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DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

JODHPUR INSTITUTE OF ENGINEERING AND TECHNOLOGY NH – 65, MOGRA, JODHPUR 342 002.

PRACTICAL TRAINING REPORT

ON

CHARACTERIZATION OF MCT USING HALL MEASUREMENT

TRAINING AT

SOLID STATE PHYSICS LABORATORY

DRDO TIMARPUR

DELHI - 110054

SUBMITTED BY UDAY KUMAR

(VII SEMESTER) (2011-12)

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Certificate This to certify that Mr. Uday Kumar student of 7th semester ECE, JIET

Jodhpur has undergone 4week summer training programme in INFRARED division from July 1, 2011 to July 31, 2011 on HALL MEASUREMENTS. This candidate had a good code of conduct and sincerity towards his tasks during the course of training.

I wish him success in all his future endeavors.

Dated:

Dr Rachna Manchanda

(Scientist ‘E’ SSPL,DRDO)

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Acknowledgments I would like to express my deep sense of gratitude and grateful to , Director SSPL for allowing me to carry out my training in this establishment.

While presenting this report I would like to express my deep feeling to my guide Dr Rachna Manchanda (Scientist ‘E’) and entire SSPL staff who were indispensable part of my training giving me mending guidance, inspiration, encouragement and providing me a conductive environment throughout my training in this establishment and making it a truly memorable one.

I also wish to thanks all IR group staff for their support and guidance.

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Table of Contents Contents Page

Certificate……………………………………………………………………………………………………………………………………….2

Acknowledgment……………………………………………………………………………………………………………………………...3

1.Semiconductor……………………………………………………………………………………………………………………………….6 1.1Energy Band Model………………………………………………………………………………………………………................6 1.2Intrinsic Semiconductor…………………………………………………………………………………………….…………….8 1.3Extrinsic Semiconductor………………………………………………………………………………………….…..............8 1.4Semiconductor Doping………………………………………………………………………………………………………….….9 1.5Types of Extrinsic Semiconductor…………………………………………………………………………...............10 1.5.1N Type………………………………………………………………………………………………………………………………….10 1.5.2P Type………………………………………………………………………………………………………………………………….11 1.6Conductivity of a Semiconductor…………………………………………………………………..….………………….13 1.7Effects of Temperature and Doping on Mobility of a Semiconductor………………………….13 1.8Temperature Dependence of Carrier Concentration……………………………………..…………………14 1.9Temperature Dependence of Conductivity for a Semiconductor………………..…………………15 2.Electrical Characterization Using Hall Measurement………………………………………………………..17 2.2The Hall Effect…………………………………………………………………………………………………………………………17 2.3Hall effect in semiconductors……………………………………………………………………………………………….19 2.4 The van der Pauw Technique………………………………………………………………………………………………..20 2.5 Procedure for Resistivity Measurement……………………………………………………………………………22 2.5.1 Resistivity Calculations……………….………………………………………………………………………………….23 2.6 Procedure for Hall Voltage Measurements………………………………………………………………………23 2.6.1 Hall Coefficient Calculations…………………………………………………………………………………………….24 2.6.2 Hall Mobility Calculation…………………………………………………………………………………………………….25 2.7 Experimental Setup for Hall Measurement………………………………………………………………………25 2.8 Recommended Equipments……………………………………………………………………………………………………26

3.MCT……………………………………………………………………………………………………………………………………………….30 3.1 Growth Techniques………………………………………………………………………………………………………………….30 3.2 Growth of HgCdTe by Liquid Phase Epitaxy……………………………………………………………………30 3.3 Three main approaches for LPE growth of MCT………………………………………………………………31 3.3.1 Tipping LPE………………………………………………………………………………………………………………………..31 3.3.2 Dipping LPE……………………………………………………………………………………………………………………….31

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3.3.3 Sliding Boat LPE………………………………………………………………………………………………………………32 3.4 Properties…………………………………………………………………………………………………………………………………32

Result……………………………………………………………………………………………………………………………………………….34 References………………………………………………………………………………………………………………………………………35

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1. Semiconductor

A semiconductor is a material with electrical conductivity due to electron flow (as opposed to ionic conductivity) intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter. Semiconductor materials are the foundation of modern electronics, including radio, computers, telephones, and many other devices. Such devices include transistors, solar cells, many kinds of diodes including the light-emitting diode, the silicon controlled rectifier, and digital and analog integrated circuits. Similarly, semiconductor solar photovoltaic panels directly convert light energy into electrical energy. In a metallic conductor, current is carried by the flow of electrons. In semiconductors, current is often schematized as being carried either by the flow of electrons or by the flow of positively charged "holes" in the electron structure of the material. Actually, however, in both cases only electron movements are involved.

Common semiconducting materials are crystalline solids, but amorphous and liquid semiconductors are known. These include hydrogenated amorphous silicon and mixtures of arsenic, selenium and tellurium in a variety of proportions. Such compounds share with better known semiconductors intermediate conductivity and a rapid variation of conductivity with temperature, as well as occasional negative resistance. Such disordered materials lack the rigid crystalline structure of conventional semiconductors such as silicon and are generally used in thin film structures, which are less demanding for as concerns the electronic quality of the material and thus are relatively insensitive to impurities and radiation damage. Organic semiconductors, that is, organic materials with properties resembling conventional semiconductors, are also known.

Silicon is used to create most semiconductors commercially. Dozens of other materials are used, including germanium, gallium arsenide, and silicon carbide. A pure semiconductor is often called an “intrinsic” semiconductor. The electronic properties and the conductivity of a semiconductor can be changed in a controlled manner by adding very small quantities of other elements, called “dopants”, to the intrinsic material. In crystalline silicon typically this is achieved by adding impurities of boron or phosphorus to the melt and then allowing the melt to solidify into the crystal. This process is called "doping".

