MM 765: Semiconductor Devices

Electronic Materials Overview

Understanding the fundamental differences between metals, semiconductors, and insulators is the first step in solid-state physics.

Parameter	Metals	Semiconductors	Insulators
Conductivity (RT)	High (~10⁷ S/m)	Intermediate (10⁻⁶ - 10⁴ S/m)	Low (~10⁻²⁰ - 10⁻⁷ S/m)
Band Structure	Overlapping / filled bands	Intermediate bandgap (0.6 - 3 eV)	Large bandgap (> 3 eV)
Temp. Response	Conductivity decreases with T	Conductivity increases with T	Conductivity increases with T
Charge Carriers	Unipolar (electrons)	Bipolar (electrons & holes)	Bipolar (electrons & holes)
Examples	Pt, Au, Ag, Cu	Si, Ge, GaAs	Diamond, Glass

Course Syllabus

Basic Semiconductor Physics

Intrinsic & Extrinsic Concepts
Energy Band Models & E-k diagrams
Fermi-Dirac Distribution
Drift, Diffusion & Mobility
Generation & Recombination (SRH Theory)

Electronic Devices

P-N Junctions & Depletion Layers
Metal-Semiconductor & MOS Capacitors
MOSFETs, CMOS, & Threshold Voltage
Bipolar Junction Transistors (BJTs)
Advanced Devices (HEMTs, FinFETs, JFETs)

Photonic Devices

Light Emitting Diodes (LEDs)
Photodetectors (PIN, APD)
Lasers & Optical Cavities
Charge-Coupled Devices (CCDs)
QWIPs & Advanced Imagers

Extrinsic Semiconductors & Doping

Learn how intentionally introducing impurities into a pure semiconductor lattice drastically alters its electrical conductivity by generating excess free electrons or holes.

N-Type (Donors)

Doping with Group V elements (like Phosphorus). They have 5 valence electrons. 4 form bonds, leaving the 5th loosely bound. It easily becomes a free conduction electron.

Majority carriers: Electrons
Minority carriers: Holes
Ion concentration: Positive donor ion concentration N_D > negative acceptor ion concentration N_A

P-Type (Acceptors)

Doping with Group III elements (like Boron). They have only 3 valence electrons, leaving an empty spot (a hole) in the lattice bonding. Other electrons can hop into this hole.

Majority carriers: Holes
Minority carriers: Electrons
Ion concentration: Negative acceptor ion concentration N_A > positive donor ion concentration N_D

Interactive Lattice Simulation

Switch doping types to observe changes in carrier concentrations and movement.

Current State

In pure (intrinsic) silicon, the only charge carriers are thermally generated electron-hole pairs.

Legend

Si
Silicon Atom
P
Phosphorus (Donor)
B
Boron (Acceptor)
-

Free Electron
+

Hole (Valence Band)

Physics Foundations

Intrinsic & Doped Semiconductors

An intrinsic semiconductor contains only native atoms. At absolute zero (0 K), it acts as an insulator. As temperature rises, thermal energy breaks bonds, creating an equal number of free electrons ( $n_{0}$ ) and holes ( $p_{0}$ ).

Intrinsic Equation

n_{0} = p_{0} = n_{i}

Factors Impacting Carrier Generation

Thermal Generation (Temperature)
Carrier concentration strongly depends on temperature. As temperature increases, more thermal energy is available to break covalent bonds across the bandgap ( $E_{g}$ ), exponentially increasing intrinsic concentration ( $n_{i}$ ).
Optical Generation (Light)
When incident photons possess energy greater than or equal to the bandgap ( $h ν \geq E_{g}$ ), they are absorbed by valence electrons. This excites the electrons into the conduction band, creating excess electron-hole pairs and increasing overall conductivity.

Governing Equations

The Electroneutrality Equation

Despite having mobile charges, a semiconductor crystal remains electrically neutral overall. Immobile dopant ions balance the mobile charges.

p_{0} - n_{0} + N_{D} - N_{A} = 0

The Mass Action Law

In thermal equilibrium, the rate of generation equals the rate of recombination, linking the majority and minority carrier concentrations.

n_{0} p_{0} = n_{i}^{2}

Refreshing Quantum Mechanics

While classical mechanics perfectly describes the macroscopic world, it becomes highly inconsistent at the microscopic scale. To understand the behaviour and characteristics of electrons in semiconductors, we rely on the formulation of wave mechanics.

Quantization of Energy

Energy is not continuous but exists in discrete packets (quanta/photons). This explains phenomena like blackbody radiation and the photoelectric effect.

Wave-Particle Duality

Matter and light exhibit both wave-like (diffraction, interference) and particle-like (momentum, localized impacts) properties simultaneously.

Uncertainty Principle

It is fundamentally impossible to measure conjugate variables (like position and momentum) simultaneously with absolute precision.

