built from them are the building blocks of all electronic systems:

simple componentsresistor (R), capacitor (C), inductor (L);

more complexpn junction (diode), transistor;

special devicesoptoelectronic (LED, photodiode, solar cell) and control devices.

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Worked examples (Lesson 1)

Example 1.1.→The concentration of free electrons in pure silicon at room temperature is 1.5 × 10¹⁰ cm⁻³. What is the concentration of holes and the density of charge carriers in total? Because electrons and holes are created in pairs, p = n = 1.5 × 10¹⁰ cm⁻³. The total number of carriers is 3.0 × 10¹⁰ cm⁻³. (Compare this with a copper conductor that has about 8 × 10²² electrons per cm³: a pure semiconductor is a very poor conductor.)

✍️ Worked examples

Example 1.2.
Explain what happens to the conductivity of pure silicon when it is heated from 300 K to 350 K.
More bonds are broken per second, so n and p increase until a new thermal equilibrium; the conductivity increases.
For a metal, the resistance rises instead.

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Why dope?

The conductivity of pure silicon is small and strongly temperature-dependent.
Adding a very small amount of a different element (an impurity), typically one atom in a few million, changes it enormously; this is called doping.
Doping makes it possible to produce a semiconductor with a chosen kind and number of carriers.

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n-type semiconductor (donor impurities)

Add a pentavalent element (5 outer electrons), such as phosphorus (P), antimony (Sb) or arsenic (As).
An atom of the impurity replaces a silicon atom in the crystal and forms bonds with four neighbours using four of its electrons.
The fifth electron is left over and is only weakly attracted to its parent atom, so it can easily be detached and becomes a free electron.
The impurity atom, having lost an electron, becomes a positive ion (fixed in the crystal and not a free carrier).

The impurity atoms are called donors (they give electrons). Their concentration is N_D.
Free electrons now come from two sources broken bonds and donors. In thermal equilibrium the total positive charge equals the total negative charge: n = p + ND (8-1)
- Since n > p, electrons are the majority carriers and holes the minority carriers.
- The material is called n-type (n for negative carriers).
- It is electrically neutral as a whole.

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p-type semiconductor (acceptor impurities)

Add a trivalent element (3 outer electrons), such as aluminium (Al), boron (B) or gallium (Ga).
The impurity atom has one electron too few to complete four bonds; it takes an electron from a neighbouring bond, creating an extra hole, and itself becomes a negative ion.

These atoms are called acceptors (they take electrons). Their concentration is N_A.
In thermal equilibrium p = n + NA (8-2)
Holes are the majority carriers (p > n); the material is called p-type.

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The law of mass action

For any semiconductor in thermal equilibrium (doped or not):
(8-3)

where nᵢ is the concentration of electrons (or holes) in the pure semiconductor at the same temperature.
If doping makes n larger, p becomes smaller by the same factor (more electrons mean more recombination, so fewer holes remain), and vice versa.
Approximations (when the doping is much larger than nᵢ):

n-type n ≈ ND and p = nᵢ²/ND (8-4, 8-5)
p-type p ≈ NA and n = nᵢ²/NA
Note that doping raises the total carrier concentration enormously (the majority carriers) and hence the conductivity, while the semiconductor remains neutral.
If donors and acceptors are both present, the net doping is ND − NA.
If NA = ND, the semiconductor returns to being pure (compensation).

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Summary comparison

Comparison aspect	n-type	p-type
Impurity	pentavalent: P, Sb, As	trivalent: Al, B, Ga
Impurity atom called	donor	acceptor
Ion left in the crystal	positive	negative
Majority carriers	electrons	holes
Minority carriers	holes	electrons
Charge balance	n = p + N_D	p = n + N_A
Approximate concentrations	n ≈ N_D; p = nᵢ²/N_D	p ≈ N_A; n = nᵢ²/N_A

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Worked examples (Lesson 2)

Example 2.1 — n-type. Pure silicon has nᵢ = 1.5 × 10¹⁰ cm⁻³. It is doped with phosphorus at N_D = 3 × 10¹⁶ cm⁻³. Find n and p.
n ≈ ND = 3 × 10¹⁶ cm⁻³; p = nᵢ²/n = (1.5 × 10¹⁰)²/3 × 10¹⁶ = 2.25 × 10²⁰/3 × 10¹⁶ = 7.5 × 10³ cm⁻³.
Majority electrons exceed holes by a factor of 4 × 10¹².
The material is n-type.
Example 2.2 — p-type. With nᵢ = 1 × 10¹⁰ cm⁻³ and boron N_A = 5 × 10¹⁵ cm⁻³: p ≈ 5 × 10¹⁵ cm⁻³ and n = 10²⁰/5 × 10¹⁵ = 2 × 10⁴ cm⁻³.
Example 2.3 — compensation. An n-type silicon sample has N_D = 4 × 10¹⁴ cm⁻³. What acceptor concentration returns it to pure silicon? N_A = N_D = 4 × 10¹⁴ cm⁻³ (each acceptor takes an electron from a donor).