1.1 Energy-band Model

The energy-band model is applied to represent the conditions (esp. the energy levels) of the electrons in a solid. In this model the assumption is made that electrons can only take on discrete energy levels (W) inside the bands, all levels between the bands are not permitted. In solids, there are two basically distinct possibilities. If the highest energy-band (conduction band) is only partly occupied by electrons, then the solid is called a conductor because the electrons find enough unoccupied energy levels in the conduction band, which makes charge transport easy. If the highest energy-band is completely occupied at the temperature of 0 Kelvin, then we deal with either a semiconductor (SC) or an insulator. Semiconductors differ from insulators in the width of the gap between the fully occupied valence band (WV) and the empty conduction band (SC < 5eV, insulator > 5eV).

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Fig. 1: Energy-band model for metals, semiconductors and insulators

With semiconductors, it is possible to convert the energy of the solar radiation into electric energy. Theoretically, each absorbed light quantum (photon) could generate an electron-hole pair. If the energy of the photon surpasses the band gap, then such a generation takes place. The surplus energy is converted into heat. In order to generate more than one electron-hole pair, the photon must provide a multiple of the energy of the band gap. This generation process is called intrinsic photoelectric effect; in contrast to the extrinsic photoelectric effect where electrons come out of the solid, here, the electrons stay inside the solid as free charge-carriers.

Since different semiconductor materials have different band gaps, a material has to be selected that is suitable to the solar radiation spectrum. The maximum photovoltaic efficiency represents the percentage of the solar radiation energy that can be transformed into charge carrier pairs.

By means of the maximum photovoltaic efficiency, those materials can be selected which are especially suitable for the solar spectrum

Fig. 3: Maximum efficiency values of several semiconductors

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The diagram shows the relation between the maximum efficiency and the band gap. Moreover, it shows the band gaps of some semiconductors. We can see that the band gap of silicon lies very near to the optimum of 0.44. This representation is only correct if we assume that every photon is absorbed; in reality this is not attainable. In addition, there are losses due to reflection and transmission, which are also neglected.

1.2 Intrinsic Semiconductor

An intrinsic semiconductor, also called an undoped semiconductor or i-type semiconductor, is a pure semiconductor without any significant dopant species present. The number of charge carriers is therefore determined by the properties of the material itself instead of the amount of impurities. In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p.

The electrical conductivity of intrinsic semiconductors can be due to crystal defects or to thermal excitation. In an intrinsic semiconductor the number of electrons in the conduction band is equal to the number of holes in the valence band. An example is Hg0.8Cd0.2Te at room temperature.

An indirect band gap intrinsic semiconductor is one where the maximum energy of the valence band occurs at a different k (k-space wave vector) than the minimum energy of the conduction band. Examples include silicon and germanium. A direct band gap intrinsic semiconductor is one where the maximum energy of the valence band occurs at the same k as the minimum energy of the conduction band. Examples include gallium arsenide.

A silicon crystal is different from an insulator because at any temperature above absolute zero temperature, there is a finite probability that an electron in the lattice will be knocked loose from its position, leaving behind an electron deficiency called a "hole".

If a voltage is applied, then both the electron and the hole can contribute to a small current flow.

The conductivity of a semiconductor can be modeled in terms of the band theory of solids. The band model of a semiconductor suggests that at ordinary temperatures there is a finite possibility that electrons can reach the conduction band and contribute to electrical conduction.

The term intrinsic here distinguishes between the properties of pure "intrinsic" silicon and the dramatically different properties of doped n-type or p-type semiconductors.

1.3 Extrinsic semiconductor

An extrinsic semiconductor is a semiconductor that has been doped, that is, into which a doping agent has been introduced, giving it different electrical properties than the intrinsic (pure) semiconductor.

Doping involves adding dopant atoms to an intrinsic semiconductor, which changes the electron and hole carrier concentrations of the semiconductor at thermal equilibrium.

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Dominant carrier concentrations in an extrinsic semiconductor classify it as either an n-type or p-type semiconductor. The electrical properties of extrinsic semiconductors make them essential components of many electronic devices.

1.4 Semiconductor doping

Semiconductor doping is the process that changes an intrinsic semiconductor to an extrinsic semiconductor. During doping, impurity atoms are introduced to an intrinsic semiconductor. Impurity atoms are atoms of a different element than the atoms of the intrinsic semiconductor. Impurity atoms act as either donors or acceptors to the intrinsic semiconductor, changing the electron and hole concentrations of the semiconductor. Impurity atoms are classified as donor or acceptor atoms based on the effect they have on the intrinsic semiconductor.

Donor impurity atoms have more valence electrons than the atoms they replace in the intrinsic semiconductor lattice. Donor impurities "donate" their extra valence electrons to a semiconductor's conduction band, providing excess electrons to the intrinsic semiconductor. Excess electrons increase the electron carrier concentration (n0) of the semiconductor, making it n-type.

Acceptor impurity atoms have less valence electrons than the atoms they replace in the intrinsic semiconductor. They "accept" electrons from the semiconductor's valence band. This provides excess holes to the intrinsic semiconductor. Excess holes increase the hole carrier concentration (p0) of the semiconductor, creating a p-type semiconductor.

