# Bang Gap of Semiconductors: Exploring the Brus Approximation

• String_man
In summary, the "Brus Approximation" is a model developed by Brus to predict the band gap energy of nanocrystallites, quantum dots, and other small spherical structures. It takes into account the discrete energy states of single atoms and the energy bands of bulk semiconductors, using a "particle-in-a-box" term and a Coulomb-attraction term. While it is accurate for structures of intermediate size, it is not reliable for very small structures due to the use of effective masses.

#### String_man

Can anyone tell me what is the "Brus Approximation" in case of the bang gap of semiconductors?

what is "bang gap" ?

sorry ! its just a typing mistake. You can understand what i want to say.

ok, Band Gap.

I have never heard of Brus Approximation, is that also a typo? Can you elaborate a bit?

Single atoms show discrete energy states. Bulk semiconductors show energy bands. So one would expect the band gap behaviour to change with the size of the solid. For example one can tune the color of the emission of colloidal quantum dots just by varying their size.

Brus developed a model to predict the band gap energy of nanocrystallites, quantum dots and other small spherical structures with radius R. Roughly speaking, the approach is to start with the bulk value of the energy gap, add a "particle-in-a-box" like term for electrons and holes using an effective mass approximation for the masses of both and subtracting a term, which corresponds to the Coulomb-attraction between electrons and holes. The particle-in-a-box-term scales with 1/R² and the attraction term scales with 1/R, so in small structures the 1/R²-term dominates.

However this approach uses effective masses, which do not depend on the size of the structure. Therefore the results are ok for structures of intermediate size, but are rather wrong for very small structures.

## 1. What is the band gap of a semiconductor?

The band gap of a semiconductor is the energy difference between the top of the valence band (where electrons are usually found) and the bottom of the conduction band (where electrons can move freely). It is an important property that determines the conductivity and optical properties of the material.

## 2. How is the band gap of a semiconductor measured?

The band gap of a semiconductor can be measured using various experimental techniques such as optical absorption spectroscopy, photoemission spectroscopy, and electrical conductivity measurements. These methods involve studying the energy levels of electrons in the material and determining the energy difference between the valence and conduction bands.

## 3. What is the Brus approximation in relation to the band gap of semiconductors?

The Brus approximation is a theoretical model that describes the behavior of the band gap in small semiconductor particles (nanocrystals). It states that the band gap of a semiconductor particle is inversely proportional to the square of its diameter.

## 4. How does the band gap of a semiconductor affect its properties?

The band gap of a semiconductor has a significant impact on its properties. A larger band gap means that the material has a wider range of energy levels that cannot be occupied by electrons, making it an insulator. A smaller band gap indicates that more electrons can be easily excited to the conduction band, making the material a better conductor.

## 5. Can the band gap of a semiconductor be engineered?

Yes, the band gap of a semiconductor can be engineered by altering its composition, structure, or size. This is a crucial aspect of semiconductor technology, as it allows for the design and fabrication of materials with specific properties for various applications such as solar cells, LEDs, and transistors.