Semiconductor Electronics, P–N Junctions, Atomic Models & AC Physics

Posted on Feb 18, 2026 in Physics

Semiconductor Electronics

Semiconductor

Semiconductor — These materials whose electrical conductivity lies between a conductor and an insulator are called semiconductors. At absolute zero they behave as insulators and at room temperature they behave as conductors.

Examples: Ge, Si, GaAs, CdS, CdSe, InP, etc.

Classification by Energy Band Theory

In solids there are three energy bands:

• The lower band is completely filled by electrons and is called the valence band (VB).
• The upper band is called the conduction band (CB), which may be empty or partially filled.
• There is a gap between VB and CB called the forbidden gap (energy gap).

1. Metals (Conductor)

In metals the valence band overlaps with the conduction band. Both VB and CB are partially filled; hence electrons are able to move freely from VB to CB. Therefore metals conduct electricity.

2. Insulator

In insulators there is a large energy gap (Eg > 3 eV) between VB and CB. Even an applied electric field cannot give enough energy to electrons to move from VB to CB. Hence insulators do not conduct electricity.

3. Semiconductor

At 0 K the conduction band is empty and the valence band is filled, so the material is an insulator at 0 K. At room temperature some valence electrons acquire thermal energy and jump to the conduction band where they are free to conduct electricity. Thus a semiconductor acquires a small conductivity at room temperature.

Doping

Doping — The process of adding a desirable impurity to a pure semiconductor so as to increase its conductivity is called doping. The impurity atoms added are called dopants, and semiconductors doped with impurity atoms are called extrinsic semiconductors.

Examples of dopants:

• Pentavalent dopants: Sb, P, Arsenic (As).
• Trivalent dopants: Indium (In), Boron (B), Aluminium (Al).

Extrinsic Semiconductor

An extrinsic semiconductor is a semiconductor doped with suitable atoms so as to increase its conductivity.

P–N Junction Diode

P–N Junction Diode

P–N junction diode — It is a single crystal of, e.g., Ge or Si, doped in such a manner that one half portion acts as a p-type semiconductor and the other half as an n-type semiconductor. The junction implies the boundary between n-type and p-type semiconductor.

Depletion Layer

Depletion layer — When a P–N junction is formed, the P-side of the junction has a higher concentration of holes and the N-side has a higher concentration of electrons. Due to the concentration gradient at the junction, holes begin to diffuse from P-side to N-side and electrons begin to diffuse from N-side to P-side. As holes diffuse from P → N side, they leave behind negative ions which set up a layer of negative charge on the P-side of the junction. Similarly, as the electrons diffuse from N → P side, they leave behind positive ions which set up a layer of positive charge on the N-side. These layers are called the depletion layer.

Barrier Potential (V₀)

Barrier potential (V₀) — The accumulation of negative charge on the p-side and positive charge on the n-side sets up a potential difference across the junction. This acts as a barrier and is called the barrier potential (V₀).

Diffusion Current

Diffusion current — The diffusion of minority charge carriers across the junction gives rise to an electric current from P → N side; this is called diffusion current.

Biasing of a Diode

1. Forward bias — If the P-side of the diode is connected to the positive terminal and the N-side is connected to the negative terminal of the battery, the diode is said to be forward biased. When V_f exceeds V₀ (V_f > V₀), the majority charge carriers start flowing across the junction and set up a large current (mA) called the forward current in the circuit. The current increases with the increase in applied voltage.
2. Reverse bias — If the P-side of the diode is connected to the negative terminal and the N-side is connected to the positive terminal of the battery, the diode is said to be reverse biased. At room temperature there are always some minority charge carriers like holes in the N-side and electrons in the P-side. Reverse biasing pushes them away from the junction, setting a current called a reverse or leakage current in the circuit, in the opposite direction. As the minority charge carriers are much fewer in number than the majority carriers, the reverse current is small.

I–V Characteristics of a P–N Junction Diode

1) Forward characteristics — The I–V graph is not a straight line. A junction diode does not obey Ohm’s law. Initially the current increases very slowly, almost negligible, until the voltage across the diode crosses a certain value, called the cut-in voltage (threshold or knee voltage). The value of cut-in voltage is about 0.2 V for a germanium (Ge) diode and 0.7 V for a silicon (Si) diode.

2) Reverse characteristics — When the diode is reverse biased, the reverse bias produces a very small current, about a few microamperes (µA), which almost remains constant with bias. This current is called the reverse saturation current; it is due to the drift of minority charge carriers across the junction.

When the reverse voltage across the junction reaches a sufficiently high value, the reverse current suddenly increases to a large value. This voltage at which breakdown of the diode junction occurs is called the breakdown voltage of the diode.

