determination of the type and the density of carriers...

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International Journal of Advanced Research in Engineering and Technology

(IJARET) Volume 7, Issue 3, May–June 2016, pp. 01–13, Article ID: IJARET_07_03_001

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ISSN Print: 0976-6480 and ISSN Online: 0976-6499

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DETERMINATION OF THE TYPE AND THE

DENSITY OF CARRIERS IN MOTE2

MASSIVE BY MEASURING THE HALL

EFFECT

Aly Mallouky

Laboratory of Computer Networks and Multimedia Technology (RITM)

EST - Hassan II University, Casablanca, Morocco

Mariam Benhadou, Abdellah Haddout

Laboratory of Industrial Management and Energy and Technology of Plastic and

Composite Materials ENSEM - Hassan II University, Casablanca, Morocco

ABSTRACT

The continuous measurements of halleffect made on monocrystalline

MoTe2 needles showed good linearity of current contacts (longitudinal). The

influence of magnetic induction on the Hall voltage VHa has been studied. Two

areas are observed: a linear growth area where the Hall RH coefficient is

almost constant and a saturation region where the Hall voltage doesn't

practically vary with induction.

In the first area, a carriers concentration about 6 1020

/m3and could be

determined through the constant area. VH behavior in the saturation zone is

explained by depletion of charge carriers by magnetic deflection. The

resistivity is studied in a temperature range from ambient to the temperature

of liquid nitrogen.

Key words: Charge Carriers, Hall Effect, Magnetic induction, Alternative

Measurement, Continuous Measurement.

Cite this article Head: Aly Mallouky, Abdellah Haddout, Mariam Benhadou.

Determination of the type and the density of carriers in MoTe2 massive by

measuring the Hall Effect. International Journal of Advanced Research in

Engineering and Technology, 7(3), 2016, pp 01–13

http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=7&IType=3

Aly Mallouky, Abdellah Haddout, Mariam Benhadou


1. INTRODUCTION

The electrical properties of compounds, having a lamellar structure type MX2 (where

M is a metal and X a chalcogen group VI B: Se, Te or S), have been studied by many

authors because of their importance in applications in devices infrared and

photovoltaic and thermoelectric.

Most results were summarized by Wilson and Yoffe [1]. In many of these studies, it

was shown that the electrical conductivity decreases exponentially when the

temperature increases. The activation energy derived from the slopes of the graphs Ln

σ = f (

), regularly grow [2, 3]. Thermoelectric power measurements (P.T.E.) obtained

by some authors in different temperature conditions and with various composition

[4,5] establishes the semiconductor character of MoTe2.Various models of band

structures have been deducted from these results [6, 7, 8]. Oslo, few authors who have

studied the Hall effect in the MoTe2. In order to supplement the results regarding

MoTe2, we performed a full characterization by Hall effect measurement. Indeed, the

Hall effect measurements allow simultaneous access to the type and the concentration

of carriers.

2. HALL EFFECT

We consider a cuboid sample subjected to the simultaneous action of orthogonals:

electric field a and magnetic induction .

The electric field animates the free charge carriers of a drive speed e carried in

the direction of a.

The magnetic induction exerts on the carriers a known force as Lorenz:

= q ˄ e (1) when the carriers are n type (electron)

= -q ˄ e (2) in the case of p type carriers (holes).

q: a hole charge (–q electron charge).

˄: Symbol of the cross product.

Figure 1 Mechanism of the hall effect

Under the effect of the Lorenz force, the trajectory of the carriers undergoes a

deviation from the direction of the applied field a and a transverse current can

appear in the sample. If the charges are not evacuated laterally, a transverse electric

field H nominated Hall field appears, opposing charge's lateral movement. This derived field in the Hall voltage, which we denote VH (Fig. 1).

At the appearance of the Hall field H, the carriers are subject to the action of a

resultant field :

= a + H (3)

Determination of The Type and The Density of Carriers In Mote2 Massive by Measuring The

Hall Effect


a is relied to the current density resulting by:

a = ρ (4)

with ρ = ; ρ denotes the electrical resistivity and σ the conductivity.

