Semiconductors, Diodes & LED - Page-by-Page Notes

Page 1

• Topic: 18-100 Introduction to Electrical and Computer Engineering

• Focus: Semiconductors, Diodes, and LED

• Source notes: Presentation slides by Jimmy Zhu for 18-100/18-100F25 L02

Page 2

• Conductors vs. Insulators

• Examples:

  • Conductors: copper (Cu)

  • Insulators: general insulating materials (no specific example given on this slide)

Page 3

• Copper (Cu) example

• Concept: A lone electron in the outer shell of copper is used as a representative charge carrier in conductors

• Emphasis: Outer-shell electrons can participate in conduction

Page 4

• Copper (Cu) wire

• Key idea: The outer shell electrons become “non-local” in a conductor, enabling current flow when a voltage is applied

Page 5

• Copper wire under applied voltage

• Concept: Electrons flow under the applied voltage

• Directional note: Conventional current direction is from the positive side to the negative side, while electron flow is opposite

Page 6

• Conductors: Charge is carried by electrons

• Definitions and constants:

  • Electron charge: $e = 1.6 \times 10^{-19} \ \text{C}$

  • Current definition: $I = \frac{\Delta Q}{\Delta t}$

  • Charge per electron: $\Delta Q = (-e) \times N_{e}$, so the current can be viewed as the rate of charge transfer

• Example: Number of electrons per second for a given current

  • For $I = 1\ \text{mA}$, number of electrons per second is $\frac{I}{e} = \frac{1\times 10^{-3}}{1.6\times 10^{-19}} \approx 6.25\times 10^{15}\ \text{electrons/s}$

• Relationship: A current of $1\ \text{mA}$ corresponds to about $6.25\times 10^{15}$ electrons per second

Page 7

• Semiconductor basics: Si has a valence of 4 electrons

• Intrinsic Si schematic shows four valence electrons per silicon atom and the +4 oxidation state indicators on the diagram

• Intrinsic silicon is shown with multiple +4 signs; intrinsic Si has 4 valence electrons per atom

Page 8

• Intrinsic semiconductor: Almost an insulator

• Notation: Intrinsic Si is shown with charge neutrality and very low free carrier concentration (I ≈ 0)

Page 9

• Reiteration: Intrinsic semiconductor — 4 valence electrons per atom in silicon

• Si illustrated with +4 valence contributions on the bonding diagram

Page 10

• Effect of dopants: Donors (n-type)

• Dopant example: Phosphorus (P) with 5 valence electrons per atom

• Donor doping creates free electrons

• Doping concept: P atoms contribute extra electrons to the conduction process

• Notation on the diagram: P has 5 valence electrons, compared to Si’s 4

Page 11

• Donor dopants: Donor elements (e.g., phosphorus) introduce electrons as charge carriers

• Type: n-type semiconductor (donor dopants)

• Charge carriers in n-type: electrons

• Symbolic reference: $e^-$ (electron) as the mobile charge carrier

Page 12

• n-type semiconductor depiction

• Visual: n-type region with donors and free electrons as majority carriers

Page 13

• Recap: intrinsic silicon with 4 valence electrons per atom

• Intrinsic Si labeled again in the intrinsic context

Page 14

• Doped Silicon: Creating holes via boron doping

• Dopant example: Boron (B) with 3 valence electrons per atom

• B substitution creates holes (positive charge carriers) in the silicon lattice

• Diagram shows B replacing Si atoms to form holes

Page 15

• Doped Silicon: Holes moving under applied voltage

• Key idea: Holes (positive charge carriers) can move under applied voltage in p-type material

• Doping description: B has 3 valence electrons per atom; the absence of one electron creates a hole that can move

Page 16

• Doped Silicon: Holes can move under applied voltage (continued)

• Emphasizes hole mobility under an external field

Page 17

• Doped Silicon: Holes moving under voltage (reiterated)

• Visual emphasis on hole conduction in p-type material

Page 18

• Properties of Doped Silicon: Acceptor (p-type semiconductor)

• Dopant example: Phosphorus? (note: in the slide, Acceptor is labeled with B but text shows P-type/Acceptor context; emphasis on acceptor behavior and p-type conduction)

• Voltage applied across doped silicon

Page 19

• Properties of Doped Silicon: Acceptor

• p-type semiconductor: number of holes equals number of dopant atoms (for acceptor dopants like boron)

• Visual cue: + signs indicating holes being created

Page 20

• Properties of Doped Silicon: Acceptor

• Charge carriers in p-type semiconductors are holes ($h^+$)

• Equation reference: $ ( ) e^+ q $ is shown to indicate hole charge convention

Page 21

• n-type semiconductor in a circuit context

• Forward bias depiction with p-type and n-type regions and holes in p-type region

• Visual cues show current flow directions in a PN junction under bias

Page 22

• P-type and N-type semiconductors

• Illustration of both types side by side

• Notation: “p-type” and “n-type” with associated charge carriers (holes vs electrons)

Page 23

• PN junction: Formation of a diode

• Concept: The interface between p-type and n-type regions forms a diode (PN junction)

