A History of the Photoelectric Effect and Its Role in Solar PV

Solar cells are fueled by the light of the sun. Knowing this, the first question we should ask is “what is light?” followed closely by “how is it possible to convert light into electricity?” These are not easily answered questions.

Understanding the nature of light has been a challenging task for the centuries of philosophers and scientists working on this subject. Optics is one of the oldest disciplines studied by men, and the process of converting light into electricity started from casual observation.

Far from being a formal study of quantum physics, this article aims to teach key discoveries from some of the scientists and philosophers who devoted their work to the study of light and its applications. It sets the foundation for understanding how solar cells can convert light into electrical current.

Note: The unit systems employed in this article are the International System of Units (SI) and units accepted for use with the SI.

 

The Beginnings of Understanding Light

Research on the nature of light is known to start in ancient Greece, where philosophers like Plato, Socrates, Aristotle, Pythagoras, and Euclid (Optics) gave opinions on the matter. During medieval times in the Islamic world, scientists like Abu Ali Mohammed Ibn Al Hasn Ibn Al Haytham, known now as Alhazen, worked on theories of light and vision.

From the 1600s to the 1930s, many famous scientists also made significant steps toward our understanding of what light is and how it works. In 1672, Isaac Newton stated that particles, not waves, make light (corpuscular theory). Christiaan Huygens, Thomas Young, and Augustin-Jean Fresnel believed that light was a wave. James Clerk Maxwell theoretically predicted the existence of electromagnetic waves. Max Planck thought black bodies emitted energy in discrete packets, and Albert Einstein alleged that light came in bundles of energy.

 

Proving Light Moves in Waves

In 1678, Christiaan Huygens developed a useful technique for defining how and where light waves propagate. Huygens' principle of light passing through a slit helped prove that light is a wave. However, by that time, this principle was not considered evidence enough to show that light was a wave, mainly due to Isaac Newton's disagreement and his reputation among the scientific society.

In 1801, Thomas Young did his double-slit interference experiment. This experiment showed that waves of light passing through two slits overlap (add or cancel each other) and form an interference pattern. Water waves, sound waves, and waves of all different types display this same interference phenomenon. This experiment’s results proved the wave character of light.

In 1865 James Clerk Maxwell showed in his publication A Dynamical Theory of the Electromagnetic Field that a beam of light is a traveling wave of electric and magnetic fields, i.e., an electromagnetic wave. Comparing the velocity of the waves with the speed of light, as measured by Fizeau and Foucault, he concluded:

"The agreement of the results seems to show that light and magnetism are affections of the same substance and that light is an electromagnetic disturbance propagated through the field, according to electromagnetic laws."

Huygens' wave theory for light was mathematically less complicated than Maxwell’s electromagnetic theory.

 

Calculating Light Wavelength and Frequency

The color of the light depends on the wavelength, understanding the light as an electromagnetic wave. In a periodic wave, wavelength (λ) is the distance from crest to crest or from trough to trough on the wave shape. The usual units of wavelength are meters, centimeters, millimeters, and nanometers.

In the visible spectrum, violet has the shortest wavelength and red has the longest. The wavelength of ultraviolet (UV) radiation is shorter than that of violet light. Likewise, the wavelength of infrared radiation is longer than the wavelength of red light.

 

Figure 1. The visible spectrum is the portion of the electromagnetic spectrum visible to the human eye. Image courtesy of Michigan State University.

 

Wave frequency f is the number of waves that pass a fixed point per unit of time, measured in Hertz (Hz). One Hertz equals one wave passing a fixed point in one second. Still in use is the former term cycles per second.

The period T = 1/f is the time it takes a periodic wave to go through one complete cycle of its motion. The SI unit is the second (s).

It is essential to point out that, before connecting the concepts of wavelength, frequency, and period, light is a traveling wave. A traveling wave moves in a direction and travels a distance of one wavelength λ in a time equal to one period T. If it travels, it has a speed v. This speed relates to frequency and wavelength through the expression v = λ/T = λ · f.

The accepted speed of light is 299,792,458 m/s, rounded to 2.998 x 10⁸, and expressed as c. Every time conversion of wavelength to frequency (or vice versa) is required, the expression c = λ · f  is used.

 

Figure 2. A diagram of electromagnetic waves. Image courtesy of the National Weather Service. 

 

The electromagnetic spectrum is separated by order of increasing wavelength into the following regions: gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves, and radio waves. Electromagnetic energy from the sun consists primarily of visible and infrared wavelengths, with small amounts of ultraviolet, microwave, and radio-wave radiation.