H is defined by:

H = RH. ˄ (5)

Where RH means the Hall constant

resultant field is then: = ρ + H=ρ + RH. ˄ (6) The Hall voltage VH is written (Fig. 1): VH = VM’ – VM=EH.b (7)

EH: Standard H supported by the axis Oy.

In the case of a sample having the bar shape with a rectangular section b and a

thickness a, VH may be written: VH=

.Bz.Ix (8)

Bz : component of of the axis Oz

Ix : current due to the applied field a (flowing in the direction Ox). In the case of a material containing only one type of carriers (N for example) and

subjected to a strong magnetic field, EH exerts a force H such as:

H = q. H (9)

In permanent state, FH balance the Lorentz force Fn, so that we can write:

H = - < e>˄ (10)

< e>: average training speed of the carriers.

Knowing that the flow of electrons is:

n = - ne < e> (11) e : elementary charge (e = -q).

The Hall field can be written as:

H = - (-

) ˄ (12)

Comparing to the equation (5), we can write:

RH = -

(13)

By analogy we can write RH for a type of sample P:

RH =

(14)

p: hole concentration in the sample.

Knowledge of the Hall constant and electrical conductivity provides access to the Hall

mobility of the carriers μH :

μH=׀RH׀σ (15)

3. EXPERIMENTAL PROCEDURE 3. 1 Study of the Hall Effect continuously 3.1.1 Sample Preparation

We worked on samples of MoTe2 in the needles form. On this type of samples,

making side contacts, (contact area) is not very easy. For connection to the sample

body, we used copper son.

To ensure electrical contact with the sample, we dip the end of the copper son in

silver lacquer. The silver ball, is then carefully adhered to the sample surface as

shown in Figure 2:



Figure 2 Sample preparation

3.1.2 Sampling of the Hall voltage.

Problem of misalignment of Hall contacts

The values of the voltages collected on contacts Hall (side contacts) are very low.

These are the order of tens of microvolts. Thus, misalignment of the lateral contacts

can be accompanied by a voltage drop in the body of the sample of the same order of

magnitude of the Hall voltage.

Δl is the misalignment (Fig. 3). If ρ is the resistivity of the bar, its section S and I the

current flowing through it in the longitudinal direction (electrically insulated sides),

the resistance ΔR of the volume portion (S.Δl) of the sample is expressed by :

ΔR = ρΔ

(16)

The voltage drop Vd due to misalignment Δl is written:

Vd = ΔR.I = ρ.Δ

.I (17)

If the current is constant and the section is uniform, Vd is proportional to the

misalignment. If the measurements of the Hall voltage VH are taken without

compensation of misalignment, the measured voltage V would be:

V = VH + Vd (18)

So the actual Hall voltage is no longer accessible especially as Vd is of the same order

of magnitude as VH.

In order to minimize the error introduced by the misalignment of the contact area, we

have created a voluntary misalignment as shown in Figure 3 where:

Rv: precision potentiometer (Ten Towers)

uV: high resolution microvoltmeter

I: longitudinal current due to the applied electric field a.

Figure 3 Misalignment compensation


Hall Effect


Measurement methodology

• In the absence of magnetic field, we set the resistance RV in order to obtain the

microvolt measurement near zero voltage.

• We then apply a magnetic induction B. The indication of microvoltmeter is then the

only contribution of the Hall effect.

By artifice, we could reverse the effect of the misalignment. The value of RV is

chosen sufficiently high so as not to shunt the sample volume between the contacts 1

and 2 (Fig. 3).

3.1.3 Amplification of the Hall voltage

In addition to the stress due to misalignment, the voltages induced by the surrounding

noise can affect the measurement of VH. Furthermore, the measuring circuit must

have a sufficiently high input resistance to avoid the evacuation of lateral loads (Hall

of expenses).In order to minimize the effect of noise, the Hall voltage VH is measured

using shielded cables. A measuring amplifier carefully designed is called upon to

interface the sample and microvoltmeter (Figure 4).

