Electrical Properties of Material

School of Materials Science & Engineering Second Year Undergraduate Experiment MS2082 Laboratory

Formal Report For EB1 Electrical Properties of Materials

Name: Joseph Ong Jia Jie Matric: U1720090F Lab Group: GB9

Academic Year 2018/19

Nanyang Technological University

Table of Contents 1. Objectives................................................................................................ 3 2. Introduction ............................................................................................ 3 3. Theory ..................................................................................................... 3 4. Equipment and Materials........................................................................ 7 5. Experimental Procedures ........................................................................ 7 6. Results and Discussion ............................................................................ 7 7. Conclusion ............................................................................................. 12 8. References............................................................................................. 13

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1. Objectives The aims of this experiments are to: i) ii) iii) iv)

Familiarize with the technique used to measure the electrical resistivity or conductivity of solid materials Distinguish between conductors and semiconductors Explain the role of deformation and impurity in the conductivity of metals Identify the important effect of doping on the electrical conductivity of semiconductors.

2. Theory Electrical conductivity and resistivity Electrical resistivity and conductivity are significant electrical properties of a solid material. The electrical conductivity represents the ease of how electrons flows in a solid material and also conducts electricity throughout the whole material while electrical resistivity indicates how resistive the solid material is towards electrical current. Both are intrinsic properties that are related by the following relationship: đ?œŽ=

1

(1)

Ď

Electrical resistance is defined by the following equation: đ?‘™

đ?‘… = Ď A

(2)

From Ohm’s Law, �=

V đ??ź

(3)

Thus we get: đ?‘…=

VA I đ?‘™

(4)

Where l is the length, A is the cross-sectional area of the material used, V is the voltage and I is the current. From Equation (4), we know that the electric resistivity and conductivity can be calculated if both the current passing through the material and applied voltage is known.

Factors determining conductivity of material Electric current rises from the motion of charged particles such as electrons, ions and even ‘holes’ that are within the material and the most important factor is the

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amount of free particles available in the material. Taking electrons as the charged particles, the electrical conductivity of a material is represented by: đ?œŽ = đ?‘›|đ?‘’|Âľđ?‘’

(5)

Where n is the number of free or conducting electrons and |e| is the absolute magnitude of the electrical charge of an electron (1.6 x 10-19 C), and Âľe is the electron mobility (m2/V-s). Electron mobility is affected by electron scattering events and centers which slow down the motion of electron flow. Centers are created by point defects, line defects, crystallographic impurities and thermal vibrations which causes scattering and reduces electron mobility.

Conductors, Semiconductors and Insulators We commonly classify solid materials under 3 groups which are metals, semiconductors and insulators. The difference in the electronic energy structure is the most significant characteristic between these 3 classes of solid materials.

According to quantum mechanics, the allowed electrons in the materials are arranged in energy bands with each band having quantum mechanically restricted ranges. Valence band are the lower energy bands which are completed filled and the conduction band is the first energy band which is empty or partially filled. The difference in energy between the top of the valence band and the bottom of the conduction band is known as the energy band gap. When electrons in the valence band are excited across the energy gap and into the conduction band, they can move freely and thus contribute to electric current when a voltage is applied across the material. The distance of the band gap determines the type of the above 3 materials, conductors, semiconductors or insulators.

Figure 1. Possible band gap structures in metals, semiconductors and insulators.

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Metals are good conductors of electricity and their conductivity can be expressed by equation (5). The conduction band and valence band negligibly close together which allows electrons to freely move into the conduction band to conduct electrical current easy without much energy supplied. Inversely, the band gap in the insulator is large that the conduction band is always empty. The number of free electrons in a metal is determined by the valence electrons per atom of the metal which does not change with temperature of plastic deformation. However, the increase in temperature, plastic deformation and introduction of impurity atoms can affect the electrical conductivity due to the thermal vibration of atoms and increased lattice imperfections serving as scattering centers.