Intrinsic semiconductor Donor atoms Acceptor

atoms

Group IV semiconductors

Silicon, Germanium

Phosphorus, Arsenic

Boron, Aluminium

Group III-V semiconductors

Aluminum phosphide, Aluminum arsenide, Gallium arsenide, Gallium nitride

Selenium, Tellurium, Silicon, Germanium

Beryllium, Zinc, Cadmium, Silicon, Germanium

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Semiconductors and dopant atoms are defined by the column of the periodic table of elements they fall in. The column definition of the semiconductor determines how many valence electrons its atoms have and whether dopant atoms act as the semiconductor's donors or acceptors.

Group IV semiconductors use group V atoms as donors and group III atoms as acceptors.Group III-V semiconductors, the compound semiconductors, use group VI atoms as donors and group II atoms as acceptors. Group III-V semiconductors can also use group IV atoms as either donors or acceptors. When a group IV atom replaces the group III element in the semiconductor lattice, the group IV atom acts as a donor. Conversely, when a group IV atom replaces the group V element, the group IV atom acts as an acceptor. Group IV atoms

can act as both donors and acceptors; therefore, they are known as amphoteric impurities.

1.5 Types of extrinsic semiconductor

1.5.1 N type semiconductors

Band structure of an n-type semiconductor. Dark circles in the conduction band are electrons and light circles in the valence band are holes. The image shows that the electrons are the majority charge carrier.

Extrinsic semiconductors with a larger electron concentration than hole concentration are known as n-type semiconductors. The phrase 'n-type' comes from the negative charge of the electron. In n-type semiconductors, electrons are the majority carriers and holes are the minority carriers. N-type semiconductors are created by doping an intrinsic semiconductor with donor impurities. In an n-type semiconductor, the Fermi energy level is greater than that of the intrinsic semiconductor and lies closer to the conduction band than the valence band. N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material (e.g. phosphorus in silicon). This creates an excess of negative (n-type) electron charge carrier. Semiconductors

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are defined by their unique electric conductive behavior. Metals are good conductors because at their Fermi level, there is a large density of energetically available states that each electron can occupy. Electrons can move quite freely between energy levels without a high energy cost. Metal conductivity decreases with temperature increase because thermal vibrations of crystal lattice disrupt the free motion of electrons. Insulators, by contrast, are very poor conductors of electricity because there is a large difference in energies (called a band gap) between electron-occupied energy levels and empty energy levels that allow for electron motion.

Insulator conductivity increases with temperature because heat provides energy to promote electrons across the band gap to the higher electron conduction energy levels (called the conduction band). Semiconductors, on the other hand, have an intermediate level of electric conductivity when compared to metals and insulators. Their band gap is small enough that small increase in temperature promotes sufficient number of electrons (to result in measurable currents) from the lowest energy levels (in the valence band) to the conduction band. This creates electron holes, or unoccupied levels, in the valence band, and very loosely held electrons in the conduction band. An intrinsic semiconductor is made up ideally of one pure element, typically silicon. At room temperature, the conductivity of intrinsic semiconductors is relatively low. Conductivity is greatly enhanced by a process called doping, in which other elements are added to the intrinsic crystal in very small amounts to create what is called an extrinsic semiconductor. When the dopant provides extra electrons to the host, the product is called an n-type semiconductor. The process of doping is described as it introduces energy levels into band gap; those levels are filled with electrons and lie close to the conduction band so that even slight thermal agitation can release them into the conduction band.

It should be noted, that the negative charge of the electrons is balanced by an equivalent positive charge in the center of the impurity atoms. Therefore, the net electrical charge of the semiconductor material is not changed.

1.5.2 P-type semiconductors

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Band structure of a p-type semiconductor. Dark circles in the conduction band are electrons and light circles in the valence band are holes. The image shows that the holes are the majority charge carrier

As opposed to n-type semiconductors, p-type semiconductors have a larger hole concentration than electron concentration. The phrase 'p-type' refers to the positive charge of the hole. In p-type semiconductors, holes are the majority carriers and electrons are the minority carriers. P-type semiconductors are created by doping an intrinsic semiconductor with acceptor impurities. P-type semiconductors have Fermi energy levels below the intrinsic Fermi energy level. The Fermi energy level lies closer to the valence band than the conduction band in a p-type semiconductor.

P-type semiconductor (P for Positive) is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers (in this case positive).When the doping material is added, it takes away (accepts) weakly bound outer electrons from the semiconductor atoms. This type of doping agent is also known as an acceptor material and the vacancy left behind by the electron is known as a hole.

The purpose of P-type doping is to create an abundance of holes. In the case of silicon, a trivalent atom (typically from Group 13 of the periodic table, such as boron or aluminium) is substituted into the crystal lattice. The result is that one electron is missing from one of the four covalent bonds normal for the silicon lattice. Thus the dopant atom can accept an electron from a neighboring atom's covalent bond to complete the fourth bond. This is why such dopants are called acceptors. The dopant atom accepts an electron, causing the loss of half of one bond from the neighboring atom and resulting in the formation of a "hole". Each hole is associated with a nearby negatively charged dopant ion, and the semiconductor remains electrically neutral as a whole. However, once each hole has wandered away into the lattice, one proton in the atom at the hole's location will be "exposed" and no longer cancelled by an electron. For this reason a hole behaves as a quantity of positive charge. When a sufficiently large number of acceptor atoms are added, the holes greatly outnumber the thermally excited electrons. Thus, the holes are the majority carriers, while electrons are the minority carriers in P-type materials. Blue diamonds (Type IIb), which contain boron (B) impurities, are an example of a naturally occurring P-type semiconductor.

Therefore, to a first approximation, sufficiently doped P-type semiconductors can be thought of as only conducting holes.

1.5.3 Utilization of extrinsic semiconductors

Extrinsic semiconductors are components of many common electrical devices. A semiconductor diode (devices that allow current in only one direction) consists of p-type and n-type semiconductors placed in junction with one another. Currently, most semiconductor diodes use doped silicon or germanium.