In the diagram of Figure 4, control elements introduced therein to compensate for the

various offset voltages and currents. Similarly, operational amplifiers are selected

according to the above measurement conditions:

Ao1 = Ao2 = LF351

Ao3 = LM725The differential mode gain of the amplifier is given by:

=

(1

+ 2

) (19)

Figure 4 Amplifier for measuring the Hall voltage

The amplifier characteristics: R1 = R3; R’1 = R’3; R2 = R4

• adjustable gain of 1 to 1000 • Input impedance of common mode: 1012Ω • Offset current at the entrie 1 pA. • Common Mode Rejection: 110 dB

• Non-linearity of about 0.01% • Differential input impedance: 1012Ω

The Hall voltage is collected between the entries E+ and E

-. The gain of the amplifier

is set at 100 for our measurements. The voltage measured by the microvolt is:

VS = 100 VH (20) Where VH is the Hall voltage sought (real).



3.1.4 sample Linearity

This is to check the ohmicity (no rectifier effect) of the contacts convey the

longitudinal current. Figure 5 shows the principle steps for construction of the sample

linearity curve.

Figure 5 Sample linearity curve

3.1.5 Effect of the magnetic induction B on the Hall voltage VH

Measurement circuit

The Hall Effect is palpable through the Hall voltage VH such that:

VH = RH (BzIx/a) (21)

a: specimen thickness (about 1 mm)

Bz: magnetic induction existing in the gap of electromagnet BRUKER type

Ix: longitudinal current supplied by a Keithley current source, VH is measured after

amplification using a Keithley microvoltmeter. Continuous measurements were

performed at ambient temperature. The measuring device is described in Figure 6.

Figure 6 Schematic of measuring circuit of the Hall voltage

Les notations qui apparaissent dans cette figure sont explicitées ci-après :

The notation that appear in this figure are explained below: E: MoTe2 sample

(R, A) amplifier made for continuous measurements (R allows zero adjustment to

make up for misalignment and A is the amplification coefficient)

I : Power source; uV: Microvoltmeter; B: Magnetic field.

3.2 Alternative measurement of Hall Effect

3.2.1 Interest of the alternative method (AC) The method of measuring the Hall voltage AC is to use a current and a magnetic

induction both alternative. The Hall voltage is proportional to the BI product

(respectively intensity of induction and the longitudinal current), it is then presented

to either the sum frequency or at the frequency difference of the current and the

magnetic field. In practice it holds the signal at the difference frequency detected by

comparing it with a reference signal having the same frequency.


Hall Effect


These considerations give the method the following advantages:

- Elimination of the sensors misalignment effect

- Removing thermovoltages

- Tensions due to noise playing in the 1/f (f is the frequency of the signal), they can be

minimized by adjusting the frequency of games magnitudes.

- The selectivity of the detector (a bandwidth of 0.05 Hz) virtually eliminates all

signals having a frequency different from the reference signal.

The AC method allows a more precise measure than continuous measurements.

However, the continuous method remains essential for the determination of crystal

types. The AC method has the disadvantage of the occurrence of stray voltage with

reference signal frequency when the contacts are not perfectly ohmic.

3.2.2 Sample Preparation

The AC method eliminating the effect of misalignment of the hall contact, we can be

content to draw here two side contacts only (Fig. 7). Setting these contacts is very

delicate, this method offers considerable

Figure 7 The Hall contacts for alternative measures time savings.

3.2.3 Description of the measuring device

3.2.2.1 Hall effect measurement

The device for measuring the Hall voltage is composed mainly of:

1- A quartz oscillator with minimum frequency 5MHz. This oscillator will provide the

reference signal.

2- An amplifier coupled to an electromagnet. The set used to generate the magnetic

field.

3- A current source for supplying the longitudinal current in the sample.

4- A measuring amplifier which serves to adapt the Hall voltage.

5- An analog multiplier that will ensure BI product. This product will be extracted the

reference voltage.

The device thus formed is coupled to a digital microvoltmeter that supports the

measurement and display of the Hall voltage.

3.2.2.2 The device of temperature variation

Our measurement range is from ambient to the temperature of liquid nitrogen (about

77K). To make measurements in this range, we have a poly cryostat to achieve the

temperature of liquid helium. The electromagnet is installed at the bottom of this

cryostat permanently while the sample holder is introduced only during the

measurements.