 

Figure 3.Visible light colors and wavelengths.

 

The visible light colors and wavelengths are: 

• Violet (400-450 nm)
• Indigo (420-450 nm)
• Blue (450-495 nm)
• Green (495-570 nm)
• Yellow (570-590 nm)
• Orange (590-620 nm)
• Red (620-750 nm)

The human eye perceives this mixture of colors as white, with wavelengths from 400 nm to 750 nm. White light consists of components from virtually all of the colors in the visible spectrum with roughly uniform intensities. When passed through a prism, white light is diffracted into all the colors.

 

Figure 4. White light is a mixture of all colors of light.

 

Newton was the first to succeed in separating white sunlight into its colored components.

 

Black Body Radiation and Planck’s Constant

In 1860, Gustav Kirchhoff stated some objects absorb and then emit all the energy that hit them. He called this occurrence black body radiation. Kirchhoff and Robert Bunsen researched the solar spectrum and published a paper in 1861, where they identified the chemical elements in the sun's atmosphere and the spectra of those elements. Kirchhoff was awarded the Rumford Medal for his research on this topic in 1862.

In 1900, Max Planck did a thorough study of black body radiation and concluded that the amount of energy radiated was proportional to the frequency of the electromagnetic waves the black body absorbed. This energy emission was in the form of small, discrete packets of energy that he called "quanta" (quantum is the singular form, from the Latin for "how much, how many"). These quanta could only acquire specific discrete values in multiples of a constant. Today, this concept is known as the Planck constant.

In 1901, Planck showed that assuming radiant energy consists of an integral number of “energy elements.” The energy element E must be proportional to the frequency f, thus:

E = h · f   

where:

        E = energy element

        h = Planck’s constant (6.626 10ˉ³⁴ J s)

        f = frequency of the electromagnetic radiation

These values are said to be quantized, and this demonstration was the first crucial step in the development of quantum physics, which studies the nature of minute elementary particles. It was the first time that someone noticed the energy quantized.

However, Planck did not believe that radiation was broken up into little bits, as his mathematical analysis showed. He considered E = h · f  to be a mathematical trick or convenience that gave him the right answers to solve a technical problem with black bodies, and never appears to have thought deeply about its physical meaning. In his own words:

“If the quantum of action was a fictional quantity, then the whole deduction of the radiation law was in the main illusory and represented nothing more than an empty non-significant play on formulae."

 

Hertz and Hallwachs Work to Understand the Photoelectric Effect

The photoelectric effect has been studied for many years and is not yet fully understood.

In 1887 Heinrich Hertz designed some experiments with a spark gap generator to test Maxwell's hypothesis. These experiments produced the first transmission and reception of electromagnetic waves.

Sparks generated between two small metal spheres in a transmitter induced sparks that jumped between two polished brass knobs in a copper wire loop that worked as a receiver. A tiny spark jumped between these two electrodes. Hertz noticed that he could make receiver spark more vigorous by illuminating the electrodes with ultraviolet light. He did not create any theory that could explain the observed phenomenon, but this was the first observation of the photoelectric effect.

A year later, Wilhelm Hallwachs confirmed these results and showed that ultraviolet light shining on an evacuated quartz bulb with two zinc plates as electrodes and connected to a battery generated a current due to electron emission, or photoelectric current.

 

Stoletov and the Photo Effect

From 1888 to 1891, Russian physicist Alexander Stoletov performed an analysis of the photo effect. He discovered the direct proportionality between the intensity of light and the induced photoelectric current. Today, this is known as Stoletov's law.

 

The Discovery of Electrons

In 1897 JJ Thomson discovered electrons, which he called "corpuscles." He then went on to propose a model for the structure of the atom, popularly known as the "plum pudding model” because it was a uniform sphere of positively charged matter with embedded electrons. In 1899, he showed that the increased sensitivity in Hertz's experiments was the result of light pushing on corpuscles. Thomson recognized that UV caused the emission of electrons, the same particles found in cathode rays.

In 1911, JJ Thomson's student Rutherford proposed a model that described the atom as a positively charged core (nucleus) concentrating nearly all the mass and around which the electrons (negative charges) circulate at some distance, like a planetary system.

In 1899, Philipp Lenard showed that irradiating metals with ultraviolet light may produce emission of negative charges or photoelectrons. He found that the kinetic energy of the emitted photoelectrons was independent of the intensity of light of the same frequency. Yet, in agreement with the law of conservation of energy, more photoelectrons were ejected by a bright source than a dim source.