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Transistors (devices that enable current switching) also make use of extrinsic semiconductors. Bipolar junction transistors (BJT) are one type of transistor. The most common BJTs are NPN and PNP type. NPN transistors have two layers of n-type semiconductors sandwiching a p-type semiconductor. PNP transistors have two layers of p-type semiconductors sandwiching an n-type semiconductor.

Field-effect transistors (FET) are another type of transistor implementing extrinsic semiconductors. As opposed to BJTs, they are unipolar and considered either N-channel or P-channel. FETs are broken into two families, junction gate FET (JFET) and insulated gate FET (IGFET).

Other devices implementing the extrinsic semiconductor:

• Lasers • Solar cells • Photodetectors • Light-emitting diodes • Thyristors

1.6 Conductivity of a Semiconductor

The conductivity of a semiconductor is given by:

σ µ µ= +q n pn p( ) ……….(1)

where µn and µp refer to the mobilities of the electrons and holes, and n and p refer to the density of electrons and holes, respectively. A doped semiconductor, majority carriers greatly outnumber minority carriers, so that Equation 1 can be reduced to a single term involving the majority carrier.

1.7 Effects of Temperature and Doping on Mobility of a Semiconductor

Conductivity of a material is determined by two factors: the concentration of free carriers available to conduct current and their mobility (or freedom to move). In a semiconductor, both mobility and carrier concentration are temperature dependent. Thus, it is important to view the conductivity as a function of temperature which is expressed by: ( ) ( ) ( ) ( )[ ]σ µ µ= +q T n T T p Tn p …………… Error! Bookmark not defined.

There are two basic types of scattering mechanisms that influence the mobility of electrons and holes: lattice scattering and impurity scattering. We have already discussed lattice scattering in the context of metals; we know that lattice vibrations cause the mobility to decrease with increasing temperature.

(2)

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However, the mobility of the carriers in a semiconductor is also influenced by the presence of charged impurities. Impurity scattering is caused by crystal defects such as ionized impurities. At lower temperatures, carriers move more slowly, so there is more time for them to interact with charged impurities. As a result, as the temperature decreases, impurity scattering increases, and the mobility decreases. This is just the opposite of the effect of lattice scattering.

The total mobility then is the sum of the lattice-scattering mobility and the impurity-scattering mobility. Figure 1 shows how the total mobility has a temperature at which it is a maximum. The approximate temperature dependence of mobility due to lattice scattering is T-3/2 , while the temperature dependence of mobility due to impurity scattering is T+3/2 (see Figure 1). In practice, impurity scattering is typically only seen at very low temperatures. In the temperature range we will measure, only the influence of lattice scattering will be expected.

T(K)(log scale)

( )µ cm V s2 / ?(log scale)

Impurity Latticescattering scattering

T 32 T − 3

2

Figure1. Approximate temperature dependence of mobility with both lattice and impurity scattering

1.8 Temperature Dependence of Carrier Concentration

The carrier concentration in a semiconductor is also affected by temperature. The intrinsic carrier concentration is governed by:

ni T( ) = 22πkT

h2

32

mn*mp

*( )34 exp

−Eg

2kT

…………. (3)

where the exponential temperature dependence dominates ni(T). To determine the total carrier concentration, we must also consider space-charge neutrality:

n T( ) = ND+ T( )− NA

− +ni

2 T( )n T( )

and: p T( ) = NA− T( )− ND

+ T( )+ni

2 T( )p T( )

…… (4)

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For a doped semiconductor, the temperature dependence of electron concentration can be seen in Figure 2. At very low temperatures (large 1/T), negligible intrinsic electron-hole-pairs (EHPs) exist (ni is very small), and the donor electrons are bound to the donor atoms. This is known as the ionization (or freeze-out) region. As the temperature is raised, increased ionization occurs and at about 100K all of the donor atoms are ionized, at which point the carrier concentration is determined by doping. The region where every available dopant has been ionized is called the extrinsic (or saturation) region. In this region, an increase in temperature produces no increase in carrier concentration. Referring to Equation 4, this is the region where ( )N T ND D

+ = , ( )N T NA A− = , and ( )n T N Ni D A<< − . At high temperatures, the

thermally generated intrinsic carriers outnumber the dopants (ni> N ND A− ). In this intrinsic region, carrier concentration increases with temperature as shown in Equation 3 because ni has become the dominant term of Equation 4.

0 2 4 6 8 10 12

Extrinsic

Intrinsic

Ionization

1000/T (K)-1

1011

1013

1012

1017

1016

1015

1014n0 (cm-1)

Figure 2. Carrier concentration vs. reciprocal temperature for silicon doped with 1015 donors/cm3

1.9 Temperature Dependence of Conductivity for a Semiconductor

Remember that Equation 1 showed that conductivity depends on both carrier concentration and mobility, so there are a variety of possible temperature dependencies for conductivity. For instance, at fairly low temperatures (less than 200K), the dominant

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scattering mechanism might be impurity scattering (µ α T3/2) while the carrier concentration is determined by extrinsic doping (n = ND+), therefore, conductivity would be seen to

increase with temperature (σ α T3/2). Other possibilities, depending on the material, doping, and temperature will show different temperature dependence of conductivity. One particularly interesting case occurs at high temperatures (above 400K or higher) when carrier concentration is intrinsic (Equation 4) and mobility is dominated by lattice scattering (µ α T-3/2). In such cases, the conductivity can easily be shown to vary with temperature as:

σ ∝ exp−Eg

2kT

…………. (5)

In this case, conductivity depends only on the semiconductor bandgap and the temperature. In this temperature range, measured conductivity data can be used to determine the semiconductor bandgap energy, Eg.