4. RESULTS AND DISCUSSION 4. 1 Continuous Measurement

The continuous measurements have led to the results on the curves of Figures 8 and 9.

Prior to study the influence of induction to the Hall voltage, it is helpful to check the

linearity of the Hall contact.

4.1.1 Study of linearity The results of measurements performed for this purpose are plotted on the curve of

Figure 8. These results were obtained by varying the longitudinal current and

measuring the corresponding voltage drop along the sample.

The linearity curve thus obtained (Fig. 8) showed good linearity of a test sample (stick

of molybdenum di telluride MoTe2). This curve shows no rectifier effect in the

sample.

Figure 8 Linearity contacts (longitudinal current I1 in function of the longitudinal tension V1)

4.1.2 Effects of induction and the longitudinal current

The measurements allowed the reporting of a network of curves shown in Figure 9.

These curves represent the variations of the Hall voltage as a function of magnetic

field (in gauss) or current IB in the coil (in amps). These curves are parameterized by

the longitudinal current, flowing along the sample.

The curves in Figure 9 show that the magnetic induction and the current I in the sample have different effects on the Hall voltage.

Influence of induction . The influence of the magnetic induction is studied for different values of the

longitudinal current I. For a given value of current I (here -1mA), the curve VH (B)

has two distinct zones (Figure 9):

Figure 9 Evolution of the Hall voltage as a function induction B to I = -1mA


Hall Effect


- A quasi linear evolution zone where VH varies in proportion to the intensity of . In

this area, the Hall coefficient RH remains almost constant. It is in this region that can

determine the concentration of free charge carriers.

- A saturation zone where the Hall voltage does not vary with the induction . This behavior can be explained by the fact that the carriers are practically all deflected seen

intense values of induction. It is therefore a drainage zone.

Effect of variation of the current I on VH.

In this phase of the study, we vary the intensity of the magnetic induction, and we

note the corresponding variations of the Hall voltage VH, current I (longitudinal)

being taken as a parameter.

The curves obtained show a double influence of the current intensity and its sign.

- For increasing intensity, the curves are more "high" corresponding to larger values

of VH. This behavior is already provided in the study of the effect of the influence of

. - If we focus on the only effect of the current I sign, we can observe the following

phenomena:

In the linear zone, the slope of the curves (RH), is lower for the negative currents as for the positive current (for the same value of the intensity).

At the border of the two zones, the radius of curvature is greater in the case of

negative currents.

Previous effects result in higher saturation areas (expressed as VH values) when the current sign is positive and more particularly to low intensities.

a b Figure10. Joint effects of longitudinal current I and induction B (in Gauss) on the Hall

voltage VH.

a: The entire curve network; b: Scale expansion to better see the low VH curves.

4.1.3 Determining the charge carrier type

We are leveraging a sample of Bismuth, taken as reference, whose type is known. We

connect then the samples submitted for consideration (MoTe2) in the same way as the

reference sample and observe the sign of the Hall voltage VH. We then deduce the

sign of the Hall constant RH allowing access to the type of carriers.

The experience leads us to conclude that our samples are of type P. The concentration

p of carriers searched is that of the holes.

2000 4000 6000 8000 10000 12000 14000 16000 180000,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

VH(m

V)

B(Gauss)

I=-0.1mA

I=-0.01mA

I=0.01mA

I=0.1mA



4.1.4 Carriers concentration at ambient temperature. The charge carriers are holes, the concentration p can be deduced from equation (14) that

expresses RH function of p. The RH value is determined in the straight portion of the curves

representing the Hall voltage change VH according to the magnetic induction (Fig. 9), with

the relation (21). The results are summarized in Table 1

Table 1Holes Concentration in MoTe2 solid at ambient temperature

I (μA) -1000 -100 -10 +10 +100

RH (unit IS) 11,2 10-3

10,2 10-3

6,8 10-3

11,2 10-3

11,6 10-3

P (Hole/m3) 5,57 10

20 6,13 10

20 9,19 10

20 5,57 10

20 5,37 10

20

These results show that the holes concentration in the MoTe2 samples studied is about

6 1020

/m3. It is also very sensitive to the longitudinal current. The values found for the

carrier concentration are similar to those obtained by Jubier Jassim and al [14] in thin

layers of PbTe obtained by thermal evaporation at ambient temperature. These values

are also comparable to the manufacturer data for the doped germanium [15].

