# Hall Effect In A Semiconductor Engineering Essay

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In this experiment, Hall voltage was measured by using electrometer at room temperature. The Hall coefficient and charge carrier concentration could be determined from the Hall voltage.

Theory

When a current passes through a sample across a magnetic field, it is well-known that a Hall voltage is establish, such that

Where is the Hall coefficient, is the transverse electric field, the current density, the magnetic field strength. x, y and z are their mutually orthogonal directions. When a semiconductor carries both types of charge carriers, namely, electrons and holes, the hall coefficient is then given by

where , b the electron to hole mobility ratio, n, and p are respectively electron and hole concentrations.

To measure the Hall voltage, and hence to evaluate the Hall coefficient, traditionally, DC measurement has been employed. The drawback of this method is the spurious voltages arise from various causes, such as contact, earth environmental interference, etc. Measurement should be performed by reversing the magnetic field direction or by reversing the current direction. In our case, for simplicity, we only reverse the magnetic field direction, their relations are given by

where is the Hall voltage, and are spurious voltages from varuous sources. To eliminate them

the voltage is negligibly small.

Traditional shape of the sample is a long bar with small end contacting pads. This is difficult to prepare such sample, as most semiconductors are brittle. Instead, for a laminated van der Pauw sample with small contact electrodes,

The Hall coefficient and the sheet Hall Coefficient are given by

and

where , is the current through terminals 1 and 3 respectively. The thickness of the boron doping layer .

## Apparatus

Sampler holder, p-doped semiconductor sample, TR 8652electrometer, DC power supply, Magnet power supply.

## Procedures

The sample was mounted with sample holder in the gap between the cores of the electromagnet, the gap should not be exceed 1 cm. Foams were inserted between the sample holder and the magnet cores, in order to avoid direct contact. The direct contact would otherwise occur when a magnetic field was applied and the sample holder deforms due to the magnetic force.

## Figure 1

The current supply of the electromagnet was connected.

The circuit was connected as shown in Figure 1. Terminals 1 and 3 were connected in series with the DC power supply and an DC ammeter.

Terminals 2 and 4 were connected to the electrometer. At the electrometer, VDC input was selected. AUTO was pressed to select Manual range, the M RNG signal appeared at the bottom of the display panel. The mV range was selected by pressing the &acirc;-¼ key. The SHIELD DRIVE was pressed to OFF position at the right side of the front panel. The cable was connected such that the Black and Blue probes to terminal 2 and Red probe to terminal 4.

The INTEG time key was pressed sequentially until the panel displayed MED, the COMPUTE button was pressed so that the output reading displayed the average value after 40 samplings. The knob was turned to ZERO.

The variable resistance value was adjusted to obtain a current of 5 mA. The power supply of the electromagnet was switched on. The reading at the electrometer was observed. The electrometer needs a few minutes to be stable.

The Hall voltage was measured, at zero magnetic field, by pressing RUN key of the electrometer. Notice that this was a non-zero reading.

The NULL key was pressed, and, the Hall voltage was measured again. Noticed that at this time, the Hall voltage was offset such that for .

The supply current to the electromagnet was slightly increased, in step of 0.5 A. The corresponding magnetic field could be determined from the calibration curve provided at the end of this report.

After the readings had been stabilized, the corresponding Hall voltage was measured by pressing RUN.

Step 10 was repeated by increasing the supply current in step of 0.5 A, until the supply current reached 3 A. (Due to the instability of the sample, especially at the contacts, both the sample current and the magnet should not attain high value, exceeding the suggested values)

The sample current I13 was increased in step of 5 mA to 15 mA. Steps 6-11 were repeated

The electromagnet power supply was switched off. Waiting for a while to let it discharge. The polarity of the supply current was reverted. This would in effect revert the direction of the magnetic field across the sample. In this time the measured Hall voltage was denoted by . Steps 6-12 were repeated. The same setting of sample currents and magnetic fields as in Step 9 and Step 12 was used.

against B was plotted for each sample current.

## Results

Sample current I13 at 5 mA

V24 (+) offset = 0.001V V24 (-) offset = 0.000V

## Table 1

Measured data at Sample current I13 5 mA

## V24[V]

0.5

1.18893

0.003 V

-0.002

0.003

-0.003

0.006

1

1.54728

0.007

-0.005

0.007

-0.006

0.013

1.5

1.90563

0.011

-0.009

0.011

-0.01

0.021

2

2.26398

0.014

-0.012

0.014

-0.013

0.027

2.5

2.62233

0.017

-0.014

0.017

-0.015

0.032

3

2.98068

0.019

-0.017

0.019

-0.018

0.037

Sample current I13 at 10 mA

V24 (+) offset = 0.001V V24 (-) offset = 0.000V

## Table 2

Measured data at Sample current I13 10 mA

## V24[V]

0.5

1.18893E-08

0.007

-0.007

0.008

-0.007

0.015

1

1.54728E-08

0.014

-0.015

0.015

-0.015

0.03

1.5

1.90563E-08

0.021

-0.023

0.022

-0.023

0.045

2

2.26398E-08

0.029

-0.031

0.03

-0.031

0.061

2.5

2.62233E-08

0.035

-0.039

0.036

-0.039

0.075

3

2.98068E-08

0.041

-0.045

0.042

-0.045

0.087

Sample current I13 at 15 mA

V24 (+) offset = 0.000V V24 (-) offset = 0.000V

## Table 3

Measured data at Sample current I13 15 mA

## V24[V]

0.5

1.18893E-08

0.011

-0.008

0.011

-0.008

0.019

1

1.54728E-08

0.022

-0.017

0.022

-0.017

0.039

1.5

1.90563E-08

0.032

-0.028

0.032

-0.028

0.06

2

2.26398E-08

0.041

-0.04

0.041

-0.04

0.081

2.5

2.62233E-08

0.05

-0.05

0.05

-0.05

0.1

3

2.98068E-08

0.059

-0.059

0.059

-0.059

0.118

Note: Actual V24 (+) = Measured V24 (+) - V24 (+) offset

Actual V24 (-) = Measured V24 (-) - V24 (-) offset

V24 = Actual V24 (+) - Actual V24 (-)

Corresponding Magnetic Field is calculated from Figure 4 in appendices

## Figure 2

V24 against Corresponding Magnetic Field at different sample current I13

5

1.7381 x 106

10

4.0742 x 106

15

5.5732 x 106

## Figure 3

Slope S against sample current I13

S = 2RHsI13

Slope S&acirc;€™ = 2RHs = 0.3835 x 109

Sheet Hal l coefficient RHs = 0.3835 x 109/2 = 0.19175 x 109 m2s-1A-1

Hall coefficient RH = RHSd d is thickness of the sample

= (0.19175 x 109)(0.4 x 10-6)

= 76.7 m3s-1A-1

## Carrier concentration

and q=1.602 x10-19 C

= 1/(76.7 x1.602 x10-19 )

=8.13846 x 1016 m3

=8.13846 x 1010 cm3

In

P