# Density of states arbitrary units

• miljohns60
In summary: In this case, it would be best to contact the authors for clarification on the units and how to convert them to a more standard unit, such as #(number of states)/(cm^3 eV).

#### miljohns60

So the problem is following. The density of states in energy space (3D case) represents the number of states per unit volume per energy. This means that the unit is #(number of states)/(cm^3 eV). This result can be seen in many solid-state physics books.
I am reading some articles where the density of states for different layers is calculated using computer simulations and where the density of states is given in arbitrary units in energy space. What is the meaning of using the arbitrary units for DOS? Shouldn't it be in some form of number of states per unit volume (area or length) per energy? How do I convert that results to #/(cm^3 eV)

miljohns60 said:
What is the meaning of using the arbitrary units for DOS?
They likely were focusing on reporting qualitative features of the DOS. It is a tad annoying; I agree. But it’s pretty standard practice, especially in computational papers.

Another place where you see arbitrary units used frequently is in spectroscopy, where line intensity will generally be reported in arbitrary units unless the paper is specifically reporting absolute oscillator strength. This is because 1) line intensity depends on the intensity of the excitation source, and 2) the most salient features of most spectra (wavelength/frequency, relative intensity between lines, linewidth, etc.) are not related—or are only weakly related—to absolute intensity.
miljohns60 said:
Shouldn't it be in some form of number of states per unit volume (area or length) per energy? How do I convert that results to #/(cm^3 eV)
Yes, it should, and you can’t. There’s no way to know what the units correspond to; they’re arbitrary.

## 1. What is the "Density of states" in terms of arbitrary units?

The density of states refers to the number of energy states per unit volume in a material. In terms of arbitrary units, it is a measure of the number of energy states per unit volume that are available to a particle in a particular energy range.

## 2. How is the density of states related to the electronic structure of a material?

The density of states is directly related to the electronic structure of a material, as it describes the distribution of energy levels that are available for electrons to occupy in the material. This information is crucial in understanding the electrical and optical properties of a material.

## 3. What are some common units used to measure the density of states?

The density of states can be measured in units of energy, such as electron-volts (eV), or in units of energy per volume, such as eV/cm3. It can also be expressed in terms of the number of states per energy range, such as states/eV.

## 4. How does the density of states vary in different materials?

The density of states can vary significantly between different materials, as it depends on factors such as the composition, crystal structure, and electronic properties of the material. For example, metals typically have a high density of states near the Fermi level, while insulators have a lower density of states in this region.

## 5. How is the density of states related to the band structure of a material?

The density of states is closely related to the band structure of a material, as it provides information about the distribution of allowed energy levels for electrons in the material. The shape and characteristics of the band structure can affect the density of states and vice versa, making it an important factor in understanding the electronic properties of a material.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8977707,"math_prob":0.96007115,"size":1051,"snap":"2023-40-2023-50","text_gpt3_token_len":237,"char_repetition_ratio":0.14422159,"word_repetition_ratio":0.71657753,"special_character_ratio":0.226451,"punctuation_ratio":0.04950495,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9809353,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-10T04:51:33Z\",\"WARC-Record-ID\":\"<urn:uuid:63719d32-68c7-4a48-a208-be6840a5d33f>\",\"Content-Length\":\"70219\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b528c126-63ad-435c-8399-857cb0dc71b1>\",\"WARC-Concurrent-To\":\"<urn:uuid:1251f3cf-549a-4441-bd72-9c160fc14995>\",\"WARC-IP-Address\":\"172.67.68.135\",\"WARC-Target-URI\":\"https://www.physicsforums.com/threads/density-of-states-arbitrary-units.543552/\",\"WARC-Payload-Digest\":\"sha1:TYKNEPLXICOP3LGNAFSANO2QV7SXNGLK\",\"WARC-Block-Digest\":\"sha1:XAT43JKGSC6H4O4UJHX3OX3H74RMD6OZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679101195.85_warc_CC-MAIN-20231210025335-20231210055335-00337.warc.gz\"}"}