 

How Einstein Combined Newton's Corpuscles and Planck's Energy Elements

Albert Einstein attempted to explain the photoelectric effect by resurrecting the idea of light corpuscles advocated by Isaac Newton. Also, in 1905, he was the first scientist to take Planck's energy elements seriously, proposing that light comes in bundles of energy. In a beam, there are bundles of "quanta." He did not say that light is a "particle." According to Einstein, a "light quantum" energy Eᵧ is:

Eᵧ = h · f      

where, as before:

h = Planck’s constant (6.626 10ˉ³⁴ J s)

f = frequency of the electromagnetic radiation

 

Einstein recognized that Planck's model was real. What we perceive as a continuous wave of electromagnetic radiation is a stream of discrete quanta. This essential formula for quantum physics is also known as the Planck-Einstein relation, giving credit to Planck's work as well.

Einstein’s prediction was:

Eē = ½ · m · v² = Eᵧ - W = h · f - W      

where:

Eē = energy of electron

v = speed of electron

m = mass of electron

Eᵧ = energy of the light quantum

W = work function (constant dependent on the metal)

The work function W is the energy needed to release an electron from a specific metal (some sort of release energy). It depends on the metal, its crystalline structure, and how polished the surface is.

Einstein stated that when a light quantum supplies energy Eᵧ to metal, some of it goes to the work function and the rest goes to electrons as kinetic energy. Metals release electrons with zero velocity if the energy supplied is precisely its work function. We can also judge from this equation that not all light frequencies will release electrons on a particular metal.

The experimental data was inaccurate at that time, and it was after ten years of measurements of the energy of the photoelectrons that, in 1916, Robert Andrews Millikan verified Einstein's conjecture.

Einstein also proposed that quanta have momentum. In 1917, he developed his theory by assigning a momentum of p = Eᵧ/c = h · f/c = h/λ to the light quantum. Only then did it have the properties of a real particle. He confirmed that light behaves like waves and like particles.

In 1921, Einstein was awarded the Nobel Prize in physics for “his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect." He received it one year later, in 1922.

In 1923, Compton validated the assumptions about the light’s quantum energy and momentum experimentally, employing his scattering experiment, and bombarding electrons with x-ray quanta.

 

Gilbert Lewis’ Discovery of Photons

Although one can hear and understand the term light quantum, it is customary to speak and write about photons. In 1926, Gilbert Lewis, a physical chemist, proposed that instead of the light quantum, one should consider a new kind of atom — what he called a photon — as the carrier of light.

However, Lewis' photon was a concept that diverged from Einstein's proposals.  The story is too long to describe here, but from the late 1920s, physicists considered the term photon to be a suitable synonym for the light quantum that Einstein introduced in 1905.

The photoelectric effect occurs when light shines on a metal. Image courtesy of Feitscherg (CC BY-SA 3.0)

Figure 5. The photoelectric effect occurs when light shines on a metal. Image courtesy of Feitscherg (CC BY-SA 3.0)

 

Review: Properties of the Photoelectric Effect

The following properties summarize the experimental observations on the photoelectric effect:

• Polished metal plates irradiated with light may emit electrons, named photoelectrons, creating a photoelectric current.
• For a given photosensitive material, there is a critical frequency of the light below which nothing happens. As frequency increases, the process starts to work, releasing photoelectrons. This magnitude is the threshold frequency fₒ, and there is a current only for f > fₒ, no matter how high the intensity may be. fₒ depends on the metal, its surface condition (i.e., how polished it is), and on the free electrons in the crystalline structure of the metal.
• The magnitude of the current is directly proportional to the intensity of the light, provided that f > fₒ.
• A crucial property is that the energy of the photoelectrons is independent of the intensity of the light.
• The energy of the photoelectrons linearly increases with the frequency of the light. This property of the photoelectric effect is not easy to understand, considering light as a wave. Einstein came up with an answer: light comes in bundles of energy.

It is important to understand the nature of light as well as the phenomenon through which light can produce electrical energy to help better understand how solar cells work.

Light behaves like both waves and particles. Light shone on metal expulses electrons from its surface. This phenomenon is the photoelectric effect, and the electrons are called photoelectrons. Experiments indicate that by increasing light frequency, the kinetic energy of the photoelectrons increases, and by intensifying the light, the current increases.

 

Next article

The next article in our series on the photoelectric effect and solar PV deals with the energy distribution in the solar spectrum and describes some basic terms used in the photovoltaic industry.