• Visual cue: A diagram showing the junction and carriers on each side

Page 24

• Forward bias of a PN junction (VS = 1.5 V)

• Mechanism: Holes in the p-region move toward the junction; electrons move toward the p-region; they meet near the junction, recombine, and release energy (photon or heat)

• Forward bias description: Recombination event injects a new hole into the p-region and a new electron into the n-region from the power source

• Net carrier numbers in the two regions remain unchanged under steady forward bias

• Notation: V_S = 1.5 V, forward-bias operation

Page 25

• Forward bias: Diode behaves as a short circuit under forward conduction

• Example: VS = 1.5 V, diode drop effectively clamped near V_ON, current flows freely

• Notation: I, R, and approximate short-circuit behavior

• Power/voltage relationships shown in schematic with a resistor and diode in forward bias

Page 26

• Reverse bias of a PN junction

• Forward vs reverse: In reverse bias, carriers are pulled away from the junction; no current flows through the junction (I ≈ 0 in ideal case)

• Concept: Reverse-bias condition acts like an open circuit

Page 27

• Reverse bias (continued)

• Summary: I = 0 for reverse bias in the ideal diode model

Page 28

• Reverse bias (emphasized): I = 0 under reverse bias; junction behaves as open circuit

• VS = 1.5 V used in examples

Page 29

• I-V Characteristics of a diode (example: red LED)

• Key takeaways:

  • Very different from a resistor

  • No current for negative voltage (OFF region)

  • Very sharp rise in current after threshold voltage

  • After ON, current rises sharply with voltage

  • Threshold voltage (V_ON) for turn-on: silicon ~0.6 V; red LED ~1.8 V; green LED ~2.7 V

• Observed plot ranges: Diode Current I (mA) vs Diode Voltage V (V) with a turn-on region around V_ON

Page 30

• Identify the state of diode (Step 1)

• Procedure: Remove the diode and measure open-circuit voltage (VOC)

• If VOC < V_ON and I = 0, the diode is OFF under the given bias (reverse or no conduction)

• Example context from the slide uses VOC = -2 V indicating OFF state

• Additional data: For reverse bias, I ≈ 0, VOC < V_ON

Page 31

• Identify Forward Bias to see if Diode is ON (Step 2)

• Procedure: With a supply VS = 5 V and VOC measured, determine if the diode is ON by comparing VOC to V_ON

• If VOC > V_ON and I > 0, the diode is ON

• Observation: When ON, the diode voltage remains approximately equal to V_ON (diode drop clamps)

Page 32

• Forward bias confirmation (continued)

• When ON, VD ≈ VON

• Visuals show diode current I and diode voltage V with V ≈ V_ON while conducting

Page 33

• Forward bias calculation using Ohm’s law for a simple case

• Given: VS = 5 V, R = 100 Ω, V_ON is the diode drop in forward conduction

• Current through resistor (and through the diode branch) is:

  • $I = \frac{VS - V_{ON}}{R}$

  • For example: $I = \frac{5 - 0.6}{100} = 0.0438\ \text{A} = 43.8\ \text{mA}$

• In the diagram, the breakdown shows VR, VON, and the overall supply voltage balance

• Relationship: The resistor drop VR = I × R, and the diode drop is VON, with VS ≈ VR + VON

Page 34

• Silicon diodes (symbol): Anode (+) and Cathode (−)

• Diagram reference from Carnegie Mellon: shows diode symbol and orientation

Page 35

• Turn-on voltages for various diodes (rough values):

  • Schottky diode: $V_{ON} \approx 0.3\ \text{V}$

  • Silicon diode: $V_{ON} \approx 0.6\ \text{V}$

  • Red LED: $V_{ON} \approx 1.8\ \text{V}$

  • Green LED: $V_{ON} \approx 2.7\ \text{V}$

• Diagram shows diode indicator vs current on plots for different diode types

Page 36

• LED applications: Lighting and display

• Mentions micro-LED display and general LED lighting usage

Page 37

• LED overview

• LED is a diode specifically designed to emit light when forward biased

Page 38

• LED polarity dependency

• Forward bias vs reverse bias illustrated with a 5 V source and 5 kΩ resistor in separate configurations

• Notation shows + and − terminals for the LED circuit

Page 39

• LED forward bias context

• Intrinsic semiconductor in the LED under forward bias enables recombination to emit photons

Page 40

• LED forward bias (continued)

• Emission mechanism described in the forward-bias region

Page 41

• Photon emission in LED under forward bias

• Observations:

  • For modern LEDs, about 50% of recombinations yield photon emission; the remaining recombinations release heat

  • In the intrinsic region, electrons and holes recombine to emit photons or release heat

• Forward bias behavior: Recombination is followed by injection of a new electron into the n-side and a new hole into the p-side from the power source

• Efficient LED operation relies on recombination events that produce photons

Page 42

• Quantum efficiency of LED

• Definition: $\eta = \frac{N<em>{\text{photons}}}{N</em>{e-h}}$ where

  • $N_{\text{photons}}$ = number of emitted photons per unit time

  • $N_{e-h}$ = number of recombined electron-hole pairs per unit time

Page 43

• Bandgap concept

• Band structure terms: Conduction band, Valence band, and the Forbidden bandgap (Eg)