Semiconductors have a small energy band gap between the top of the valence band and bottom of the conduction band. Therefore, the electrons from the valence band needs to be excited by an external source of energy, such as thermal or photon energy, to become free in the conduction band and accelerate from the influence of an electric field. Carriers in a semiconductor are classified to 2 types, holes (p-type) and electrons (n-type). Holes are created when an electron jumps from the valence band into the conduction band. They can be seen as a positive electric charge moving in the opposite direction of an electron. The electrical conductivity of a semiconductor can be represented by following equation: đ?œŽ = đ?‘›|đ?‘’|Âľđ?‘’ + đ?‘?|đ?‘’|Âľâ„Ž

(6)

Whereby p/n is the carrier concentration and Âľe / uh is the electron/hole mobility.

Equation (6) refers to intrinsic semiconductors (pure, no doping involved) which are free of impurity atoms and both the number of electrons and holes are the same.

When a semiconductor is doped with impurity atoms such as group V elements such as phosphorous or Antimony and introduces an extra electron per impurity atom, the semiconductor is classified as n-type conductor. If the semiconductor is doped with an impurity atom such as Boron or Aluminium and an electron is missing per impurity atom added, the semiconductor is classified as a p-type semiconductor.

Thus Equation (6) becomes đ?œŽ ≊ đ?‘?|đ?‘’|Âľâ„Ž

(7)

For a p-type semiconductor where holes are the dominant charge carrier, đ?œŽ ≊ đ?‘›|đ?‘’|Âľđ?‘’

(8)

For a n-type semiconductor where electrons are the majority charge carrier.

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Figure 2. p type semiconductor.

Figure 3. n type semiconductors.

Thus, the electrical resistivity and electrical conductivity of a semiconductor can be modified over a wide range by controlling the amount of doped atoms in both p-type and n-type semiconductors.

Measurement of electrical resistivity/conductivity of solid materials Four-point probe technique is used to measure the resistivity or conductivity across the sample. The four-point probes are four thin equally spaced metal probes which makes contact with the samples during test. Current flows through the two outer probes while voltage is measured with the inner probes without drawing any current.

The sample in our experiment has thickness equivalent to 0.05cm and the sheet resistivity is measured by the following equation. Ď đ?‘Ąâ„Žđ?‘–đ?‘› = 4.53đ?‘Ą

đ?‘‰ đ??ź

(9)

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3. Equipment and Materials Equipment used This experiment requires a 4-point probe station for probing the surface of the specimens, a Keithley 2400 source meter which provides the current source and a Keithley 2182 nanovolt meter which measures the voltage. The specification of the probe stations is listed in table 1.

Probe Type Tip spacing Tip radius Spring load Tip Materials T For 1.02 mm 0.04 mm 100 g Tungsten carbide a Semiconductors (TC) b and Metals l Table 1. Specification of the probe used in the experiment.

Material used The thickness of the sample provided is about 0.0005m. ie. The t/s ratio is less than 0.5, thus Equation (9) can be applied for bulk resistivity.

Metals M1: Commercial pure iron M2: Stainless steel (Fe-18%Cr-9%Ni)

Semiconductors Pure Si: Sample No: PS n-type Si with various amount of Pdoping: Sample No. Sn1, Sn2, Sn3 M3: Cold-rolled stainless steel p-type Si with various amount of Bdoping Sample No. Sp1, Sp2, Sp3 Table 2. List of known materials used.

Specimen Number U1 U2 U3

Description One of these specimens is intrinsic semiconductor; the other two are extrinsic semiconductor. You have to identify which is intrinsic and which are extrinsic, and of the two extrinsic, which has more doping.

Table 3. List of three unknown material.

4. Experimental Procedures i) Source meter and the nanovolt meter was switched on and set to DC mode. ii) Sample was placed onto the probe stage and was secured by switching on the vacuum pump. iii) Toggle switch was flipped from ‘neutral’ to ‘position.’

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iv) Probe casing was lowered and watched until it stabilise on the sample. v) Then, the toggle switch was returned to the ‘neutral’ position. vi) Current source was subsequently switched on. vii) Current was set to 4.53mA for extrinsic samples and 4.53µA for intrinsic samples.

