In your science career, you will find that Albert Einstein laid the foundation for many technologies. Here we will discuss Einstein's theory of the Photoelectric Effect which led to the formulation of the Theory of Quantum Mechanics. This article will discuss the Photoelectron Spectroscopy method, emphasizing theory and applications.
- This article is about photoelectron spectroscopy.
- First, we will talk about the basics of photoelectron spectroscopy (PES).
- Then, we will look at X-ray photoelectron spectroscopy.
- After, we will analyze the features of photoelectron spectroscopy graphs.
- Subsequently, we will explore angle-resolved ultraviolet photoelectron spectroscopy.
- Finally, we will go over the main fields of application of PES and suggest areas for further study.
Background: Photoelectron Spectroscopy
Before we dive straight into photoelectron spectroscopy, let's cover the important background information.
Quantum: a packet of energy, or energy of a quantum state. The plural of quantum is quanta.
Quantum State (Energy state) refers to the energy of an electron in orbit about the nucleus of a molecule.
Excited State: when an electron in a substance absorbs a quantum and is promoted to a higher energy state.
Electromagnetic (EM) radiation: any type of light (e.g., UV, IR, Visible, etc.) or particle rays (like X-rays).
The Photoelectric Effect
Photoelectron Spectroscopy (PES) is based on the theory of the photoelectric effect:
The photoelectric effect is observed when electromagnetic (EM) radiation, such as UV light or X-rays, reflects off of the surface of a solid. In other words, the photoelectric effect occurs when a quantum of EM radiation ionizes an electron from a molecule in a solid.
Figure 1: Schematic of photoelectric effect experiment. Vaia Original
The photoelectric effect occurs when light, used to probe the surface of a solid, possesses a quantum (hν ) that has an energy that exceeds the binding energy of an electron bound to a surface molecule.
$$BE_{electron}=h\nu_0$$
The interaction of a quantum of EM radiation with a molecule on the surface of a probed solid will excite a molecularly bound electron from the ground state to an excited, "positive ion state" (please see figure 2).
Figure 2: Energy Diagram - Excitation of a ground state electron, bound to a molecule, -M-, within a solid, by a quantum of EM radiation.
We note that any excess energy (hν) past the energy needed to excite an electron from a molecular ground state to a positive ion state ( BEelectron = hν0 ) will be converted to the kinetic energy of the outgoing electron. This kinetic energy (KEelectron ) moves the ionized electron past the surface of the solid into the vacuum (please see figure 3).
Figure 3: Energy Diagram - Excitation of a ground state electron into the vacuum by a quantum of EM radiation.
For a detailed explanation of the terms, formulas, and processes involved in the above figure, please refer to the next section, "Photoelectron Spectroscopy Theory".
Photoelectron Spectroscopy Theory
The energy of a quantum of EM radiation from the light source is hν :
$$E_{quantum}=h\nu$$
Where:
According to Einstein's theory of the photoelectric effect, the kinetic energy, (KEelectron ), of an electron that is knocked off of a molecule on the surface of a solid is:
$$KE_{electron}=h\nu-h\nu_0$$
Where:
In terms of the electron binding energy, (BEelectron = hν0), the kinetic energy of the electron emitted from the surface of the solid is:
$$KE_{electron}=h\nu-BE_{electron}$$
Then, moving (BEelectron ) to the left-hand side, we get:
$$KE_{electron}+BE_{electron}=h\nu=E_{quantum}$$
Where:
hν = Equantum is the energy of the incoming EM radiation.
KEelectron is the kinetic energy of the electron emitted from the surface of the solid.
BEelectron is the binding energy of an electron in a molecule on the surface of a solid.
Lastly, we note that the binding energy of an electron in a molecule on the surface of a solid material is:
$$BE_{electron}=E_{quantum}-KE_{electron}$$
X-ray Photoelectron Spectroscopy
Now let's look at some examples using x-ray photoelectron spectroscopy.
An X-ray source illuminates the surface of a small silver plate located within a vacuum tube that is transparent to X-rays. Typical X-ray sources emit quanta at energies ranging from 124 eV to 145 eV (eV is short for electron-volts). If a quantum of 135 eV is emitted from the source, what would the frequency of this radiation be? What would the energy per mole of the X-ray packets be?
