Methods of characterization of materials/ fourth part

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(Edited)

Welcome to a new installment of my material characterization series where I share the different techniques, methods or experimental procedures for the study of semiconductor compounds.

Before starting this new material is advisable to read previous installments, in order to get a better understanding of the subject and can digest it more easily.

Here I will leave you the links:

Part 1

Part 2

Part 3

Let's remember some basic concepts:

Electrical conductivity "(σ)" is nothing more than the ability to conduct electric current when a potential difference, i.e. a voltage, is applied to it. It is undoubtedly one of the most important physical properties of a semiconductor or solid. In a sample of a totally homogeneous semiconductor, this depends on the concentration and mobility of the load carriers.

Similarly we must know that the electrical resistivity "ρ" is:

The physical magnitude known by the difficulty to which a specific material opposes the flow of the load carriers. It is also known as one of the most sensitive indicators of changes in the nature of chemical bonds.

Also to mention that it is very important the correct preparation of the samples of a semiconductor, since if we present errors in these procedures the results of the measurements can present errors, in the same way the calibration of the equipments is essential, to verify each connection, each cable, supply of correct electrical current not to cause damages to these experimental equipments.

In this opportunity I will share with all of you an important or better said essential tool for us scientists in the area of semiconductors called the Hall Effect.

The characterization of materials, in particular the electrical characterization is an essential part in the study of semiconductor compounds. Knowing the properties of a certain material can give us an idea of its future use, that is, the application that this material can have in the technological field.

The Hall effect is a very important method for scientists today and is part of an indispensable study in semiconductor laboratories, due to the growing demand of industries for the creation of new devices more efficient, versatile, economical and long-lasting. This method is very simple and easy to apply, due to its low cost and simplicity is a favorite for us, apart from giving us a very clear and precise idea of what we can do with the material in the future. Basically it is the starting point for the study of new materials.

The Hall Effect arises from the importance of studying different electrical properties in a material such as; charge carrier density, electrical resistivity, and charge carrier mobility in semiconductors and metals, (very important this).

Now we are going to know the concept of Hall Effect...

Wiki tells us that:

The Hall Effect is the appearance of an electric field by separation of charges, inside a conductor through which a current circulates in the presence of a magnetic field with a component perpendicular to the movement of charges. This electric field (Hall field) is perpendicular to the movement of the charges and to the perpendicular component of the applied magnetic field. It is named after its first modeler, the American physicist Edwin Herbert Hall (1855-1938).

Fact...

in 1985 and 1998 two Nobel prizes were awarded for the discovery of the Quantum Hall Effect, which has the same principle but occurs under more extreme conditions: electrons participating in the current must be restricted to moving in a plane and be subjected to the action of an intense magnetic field, while the system is kept at an extremely low temperature, and conduction electrons in the two-dimensional system can only be found in certain discrete states, and each of these states can contain only a finite number of electrons[1].


The Hall effect for different directions of electric current and magnetic field. CC BY-SA 3.0

The fundamental principle that is involved within the Hall effect is the Lorentz force, this phenomenon is located below the Hall effect, ie this happens when an electron is mobilized within the electric field perpendicular to the magnetic field that is applied, therefore this field experiences a force in both directions that moves constantly as a response of magnetic force and force within the electric field of the material.

It works for any semiconductor, for example; if we have a semiconductor material with a negative conductivity type, we know very well that because it is type n the majority carriers would be the electrons that occupy a greater density in the sample. It can be assumed that the current circulating inside the semiconductor bar flows constantly in the X coordinate axis from left to right of a Z magnetic field as shown in the following diagram.


Hall Effect in a semiconductor

Now, if the majority load carriers in the semiconductor sample that are held by the Lorentz force at the beginning move away from the current that this direction toward the Y-axis, thus producing an excess load in the material. If we have a clean displacement of electrons in a direction and being the material zero, an equal and opposite clean charge must appear in the other side of the semiconductor material, giving for consequence the appearance of an electric field EH, and a difference of voltage that was called voltage Hall VH [2-3].

If we have two separate continuous charges, the free load carriers must make the electric force exerted within a transverse electric field EH in the material equal the Lorentz force, this can be observed by the following expression:

On the other hand, if in the semiconductor rod we call its width "w", the opposite sides of the rod will have a difference of potential VH:

We now consider the current density j ̅ and the average velocity of the electrons or majority charge carriers v using the following relationship:

Bearing in mind that n is the concentration of the charge carriers.

The Hall voltage can be represented by the following expression:

RH is the Hall coefficient.

If we express the equality of current intensity I, we have the following:

The charge carriers are subjected to the electric field which is parallel to the electric current,

Now the speed of the carriers is given by the following expression:

Where µ is called the mobility of the charge carriers q and mass m.

If we base ourselves on the famous Ohm's law, we can find the electrical conductivity σ in the semiconductor rod by means of:

For measurements as a function of temperature T in an intrinsic material we have:

KB: Boltzmann constant = 8.625x10-5 eV.K-1.

σ: electrical conductivity at high temperatures.

Eg: energy gap between the conduction and valence band.

And finally after developing all this set of equations and from equation (11) we can find the real value of the electrical conductivity of a semiconductor by means of the following expression:

R0: plate resistance.

l: the length of the plate.

S: the area of its cross section.

and finally µHO Hall mobility at room temperature[4].

In this way we can find some of the electrical properties in semiconductor compounds.

It is probable that you will find the development of these equations in some books, I don't know if completely equal to this content. Similarly there are different ways or methods to find the electrical conductivity and charge concentration, as well as the energy gap that I will show in my next delivery, but this method is the most effective to obtain viable results and I say this with authority because of my experience in the area.

You can read my Spanish version by clicking here or just use your browser's translator.

Thank you very much for taking the time to read my content, see you in an upcoming installment of my material characterization series.

Bibliography consulted

  • [1]. Pedro Gonzáles Mozuelos. El Efecto Hall Cuántico Fraccionario in http://www.hemerodigital.unam.mx/ANUIES/ipn/avanpers/ene99/efecto/efecto.html
  • [2].NIST National Institute of Standards and technology. Hall Effect Measurements.
  • [3]. José Rogan C. Gonzalo Gutierrez G. Eduardo Menendez P. Introducción a la física de sólidos.
  • [4]. Efecto Hall en germanio.(2010). Laboratorio de electricidad y Magnetismo departamento de Física. Universidad Carlos III de Madrid.
  • Marin, G. (2001). Preparación para diferentes técnicas, estudios comparativos de las propiedades ópticas y eléctricas en función de la temperatura de los semiconductores CuInTe2 y CugaTe, Tesis de Maestría. Mérida, Universidad de los Andes.
  • Charles Kittel. (2004). "Introducción a la física del estado sólido". Segunda edición. México. Editorial Reverte.
  • Smith, W; Hashemi. (2006) Fundamentos de la ciencia e ingeniería de los materiales. Cuarta Edición. México. Editorial McGraw Hill, pag 791-796.
  • Electron mobility
  • Hall effect
  • Hall Effect
  • Electrical Conduction in Metals and Semiconductors
  • Lorentz force
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