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Formation of the junction

A p-n junction is made by converting part of a crystal of one type into the opposite type (for example, by doping one end with donors and the other with acceptors).
The name "pn" refers to the p-region and n-region, not "positive-negative".
It is not two crystals glued together but one continuous crystal.
At the instant of formation:

The p-side has a high concentration of holes, the n-side a high concentration of electrons. By diffusion (from high to low concentration), holes move from p to n and electrons from n to p. The movement produces a diffusion current.
Each region was neutral. When an electron leaves the n-side, an equal number of positive donor ions are left uncovered; when a hole leaves the p-side, an equal number of negative acceptor ions are left uncovered.
This creates a middle layer with positive ions on the n-side and negative ions on the p-side, with practically no free electrons or holes: the transition (depletion) region. The width of this region is of the order of a micrometre.
An electric field is set up in the transition region, directed from the positive ions to the negative ions (from n to p). It opposes the further diffusion of the majority carriers and causes a drift current of minority carriers in the opposite direction to the diffusion current.
At equilibrium the diffusion current equals the drift current, so the net current is zero. A potential difference (the barrier potential, about 0.7 V for silicon) is established across the junction.

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Biasing the junction

Forward bias:

the p-region is connected to the positive terminal of a battery and the n-region to the negative terminal.
The field due to the battery opposes the internal field; it narrows and weakens the barrier.
Majority carriers can cross the junction in large numbers, and a large current flows (it rises rapidly once the applied voltage exceeds about 0.7 V for silicon).
Reverse bias:

the battery is reversed (p to negative, n to positive).
The battery field adds to the internal field, widens the transition region and strengthens the barrier.
Only a tiny current of minority carriers flows (almost zero, the reverse saturation current).
Beyond a high reverse voltage the junction breaks down.
The behaviour is shown by the current-voltage (I-V) characteristic: practically zero current for negative voltage, a very small current until about 0.7 V, then rapid increase for positive voltage.

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The diode as a switch and as a rectifier

A pn junction acts as a diode a device that conducts well in one direction (a closed switch in forward bias, with a small resistance) and hardly at all in the other direction (an open switch in reverse bias, with a very large resistance).
The symbol shows an arrow (the p-side, anode) pointing toward a bar (the n-side, cathode): conventional current flows in the direction of the arrow.
To check a diode, use an ohmmeter it should show a small resistance in one direction (forward) and a very large resistance in the other.
Rectification:

because of this one-way behaviour, a diode is used to convert alternating current to direct current (it passes only the half-cycles in which it is forward biased).
Rectifiers are found in every power supply and battery charger.

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Electronic tuning (the varactor)

To tune a radio or TV to a particular station, we adjust a capacitor in a resonant circuit so that the circuit’s frequency equals that of the station (resonance).
In modern receivers the variable capacitor is replaced by a reverse-biased pn diode.
The transition region is like the insulator of a capacitor, with the fixed ion layers on both sides acting as the two plates.
When the reverse voltage increases, the transition region widens and more fixed ions are uncovered; the capacitance falls (plates farther apart).
So the capacitance can be controlled electronically by changing the reverse voltage.
This is called electronic tuning, and the diode used is a varactor.

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Worked examples (Lesson 3)

Comparison aspect	Main idea	Keywords
Example 3.1.	A diode has a forward resistance of 50 Ω and infinite reverse resistance. It is connected in series with a 3 V battery. Find the current for forward and reverse connection. Forward: I = 3/50 = 60 mA. Reverse: I = 0	diodeforwardresistanceinfinite
Example 3.2.	A silicon diode and a 200 Ω resistor are connected in series to a 6 V battery in the forward direction. Taking the voltage drop across the conducting diode as 0.7 V: I = (6 − 0.7)/200 = 26.5 mA	silicondioderesistorconnected

✍️ Worked examples

Example 3.3.
Explain what happens to the width of the transition region when the reverse bias is increased from 2 V to 10 V.
It increases, since more ions are uncovered, and the diode capacitance decreases.