4.2 Alternative Measurements

4.2.1 Study of the Hall constant (RH) as a function of temperature The Hall constant is studied in a temperature range extending from ambient to the

temperature of liquid nitrogen. Measurements are made in three different samples. The results

are shown in Figure 11. We observe on the curves of figure 11 a similarity great in the

behavior of samples in the vicinity of ambient temperature. RH increases precipitously when

the temperature decreases from ambient to 230 K.

Figure 11 Variation of Hall coefficient RH as function of the temperature.

We can deduce that in this temperature range, the hole' concentration increases

rapidly with temperature. This behavior is typical of the intrinsic regime where

conduction occurs primarily by thermally activated jumps. At intermediate

temperatures (250K to 200K), Ln(RH) stops increasing and passes through a

maximum that corresponding to the exhaustion domain. A notorious dispersion

appears on the value of the Hall constant at very low temperatures, RH varies little.

This dispersion is probably due to the presence of acceptor states located in the

valence band.

These states contribute with a specific density NA, which ceases to be negligible

compared with the intrinsic density of holes at low temperatures. To try to explain this

singular phenomenon, we recall that the Hall constant depends on the temperature

only through the carrier concentration. Indeed, for an intrinsic semiconductor, a

3 4 5 6 7 8 9 10 11

0

2

4

6

8

10

12

14

Ln

(RH)

(1000/T)K-1

1

2

3


Hall Effect


statistical thermodynamics and solid state physics show that the carrier concentration

n at low temperatures are expressed by: n = T3/2

(22)

EC: Energy of the lowest level of the conduction band

EV: Energy from the top of the valence band

T: Absolute temperature

kB: Boltzmann's constant

For a semiconductor P-type, the hole concentration remains substantially constant

(and low) at low temperatures. It increases rapidly as the temperature begins to

approach the ambient. This explains the sharp drop of RH at about ambient

temperature first, and stabilization on low temperatures as shown by the curves in

Figure 11.

4.2.2 Study of the resistivity as a function of temperature and frequency

We investigated the resistivity of monocrystalline MoTe2 samples both depending on

the temperature (low temperature) and as a function of frequency. Les résultats de

mesures faites en fonction de la température et à fréquence constante, sont reportés

sur la figure 12, tandis que ceux de l’étude en fréquence sont résumés sur la figure 13.

A comparative study of the resistivity obtained by the continuous method (DC) and

the alternative method (AC) is reported in Figure 14. The resistivity is investigated

through the sample resistance because both are proportional, and the second is more

easily accessible by the measurement.

4.2.2.1 Study of the resistivity as a function of temperature

For an isotropic sample the electric conductivity is given by: σ =

<ζ˃ (23)

n : electron concentration (number of electrons per volume unit)

q : elementary charge

m : mass of an electron

<ζ˃ : average relaxation time

The electrical resistivity ρ being the inverse of the conductivity, it can be expressed

by: ρ(T) =

(24)

So ρ depends on the temperature through average relaxation time <ζ˃ and more

particularly of the carrier concentration p or n. Theoretically, the resistivity varies

inversely with the concentration of carriers and thus with the temperature. That's the

evolution that can be observed on the curves in Figure 12.

Figure 12 Evolution of the resistivity with temperature at constant frequency

3 4 5 6 7 8 9

2

3

4

5

6

7

Ln

(Rac/1

k

)

(1000/T) K-1

f/f0 (kH)=0,1 f/f

0 (kH)=1

f/f0 (kH)=5 f/f

0 (kH)=60

f/f0 (kH)=100 f/f

0 (kH)=150

f/f0 (kH)=200



4.2.2.2 Study of the resistivity as a function of the frequency

In order to improve the investigations, we studied the variations in the resistivity as a

function of the frequency of the magnetic field for various values of temperature. The

measurement results are summarized in Figure 13. The network of curves show that

the resistivity is not affected by changes of frequency in a frequency range. Moreover,

outside this range, it varies inversely with the frequency, particularly as the

temperature of the sample decreases.

