# Why is Si indirect semiconductor

• vani_lj
In summary, Silicon has an indirect band gap due to the different energy levels of the valence and conduction bands.

#### vani_lj

Can anybody explain...

what makes silicon indirect band semiconductor?

Vani

Look at the band structure diagram.

http://en.wikipedia.org/wiki/File:Si-band-schematics.PNG
http://en.wikipedia.org/wiki/File:Si-band-schematics.PNG

Find the maximum of the valence band and the minimum of the conduction band.

They are not at the same k-vector.

Holes and conduction electrons will be found near the maximum/minimum. In order for a hole/electron pair to recombine they must "get rid" of the difference in k. An optical photon carries next to no momentum, so some other elementary excitation like a phonon has to be created.

In GaAs on the other hand, min and max occur at the same k. Holes and electrons can recombine and emit just a photon.

The same hold vice-versa for absorption of a photon.

@M Quack, thanks for the explanation...

But I am still searching for answer that what makes energy band minima to occur at k other than zero in Si.

Hmm, that is just the way the band structure works out with the number of electrons on Si, covalent bonds, and so on. I don't think that you can find an argument based on symmetry.

BTW, Ge and diamond also have indirect band gaps.

The "stretched silicon" invented in the 90's reduced the degree of indirectness of the gap and allowed for more efficient silicon switching speeds. The idea was to grow silicon layers on mismatched substrates that were hot. When the wafer cooled, the silicon was stretched into a slightly different lattice constant.

I suppose there should be some qualitative argument using e.g. tight binding approximation on how the valence band and conduction band change at k=0 with k using kp-perturbation theory. As both bent downward, the band gap must be indirect.

The valence and conduction band are qualitatively due to the s and p orbitals of Si. The s orbitals are lower in energy than p. On the Gamma point, the total bonding-antibonding splitting is larger for s than for p orbitals. Taken together, the lowest valence band has s-character and is well separated from the highest valence band which has pure p character. The mainly anti-bonding p and s type conduction bands are nearly degenerate in energy. Once the Gamma point is left, the kp term will mix s and p bands. The p type valence band and s-type conduction band will repell whence the valence band has a maximum at k=0. On the other hand the s and p type conduction bands will repell even stronger as they are nearly degenerate. Hence the lowest conduction band will also have a maximum at k=0. If we believe in k=0 being the absolute maximum of the valence band then Si has to have an indirect band gap.

@DrDu, Thanks for the explanation...

## 1. Why is silicon an indirect semiconductor?

Silicon is an indirect semiconductor because its bandgap has a minimum energy point at a different momentum than its maximum energy point. This means that electrons and holes have different minimum energy levels and therefore require more energy to be excited, making it less efficient for use in electronic devices.

## 2. What is the significance of silicon being an indirect semiconductor?

The indirect bandgap of silicon makes it less efficient for use in electronic devices compared to direct bandgap semiconductors. This is because indirect semiconductors have a lower rate of light emission and absorption, leading to lower performance in optoelectronic devices such as LEDs and solar cells.

## 3. How does the indirect bandgap affect the properties of silicon?

The indirect bandgap of silicon affects its optical and electronic properties. It has a lower absorption coefficient, meaning it absorbs less light, and a lower rate of light emission, making it less efficient for use in optoelectronic devices. It also has a lower electron mobility, affecting its ability to conduct electricity.

## 4. Can silicon be converted into a direct semiconductor?

It is possible to modify the band structure of silicon to make it a direct semiconductor. This can be achieved by introducing strain or alloying with other materials. However, this process is complex and expensive, and direct bandgap materials are often preferred for applications that require efficient light emission or absorption.

## 5. What are the advantages and disadvantages of silicon being an indirect semiconductor?

The main advantage of silicon being an indirect semiconductor is its abundance and low cost, making it the most widely used material in the semiconductor industry. However, its indirect bandgap also leads to lower performance in certain electronic and optoelectronic devices, making it less suitable for those applications. Additionally, the process of modifying silicon to become a direct semiconductor can be costly and time-consuming.