Methods of characterization of materials/ third part

In my two previous 1,2 installments I talked about conductivity and resistivity in semiconductors, some fundamental concepts to understand the behavior of this physical property in these materials.

Let us remember the following:

Electrical conductivity "(σ)" is nothing more than the ability to conduct electrical 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.

also that,

The electrical resistivity "ρ" is that physical magnitude known by the difficulty to which a specific material opposes to 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.

It showed that these characterization methods are very important because it gives us essential information about the activation energy and the concentration of the main charge carriers (electrons, type n, hollows, type p), is electrical resistivity.

To be able to obtain this information we must comply with some parameters, first of all, to carry out the growth synthesis of the semiconductor compound. After obtaining the ingot, a small portion must be cut and prepared for its respective measurement. For electrical resistivity measurements we must have a small portion of the semiconductor ingot in the form of a parallelepiped as we can see in figure 1.

^{Figure 1. Diagram and actual assembly of the semiconductor sample for measurements of electrical resistivity and hall effect at the end of the bar or 6-point method.}

Now, to perform this experiment we must have the following equipment available: Temperature control, power supply, Oven, current-voltage source, current cables and computerized software.

The following photo shows the real experimental set-up that is carried out in our laboratory, whose experimental configuration is thanks to Dr. Giovanni Marín @iamphysical. In the photo you can see all the equipments used in the experiment, they are a little disordered, I couldn't take a better capture, but next I will explain you how the system of electrical resistivity measurements works step by step depending on the temperature.

^{Actual experimental set-up of electrical resistivity measurements as a function of temperature}

1. Temperature control.

2. Voltage source.

3. Oven.

4. Semiconductor.

5. Support.

6. Power supply.

7. Cables through which current and voltage circulate.

8. Software.

The sample of the semiconductor compound fully ready for measurement must be introduced into the furnace, the main function of this furnace is to be able to maintain the temperature in the sample, i.e. it does not escape. The sample as explained in my two previous deliveries must be placed on a bakelite, this bakelite must have 6 copper wires through which the current and voltage will circulate to the semiconductor sample through the current wires that come from their respective sources. From one of these, data will be collected on the variation of voltage depending on the current, and the other will be responsible for providing current to the sample.

Temperature control is a very important piece of equipment within this measurement system, since by means of it we are going to vary the temperature of the sample starting from very low levels to very high levels, up to the melting point of the indium where this material will be detached from the semiconductor sample and the data collection will be finished. It should be noted that the temperature controller is connected to the main power supply, which takes the voltage variation data as a function of its temperature, and this source likewise takes the signal of the data collected to the computer where we have the automated measurement system that will show below.

^{An example of automated software simulation for temperature-dependent electrical resistivity measurements (microsoft excel program)}

As we can see in the previous image, the program presents particular characteristics for the measurement system, in which we can modify the passage current and voltage to the sample, without having to do it manually in the source, we can also place the time of sweeping of the sample, among others. This program is designed by the technical staff of the laboratory explicitly for measurements of electrical resistivity, which is a great advantage for scientists in the area of semiconductors since this type of software after different reliability tests showed an efficiency of 99%, which is a great advantage for all of us, since previously the measurements were taken manually.

After the sweep of the sample is finished, the program records all the data obtained from the current, voltage and temperature, and then exports them to any graphics program, such as Origin. There we can annex these data and observe the electrical resistivity curve of the semiconductor compound as represented in figure 2.

^{Figure 2. Electrical resistivity curve vs temperature}

Another way to calculate electrical resistivity is by the following equation:

where:

a is the width of the sample.

e sample thickness.

d distance of contact points.

v voltage.

i current.

Conclusions: It is important to emphasize that the information provided in this publication is extremely basic, to determine the electrical resistivity and other important characteristics of the properties of a semiconductor requires deeper or advanced studies, by this I mean in the concentration of charge carriers and electrical conductivity of a semiconductor compound requires the analysis of more complex equations. In this opportunity it was presented how to make the correct configuration of a system of analysis of electrical resistivity measurements, since without a correct experimental procedure.

If you want more information about the subject you can visit the following links:

Electrical resistivity and conductivity

Semiconductor Basics

Resistivity

(1)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.

Marin, G. Wasin M,S. Sanchez, G. Perez. Mora, A. (1998). Caracterización estructural y de composición del CuInTe2 obtenido por la técnica de evaporación del Te.CIENCIA 6(2), pag 129-137.

Charles Kittel. (2004) Introducción a la física del estado sólido ". Segunda edición. Editorial Reverte.

Smith, W; Hashemi. (2006) Fundamentos de la ciencia e ingeniería de los materiales. Cuarta Edición. Méjico. Editorial McGraw Hill.

ASTMF43-09. Internacional. (2011). Estándar (2010) Métodos de prueba de resistividad de materiales semiconductores Vol. 10.05.

ASTMF42-02. Standard (2003) Test Methods for Conductivity Type of Extrinsic Semiconducting Materials Conyained in Vol 10.05.

Smith, W; Hashemi. (2006) Fundamentos de la ciencia e ingeniería de los materiales. Cuarta Edición. México. Editorial McGraw Hill, pag 791-796.

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