F. Revolutions in Modern Physics: Quantum Mechanics and Special Relativity · Quantum MechanicsQuantum Technologies I: Solar Cells, Digital Cameras, LEDs and Lasers
F1.2 F2.1 F1.1 F2.2About 70 minutes
Learning goals- I can explain how solar cells and digital camera sensors use the photoelectric principle (photons freeing electrons).
- I can explain how LEDs and lasers produce light, using energy levels and stimulated emission.
- I can calculate quantities such as cut-off wavelengths, photon counts and power output for these devices.
- I can assess the importance of quantum mechanics to these technologies and their effects on society and the environment, including Canadian contributions.
Words to know
photovoltaic cell (solar cell)
A device in which absorbed photons free electrons in a semiconductor, producing an electric current directly.
semiconductor
A material such as silicon whose electrons need a small energy (the band gap) to become free to conduct.
band gap
The minimum energy needed to free an electron in a semiconductor (about 1.1 eV for silicon).
CCD / CMOS sensor
Light sensors made of millions of pixels; in each pixel, photons free electrons and the charge is counted.
stimulated emission
When a photon causes an excited atom to drop to a lower level and emit a second photon identical to the first.
population inversion
A state in which more atoms are in an excited level than in the lower level; needed for a laser.
laser
Light Amplification by Stimulated Emission of Radiation: a source of coherent, single-wavelength, highly directional light.
coherent light
Light whose waves are in step (same frequency and constant phase relationship).
Quantum physics in your pocket
The photon ideas from earlier in this unit are not just history. Count the quantum devices near you: your phone's camera sensor, its LED flashlight and screen, the laser in a barcode scanner at the grocery checkout, the solar panels on a roof down the street. None of them could have been designed with classical physics alone. This lesson looks at how four of them work, and what they mean for society.
Solar cells: the photoelectric effect at work
A solar cell is a thin wafer of silicon with two layers made slightly different (called n-type and p-type). Where they meet, a built-in electric field forms at the junction.
- A photon with energy greater than silicon's band gap (about 1.1 eV) is absorbed and frees an electron, leaving behind a "hole" (a missing electron, which acts like a positive charge). This is the internal version of the photoelectric effect: the electron does not leave the material, but it becomes free to move.
- The junction's field pushes the electrons one way and the holes the other.
- Connect a wire, and the electrons flow through the external circuit, doing work in a load.
Photons below the band gap (wavelengths longer than about 1100 nm) do nothing. Photons far above it waste their extra energy as heat. That is one reason ordinary silicon panels convert only about 20% of the sunlight's energy into electricity.
Worked exampleExample 1: Silicon's cut-off wavelength
Silicon's band gap is 1.12 eV. What is the longest wavelength of light a silicon solar cell can use? Can it use visible light? Infrared?
- The photon must have at least 1.12 eV: λ(max) = hc/E = 1240 eV·nm ÷ 1.12 eV.
- λ(max) = 1107 nm, about 1100 nm.
About 1100 nm. All visible light (400 nm to 700 nm) works, and so does near-infrared from 700 nm to about 1100 nm. Longer infrared wavelengths pass through unused.
Worked exampleExample 2: Power from a panel
A rooftop panel has an area of 1.6 m² and an efficiency of 20%. On a clear summer day, about 1000 W/m² of sunlight reaches it. Find its electrical power output and the energy it produces in 6 hours of such sunlight.
- Incoming power = (1000 W/m²)(1.6 m²) = 1600 W.
- Electrical power = 0.20 × 1600 W = 320 W.
- Energy in 6 h = 320 W × 6 h = 1920 Wh = 1.9 kWh.
320 W of output and about 1.9 kWh in 6 hours. (A Canadian winter day gives far less: shorter days, a lower Sun, and snow on the panels.)
Digital cameras: counting photoelectrons
A camera sensor is a grid of millions of tiny light-sensitive pixels, each a small piece of silicon. Photons striking a pixel free electrons, which are stored as charge. After the exposure, the charge in each pixel is measured: more photons → more electrons → brighter pixel. Coloured filters over neighbouring pixels (red, green or blue) let the camera build a full-colour image.
The first practical design, the charge-coupled device (CCD), was invented in 1969 at Bell Labs by Willard Boyle, a physicist born in Amherst, Nova Scotia, and George E. Smith. It shifted each pixel's charge along the rows, "bucket brigade" style, to be read out. Boyle and Smith shared half of the 2009 Nobel Prize in Physics for it (the other half went to Charles K. Kao for optical fibres). CCDs transformed astronomy (including the Hubble Space Telescope) and medical imaging. Most phone cameras now use CMOS sensors, which read each pixel with its own tiny circuit; the physics of photon in, electron out is the same.
Worked exampleExample 3: Photons in one pixel
During an exposure, one pixel receives 1.0 × 10⁻¹⁵ J of green light (550 nm). If 60% of the photons free an electron, how many electrons are stored?