1. Calculation of the frequency of the X-ray packet:
Given that the X-ray quantum has an energy of 135 eV, we first convert electron-volts, eV, to kilo Joules, kJ, by the following conversion factor:
$$1eV=1.6022X10^{-22}kJ$$
Notice that, conversion factors are another form of the number one, which can be seen in the present case by the following rearrangement:
$$1=\frac{1.6022X10^{-22}kJ}{1\,eV}$$
Then, multiplying the energy of the X-ray quantum by the conversion factor, in order to cancel the dimension of electron-volts, eV, we get an energy, in kilo Joules, kJ:
$$E_{X-ray}=135\,eV*\frac{1.6022X10^{-22}kJ}{1eV}=2.16X10^{-20}kJ$$
Now, we can calculate the frequency associated with this energy by using the relation:
$$E_{X-ray}=h\nu_{X-ray}=2.16X10^{-20}kJ$$
Using Planck's constant in the dimensions of Joules-seconds:
$$h=6.626X10^{-34}J*s$$
And isolating for the frequency, ν X-ray, we get:
$$\nu_{X-ray}=\frac{E_{X-ray}}{h}=\frac{2.16X10^{-20}kJ}{6.626X10^{-34}J*s}*\frac{1000\,J}{kJ}=3.26X10^{12}*s^{-1}$$
2. Calculation of energy of X-ray quanta per mole:
Again using the conversion for one electronvolt, eV, to kilo Joules, kJ:
$$1\,eV=1.6022X10^{-22}kJ$$
Then as before, for the X-ray quantum at 135 eV, we would get:
$$E_{X-ray}=135\,eV*\frac{1.6022X10^{-22}kJ}{1eV}=2.16X10^{-20}kJ$$
Now to convert this energy to mega Joules per mole, MJ/mol, we use another conversion factor involving Avogadro's number:
$$1\,mol=6.022X10^{23}$$
Then:
$$1=\frac{6.022X10^{23}}{1\,mol}$$
And multiplying this conversion factor, we get:
$$E_{X-ray}=2.16X10^{-20}kJ*\frac{6.022X10^{23}}{mol}*\frac{1\,MJ}{1000\,kJ}=13\,MJ*mol^{-1}$$
This then is the energy per mole of the X-ray quanta.
Photoelectron Spectroscopy
Now, let's talk about what photoelectron spectroscopy is in more detail.
PES is used to measure the ground's relative energies and electrons' excited states within a molecule.
The relative energy of an electron ground state versus an excited, positive ion state is measured in PES.
Photoelectron spectroscopy (PES) - the application of Einstein's photoelectric effect theory to obtain an electronic spectrum. PES utilizes EM radiation (UV-light or X-rays) to obtain electronic spectra.
Electronic spectrum - electronic signals detected as a result of the irradiation of a sample with EM radiation.
- Irradiation: to shine EM radiation (e.g., UV light or X-rays) on a material.
Photoelectron Spectroscopy Graph
Here we consider the PES graph of a hypothetical material. Notice the graph is in terms of the binding energy versus the relative number of electrons detected after irradiation of the sample.
Figure 4: Hypothetical Photoelectron Spectroscopy (PES) experiment. (Inset: Energy Diagram)
We note that the abscissa, or vertical axis, for the Photoelectron spectrum is in terms of the "Relative number of electrons." For example, the spectrum for Lithium metal, which is made up of two 2s (inner core) electrons and one 2p (valence) electron, would have a PES graph that looks something like this:
Figure 5: Approximate PES graph of Lithium.
Thus, the vertical axis of the PES graph maps the relative numbers of electrons within an electron shell. This information and the binding energy associated with peaks can be used to identify the atoms that make up a material.
Please refer to the article on "Valence Electrons" and "Orbitals" if you need a refresher on these topics!
Let's continue with this example and calculate the binding energy for Lithium's valence (2s1 ) electron. Using the X-ray quantum for which we calculated the energy, we would have:
$$E_{X-ray}=13\,MJ\cdot mol^{-1}=KE_{electron}+BE_{electron}$$
If we are further given the information that the measured kinetic energy of the emitted electron was, \(KE_{electron}=12.49\,MJ\cdot mol^{-1}\), we would then have a binding energy for the valence electron of Lithium:
$$BE_{electron}=E_{X-ray}-KE_{electron}=0.51\,MJ\cdot mol^{-1}$$
Practical Surface Analysis by Auger and X-ray Photoelectron Spectroscopy
The surface analysis by Auger and X-ray spectroscopy is used to:
Probe the surface of a solid material in greater detail, yielding information about molecular geometry and the electronic structure of molecules.
Probe quantum states of molecules at the surface of a solid material.
Produce images in electron microscopes.
Angle-Resolved Ultraviolet Photoelectron Spectroscopy
The angle-resolved ultraviolet photoelectron spectroscopy (ARPES) technique is used to:
Probe the surface of a solid material to obtain information about the allowed energies and momentum of conduction electrons in a metal.
Map the material band structure, or conduction band energies, on a metal surface.
Probe the quantum mechanical structure of conduction electrons in a metal or semiconductor like Silicon.
Application of Photoelectron Spectroscopy (PES)
The applications of PES are mainly in condensed matter physics, electron microscopy, electronic mapping conduction in metals, and characterizing quantum effects in metals and semiconductors.
Although this is a brief survey of the PES technique, the ability to probe the quantum mechanical nature of molecules at the surface of solids might appeal to some of you. I would suggest that students interested in PES study quantum mechanics, chemical physics, and condensed matter physics at the college level would lead research work utilizing PES in the lab. Best of luck in your future studies.
Photoelectron Spectroscopy - Key takeaways
- The photoelectric effect occurs when a quantum of EM radiation ionizes an electron from a molecule in a solid.
- Quantum - a packet of energy, or energy of a quantum state.
- The binding energy of an electron in a molecule on the surface of a solid material is given by the formula: \(BE_{electron}=E_{quantum}-KE_{electron}\)
- The relative energy of an electron ground state versus an excited, positive ion state is measured in PES.
- The vertical axis of the PES graph yields the number of electrons within an electron shell.
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