Nanovolt meter then reads the value of the voltage. viii) Resistivity was calculated using equation 9 with the t value being 0.05cm. ix) The current source was shut off after measurement was completed. x) Probe station toggle switch was flipped from ‘neutral’ to ‘up’. xi) Toggle switch was then put back to ‘neutral’ position after the probe casing was all the way up. xii) Steps (iii) to (xi) was repeated for other samples. xiii) After all measurements are done, the source meter and nanovolt meter are switched out.

Calculation Equation (9) was used to calculate the electrical resistivity and Equation (1) to calculate the conductivity of all materials. Charge concentration can be determined by using Equation (7) and (8) (number of charges per cubic cm) for the semiconductor materials measured, assuming hole mobility and electron mobility at room temperature are 500 cm2/V-s and 1400 cm2/V-s respectively, and e= 1.6x1019C.

5. Experimental Results Sample M1 M2 M3

Current(A) 45.3 E-03 45.3 E-03 -

0.0016 0.014 -

Voltage 0.0025 0.0145 -

PS Sn1 Sn2 Sn3 Sp1 Sp2 Sp3 U1 U2 U3

0.0022 0.0144 -

Average V 0.000002 0.000014 -

Voltage Unit mV mV -

4.53E-06 4.53E-03 4.53E-03 4.53E-03 4.53E-03 4.53E-03 4.53E-03

0.77025 0.31561 62.5871 0.73768 0.37071 0.1 0.71310

0.98752 0.31531 63.1203 0.72861 0.37601 0.11895 0.71310

0.88091 0.31502 60.5262 0.72842 0.37563 0.12118 0.70307

0.87956 0.003153 0.062078 0.73157 0.000374 0.12036 0.711986

V mV mV V mV V V

4.53E-06 4.53E-03 4.53E-03

0.409 0.373 60.706

0.418 0.265 61.776

0.443 0.289 60.627

0.423333 0.000309 0.061036

V mV mV

Table 4. Raw data obtained from experiment.

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Sample No.

Resistivity/ (Ohm.cm)

Conductivity /(Ohm.cm)^-1

Majority carrier

Charge Concentration (cm-2)

M1 M2 M3

1.00E-05 7.00E-05 8.00E-05

1.00E+05 1.43E+04 1.25E+04

electrons electrons electrons

-

PS Sn1 Sn2 Sn3 Sp1 Sp2 Sp3

4.40E+04 1.16E-02 3.10E+00 3.67E+01 1.87E-02 6.02E+00 3.56E+01

2.27E-05 8.62E+01 3.23E-01 2.72E-02 5.35E+01 1.66E-01 2.86E-02

no dominant electrons electrons electrons Holes Holes Holes

7.47E+10 3.85E+17 1.43E+15 1.21E+14 6.91E+17 2.06E+15 3.58E+14

U1 U2 U3

2.12+04 1.55E-02 3.05E+00

4.72E-05 6.47E+01 3.28E-01

-

-

Table 5. Results of Measurements and Calculation.

6. Discussion Explain why there is a large difference in electrical resistivity between metals and semiconductors? How does your experiment findings relate to the theory?

The magnitude of electrical conductivity is strongly dependent on the number of free electrons available in the conducting band. The number of free electrons in a material is related to the arrangement of the electron states or level with respect to energy, and the manner which electrons occupy the states. For metals, the highest allowed energy band gap is always partially filled, as the partially filled conduction band allows electrons to move freely. This leads to free electrons being available in the conduction band. However, for semiconductors, there are small energy gap between the filled valence band and empty conduction band. To become free so that they can contribute to the conductivity in the semiconductor, electrons must be promoted across the energy gap into the empty states at the bottom of the conduction band. This is only possible by supplying the energy difference of the band gap. Thus, few electrons can jump across the energy gap and stay in conduction band, and the conductivity of a semi-conductor would be lower than metals. Since conductivity is inversely proportional to resistivity, the resistivity of semiconductors would then be higher than metals. Experimental findings have shown that resistivity of semiconductors are higher than metals. This tallies with the theory, and further confirms that metals have higher electrical conductivity than semiconductors.

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If there is a difference in the resistivity values measured for the three metals samples, explain why? Compare the experimental results of M1, M2 and M3. Are the results as expected?