- Energy per photon: E = hc/λ = 3.62 × 10⁻¹⁹ J.
- Photons = 1.0 × 10⁻¹⁵ ÷ 3.62 × 10⁻¹⁹ = 2.76 × 10³.
- Electrons = 0.60 × 2.76 × 10³ = 1.66 × 10³.
About 1700 electrons. Because light arrives in whole photons, a very dim image has random speckle ("noise"): the photon counts in neighbouring pixels naturally vary a little.
LEDs
In the investigation lesson you saw that an LED emits a photon each time an electron drops across its energy gap: hf ≈ E(gap). Engineers choose the semiconductor material to set the gap and so the colour. Red LEDs were available in the 1960s, but bright blue LEDs (gap near 2.7 eV) were very hard to make; Isamu Akasaki, Hiroshi Amano and Shuji Nakamura shared the 2014 Nobel Prize in Physics for succeeding in the early 1990s. Blue LEDs made white LED lighting possible (a blue LED coated with a material that glows yellow). LED bulbs use several times less electricity than incandescent bulbs for the same light, which cuts energy use for lighting around the world.
Lasers: stimulated emission
In 1917 Einstein predicted a third way atoms interact with light. Besides absorbing a photon and spontaneously emitting one in a random direction, an excited atom can be stimulated by a passing photon of exactly the right energy to drop down and emit a second, identical photon: same energy, same direction, same phase.
A laser uses this:
- Energy is pumped in (by a flash lamp, electric current or another laser) to create a population inversion: more atoms in the excited state than in the lower one.
- A photon from one spontaneous emission stimulates another, and those two stimulate more, in a chain.
- Mirrors at each end bounce the light back and forth through the material, building it up. One mirror lets a little escape as the beam.
The result is light that is monochromatic (one wavelength), coherent (in step) and highly directional. Theodore Maiman built the first laser, using a ruby crystal, in 1960. Today lasers read barcodes, carry internet data through optical fibres, cut steel, measure distances, and correct vision.
Canadian connection: Donna Strickland, a physicist at the University of Waterloo, shared the 2018 Nobel Prize in Physics with Gérard Mourou for chirped pulse amplification, a way of making extremely short, intense laser pulses without destroying the amplifier. It is used in laser eye surgery and precision machining. (Arthur Ashkin received the other half of that prize, for optical tweezers.)
Weighing the effects on society (F1.2)
Solar cells: clean electricity with no fuel or emissions while operating; useful far from the grid, for example in some remote First Nations communities that have built solar projects, often community-owned, to reduce their reliance on diesel generators. Costs include mining and refining materials, energy used in manufacturing, and recycling panels at the end of their life.
Digital imaging: cheap, instant photography for everyone, new science (astronomy, medical imaging) and citizen journalism; also raises issues of privacy, surveillance and image manipulation.
LEDs: large energy savings; concerns about light pollution and glare at night.
Lasers: communications, medicine and manufacturing; eye hazards (even a pointer can damage the retina), and laser strikes on aircraft are a serious crime in Canada.
Just for funThe word laser began as an acronym: Light Amplification by Stimulated Emission of Radiation. Physicists joked early on that it was "a solution looking for a problem." It has since found thousands.
Hands-on activitySolar cell investigation
You need: a small solar-powered calculator or garden light (one with a visible solar cell), a flashlight, a sheet of paper, and coloured transparent plastic (candy wrappers, coloured report covers or sunglasses).
- Calculator: in a dim room, cover the solar strip with your finger. The display fades (if it also has a battery, choose a solar garden light instead). Uncover it under a lamp: it works.
- Garden light: these turn on when it is dark. In daylight, cover the cell with your hand: the light switches on, because the cell senses darkness by its current dropping.
- Shine a flashlight on the cell from 10 cm, then 20 cm, then 40 cm. Does the calculator display or garden light respond differently?
- Try covering the cell with red, then blue plastic. Which lets the device keep working better? (Hint: the cell responds to any colour above its cut-off, but coloured plastic blocks different amounts of light.)
What to look for: the cell responds to the number of photons reaching it: more light (closer flashlight) gives more current. Any visible colour can free electrons in silicon, since all visible photons have more than 1.1 eV; the differences you see come from how much light each filter blocks.
Your turn
1What happens inside a solar cell when a photon with more energy than the band gap is absorbed?
It frees an electron and leaves a hole; the junction's electric field separates them, and the electrons flow through the external circuit as current.
2A solar cell is made from a semiconductor with a band gap of 1.4 eV. Find its cut-off wavelength.
λ = 1240 ÷ 1.4 = 886 nm (about 890 nm).
3A 2.0 m² panel with 18% efficiency receives 800 W/m². Find its electrical output.
P = 0.18 × 800 × 2.0 = 288 W (about 290 W).
4In a camera sensor, why does a brighter part of the scene appear brighter in the image?
More photons reach those pixels, so more electrons are freed and stored; the camera reads the larger charge as a brighter pixel.
5What are three special properties of laser light?