• Doping typically does not change the bandgap Eg

• Diagram shows intrinsic conduction/valence bands and the bandgap in-between

Page 44

• Energy view of bandgap

• Emitted photon energy equals the bandgap energy (approximately):

  • If a photon is emitted during recombination, its energy is approximately $E<em>{\text{photon}} \approx E</em>g$

• Turn-on voltage is related to the bandgap but is typically smaller than the actual bandgap energy

Page 45

• LED efficiency exercise: Given an LED operating at 10 mA with 55% quantum efficiency, compute photon emission rate

• Steps:
  1) Number of electron-hole pairs injected per second:
  $N<em>{e-h} = \frac{I}{q} = \frac{10\times 10^{-3}}{1.6\times 10^{-19}} = 6.25\times 10^{16} \ \text{s}^{-1}$ 2) Number of photons emitted per second: $N</em>{\text{photons}} = \eta \times N_{e-h} = 0.55 \times 6.25\times 10^{16} = 3.43\times 10^{16} \ \text{s}^{-1}$

• Result: Approximately $3.43\times 10^{16}$ photons per second

Page 46

• LED circuit schematic (multi-branch)

• Nodes: VS = supply; VA is a node; Branches include resistors and diodes (Di with turn-on voltage VON)

• Components: R0, R1, R2, R3, R4, and an LED network

• Concept: Each branch contains a diode with a forward drop V_ON and a resistor; node VA links branches

Page 47

• LED circuit analysis using Kirchhoff’s Current Law (KCL)

• KCL formulation (illustrative):

  • Total source current equals the sum of branch currents: $I = I<em>1 + I</em>2 + I<em>3 + I</em>4$

• Branch currents depend on branch voltages and resistances, with the diode drop approximated as V_ON in forward-biased branches

• Example states which branches are ON vs OFF and uses a node-voltage approach to solve for VA and branch currents

• Resulting equations combine: $V<em>S, V</em>{ON}, R<em>k, V</em>A, I_k$ to determine which branches conduct

Page 48

• Excise Quiz: Determine current through resistor in parallel to a diode

• Circuit: VS = 3 V; Rp = 120 Ω; Rs = 240 Ω; Observations indicate the diode is ON (forward-biased threshold exceeded)

• Calculation approach: If diode is ON, the resistor in parallel with the diode sees the diode’s forward drop V_ON across it

• Voltage across the parallel resistor equals the diode forward voltage (approximately)

• Current through the resistor Rx:$I<em>P = \frac{V</em>{ON}}{R_P}$

Page 49

• Answer to the Excise Quiz (final): The current through the resistor in parallel to the diode is 5 mA

• Calculation: With VON ≈ 0.6 V and Rp = 120 Ω, $I</em>P = \frac{V<em>{ON}}{R</em>P} = \frac{0.6}{120} = 0.005\ \text{A} = 5\ \text{mA}$

Summary of key concepts and formulas (quick reference)

• Current and charge transport in conductors:

  • $I = \frac{\Delta Q}{\Delta t}$, $\Delta Q = -e \cdot N<em>{e}$, hence $I = -e \cdot \frac{dN</em>e}{dt}$

  • Number of electrons per second for a given current: $N_{e\text{,s}} = \frac{I}{e}$

• Electron charge: $e = 1.6\times 10^{-19}\ \text{C}$

• Intrinsic semiconductor behavior:

  • Silicon (Si) has 4 valence electrons per atom

  • Intrinsic Si acts as an insulator with very low free carriers (I ≈ 0)

• Doping and charge carriers:

  • Donors (n-type): dopants with extra valence electrons (e.g., P) → free electrons as majority carriers

  • Acceptors (p-type): dopants with fewer valence electrons (e.g., B) → holes as majority carriers

• PN junction and diode basics:

  • PN junction forms a diode when p-type and n-type regions are joined

  • Forward bias: charges move toward the junction, recombine, and emit energy (photon or heat)

  • Reverse bias: current is suppressed; junction behaves as open circuit

• Diode turn-on and I-V behavior:

  • Forward-biased diode has a threshold VON; below VON, current is small; above V_ON, current rises steeply

  • Typical turn-on voltages: Schottky ≈ 0.3 V, Silicon ≈ 0.6 V, Red LED ≈ 1.8 V, Green LED ≈ 2.7 V

• LED operation and emission:

  • LED is a diode engineered to emit light when forward-biased

  • Photon emission probability ~50% per recombination in modern LEDs (quantum efficiency considerations)

  • Photon energy ~ bandgap energy: $E<em>{ ext{photon}} \approx E</em>g$

  • Quantum efficiency: $\eta = \frac{N<em>{\text{photons}}}{N</em>{e-h}}$

• Band structure and bandgap:

  • Conduction band, valence band, and forbidden bandgap (Eg)

  • Doping typically does not change the bandgap significantly

If you’d like, I can tailor these notes further (e.g., convert all figures to text-based equivalents, add quick-end-of-page flashcards, or create a condensed formula sheet).