Lesson 1: Intrinsic and Doped Semiconductors, the p-n Junction and Transistors · 19 / 26

Structure

The transistor was invented in 1947–1955 by John Bardeen, William Shockley and Walter Brattain.
It replaced the vacuum tube and made computers and mobile phones possible.
We study the bipolar junction transistor (BJT), which has three regions in sequence: either n-p-n or p-n-p:

the first region is the emitter (E), heavily doped, which emits the carriers;
the middle region is the base (B), which is very thin and lightly doped;
the last region is the collector (C), which collects the carriers.

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Operation (n-p-n, common base)

For normal (active) operation:

the emitter-base junction is forward biased,→the collector-base junction is reverse biased.

the n-type emitter injects many free electrons into the p-type base.
Because the base is very thin and lightly doped, only a small fraction (a few percent) of these electrons recombine with holes in the base; the great majority diffuse across and are swept into the collector by the strong field of the reversed collector junction.
Therefore the emitter current I_E divides into a large collector current I_C and a small base current I_B:
(8-6)

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Current ratios

Current transfer ratio (common base), αα = I_C / I_E. Because only a small fraction of the electrons are lost in the base, α is less than 1 but very close to 1 (e.g. 0.95–0.995).

Current gain (common emitter), ββ = I_C / I_B, which is large (tens to hundreds).

Relation between α and β.→Divide I_E = I_B + I_C by I_C:

1/α = 1/β + 1. Therefore

β = α/(1 − α)and α = β/(1 + β).

Examplesα = 0.99 → β = 99; α = 0.98 → β = 49; β = 100 → α = 0.990. Also IB = (1 − α) IE.

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The transistor as an amplifier

In the common-emitter arrangement, a small signal (for example from a microphone) applied to the base circuit produces a base-current change ΔIB, which causes a change in the collector current ΔIC = β ΔIB, β times larger.
If a load resistor RC is placed in the collector circuit, the corresponding voltage change across RC is much larger than that applied at the input.
So the transistor amplifies current, voltage and power; the extra power comes from the battery in the collector circuit.
This effect is called transistor action.

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The transistor as a switch (and inverter)

In the common-emitter circuit with supply V_CC, collector resistor R_C:
VCC = VCE + IC RC (8-7)
(where V_CE is the voltage between collector and emitter.)

Comparison aspect	Main idea	Keywords
Large positive base voltage (input high)	large base current, so a large collector current I_C. The voltage drop I_C R_C becomes large and V_CE falls to a very small value (about 0.2 V). The output is close to zero. The transistor is like a closed switch (saturation).	currentcollectordropbecomes
Small or negative base voltage (input low)	no base current, I_C is almost zero, so I_C R_C ≈ 0 and V_CE ≈ V_CC. The output is high. The transistor acts as an open switch (cut-off).	currentalmostzerooutput

Thus the transistor can be switched on and off by the input voltage.
Notice that a high input gives a low output and a low input gives a high output; the circuit is an inverter (NOT gate).

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Worked examples (Lesson 4)

Comparison aspect	Main idea	Keywords
Example 4.1.	A transistor has α = 0.98 and base current 60 μA. Find β, I_C and I_E. β = 0.98/0.02 = 49. I_C = β I_B = 49 × 60 μA = 2.94 mA. I_E = I_B + I_C = 3.00 mA. Check: α = 2.94/3.00 = 0.98 ✓.	transistorbasecurrentFind
Example 4.2.	In a circuit the emitter current is 5.0 mA and the base current 0.1 mA. I_C = 4.9 mA; α = 4.9/5.0 = 0.98; β = 4.9/0.1 = 49.	circuitemittercurrentbase
Example 4.3 — switch.	V_CC = 12 V, R_C = 1.8 kΩ. When saturated (V_CE = 0.2 V), I_C = 11.8/1800 = 6.6 mA. For β = 50 the base current needed is I_B ≥ 6.6 mA/50 = 0.13 mA. When cut off, I_C = 0 and V_CE = 12 V.	saturated1800basecurrent
Example 4.4 — amplifier.	Base current changes by 20 μA and the collector current by 1.5 mA. β = 1.5 mA/20 μA = 75 and α = 75/76 = 0.987	Basecurrentchangescollector

Lesson 1: Intrinsic and Doped Semiconductors, the p-n Junction and Transistors · 25 / 26

Part 26

📖

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

Physics (Thanaweya Amma 2026/2027)

Lesson 1 – Intrinsic and Doped Semiconductors, the p-n Junction and Transistors
Semiconductors (Silicon and Germanium) exhibit intermediate conductivity.
Intrinsic semiconductors conduct via thermally broken bonds (electrons and holes).
Extrinsic doping with pentavalent donors (n-type) or trivalent acceptors (p-type) dramatically boosts conductivity.
The p-n junction diode acts as a rectifier, and the transistor operates as an amplifier and switch.