Dynamic Resistance of a Diode

Dynamic resistance — It is the ratio of a small change in applied voltage ΔV to the corresponding change in current ΔI.

r_e = ΔV / ΔI

Rectifiers

Rectifier — (AC to DC converter) It is an electronic device used to convert alternating current into direct current. A P–N junction diode is commonly used as a rectifier.

1) Half-wave Rectifier

During the positive half cycle of AC, point A becomes positive and B becomes negative. The diode D is forward biased and current I flows through the load R_L. During the negative half cycle of AC, A becomes negative and B becomes positive. The diode is reverse biased and no current flows through R_L. No voltage appears across R_L during the negative half cycle.

The output voltage is unidirectional but not smooth. Since the voltage across the load resistance R_L appears only during the positive half cycle of the AC input, this process is called half-wave rectification.

2) Full-wave Rectifier

Working:

During the positive half cycle of the AC input, A becomes positive and B becomes negative. Diode D₁ is forward biased and conducts current through R_L; diode D₂ is reverse biased and does not conduct.

During the negative half cycle of the AC input, A becomes negative and B becomes positive. Diode D₁ is reverse biased and does not conduct. Diode D₂ is forward biased and conducts current through R_L.

Since during both half cycles the current through the load R_L flows in the same direction, we get a pulsating DC voltage across R_L. This process is called full-wave rectification.

Atomic Models and Experiments

Atom (L-12)

J. J. Thomson Model of Atom

In 1898, J. J. Thomson proposed that an atom is a sphere of positively charged matter with electrons embedded in it. The positive charge is uniformly distributed over the atom. The arrangement of electrons inside the continuous positive charge is similar to that of seeds in a watermelon.

Drawbacks

The Thomson model could not explain the origin of several spectral series in the case of hydrogen and other atoms. It also failed to explain the large-angle scattering of α-particles observed in Rutherford’s experiment.

α Particle

α-particle — It is a helium ion, i.e., a helium atom from which both the electrons have been removed. It has a charge of +2e and its mass is nearly four times the mass of a proton.

α-Particle Scattering Experiment

Gold foil experiment observations:

• Most of the α-particles pass straight through the gold foil, suffering only small deflections.
• A few α-particles (about 1 in 8000) get deflected through greater than 90°.
• Occasionally, an α-particle is rebounded from the gold foil, suffering a deflection nearly equal to 180°.

Distance of Closest Approach

The distance r₀ from the nucleus at which an α-particle stops momentarily and then retraces its path (i.e., is scattered through 180°) is called the distance of closest approach.

Expressions given in the notes:

r₀ = 2kze²/k_eα, r₀ = 4kze²/mv²

Impact Parameter (b)

The impact parameter is the perpendicular distance of the velocity vector of the α-particle (when it is far away from the atom) from the centre of the nucleus.

Expression:

b = (1 / 4πε₀) × (Ze² cot(θ/2)) / ((1/2) m v²)

Rutherford’s Model of an Atom

Rutherford’s model — An atom consists of a small and massive central core in which the entire positive charge and almost the whole mass of the atom are concentrated. This core is called the nucleus. The size of the nucleus (~10⁻¹⁵ m) is very small compared to the size of the atom (~10⁻¹⁰ m).

The nucleus is surrounded by a suitable number of electrons so that the total negative charge equals the total positive charge of the nucleus; hence the atom as a whole is electrically neutral. The electrons revolve around the nucleus in various orbits just as planets revolve around the sun.

Drawbacks of Rutherford’s Model

Rutherford’s model could not explain the stability of an atom. According to classical physics, revolving electrons should continuously radiate energy, lose speed and eventually fall into the nucleus. As electrons spiral inwards, their angular velocities and frequencies would change continuously, and so would the frequency of emitted light.

Bohr’s Atomic Model of Hydrogen

Postulates

1. Nuclear concept — An atom consists of a small central core called the nucleus around which electrons revolve.
2. Quantum condition — The angular momentum of a revolving electron is equal to an integral multiple of h/2π: L = m v r = n(h/2π).
3. Stationary orbits — While revolving in permissible orbits an electron does not radiate energy. These non-radiating orbits are called stationary orbits.
4. Frequency condition — An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or vice versa. If E₂ and E₁ are the energies associated with the second and first orbits, respectively, then the energy emitted or absorbed is given by: E₂ − E₁ = hν.

Alternating Current (AC) and Related Concepts

AC and DC

AC — The current which changes continuously with time and reverses its direction periodically is called AC. An instance of AC is given by I = I₀ sin ωt.