It is monochromatic (one wavelength), coherent (waves in step) and highly directional (narrow beam).
6Why does a laser need a population inversion?
Normally most atoms are in the lower level, so photons are more likely to be absorbed than to cause stimulated emission. With more atoms excited than not, stimulated emission wins and the light is amplified.
7Name a Canadian who won a Nobel Prize for a quantum technology and what it was.
Willard Boyle (co-inventor of the CCD image sensor, 2009) or Donna Strickland (chirped pulse amplification of laser pulses, 2018).
More practice: warm-up
1What does LASER stand for?
Light Amplification by Stimulated Emission of Radiation
2What is the band gap of silicon, approximately?
3In which year was the first laser built?
1960 (Theodore Maiman, ruby laser)
5In stimulated emission, how does the new photon compare with the stimulating photon?
Identical: same energy, direction and phase.
More practice: on your own
1A ruby laser emits 694 nm light. Find the photon energy and the energy difference between the two laser levels.
E = 1240 ÷ 694 = 1.79 eV; this equals the energy difference between the upper and lower laser levels.
2A 1.0 mW, 694 nm laser beam: how many photons per second?
E = 1.79 eV = 2.86 × 10⁻¹⁹ J; N = 1.0 × 10⁻³ ÷ 2.86 × 10⁻¹⁹ = 3.5 × 10¹⁵ photons/s.
3Explain why ordinary silicon cells cannot exceed a limited efficiency, giving two reasons based on photon energy.
(1) Photons with less than 1.1 eV (λ > 1100 nm) are not absorbed, so their energy is lost. (2) Photons with more than 1.1 eV free only one electron each; the extra energy becomes heat. (Other losses include reflection and resistance.)
4A pixel stores 900 electrons when 30% of the photons arriving free electrons. The light is 600 nm. How much light energy reached the pixel?
Photons = 900 ÷ 0.30 = 3000. E per photon = 1240 ÷ 600 = 2.07 eV = 3.31 × 10⁻¹⁹ J. Total = 3000 × 3.31 × 10⁻¹⁹ = 9.9 × 10⁻¹⁶ J.
5Give one positive and one negative environmental effect of large-scale solar power.
Positive: no greenhouse-gas emissions while generating, reducing fossil-fuel use. Negative: for example, energy and mining needed to make panels, land use for large solar farms, or waste when panels are retired if not recycled.
Challenge
1A white LED bulb uses 9.0 W to produce the same light as a 60 W incandescent bulb. If the bulb runs 4.0 hours a day for a year, how much electrical energy does switching save? At 13 cents per kWh, how much money?
Saving = (60 − 9.0) W × 4.0 h × 365 = 74 460 Wh ≈ 74 kWh. Cost saving ≈ 74 × $0.13 ≈ $9.70 per bulb per year.
2Explain, using the photon model, why a solar cell is more efficient with near-infrared light just above 1.1 eV than with violet light at 3.1 eV (for the same power).
Each photon frees at most one electron and gives about 1.1 eV of useful energy. A near-infrared photon of 1.2 eV wastes only 0.1 eV, about 8% of its energy. A violet photon of 3.1 eV wastes about 2 eV (65%) as heat. Also, the same power of near-infrared light contains about 2.6 times as many photons, so more electrons are freed.
3Assess the statement: "Quantum mechanics is too abstract to matter in everyday life." Use at least three technologies from this lesson.
The statement is false. Solar cells (photons freeing electrons across a band gap), camera sensors in every phone (counting photoelectrons in pixels), LED lighting (photons from electrons dropping across a band gap), and lasers (Einstein's stimulated emission) all rely directly on quantized energy and photons. They affect energy use, communication, medicine and the economy, so quantum ideas shape daily life even if we never see them directly.
Quiz
1. A solar cell produces current because absorbed photons
2. Silicon's band gap is 1.1 eV. Which light can NOT produce current in a silicon cell?
3. In a digital camera sensor, the brightness recorded by a pixel depends on
4. In stimulated emission, an incoming photon causes
5. Who co-invented the CCD image sensor and was born in Nova Scotia?
6. Which is a property of laser light?
Big idea (F1.2): solar cells, camera sensors, LEDs and lasers all depend on quantized energy: photons freeing electrons, electrons dropping across energy gaps, and stimulated emission. Canadians such as Willard Boyle and Donna Strickland made key contributions.
How to help: look around your home together and list devices that use these technologies. Discuss trade-offs: for example, the environmental costs and benefits of solar panels, or privacy questions raised by cameras everywhere.
Common difficulties:
- Thinking solar cells work like the photoelectric effect in a vacuum tube, with electrons leaving the surface. In a solar cell, electrons are freed but stay inside the material.
- Mixing up spontaneous and stimulated emission.
- Forgetting that efficiency applies to the incoming power (output = efficiency × intensity × area).
Safety: never point a laser pointer at people, pets, vehicles or aircraft; even brief exposure can damage the eye.