Energy Quantisation

Planck's Postulation (1900): Thermal radiation is emitted from a heated surface in discrete packets of energy called quanta.

Einstein (1905): Energy in a light wave is also in discrete packets called photons. This perfectly explained the Photoelectric Effect.

Classical vs Reality

Classical physics: High light intensity should overcome the work function independent of frequency (Not observed).

Reality: K.E. of emitted photoelectrons varies linearly with frequency. Below a threshold ( $ν_{0}$ ), NO electrons are emitted regardless of intensity.

Governing Equations

E = h ν

Excess energy becomes Kinetic Energy (K.E.):

K . E . = h ν - Φ = h ν - h ν_{0}

Kinetic Energy vs. Frequency

K.E. of Photoelectron

Frequency (

ν

)

ν_{0}

For $ν \geq ν_{0}$ , kinetic energy increases linearly.

Wave-Particle Duality

De Broglie postulated in 1924 that matter behaves as a wave as well. Electrons exhibit wave properties such as diffraction and interference, as evidenced in the electron microscope.

De Broglie Relation

λ = \frac{h}{p}

Where h is Planck's constant ( $6.626 \times 10^{- 34} J.s$ ) and p is momentum.

Macroscopic Particle

Consider an iron ball of 1 kg travelling at a velocity of 1 m/s.

λ = 6.626 × 10^-34 m

Conclusion: Wavelength is vastly smaller than the radius of an iron atom. The wave aspect has no practical meaning. Classical concepts work well.

Microscopic Particle

Consider an electron travelling at a typical velocity in a semiconductor lattice.

λ ≈ Nanometer scale

Conclusion: Wavelength is comparable to atomic spacing. Wave mechanics are absolutely essential to model the behavior.

Wave Description of an Electron

The Wave Packet Model

A localized free particle is represented by a wave packet, formed by a superposition of wave functions with different $k$ values.

"If the wave packet was light, we would not see the same light intensity at any x point. Standing at a single x point, we would hear or see the wave packet passing by us as a lump of sound or light, traveling with velocity v."
— S. Dimitrijev

Key Relations

Rate of phase change with time: $ω = \frac{2 π}{T}$
Wave vector: $k = \frac{2 π}{λ}$
Particle-Wave Link: $p = ℏ k$

Wave Packet Simulation

Visualization of $Re {Ψ (x, t)}$ traveling in the x-direction.

Uncertainty & The Wave Equation

Heisenberg's Uncertainty Principle (1927)

We cannot describe with absolute accuracy the behaviour of small particles. There is a fundamental relationship between conjugate variables.

Δ p \cdot Δ x \geq ℏ

Δ E \cdot Δ t \geq ℏ

Where $ℏ = h / 2 π$ . Extensively used to calculate the probability of finding an electron.

Probability Density Function

Formulated by Max Born (1926). The total wave function's squared magnitude represents the probability of finding the particle between $x$ and $x + dx$ at a given time.

{| Ψ (x, t) |}^{2} = Ψ (x, t) Ψ^{*} (x, t)

Since $Ψ (x, t) = ψ (x) e^{- j ω t}$ , the probability density is independent of time:

{| Ψ (x, t) |}^{2} = {| ψ (x) |}^{2}

Reference Texts

1

Principles of Semiconductor Devices (2nd Edition)

Sima Dimitrijev, Oxford University Press, 2012.
2

Physics of Semiconductor Devices (4th Edition)

S. M. Sze, Y. Li and K. K. Ng.
3

Semiconductor Physics and Devices - Basic Principles (4th Edition)

Donald A. Neamen.
4

Solid State Electronic Devices (7th Edition)

Ben G. Streetman and S. K. Banerjee, Pearson, 2016.

Semiconductor Devices
& Their Working Principles

Electronic Materials Overview

Course Syllabus

Basic Semiconductor Physics

Electronic Devices

Photonic Devices

Extrinsic Semiconductors & Doping

N-Type (Donors)

P-Type (Acceptors)

Interactive Lattice Simulation

Current State

Legend

Physics Foundations

Intrinsic & Doped Semiconductors

Factors Impacting Carrier Generation

Governing Equations

The Electroneutrality Equation

The Mass Action Law

Refreshing Quantum Mechanics

Quantization of Energy

Wave-Particle Duality

Uncertainty Principle

Energy Quantisation

Classical vs Reality

Kinetic Energy vs. Frequency

Wave-Particle Duality

Macroscopic Particle

Microscopic Particle

Wave Description of an Electron

The Wave Packet Model

Key Relations

Uncertainty & The Wave Equation

Heisenberg's Uncertainty Principle (1927)

Probability Density Function

Reference Texts

Principles of Semiconductor Devices (2nd Edition)

Physics of Semiconductor Devices (4th Edition)

Semiconductor Physics and Devices - Basic Principles (4th Edition)

Solid State Electronic Devices (7th Edition)

Lecture 1 Knowledge Check