DC — The current which is unidirectional (constant) is called DC.

RMS of AC

RMS (over a complete cycle) — It is defined as the square root of the mean of the square value of AC over a complete cycle:

I_rms = I₀ / √2 = 0.707 I₀

Impedance and Q Factor

Impedance (Z) — The combined opposition offered by reactance and resistance to the flow of alternating current is called impedance. It is denoted by Z.

Quality factor (Q) — The sharpness of the resonance curve is measured by the quality factor or Q factor. Mathematically it is defined as the ratio of either inductive reactance to the resistance.

Wattless Current

Wattless current — The current in an AC circuit is said to be wattless if the average power consumed in the circuit is zero. This happens in a pure inductive or capacitive circuit in which the voltage and current differ by a phase angle of π/2.

Transformer

Transformer — It is an electrical device used to convert high voltage into low voltage and low voltage into high voltage.

Two types: Step-up (converts low voltage to high voltage; N_p < N_s) and step-down (converts high voltage to low voltage; N_p > N_s).

Energy losses in transformers — copper loss, iron loss, eddy current loss, flux leakage, hysteresis.

AC Generator

AC generator — It is an electrical device used to convert mechanical energy into electrical energy.

Main parts: field magnet, rectangular coil or armature, slip rings R1 and R2, brushes B1 and B2, source of mechanical energy.

Wave Optics

Reflection and Refraction

Reflection of light — The phenomenon of bouncing back of light into the same medium after incidence on a reflecting surface (like a mirror) is called reflection of light.

Refraction of light — The phenomenon of bending of a light ray as it passes from one medium to another medium is called refraction of light.

Power of a lens — It is the reciprocal of the focal length of a lens: P = 1/f.

Critical angle — The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90° is called the critical angle of the denser medium.

Wave Front

Wave front — The continuous locus of all particles of the medium which are vibrating in the same phase at any instant is called a wave front. Types: spherical wave front, plane wave front, cylindrical wave front.

Interference of Light

Interference — When two light waves of the same frequency and having zero or constant phase difference in the same direction superpose, the intensity in the region of superposition gets redistributed, becoming maximum at some points and minimum at others. This phenomenon is called interference of light.

Fringe width — The distance between two consecutive bright fringes is called fringe width.

β = λD / d.

Diffraction at a Single Slit

Diffraction — Central maximum: at the central point O the secondary wavelets have zero path difference, i.e., they are in the same phase. They add up constructively to produce a central bright fringe. Calculation of path difference: the path difference between wavelets from L and N is given by:

P = NP = LP = NQ sin θ = LN sin θ = P = d sin θ.

Nuclei and Nuclear Quantities

Basic Nuclear Terms

1) Nucleons — Protons and neutrons present in the nuclei of atoms are collectively known as nucleons.

2) Atomic number (Z) — The number of protons in the nucleus is called the atomic number of the element.

3) Mass number (A) — The total number of protons and neutrons present in a nucleus is called the mass number of the element.

4) Number of neutrons (N)

Therefore: A = Z + N and N = A − Z.

Nuclear Mass and Related Terms

5) Nuclear mass — The total mass of the protons and neutrons present in a nucleus is often referred to in terms of mass number and nuclear mass.

Isotopes, Isobars, Isotones, Isomers

7) Isotopes — The atoms of an element which have the same atomic number but different mass numbers are called isotopes. For example, hydrogen has three isotopes:

• 1H → Protium
• 2H → Deuterium
• 3H → Tritium

Other examples: 2He4, 2He3; 3Li6, 3Li7.

8) Isobars — The atoms having the same mass numbers but different atomic numbers are called isobars.

Examples:

• 1H3, 2He3
• 17Cl35, 16S35
• 20Ca40, 18Ar40

9) Isotones — The nuclides having the same number of neutrons are called isotones.

Example: 17Cl37, 19K39 (Here N = 20).

10) Isomers — These are nuclides with the same atomic number and same mass number but existing in different energy states.

Atomic Mass Unit (amu) and Electron Volt

11) Atomic mass unit (amu) — (amu or u):

1 amu = (1/12) × mass of one C-12 atom = (1/12) × 1.99 × 10⁻²⁶ kg = 1.66 × 10⁻²⁷ kg.

12) Electron volt (eV) — If W = q × V, then 1 eV = 1e × 1 V = 1.6 × 10⁻¹⁹ coulomb × volt = 1.6 × 10⁻¹⁹ J.

13) Mega electron volt (MeV) — 1 MeV = 10⁶ eV = 10⁶ × 1.6 × 10⁻¹⁹ J = 1.6 × 10⁻¹³ J.