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2. Electrical Characterization Using Hall Measurement

2.1 Introduction

The objective is to describe the hall measurement technique for determining the carrier density and mobility in semiconductor materials. Introductory description of the hall measurement technique covering basic principles, equipment and recommended procedures.

Hall measurement is the one and only method for the characterization of materials. This method is used all over the world for characterization of materials. HgCdTe known as MCT (Mercury cadmium telluride) is a semiconductor material which is formed by Epitaxial growth processes and used in defense technologies as a sensor and has a wide range of other applications. In this sample four connections are made then without applying magnetic field resistivity measurement is done. After that magnetic field is applied and Hall measurement is done at room temperature and at 77K. Using these observations charge density, mobility of charge carriers and other behavior of material is determined.

The importance of the Hall Effect is supported by the need to determine accurately carrier density, electrical resistivity and mobility of carriers in semiconductors. The Hall Effect provides a relatively simple method for doing this. Because of its simplicity, low cost, and fast turnaround time, it is an indispensable characterization technique in the semiconductor industry and in research laboratories. Furthermore two Nobel prizes (1985, 1998) are based upon the Hall Effect.

The history of Hall Effect begins in 1879 when Edwin H Hall discovered that a transverse voltage appeared across a current carrying thin metal strip in an applied magnetic field. Until that time, electrical measurements provided only the carrier density mobility product and the separation of these two important physical quantities had to rely on other difficult measurements. The discovery of Hall Effect enabled a direct measure of the carrier density. The polarity of this transverse Hall voltage proved that it is in fact electrons that are physically moving in an electric current. Development of the technique has since led to a mature and practical tool, which today is used routinely for characterizing the electrical properties and quality of almost all of the semiconductor materials used by the industry and in research labs throughout the world.

2.2 The Hall Effect

The Hall Effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879.

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The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. It is a characteristic of material from which the conductor is made, since its value depends on the type, number and properties of the charge carriers that constitute the current. The Hall effect was discovered in 1879 by Edwin Hall while he was working on his doctoral degree at Johns Hopkins University in Baltimore, Maryland. His measurements of the tiny effect produced in the apparatus he used was an experimental tour de force, accomplished 18 years before the electron was discovered.

The Hall effect comes about due to the nature of the current in a conductor. Current consists of the movement of many small charge carriers, typically electrons, holes, ions or all three. Moving charges experience a force, called the Lorentz force, when a magnetic field is present that is perpendicular to their motion. When such a magnetic field is absent, the charges follow approximately straight, ‘line of sight’ paths between collisions with impurities, phonons, etc. However, when a perpendicular magnetic field is applied , their path between collisions are curved so that moving charges accumulate on face of the material. This leaves equal and opposite charges exposed on the other face, where there is a scarcity of mobile charges. The result is an asymmetric distribution of charge density across the Hall element that is perpendicular to both the ‘line of sight’ path and the applied magnetic field. The separation of charge establishes an electric field that opposes the migration of further charge, so a steady electrical potential builds up for as long as the charge is flowing.

It shall be noted that in the classical view, there are only electrons moving in the same average direction both in the case of electron or hole conductivity. This cannot explain the opposite sign of the Hall effect observed. The difference is that electrons in the upper bound of the valence band have opposite group velocity and wave vector direction when moving, which can be effectively treated as if positively charged particles (holes) moved in the opposite direction to that of the electrons

For a simple metal where there is only one type of charge carrier (electrons) the Hall voltage VH is given by

where I is the current across the plate length, B is the magnetic flux density, d is the depth of the plate, e is the electron charge, and n is the charge carrier density of the carrier electrons.

The Hall coefficient is defined as

where j is the current density of the carrier electrons, and Ey is the induced electric field. In SI units, this becomes

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As a result, the Hall effect is very useful as a means to measure either the carrier density or the magnetic field.

One very important feature of the Hall effect is that it differentiates between positive charges moving in one direction and negative charges moving in the opposite. The Hall effect offered the first real proof that electric currents in metals are carried by moving electrons, not by protons. The Hall effect also showed that in some substances (especially p-type semiconductors), it is more appropriate to think of the current as positive "holes" moving rather than negative electrons. A common source of confusion with the Hall Effect is that holes moving to the left are really electrons moving to the right, so one expects the same sign of the Hall coefficient for both electrons and holes. This confusion, however, can only be resolved by modern quantum mechanical theory of transport in solids.

It must be noted though that the sample inhomogeneity might result in spurious sign of the Hall effect, even in ideal van der Pauw configuration of electrodes. For example, positive Hall effect was observed in evidently n-type semiconductors.

2.3 Hall effect in semiconductors

When a current-carrying semiconductor is kept in a magnetic field, the charge carriers of the semiconductor experience a force in a direction perpendicular to both the magnetic field and the current. At equilibrium, a voltage appears at the semiconductor edges.

The simple formula for the Hall coefficient given above becomes more complex in semiconductors where the carriers are generally both electrons and holes which may be present in different concentrations and have different mobilities. For moderate magnetic fields the Hall coefficient is

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where is the electron concentration, is the hole concentration, is the electron mobility , the hole mobility and the absolute value of the electronic charge.

