Electronic band structures are caused by electron-electron interactions between neighboring atoms. The greater the degree of interaction, the wider the band generally becomes. For this reason, atoms with high coordination numbers tend to form wider bands, since more bonds are formed when coordination number is higher. If the bands are wider, the band gaps become smaller because the band covers more energy values. Base on this knowledge, if you made a single-atom layer thin film out of a semiconductor, what would you expect the bandgap of this film to be compared to a bulk (large in all 3 dimensions) semiconductor made out of the same material? Please explain why.
If you made a single-atom layer thin film out of a semiconductor, you would expect the bandgap of this film to be different compared to a bulk semiconductor made out of the same material. In most cases, the bandgap of the thin film would be different from that of the bulk semiconductor.
To understand why, let's consider the concept of band structure and how it relates to the electronic properties of materials. In a solid material, the energy levels available to electrons are organized into bands. The highest occupied band is called the valence band, while the lowest unoccupied band is called the conduction band. The energy difference between the highest valence band and the lowest conduction band is known as the bandgap.
In bulk semiconductors, the electronic behavior is determined by the collective interactions of a large number of atoms. As you mentioned, electronic band structures are influenced by electron-electron interactions between neighboring atoms. The greater the degree of these interactions, the wider the band becomes. As a result, atoms with high coordination numbers tend to form wider bands because more bonds are formed.
Now, when we consider a single-atom layer thin film, the electronic behavior is fundamentally different from that of bulk materials. In a thin film, the number of atoms in the vertical direction is greatly reduced, and the interactions between atoms in this direction are limited. As a result, the coordination number is lower in the thin film compared to the bulk material.
Due to the reduced coordination, the band structure of the thin film is modified, and the band widths may become narrower compared to the bulk counterpart. This narrowing of band widths in the thin film can lead to an increased bandgap compared to the bulk material. However, it is important to note that the specific change in bandgap will depend on the material and the specific structure of the thin film.
In summary, when you make a single-atom layer thin film out of a semiconductor, you would generally expect the bandgap of this film to be different from the bulk semiconductor made out of the same material. The bandgap may be increased in the thin film due to the reduced coordination number and the resulting narrowing of band widths. However, it is important to analyze the specific material and thin film structure to determine the exact change in bandgap.