There is a difference in the resistivity values of the three metal samples. The electrical conductivity depends on number of free charged particles in the material and mobility of the charged particles in an electric field. For metals, the difference in resistivity will be due to difference in electron mobility. Electron mobility is affected by electron scattering centers and events such as dislocations of the atoms, vacancies and impurities. M1 is pure iron, the lattice structure is relatively regular. Hence conduction electrons can move smoothly with fewer obstructions. M2 and M3 are metals with impurities. M2 is stainless steel, an alloy made up of iron, 18% chromium and 9% nickel. Chromium and nickel are considered impurities and will disrupt the lattice structure of metals because the atom sizes of impurities are different from the pure metal atoms and this will increase the number of electron scattering centers thus increasing the resistivity. M3 is a cold-rolled stainless steel.

The process of cold rolling will deform the structure of the metal. Deformation destroys the lattice structure of metals, and since the lattice structure has become more irregular, the electron mobility decreases, hence decreasing conductivity. Therefore, the resistivity of cold-rolled stainless steel is higher than common stainless steel.

Explain why the semiconductor samples possess different electrical resistivity. What is the most dominating factor? You should explain it with reference to your experimental results.

We can classify semiconductors into intrinsic and extrinsic semiconductors. Intrinsic semiconductors do not contain impurity atoms while extrinsic semiconductors are doped with impurity atoms. The extra charge carriers in extrinsic semiconductors contribute to better electrical conductivity in the material. The impurity atoms also help to bridge the energy band gap between the valence and conduction band as the impurities will introduce a charge carrier that will introduce an electron in an n-type semiconductor while introducing a hole in a p-type semiconductor (which is also viewed as a positive charge carrier). With evidence from the experimental results, the conductivity of the intrinsic semiconductor PS has lower conductivity and high resistivity as compared to the extrinsic semiconductors Sn1 and Sp1.

The amount of charge carriers is also an important factor when we are talking about the electrical conduction and resistivity of a solid material. Looking at equations (6), (7) and (8), we can note that the increase in charge carriers will increase the conductivity of the solid material and reduces its resistivity. With evidence from the experimental results, when we compare Sn1, Sn2 and Sn3, we can deduce that as the amount of charge carriers decrease, the conductivity decreases and resistivity increases. Therefore, the amount of charge carriers is the dominating factor.

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Among the three specimens listed in Table 3, indentify which is intrinsic semiconductor, and which are extrinsic semiconductor, and of the two extrinsic, which has more doping. Explain.

With reference to the experimental results, the voltage for U1 falls under the voltage range of sample PS which is an intrinsic semiconductor. The voltage for U2 falls under the voltage range of sample Sn1 and the voltage for U3 falls under the voltage range of Sn2 which both are extrinsic semiconductors. Therefore, U1 is the intrinsic semiconductor while U2 and U3 are extrinsic semiconductors. U2 is the extrinsic semiconductor that has more doping as it has much higher conductivity which suggests that it has higher concentration of charge carriers.

Explain why metals are good conductors of electricity and why semiconductors have relatively poor conductivity.

The difference in metals and semi-conductors conductivity can be explained by the band theory and atomic bonding models. From the perspective of band theory, metals are good conductors of electricity because free electrons are available in the conduction band. Metals have partially filled valence band or valence band overlapping with conduction band. It allows the electrons to move freely, giving rise to conductivity. However, for semiconductors, there is a small energy gap between the valence and conduction band.

Even though, the band gap is small. Electrons must have sufficient thermal energy to move up the band gap to the conduction band. Thus, charge carriers concentration would be lesser as compared to metals, resulting in the semi-conductors having poor conductivity.

From the perspective of atomic bonding models, the bonding in metals is metallic, and they do not bond with other atoms, so, the valence electrons are relatively free to leave an atom and join another. Under the influence of an electric field, these valence electrons will get excited; increase the number of free electrons, leading to an increase in conductivity.

However, for semiconductors, covalent bonds exist. The valence electrons are bonded with individual atoms; therefore, electrons will not be mobile to conduct electricity. Assuming electron mobility is constant, since the number of electrons in metals is higher than semiconductors, the conductivity for metals would be higher.