For large applied fields the simpler expression analogous to that for a single carrier type holds.

with

2.4 The van der Pauw Technique

In order to determine both the mobility μ and the sheet density ns, a combination of a resistivity measurement and a Hall measurement is needed. We discuss here the van der Pauw technique which, due to its convenience, is widely used in the semiconductor industry to determine the resistivity of uniform samples (References 3 and 4). As originally devised by van der Pauw, one uses an arbitrarily shaped (but simply connected, i.e., no holes or non conducting islands or inclusions), thin-plate sample containing four very small ohmic contacts placed on the periphery (preferably in the corners) of the plate. A schematic of a rectangular van der Pauw configuration is shown in Fig. 2. The objective of the resistivity measurement is to determine the sheet resistance RS. Van der Pauw demonstrated that there are actually two characteristic resistances RA and RB, associated with the corresponding terminals shown in Fig. 2. RA and RB are related to the sheet resistance RS through the van der Pauw equation Exp (-πRA/RS) + exp (-πRB/RS) = 1 ………… (3) which can be solved numerically for RS. The bulk electrical resistivity ρ can be calculated using ρ = RSd. …………. (4) To obtain the two characteristic resistances, one applies a dc current I into contact 1 and out of contact 2 and measures the voltage V43 from contact 4 to contact 3 as shown in Fig. 2. Next, one applies the current I into contact 2 and out of contact 3 while measuring the voltage V14 from contact 1 to contact 4. RA and RB are calculated by means of the following expressions: RA = V43/I12 and RB = V14/I23. ……… (5)

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The objective of the Hall measurement in the van der Pauw technique is to determine the sheet carrier density ns by measuring the Hall voltage VH. The Hall voltage measurement consists of a series of voltage measurements with a constant current I and a constant magnetic field B applied perpendicular to the plane of the sample. Conveniently, the same sample, shown again in Fig. 3, can also be used for the Hall measurement. To measure the Hall voltage VH, a current I is forced through the opposing pair of contacts 1 and 3 and the Hall voltage VH (= V24) is measured across the remaining pair of contacts 2 and 4. Once the Hall voltage VH is acquired, the sheet carrier density ns can be calculated via ns = IB/q|VH| from the known values of I, B, and q. A second type of geometry that is sometimes used includes the parallelepiped or bridge-type sample. These may be more desirable in the case of anisotropic material properties. the restrictions on shape and size are more rigid than those of the van der Pauw specimen, but measurements can be made using either a six or an eight contact configuration. The bridge-type specimen differs from the parallelepiped in that the contacts are placed on arms that branch off the main parallelepiped base. The details of this method can be obtained from the ASTM document listed in the references. There are practical aspects which must be considered when carrying out Hall and resistivity measurements. Primary concerns are (1) ohmic contact quality and size, (2) sample uniformity and accurate thickness determination, (3) thermo magnetic effects due to nonuniform temperature, and (4) photoconductive and photovoltaic effects which can be minimized by measuring in a dark environment. Also, the sample lateral dimensions must be large compared to the size of the contacts and the sample thickness. Finally, one must accurately measure sample temperature, magnetic field intensity, electrical current, and voltage.

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Fig. 2 Van der Pauw Resistivity Measurement

Fig. 3 Hall Measurement

2.5 Procedure for Resistivity Measurement

Following general procedure to measure parameter necessary to calculate sample resistivity. The procedure assumes that the sample has been stabilized at the desired operating temperature and will remain at that temperature and will remain at that temperature throughout the tests.

1. Turn on the instruments to warm up. 2. Place the models 196 and 485 in autoranging. Be sure the model 196 is in DCV

function. 3. Set the model 705 scanner to the matrix mode. 4. Program cross point 5,4 to select low or high resistivity. This cross point should be

open for low resistivity and it should be closed for high resistivity. 5. Program the model 220 current to the desired value in the range of 500fA to 100mA. 6. Close the cross points necessary to measure V1. 7. Turn on the 220 output by pressing the operate key. 8. Measure V1 by noting the reading on the model 196. Also note the current measured

by the model 485 picoammeter. 9. Turn off the model 220 output and open the crosspoints. 10. Measure and record the remaining voltages (V2 through V8) by closing the appropriate

cross points.

Table 2.1 Cross point Summary for Resistivity Measurement

Voltage Designation

Cross Points Closed (Column, Row)

Current Applied Between

Voltage Measured Between

V1 1,2 2,1 3,3 4,4 1-2 3-4

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V2 2,2 1,1 3,3 4,4 2-1 3-4 V3 2,2 1,3 3,4 4,1 2-3 4-1 V4 2,3 1,2 3,4 4,1 3-2 4-1 V5 2,3 1,4 3,1 4,2 3-4 1-2 V6 2,4 1,3 3,1 4,2 4-3 1-2 V7 2,4 1,1 3,2 4,3 4-1 2-3 V8 2,1 1,4 3,2 4,3 1-4 2-3

2.5.1 Resistivity Calculations

ρA, ρB = Resistivities in ohm cm

TS = sample thickness in cm

V 1 -V8 = Voltages measured

I = current through samples in amperes

FA,fB = geometrical factors which are based on sample symmetry and are related to two resistance ratio QA & QB.

Note : fA = fB = 1 for perfect symmetry

QA & QB can be calculated using the measured voltages

Q and f are related as follows

2.6 Procedure for Hall Voltage Measurements

1. Turn on the instruments and allow them to warm up for the prescribed period for rated accuracy.

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2. Place the model 196 and 485 in autoranging. Be sure that 196 is in DCV function. 3. Using front panel program, set the model 705 scanner to matrix mode. 4. Program crosspoint 5,4 to select low or high resistivity.This crosspoint should be open

for low resistivity and it should be closed for high resistivity. 5. Program the model 220 current to the desired value in the range of 500fA to 100mA. 6. Close crosspoint 2,1:1,3:3,4 and 4,2 then zero the model 196 and enable the model

485 in relative function. 7. Turn on the model 220 output by pressing the operate key. 8. Turn on the magnetic field and set it to the desired positive flux density(+B). 9. Measure the voltage V1 by noting the model 196 reading. 10. Note and record the current being measured by the model 485 picoammeter. 11. Measure and record V2 through V4 by closing the appropriate cross points. 12. Reverse the magnetic field and measure V5 to V8 now with negative flux (-B).