🌳 Conceptual Hierarchy Tree

Solid State Electronics

├── 1. Pure and Doped Semiconductors

│ ├── Intrinsic SiliconAt absolute zero (0 K / -273°C), all bonds intact, perfect insulator

│ ├── n-type (Doped with PentavalentPhosphorus, Arsenic): Major carriers are free electrons

│ └── p-type (Doped with TrivalentBoron, Aluminum): Major carriers are positive holes

├── 2. The p-n Junction Diode

Comparison aspect	Main idea	Keywords
│ ├── Forward Bias	Positive terminal to p-type depletion region narrows conducts easily	Positiveterminaltypedepletion
│ ├── Reverse Bias	Positive terminal to n-type depletion region widens blocks current	Positiveterminaltypedepletion
│ └── Application	AC rectification into pulsating DC	rectificationpulsating
•	└── 3. The Bipolar Junction Transistor (npn / pnp)	BipolarJunctionTransistor
├── Emitter (E), Base (B	extremely thin and lightly doped) Collector (C)	extremelythinlightlydoped
├── Current Relationship	IE = IB + IC
├── Current Amplification Ratio	βe = IC / IB
└── Operating Modes	Amplifier (common emitter) and Electronic Switch (ON / OFF)	AmplifiercommonemitterElectronic

📋 Master Teacher's Blackboard Secrets

RULE 1Both n-type and p-type semiconductor crystals are ELECTRICALLY NEUTRAL as a whole (n + NA⁻ = p + ND⁺).

RULE 2In a transistor: Emitter current IE always equals the sum of base current IB and collector current IC (IE = IB + IC).

RULE 3Transistor as an Inverter (NOT Gate): When base is forward-biased with high voltage (Input = 1), VCE drops to near zero (Output = 0).

📊 MatrixComparative Analysis: Intrinsic vs. Extrinsic Semiconductor Crystals

Feature	Pure Silicon Crystal	n-type Semiconductor	p-type Semiconductor
Doping Impurity	None (100% pure Si)	Pentavalent (P, As, Sb)	Trivalent (B, Al, Ga)
Majority Charge Carriers	Electrons = Holes (n = p)	Free conduction electrons (n >> p)	Positive holes (p >> n)
Overall Electrical Charge	Electrically Neutral	Electrically Neutral	Electrically Neutral
Conductivity at 0 Kelvin	Zero (Perfect insulator)	Zero	Zero

Lesson 1: Intrinsic and Doped Semiconductors, the p-n Junction and Transistors · 26 / 26

Curriculum

Physics

Chapter 1 - Electric Current, Ohms Law and Kirchhoffs Laws

Chapter 2 - Magnetic Effects of Electric Current and Measuring Instruments

Chapter 3 - Electromagnetic Induction and AC Dynamo and Transformer

Chapter 4 - Alternating Current AC Circuits

Chapter 5 - Dual Nature of Wave and Particle

Chapter 6 - Atomic Spectra and X-Rays

Chapter 7 - Lasers and Principles

Chapter 8 - Modern Electronics and Semiconductors

More lessons

Lesson 1: Intrinsic and Doped Semiconductors, the p-n Junction and Transistors

🌳 Concept tree

├── Conductors, insulators and semiconductors

├── The silicon crystal

├── Free electrons and holes

├── Motion of holes

├── Sensitivity of semiconductors

├── Worked examples (Lesson 1)

├── n-type semiconductor (donor impurities)

├── p-type semiconductor (acceptor impurities)

├── The law of mass action

├── Summary comparison

├── Worked examples (Lesson 2)

├── Formation of the junction

├── Biasing the junction

├── The diode as a switch and as a rectifier

├── Electronic tuning (the varactor)

├── Worked examples (Lesson 3)

├── Structure

├── Operation (n-p-n, common base)

├── Current ratios

├── The transistor as an amplifier

├── The transistor as a switch (and inverter)

└── Worked examples (Lesson 4)

✍️ Worked examples

✍️ Worked examples

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

Physics (Thanaweya Amma 2026/2027)

🌳 Conceptual Hierarchy Tree

Solid State Electronics

├── 2. The p-n Junction Diode

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