Measurement of Semiconduction Properies



THE UNIVERSITY OF HONG KONG

DEPARTMENT OF ELECTRICAL & ELECTRONIC ENGINEERING

Experiment ES11: Measurement of Semiconductor Properties

Location: Part I Lab., CYC Building, Rm. 102

Objectives: The aim of this experiment is to demonstrate the use of the principles of the 4-point probe and the Hall Effect in determining semiconductor properties. The experiment is in two parts:

Part A - 4-Point Probe

Part B - The Hall Effect

Part A - 4-Point Probe

Objective: To determine the mean resistivity of two slices of doped silicon (p- and n-type).

Apparatus: (1) 4-Point Probe

(2) Power Supply

(3) Digital Voltmeter and Ammeter

Introduction:

Theory: Resistance of a segment of an electrical circuit may be determined by measuring the potential difference across it when a known current flows. If the same two contacts that carry the current are used for measuring potential difference, errors due to contact resistance may occur. These errors can be eliminated by separating the contacts (2 for current, 2 for p.d.) and ensuring that no current flows through the voltage contacts. A knowledge of the circuit geometry will then enable the material property of resistivity to be evaluated.

In this experiment, four equidistant, co-linear probes are brought into contact with the surface of a semiconductor slice. The outer two contacts carry the current and the inner two are used to measure potential difference using a very high input impedance meter (ideally a potentiometer). With this geometric arrangement the resistivity can be calculated from the expression

[pic]

where I is the current passing, V is the measured potential difference and t is the slice thickness; t is assumed small compared with the probe separation. This expression also assumes s, the probe separation, is much less than the slice diameter and much less than the distance of any probe from the boundary.

Procedures:

1. Using the apparatus provided, measure the potential difference between the central two probes of various currents [pic]I, and for various positions of the probes on the slice.

2. Repeat for the other slice.

3. Comment on the results.

Caution: The current I should not exceed 1 mA

Take care when bringing the probes into contact with the slice and ensure that the probes are well clear before attempting to move the slice.

[pic]

Part B - The Hall Effect

Objectives: To determine the type of carriers, electrons or holes, and to calculate the carrier concentration and mobility in semiconducting p-germanium.

Apparatus: (1) Solenoid

(2) Power Supply

(3) Meters 0-5A d.c.

(4) Digital Voltmeter

(5) Hall Probe

(6) Teslameter

Introduction:

If a semiconducting (or conducting) specimen in which a current flows is placed in a magnetic field, an electric field is developed in a direction perpendicular to both the current and magnetic field directions. This effect is know as the Hall Effect.

As will be seen during the course of the experiment this effect can also be used to measure magnetic fields.

Theory: Consider a semi-conducting sheet as shown in Fig. 1, carrying a steady current Ix (referred to as IH later) immersed in as steady uniform field By normal to its plane. Assume that the current flow is due to charge carriers of one sign (+ or -) only, each having a charge of magnitude e, and having an average drift velocity VD due to an applied electric field in the x-direction.

[pic]

The magnetic field in association with the velocity VD produces a force Fz on each carrier given by:

Fz = e VD By

This force results in a build-up of charge which in turn produces an electric field in the z-direction. Under equilibrium conditions the force due to the magnetic and electric fields must balance leaving the current to flow in the x-direction as assumed. Hence:

e Ez = e VDBy

and

Ez = VD By

The field Ez is known as the Hall field and an important feature of the above expression is that the direction of Ez depends on the direction of VD. Thus a current Ix may be the result of positive charges drifting in the positive x-direction or negative charges drifting in the negative x-direction.

A measurement of Ez gives the sign of VD and hence the sign of the carriers responsible for the current. The voltage Vz (the Hall Voltage VH) between two points on opposite edges of the sheet lying on a straight line parallel to the z-axis is then

Vz = Ez b

The Hall mobility H is defined as:

[pic][pic]

The angle between the resultant field E and the x-direction is called the Hall angle* and :

[pic]

A measure of the magnitude of the Hall effect is often given in terms of the Hall coefficient. Since current density is a measure of the total charge per unit area passing a given plane in unit time we can write, for a carrier concentration n:

[pic][pic]

and

[pic]

i.e. [pic]

where RH, the Hall coefficient is defined by :-

[pic] ...................................(4)

RH is positive or negative depending on the sign of the charge carriers (-ve for electrons, +ve for holes). Since the experiment measures values for Ex, Jx, and By we can calculate the mean carrier concentration.

From equation (1), (2), (3)

[pic] ...................................(5)

and the carrier mobility can be determined experimentally form conductivity and Hall-effect measurements.

Equation (4) is appropriate for metals.

Semiconductors: For semiconductors, a more general and accurate expression for RH which includes the case where both carriers (positive carriers of density p and drift mobility p, and negative carriers of density n and drift mobility n) are contributing significantly to the conductivity is

[pic] .....................................(6)

where [pic] and k is a numerical constant.

Examination of equation (6) shows it to reduce to (4) for a single carrier, except for the constant k.

The derivation of equation (4) assumed a single constant drift velocity for all carriers. In non-degenerate semiconductors (usually the case in actual samples) the carriers have a distribution of randomly-directed velocities closely approximating a Maxwellian distribution. When appropriate averaging is done for the most common carrier scattering mechanism it is found that for lattice scattering

[pic]

For metals k=1.0 and since for semiconductors the value of k is little different from unity, the correction factor is frequently omitted.

A finite length, l, of such a strip of semi-conductor will be referred to as the Hall element.

Note: we have assumed that the Hall contacts lie at the ends of an equi-potential in the absence of the magnetic field (such assumption is relevant to the questions in procedure 3) and that the current contacts do not short out the Hall field yet provide uniform current density distribution in the central cross section of the element.

Procedures:

(1) Set up the circuit as shown in Fig. 2.

[pic]

Figure 2

(2) Measure the magnetic field, B, against solenoid current, Is, up to Is = 5 A. Note any hysteresis. Always set current by a consistent procedure so that subsequent return to the same current will produce the same flux density. Plot B vs Is.

Use the compass needle to determine the direction of magnetic flux. Remember, the earth's "North" pole is a magnetic "South" pole.

CAUTION: (*** The 2000-(F capacitor will EXPLODE if reversely connected ***)

Do not allow IH to exceed 50 mA at any time.

(3) For one fixed value of Is, measure VH against IH up to 50 mA. Check linearity by plotting values of VH vs. IH. Is VH zero when IH 0, Is = 0? What factors might cause a non-zero value of VH? Note the polarities of IH and VH.

(4) Make a number of spot measurements of VH for various combinations of Is and IH.

(5) Reconnect the digital voltmeter to the two terminals marked “A” and “B” on the P-Germanium carrier board, and measure the potential drop across the element for a number of values of IH. (Do not exceed 50 mA).

(6) Choosing the most reliable values (or averages) for the various quantities, calculate the charge-carrier mean density n, the Hall coefficient RH and the Hall mobility (H. What sign are the charge carriers ?

Remark: Hall element dimensions: 20 x 10 x 1 mm

* The Hall angle is sometimes defined as the ratio of electric field.

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