Table 2.2 Cross point Summary for Hall Voltage Measurement

Voltage Designation

Flux Cross Points Closed (Columns, Row)

Current Applied Between

Voltage Measured Between

V1 +B 2,1 1,3 3,4 4,2 1-3 4-2 V2 +B 2,3 1,1 3,4 4,2 3-1 4-2 V3 +B 2,2 1,4 3,1 4,3 2-4 1-3 V4 +B 2,4 1,2 3,1 4,3 4-2 1-3 V5 -B 2,1 1,3 3,4 4,2 1-3 4-2 V6 -B 2,3 1,1 3,4 4,2 3-1 4-2 V7 -B 2,2 1,4 3,1 4,3 2-4 1-3 V8 -B 2,4 1,2 3,1 4,3 4-2 1-3

2.6.1 Hall Coefficient Calculations

Where, RHC & RHD are Hall coefficients in cm2/C

.ts is the sample thickness in cm

B is the magnetic flux in Gauss

I is the current measured by the Model 196

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2.6.2 Hall Mobility Calculation

µΗ = Ηall mobility in cm2/Vs

RH = average Hall coefficient in cm3

ρAVG = the average resistivity in Ωcm

2.7 Experimental Setup for Hall Measurement

Fig 4 Basic Hall System Configuration

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Fig 5 Experimental Setup

2.8 Recommended Equipments

Equipment Description

Model 196 DMM Measure Sample Voltage

Model 220 Current Source

Supply Sample Current

Model 485 picoammeter Measure Sample Current

Model 705 and 706 scanners

Control Hall Effect card

Cryostat Set sample temperature

Magnet Apply Magnetic Field

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Magnet Power Supply Supply Magnet Power

Gauss Meter Used to measure actual magnetic field strength

Model 196 DMM

The model 196 is recommended for measuring the voltage across the sample under test. Important Model 196 features include:

• 100nV resolution.

• High input resistance (>1GΩ on 300mV and 3V ranges) for minimum sample loading.

• 61/2 digit display resolution.

• Autoranging.

• IEEE-488 bus configuration.

Model 220 Current Source

The Model 220 Current Source is recommended for applying the current to the sample under test. Key Model 220 features include

• ±0.5pA to ±101mA DC current output.

• 1014 Ω output resistance.

• Programmable voltage compliance limit.

• Complete IEEE-488 bus programmability.

Model 485 Picoammeter

The Model 485 picoammeter can be used to monitor the current being applied to the sample under test. Although not absolutely essential for a measurement system, the use of the Model 485 is recommended to maximize accuracy, especially when testing high resistivity samples. Important Model 485 features include

• 0.1 pA resolution, 2mA maximum input current.

• 200µV maximum voltage burden

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• Autoranging

• 41/2 digit display resolution.

• IEEE-488 bus operation

Model 705 and 706 Scanners

The Model 7065 Hall Effect Card is designed to plug into the Models 705 or 706 Scanners. The Model 705 can accommodate two cards, while the Model 706 can accommodate two cards, while the Model 706 can handle up to 10 scanner cards. Other key features common to both scanner mainframes include

• Full IEEE-488 bus programmability.

• Daisy chain operation allowing upto four slave mainframes to be controlled with one master.

• Front panel programs for easier system configuration.

• Built-in day/time clock for time stamping of data.

Cryostat

The apparatus consists of a micro-miniature refrigerator (inside the small metal vacuum enclosure, which contains a window through which you can see the semiconductor sample), a tank of high pressure nitrogen for the refrigerating fluid, and a vacuum pump and manifold. The apparatus uses the Joule-Thompson expansion of a high pressure gas to achieve enough cooling to liquefy the gas in a small reservoir underneath the sample mount. The refrigerator is made up of a laminated set of glass slides, each of which has micro-channels etched into it, providing a serpentine path for the gas to proceed through a heat exchanger.

The sample is mounted on a cold mount at the end of the refrigerator with thermal grease, which makes excellent thermal contact between the sample and the refrigerator. The sample can be cooled to 80 K from room temperature in about 10 minutes. The refrigerator also has a heater built in (thin wires) with which we can heat the sample or control the temperature stability.

Magnet and Magnet Power Supply

A magnet is used to apply magnetic field for Hall measurements. Magnet power supply systems use an automatic control system to control a power supply to provide precise current to a magnet.

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Gauss Meter

Gaussmeter designed for accurate measurement of magnetic field from 0.1G to 20kG is used in Hall Measurement.

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3. MCT MCT (Mercury Cadmium Telluride, HgCdTe) is an alloy of CdTe and HgTe and is

sometimes claimed to be the third semiconductor of technological importance after Silicon and Gallium Arsenide. HgCdTe is usually referred to as MerCad Telluride, MerCadTel, or simply MerCaT in the Infrared Sensors Community.

The amount of Cadmium (Cd) in the alloy can be chosen so as to tune the optical absorption of the material to the desired infrared wavelength. CdTe is a semiconductor with a bandgap of approximately 1.5eV at room temperature. HgTe is a semi-metal, hence its bandgap energy is zero. Mixing these two substances allows one to obtain any bandgap between 0 and 1.5eV.

3.1 Growth Techniques

• Liquid Phase Epitaxy.

• Molecular Beam Epitaxy.

• Metal Organic Vapour Phase Epitaxy.

