Occupied States

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Occupied States

Figure 3948a shows an energy-level diagram of a solid with core-level excitation and electron emission processes at solid surface. This energy-level diagram provides a detailed view of the electronic structure of a solid, highlighting the core levels (K- and L-shells), the valence band, and critical energy levels such as the Fermi level (E_F) and the vacuum level (E_vac). The diagram illustrates the primary processes of electron excitation, where external energy sources, such as X-rays or incident electrons, can eject electrons from inner core levels (K and L). This excitation can lead to various secondary emission processes, including the emission of secondary electrons, photons (light and X-rays), and Auger electrons.

The Fermi level (E_F) is shown as the energy level at which electrons are in equilibrium at absolute zero temperature, representing the dividing line between occupied and unoccupied electronic states. The vacuum level (E_vac) indicates the energy threshold an electron must exceed to escape the solid into the vacuum. The valence band, represented as a shaded region, contains delocalized states where electrons are free to move throughout the material, playing a crucial role in its conductive properties.

Energy-level diagram of a solid with core-level excitation and electron emission processes at solid surface

Figure 3948a. Energy-level diagram of a solid with core-level excitation and electron emission processes at solid surface.

In details, the diagram in Figure 3948a describes:

Energy Levels in a Solid:
- K- and L-shell Core Levels: The diagram illustrates the energy levels within an atom that are closest to the nucleus. These are known as core levels, with the K-shell being the innermost energy level (n=1) and the L-shell being the next level outward (n=2). These levels are deep within the energy well of the atom and are more tightly bound to the nucleus.
- Valence Band (Shaded Area): Above the core levels, there’s a shaded region representing the valence band. This band consists of delocalized states, meaning that the electrons are not bound to any particular atom but are free to move throughout the material. The valence band is crucial for the electrical properties of materials, as it is typically the highest range of electron energies that are still bound to atoms before the conduction band.
Fermi Level (E_F):
- The Fermi level E_F is represented as a horizontal line near the top of the shaded valence band. It signifies the energy level at which the probability of finding an electron is 50% at absolute zero temperature. In metals, the Fermi level lies within the valence band, allowing free electrons to contribute to electrical conduction.
Vacuum Level (E_vac):
- The vacuum level E_vac is the energy required for an electron to completely escape the material into the vacuum. This level is shown above all other levels, indicating that any electron reaching this energy can leave the solid.

Figure 3948b shows an example of optical interband transitions of electrons from occupied states to unoccupied states.

optical interband transition of electrons from occupied states to unoccupied states

Figure 3948b. Example of optical interband transition of electrons from occupied states to unoccupied states.

Figure 3948c shows the schematic illustration of the energy level diagrams for molecular structures with different number of atoms which are single atoms, dimers, clusters and bulk materials. Splitting of the atomic energy levels occurs when the single atoms form a diatomic molecule. As more atoms join the system, the levels split further until a quasi-continuous band structure is formed in the bulk material. In other words, quantum size effects occur when the quasi-continuous band structure of a solid state system begins to break down as more atoms are included.

Schematic illustration of the energy level diagrams for molecular structures with different number of atoms which are single atoms, dimers, clusters and bulk materials

Figure 3948c. Schematic illustration of the energy level diagrams for molecular structures with different number of atoms which are single atoms, dimers, clusters and bulk materials.

Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Occupied States