Figure 13 Evolution of resistivity with frequency, at constant temperature

This behavior has inspired us to compare the frequency effect on the resistance

measured by the continuous method (R =) on one hand, and alternative (RAC) on the

other. We obtained a network of curves Ln(

) as function of Ln(

), parameterized

by the temperature where f0 = 1 kHz. This network is presented in Figure 14.

Figure 14 Comparison of the frequency behavior of the resistance obtained by the AC and

DC methods.

-3 -2 -1 0 1 2 3 4 5 6

-1,5

-1,0

-0,5

0,0

0,5

1,0

Ln

(R=

/Rac)

Ln(f/f0)

T=120°K T=141°K

T=174°K T=193°K

T=206°K T=221°K

T=231°K T=300°K

-2 -1 0 1 2 3 4 5 63,0

3,5

4,0

4,5

5,0

5,5

6,0

6,5

7,0

Ln

(Ra

c/1

K

)

Ln(f/f0)

120 141

174 193

206 221

231 300


Hall Effect


5. CONCLUSIONS

Experimental study on molybdenum telluride samples (MoTe2) led to results that

highlight the semiconductor character of this material. This study used two methods

Hall effect measurements: the continuous measurement and the alternative

measurement.

Continues measures With such measures, made at ambient temperature, we

determined initially, the type of majority charge in the samples studied. Our

measurements reveal to the studied crystals are type P.

By studying the effect of magnetic induction to the Hall voltage, we had access to the

Hall constant and the concentration of charge carriers; it would be around 6x1020

/m3

in the samples studied. The holder concentration is highly sensitive to temperature

changes, we tried to identify this behavior by alternative measures.

AC measurements Measures AC, made of crystals on MoTe2 solid have aimed to

study:

- The evolution of the concentration of charge carriers when the temperature varies

(from ambient to the temperature of liquid nitrogen).

- The resistivity behavior for temperature or frequence variations

Concentration of charge carriers at low temperatures, the carrier concentration is

low and substantially constant (ionization mode). Around room temperature, the

concentration increases strongly with temperature, thus revealing the predominance of

the intrinsic regime.

REFERENCES

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[4] REVOLINSKY, E. and BEERNTSEN, D., J. Appl. Phys. 35 (1964) 2086.

[5] CONAN, A., GOUREAUX, G., ZOAETER, M., J. Phys. Chem. Solids 36 (1975)

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[7] COHEN, M. H., FRITZSCHE, H., OVSHINSKY, S. R., Phys. Rev.Lett. 22

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[10] Christophe BLLIF, PHD thesis N° 1787 (1998), Polytechnic School of Lausanne,

Switzerland..

[11] Manuel ARANZANA, PHD thesis (2005), PARIS VI UNIVERSITy - PIERRE

And MARIE CURIE, Paris, France.

[12] Christophe CANDOLFI, PHD thesis (2008), Polytechnic Institute of Lorraine,

Nancy, France

[13] Soumia LARDJANE, PHD thesis (2013), University of Technology of Belfort-

Montbéliard, France and University Abu BekrBelkaid, Tlemcen, Algeria.

[14] T. Ohgaki, N. Ohashi, S. Sugimura, H. Ryoken, I. Sakaguchi, Y. Adachiet H.

Haneda. « Positive Hall Coefficients Obtainedfrom Contact Misplacementon

Evident n-Type ZnO Films and Crystals ». Journal of MaterialsResearch23.09

(2008), p. 2293–2295.

[15] Najwa Jassim Jubier, SuaadGhafoori Khalil and Abbas Fadhil Essa, Journal of

Materials Science and Engineering B 1 (2011) 811-818

[16] http://www.univ-sba.dz/lpcma/images/Document_3.pdf

http://www.univ-sba.dz/lpcma/images/Document_3.pdf

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