# How to Calculate the Debye Length

Debye length is a measure for the electrostatic screening in plasma, colloids or in a semiconductor material. It is very relevant to determine the stability and the use of surfactants for colloidal solutions and also for the depth profiling technique used to measure the doping profile in semiconductor materials.

It is denoted by the Greek letter Lamda and its unit is meter. It is calculated by taking the reciprocal of Kappa (1/Kappa), where Kappa is the Debye-Huckel parameter.

Determine the known variables: Boltzmann constant, electronic charge of an ion, Avogadro's number and the permittivity of vacuum are known variables. The values of these variables are always constant:

k= 1.38*10^-23m^2kgs^-2K^-1

- Debye length is a measure for the electrostatic screening in plasma, colloids or in a semiconductor material.
- It is very relevant to determine the stability and the use of surfactants for colloidal solutions and also for the depth profiling technique used to measure the doping profile in semiconductor materials.

e=1.6022*10^-19 Columb

No= 6.023*10^23

Eo= 8.854*10^-12(F/m)

Determine unknown variables: Though temperature (T) of the solution is usually given, it should always be converted into absolute scale. The absolute temperature is measured in terms of Kelvin.

Determine the ionic charge of the solution: The ionic charge of the solution is the sum of the individual ions present in the solution. It can be represented by:

- e=1.6022
*10^-19 Columb No= 6.023*10^23 Eo= 8.854*10^-12(F/m) Determine unknown variables: Though temperature (T) of the solution is usually given, it should always be converted into absolute scale.

Ionic charge= Sum.cz *e^2, where cz is individual ions and e is the electronic charge

(1.6022*10^-19 Columb).

Determine the dielectric constant of the materials: The dielectric constant is unique to every material or solution. For a particular material used, the value will usually be given. It is the ratio of electric field produced without dielectric to the field with dielectric.

Dielectric acts as an insulator when it is placed in an electric field.

Determine Kappa: Kappa or the Dybye-Huckel parameter is determined by using this equation:

- Ionic charge= Sum.cz
*e^2, where cz is individual ions and e is the electronic charge (1.6022*10^-19 Columb). - Determine the dielectric constant of the materials: The dielectric constant is unique to every material or solution.

Kappa= 1/(sqrt(Eo_Ep_k_T)/(2000_No_Sum.cz_e^2)), where means the square root.

After determining Kappa, Debye length can be calculated by taking the reciprocal (1/K) of the Kappa.

Lamda = 1/Kappa

The unit of Kappa is inverse meter and the unit of Debye length is meter.

References

- "Principles of Colloid and Surface Chemistry"; Paul C. Hiemenz, et al.; 1997
- Davidson College: The Dielectric Constant

Tips

- Debye length has a very practical implication in colloids technology in the formation of electric double layer. It is considered to be the characteristic thickness of the double layer.

Warnings

- The temperature is always measured in absolute scale. SI units are generally used for the variables.

Writer Bio

Sushil Khadka has written business concepts since 2010. He also writes op-eds in campus-wide journals. Sushil's academic research works have been published in "American Chemical Society" and the "Journal of Physical Chemistry." Sushil likes hiking, extended traveling and current affairs. He graduated with a Bachelor of Science in biological engineering from the University of Maine.