3.2 Growth of HgCdTe by Liquid Phase Epitaxy

The technique of Liquid Phase Epitaxy (LPE) which has been a well established method for thin film growth of III –V compounds, Since the early 1960s, was not applied to MCT growth.

This is a very wide range of solvents available for LPE growth it is normal in semiconductor LPE to use one of the matrix species as a solvent. In case of MCT either Hg o Te can be described by

TL = 1102 + 250z + 420yz - 785y

Where y and z describe the Te rich liquid composition in the form (Hg1-zCdz)1-yTey and solid composition x is related to z by

x = z / (0.220 + 0.780z)

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3.3 Three main approaches for LPE growth of MCT

3.3.1 Tipping LPE

In case of MCT the tipping technique has been mainly used with sealed ampoules such that by tilting the furnace the LPE solution can be brought into contact within substrate which is held within graphite jig and then decanted off at the end of the cooling cycle by tilting the tube back to its starting position.

Advantages

• Growth equipment is very cheap as no gas flows and no means of controlling Hg pressure.

:

• The graphite fixture can be very simple since there is no need to provide an in-site source of Hg and solution removal is aided by gravity.

Disadvantages

• Substrate surface and solution may become contaminated before growth since there is no gas flow to remove desorbed gas.

:

• Multilayer growth is difficult.

3.3.2 Dipping LPE

• Used for both Hg & Te rich LPE growth of MCT and uses a vertical arrangement where in the substrate is secured on a silica or graphite holder and is dipped into an open crucible holding the growth solution.

• After layer growth the substrate holder is retracted and the solution drains off under gravity.

Advantages

• Good solution removal.

:

• Visibility of the solution surface to check TL

• Substrate rotation during growth to improve uniformity, large areas of growth per run and the ability to keep the substrate cool prior to the start of growth.

Disadvantages

• Need for large solution volumes, the difficulty of multilayer growth.

:

• Fact that the substrate surface passes through the solution surface prior to growth.

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3.3.3 Sliding Boat LPE

This is the most widely used technique for compound semiconductor LPE. It normally consists of a graphite boat with a recess in the base for holding the substrate wafer and a movable block with wells which contain the LPE solution and which allows the solution to be brought into the contact with substrate and then wiped off after growth.

• Efficient use of solution.

Advantage

• The ease of growing multilayers.

• Need for careful machining of boat components in order to get efficient removal of the solution after growth.

Disadvantages

• Need for precisely sized substrate wafers to fit into the recess in the boat.

3.4 Properties:

Properties are related to the lattice structure & band structure of HgCdTe Mercury Cadmium Telluride is a semimetal and Cadmium Telluride is a semiconductor. Both type of behaviour of properties exist in solid solution of two known as MCT.

(a) Energy Gap

Energy gap is the lowest photo energy for which appreciable absorption due to inter band transition occurs. In MCT energy gap is increasing function of x. At 0K for x below 0.16 the solid is semimetal for x above 0.16 at 0 K, the material is semiconductor. As x in Hg1-xCdxTe varies from 0 to 1, the energy gap varies from -0.3 to 1.6eV. High electron mobility makes it sensitive in IR & photo detectors.

By varying the alloy fraction (x) from 0 to 1 the band gap of MCT can be varied from that of semimetal HgTe(-0.3eV) to that of semiconductor CdTe(1.6eV). The band gap of MCT becomes 0 eV at x =0.15. The equation of forbidden energy gap (Eg) is related to x & T is g(x,T) = -0.302 + 1.93x – 0.81x2 + 0.832x3 + 5.35(1-2x)10-4 T, where Eg is in eV & T is in Kelvin.

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(b) Lattice Structure

MCT is an II – VI compound semiconductor. Both CdTe & HgTe of Hg1-xCdxTe are lattice matched to within 0.3% with lattice parameter of 6.462 A0 & 6.453 A0 respectively at 298K.

Thermal expansion coefficient of HgTe & CdTe are nearly same, with a value of 5x10-6 K-1 for T> 300K 4x10-6 K-1 for T<300K. The close lattice match & similar thermal expansion coefficient allows the formation of MCT.

HgCdTe is soft because it has large bond length (HgTe : 2.794 A0 & CdTe : 2.804 A0) and also bonds are covalent.

(c) Density

Density of MCT is given by the following expression 8.05 – 2.30x g/cm3 with uncertainty of 0.02 g/cm3. At room temperature density varies by .0001 g/cm3 for each degree rise in temperature.

(d) Intrinsic Carrier Concentration

The undoped ( or lightly doped with Nd ~1015 cm-3 or Na ~ 1016 cm-3) MCT behaves as intrinsic semiconductor at ambient temperature. E.g ni for MCT (x ~ 0.2) is approx 3x1016 cm-3. This provides another means of estimating x from room temperature carrier concentration (no) or alternatively by resistivity measurements. The most standard expression for ni comes to be.

. ni = (5.585 – 3.82x + 0.001753T – 0.001364xT) x 1014 Eg3/4T3/2 exp(-Eg/KT)

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Result

ρ(mΩ-cm) RH η(cm-3) µ(cm2V-s) D147-in situ annealed (25 µm)

1269 581 1.08E16 458

D-148-in situ annealed (23µm)

1269 769 1.32E16 536

D-85-10 (t ~ 28µm)

1186 729 7E15 607

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References

• www.en.wikipedia.org • www.nist.gov • tau.nanophys.kth.se • Yeager, J.R. Hall and Van der Pauw Measurements of semiconductors, Keithley

Instrum., App Note, 1984:510 • Properties of Narrow Gap Cadmium based Compounds by Peter Capper