Methods of characterization of materials / seventh part

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Greetings again science loving friends and welcome to my new delivery of materials characterization, where I share my knowledge and experiences in the area of materials physics, especially semiconductor compounds.

The characterization of semiconductor materials is a fundamental tool for the creation of various optoelectronic devices and other technological applications, which is why it is important to study the physical properties of these materials and for this different methods of experimental analysis are needed that give us results of their possible application in the technological field. During my stay in Steem, I have dedicated myself to share my experiences in this beautiful area of materials science and then show a new method where we can obtain very important information on the electrical behavior of a semiconductor sample through the technique of Van der Pauw.

It is advisable to read my previous installments to better understand the content.

Here I will leave you the links:

Part 1 Part 2 Part 3 Part 4 Part 5 Part 6

There are different techniques to calculate one of the most important electrical properties in a semiconductor such as "electrical resistivity", all have basically the same purpose, which is to find the mobility, the concentration of charge carriers of a material, where we involve different terms such as electrical conductivity, hall coefficient, energy gap, etc.,.

All these techniques go through different paths (when we speak of mathematical development of equations), but they serve the same purpose which is to determine the "most important electrical properties of a semiconductor material".

Van der Pauw's technique is another used to find the electrical resistivity, mobility and concentration of charge carriers in a semiconductor material... It bears the name of its creator, and unlike the techniques explained above, "Van der Pauw" uses the surface resistance of the sample to determine the values of mobility and concentration in the material, remembering that in the first we use the hall coefficient and conductivity at room temperature.

The main advantage of this technique is that it is possible to obtain mobility measurements of load carriers at different temperatures, while in the previous one we can only do it at room temperature.

With all this in mind we can express the density of carriers in a rectangular and very thin semiconductor bar in the following way:

It is very simple to apply these equations to obtain carrier density, but in this case it is advisable to use surface density ns=nd instead of volumetric density. This means that results are obtained depending on surfaces such as Rs; ns, however the volumetric values of these variables can be easily obtained with the knowledge of the sample thickness d. Therefore we would obtain the following equation;

Thus, by measuring VH and knowing each value of B,I and q, we can easily determine ns of the load carriers of the material.


Figure 1: Configuration to determine the Hall voltage using the Van der Pauw

If we have a configuration as shown in the previous figure, the Hall voltage must always be negative for a semiconductor of conductivity type n and positive for type p.

As I mentioned at the beginning of this publication through the Van der Pauw technique and by making electrical resistivity measurements in a semiconductor we can determine the surface resistance of a material. So if we know that Rs involves density and mobility in carriers, from this we can find Hall mobility in this way,

Next we have two thin rectangular semiconductor plates (see figure 2 and 3), we must bear in mind that it can also be an arbitrary sample, which does not have an exact shape although it is recommended that it is circular, square or rectangular, but above all its contacts are preferably located in the corners of the sample and that these contacts are ohmic, ie the current circulates linearly throughout the semiconductor sample. The idea of creating this technique is due to its convenience since it is widely used in industry to determine the electrical properties in a semiconductor such as resistivity in uniform samples. Another important factor that we must mention is that the sample must be free of voids or corrosion that affects the measurement results. This sample must be placed on a bakelite and connect their respective cables where the current circulates (this I have shown in my previous publications with real images of an assembly).

It is important to note that in order to determine mobility μ and surface density nsub a combination of hall effect and electrical resistivity measurements must be performed.


Figure 2: Experimental configuration for the determination of RAresistance using Van der Pauw's technique

Figure 3: Experimental configuration for the determination of RBresistance using Van der Pauw's technique

Now, after explaining both schemes of the experimental configuration of the sample based on the Van der Pauw technique we have as an essential objective the determination of the surface resistance Rs. This scientist was able to demonstrate that if there are two resistances associated to the corresponding terminals that are reflected in the previous figure, these are automatically related to Rs by means of the equation,

The electrical resistivity of volume ρ can be calculated using:

Then we must follow the following steps to obtain RA RB which are as follows:

1. Direct current must be applied I which enters contact 1 and then exits contact 2.

2. The voltage V43 is measured from contact 4 to contact 3 (see figure).

3. Subsequently, current must be applied, which must enter through contact 2 and exit through contact 3.

4. Finally, the voltage V14 is measured, from contact 1 to contact 4.

And with this RA and RB are obtained through the following expression;

In the beginning this was what we wanted to obtain and it is a very simple method when we talk about mathematical resolution. Perhaps the complexity results in the preparation of the samples since certain very important considerations must be taken into account at the time of the assembly, in order to obtain viable results of the measurements. Some of the practical aspects to carry out this type of resistivity and Hall effect measurements are for example:

  • The precision when soldering the contacts in the board, they must present a high quality and to verify this the ohmic contacts must be made if there is continuity of current in all the sample and in linear form.
  • The sample must be uniform and its thickness must be accurately determined, so that at the time of making the calculations the results are correct.
  • Verify any thermomagnetic effect due to uniform temperatures and photoconductive and photovoltaic effects that can be minimized by working in a dark environment and a balanced ambient temperature (no heat, no cold).
  • The sample should have an appropriate dimension with respect to its contacts, i.e. the contacts or solder points should not be larger than the lateral dimensions of the sample.
  • Before starting the measurement process, check the temperature of the sample, the intensity of the magnetic field and the electric field.
  • Conclusions

    The purpose of this publication was to show you how to apply the Van der Pauw technique and how to determine the surface density in a semiconductor sample by measuring the Hall voltage, which consists of a series of voltage measurements in which you must have a constant current with a magnetic field perpendicular to the sample. The figures shown in this publication serve the purpose of orienting the reader and being able to understand in a correct way the content. Similarly we can use Hall measurements to measure VH with a current I that is opposite to contacts 1 and 3 and the voltage VH24 is measured by the pair of contacts 2 and 4. After acquiring the Hall voltage we can calculate the surface density of the sample by means of ns= IB/q|VH| of I, B and q.

    And that's all on this occasion. In future publications I will continue to talk about the electrical characterization of semiconductor materials using Van der Pauw's technique.

    Sources

  • L. J. van der Pauw, "A Method of Measuring Specific Resistivity and Hall Effect of Discs of Arbitrary Shapes," Philips Res. Repts. 13, 1-9 (1958).
  • L. J. van der Pauw, "A Method of Measuring the Resistivity and Hall Coefficient on Lamellae of Arbitrary Shape," Philips Tech. Rev. 20, 220-224 (1958).
  • E.H. Hall: "On a New Action of the Magnet on Electric Currents". American Journal of Mathematics vol 2, 1879, p.287-292.
  • Marín, G.(1996). Síntesis y crecimiento del compuesto CuInTe2 por el método de Bridgman horizontal con tres zonas y sus características. Trabajo para optar al título de licenciado en física. Maracaibo. Universidad del Zulia
  • NIST National Institute of Standards and technology. Hall Effect Measurements.
  • Van der Pauw Ecopia HMS-3000 Hall Measurement System.
  • PHYWE series of publications. Hall effect in n-germanium, Hall effect in p-germanium.
  • Hall effect experiment:- Determination of charge carrier density
  • Measurement of Semiconductor Parameters. Muhammad EL-SABA
  • Temperature Dependence of Semiconductor Conductivity. (Originally contributed by Professor E.D.H. Green)
  • Hall effect
  • Hall Effect
  • Electrical Conduction in Metals and Semiconductors
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