Explain why plastic deformation (e.g cold rolling) and alloying (e.g in stainless steel) affect the electrical resistivity of metals.

Cold rolling will lead to the presence of defects. The presence of defects will lead to the increase in scattering centres which will reduce the kinetic energy of electrons, lowering the electron mobility. Alloying is the addition of a metals or non-metals to change the properties of the materials such as introducing interstitial foreign atoms distorting the planes. The existence of impurities and alloying elements will decrease the thermal and electrical conductivity causing scattering to occur more frequently when electron passes.

Since both plastic deformation and alloying leads to an increase in lattice imperfections, scattering centres increase, thus kinetic energy of the electrons will reduce, leading to a 11

decrease in electron mobility. Electron mobility is a factor that affects the conductivity.

When the electron mobility decreases, the conductivity would decrease, and resistivity would increase.

Explain the difference between intrinsic and extrinsic semiconductor.

Intrinsic semiconductor is a pure semiconductor without any impurities present. In intrinsic semiconductors, the number of free electrons equals to the number of holes. Both electron and holes contributes significantly to conduction. Its electrical conductivity is a function of temperature alone. An typical example of intrinsic semiconductor will be silicon.

Intrinsic semiconductor: σ = p|e|μh + n|e|μe σ = ni|e|(μe + μh) Where ni = n = p, μe/ μh = electron/holes mobility, |e| = electron charge, 1.6x10-19C. Extrinsic semiconductor is a semiconductor that has been doped by impurities. Conductivity by extrinsic semiconductors can be expressed by: σ = p|e|μh or σ = n|e|μe N-types semiconductors are semiconductors that have been doped with excess electrons, while p-type semiconductors are semiconductors that have been doped with excess holes.

Charge carriers which are present in excess are called dominant charger carrier. Usually a extrinsic conductor has a higher conductivity as the concentration of the dopants can be controlled. It is also a function of temperature.

Discuss the role of doping in the electrical conductivity of semiconductors.

Electrical Conductivity of semiconductors are affected by two factors, the number of free charged particles (n) in the materials and the electron mobility (μ) of charged particles.

Doping affects the two factors mentioned above. Since n and μ are directly proportionally to σ, any changes in these two factors will affect σ proportionally. Doping is the process in which the impurity atoms are added into the semiconductors. Doping will not affect intrinsic semiconductors, as both holes and electrons affect conductivity significantly. Even though the increase in charge carrier will increase the conductivity, it will also cause an increase in the scattering events, which will lead to a decrease in conductivity. However, the overall effect will be an increase in the conductivity.

7. Conclusion The conductivity and resistivity of solid materials are very dependent on the number of charge carriers and the mobility of the charge carriers in the material. Only electrons in the 12

conduction band can contribute to electrical conductivity. Presence of impurities and plastic deformation can greatly affect the charge mobility in the solid material as they act as scattering centers.

The most crucial thing to manipulating a material’s conductivity would be modifying the energy band gap, and this is done by the process of doping the material to become p type or n type semiconductor.

Therefore, metals are the best material for conducting electric current due to absence of an energy band gap followed by semiconductors which have a small energy band gap and lastly the insulators which has the largest band gap.

8. References Hyperphysics.phy-astr.gsu.edu,. (2018). Doped Semiconductors. http://hyperphysics.phyastr.gsu.edu/hbase/solids/dope.html Winner Science,. (2013). Difference between intrinsic and extrinsic semiconductors.

Retrieved September 2018, from http://www.winnerscience.com/solids-andsemiconductors/difference-between-intrinsic-and-extrinsic-semiconductors/ Chemwiki.ucdavis.edu,. (2018). Band Theory of Semiconductors - Chemwiki. Retrieved 11 February 2018, from http://chemwiki.ucdavis.edu/u_Materials/Electronic_Properties/Band_Theory_of_Semicon ductors (2018). Retrieved from http://articles.adsabs.harvard.edu//full/1952AuSRA...5..119B/0000119.000.html Lab Manual: Electrical Properties of Materials, Nanyang Technological University, 2018

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