Question

Draw the band structure expected for germanium doped with gallium. What sort of semiconductor would this be? What type of charge carrier has been added?

Short answer

When germanium is doped with gallium, the band structure retains the same conduction and valence bands, but additional energy levels are introduced due to the presence of gallium atoms. The germanium becomes a P-type semiconductor, where "P" stands for "Positive" as the charge carrier is a "hole" which acts as a positive charge carrier. This type of semiconductor allows for easier movement of electrons and enhances conductivity.

Step-by-step solution

Understanding Band Structure

Band structures in semiconductors are graphical representations of the energy levels of electrons in the material. The band gap is the energy difference between the valence band (highest energy band that can be filled with electrons) and the conduction band (lowest energy band that is unoccupied by electrons). In intrinsic semiconductors, such as pure germanium, the band gap is significant and few electrons have enough energy to cross it.

Implication of Doping

Doping is the process of introducing impurity atoms into a semiconductor crystal to change its electrical properties. Germanium being doped with gallium introduces Ga atoms, which have one electron less in the outer shell than germanium. These impurity atoms have one less electron to contribute to the germanium crystal structure, which leads to the formation of “holes”. Holes are essentially vacancies where an electron could exist, and they can move from atom to atom. They manifest as positive charge carriers, i.e., they give an effect as if a positive charge is moving which is opposite to electron movement.

Visualizing the Doped Band Structure

The gallium atoms form a donor energy level that is close to the germanium valence band. This additional energy level makes it easier for electrons to be excited from the valence to the conduction band where they are free to roam - conduct electricity. The positively charged "holes" left behind are at the energy level just above the valence band. Hence, the band structure retains the same conduction and valence bands as germanium, but now there are additional energy levels formed by the dopant.

Identifying the Doped Semiconductor

The introduction of gallium turns the germanium into a P-type semiconductor. "P" stands for "Positive" refers to the fact that charge carrier is a hole (absence of an electron) which acts as a positive charge carrier.

Identifying the Charge Carrier

The charge carrier added due to the doping process is the "hole", which is an absence of an electron, and behaves like a positive charge.