Lab 4 Study of the Hall Effect

Department of Physics

Zhang Bing

Contents1. Objectives 2. Pre-lab

Questions

3. Introduction 4. Apparatus 5. Procedure

& Equipments

6. Problems

1. Objectives

Understand the physical significance of the Hall effect. Learn how to determine the conduction type of the semiconductor sample.

Learn how to measure some characteristic quantities of semiconductor materials. Learn how to eliminate the negative effect in this experiment by taking symmetrical measuring method.

2. Pre-lab Questions

How does a charge carrier go in a uniform electric field when its initial velocity is perpendicular to the field? What kind of force is exerted by the electric field on the charge carrier?

How does a charge carrier go in a uniform magnetic field when its initial velocity is perpendicular to the field? What kind of force is exerted by the magnetic field on the charge carrier?

3. IntroductionIn 1879 E. H. Hall observed that when an electrical current passes through a sample placed in a magnetic field, a potential proportional to the current and to the magnetic field is developed across the material in a direction perpendicular to both the current and to the magnetic field. This effect is known as the Hall effect.

Edwin Herbert Hall (1855-1938) American physicist

Hall effect is the basis of many practical applications such as magnetic field measurements, position and motion detectors, etc. We also use Hall effect to study the characteristic properties of conductors or semiconductors.

Theory of the Hall effect B

Figure 1: Hall Effect principle diagram. (a) Hall Effect in N-type semiconductor (electrons are the charge carriers); (b) Hall Effect in P-type semiconductor (holes are the charge carriers)

Two forces on charge carriers: Electric force: FE qE Lorentz force: FM qv B

steady potential difference VA' A VA' VA is formed. We call this potential difference the Hall voltage, VH . In Figure 1.a, VH VA' VA 0 , the sample is N-type semiconductor. In Figure 1.b, VH VA' VA 0 , the sample is P-type semiconductor. Hall effect animation:

When steady state is reached, FM FE , and a

RH

Hall voltage:1 IB IB VH RH ne d dRH:the Hall coefficient (RH 1 ), it depends on the charge ne carrier density, and it is one characteristic quantity of the semiconductor.

I: the current passing through the semiconductor sample. B : magnetic induction of the magnetic field in which thesemiconductor sample is placed.

d: thickness of the sample.

IB VH RH d

VH IB

For the current and the magnetic field, if we keep one of them a constant and change the other, we can find the relation between the Hall voltage and the varying quantity. According to this relation, it is easy to find the Hall coefficient RH .

Keep IS (current through the sample) constant:VH

IS slope RH d

I M (B I M )

I M : the current inducing magnetic fi

eld

Keep IM constant:VH

IM slope RH d

IS

When R H is obtained, the following parameters can be determined : ﹡Determine the conduction type of the sample by the sign of R H or VH . Suppose I S and B are in the directions shown in Figure 1. If R H is negative, VH is negative and the sample is N-type semiconductor, and vise versa.

﹡Determine the density of charge carriers n by

n

1 RH e

﹡Determine the carrier mobility by R H σ , where is the conductivity of the sample.

Sample Conductivity MeasurementThe sample conductivity is measured by the probe A and C shown in Figure 1. In this measurement, we set I M zero so that there is no magnetic field. Suppose the probe A and C are separated by the distance of L, the cross-sectional area of the sample is S=bd, the current in the sample is I S , and the potential difference between A and C is V AC (or V ), then is obtained by

IS L V AC S

B

VH

Negative Effects EliminationThe voltage measured in the experiment contains some kind of additional voltages, for instance, the additional voltage is produced when the two Hall probes are not on the same equipotential surface, and some other negative effects also produce additional voltage. Since the sign of the additional voltage is related to the directions of the magnetic field and the current, we can reduce the additional voltage by changing the directions of the magnetic field and the current . In this experiment, we measure VH in four cases: (+B, +I), (+B, -I), (-B, +I), (-B, -I), then find the average value of byVH VH1 VH 2 VH 3 VH 4 / 4