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Dependence of Hall Coefficient on Temperature HEX 22

Dependence of Hall Coefficient on Temperature
Conductivity measurements in semiconductors cannot reveal whether one or both types of carriers are present, nor distinguish between them. However, this information can be obtained from Hall Effect measurements, which are a basic tool for the determination of mobilities. The effect was discovered by E.H. Hall in 1879.
Consider a simple crystal mounted as in the Fig. 1, with a magnetic field H in the z direction perpendicular to contacts 1, 2 and 3, 4. If current is flowing through the crystal in the x direction (by application of a voltage Vx between contacts 1 and 2), a voltage will appear across contacts 3, 4. It is easy to calculate this (Hall) voltage if it is assumed that all carriers have the same drift velocity. We will do this in two steps : (a) by assuming that carriers of only one type are present, and (b) by assuming that carriers of both types are present.
We know already that conduction in solids is due to the motion of the charge carriers under the influence of an applied field. We define the following symbols

 

Description

The Set-up consists of the following
1. Hall probe (Ge:p type)
2. Oven
3. Temperature sensor
4. Hall Effect Set-up, Model : DHE-22
5. Electromagnet, EMU-50V
6. Constant Current Power Supply, DPS-50
7. Digital Gaussmeter, DGM-102

1. HALL PROBE (GE : P-TYPE)
Ge single crystal with four spring type pressure contact is mounted on a glass-epoxy strips. Four leads are
provided for connections with the probe current and Hall voltage measuring devices.
2. OVEN
It is a small oven which could be easily mounted over the crystal or removed if required.
Technical details
Size : 35 x 25 x 5 mm (internal size)
Temperature Range : Ambient to 100°C
Power requirement : 12 W
3. TEMPERATURE SENSOR
Temperature is measured with Cromel-Alumel thermocouple with its junction at a distance of 1 mm from the
crystal
4. HALL EFFECT SET-UP, MODEL : DHE-22
The set-up, DHE-22 consists of two sub set-ups, each consisting of further two units.

(i) Measurement of Probe Current & Hall Voltage
This unit consists of a digital millivoltmeter and constant current power supply. The Hall voltage and probe current can be read on the same digital panel meter through a selector switch

a) Digital Millivoltmeter
Intersil 31⁄2 digit single chip ICL 7107 have been used. Since the use of internal reference causes the degradation in performance due to internal heating an external reference have been used.
Digital voltmeter is much more convenient to use in Hall Experiment, because the input voltage of either polarity can be measured.
Specifications
Range : 0-200mV (100μV minimum)
Accuracy : ±0.1% of reading ± 1 digit

(b) Constant Current Power Supply
This power supply, specially designed for Hall Probe, provides 100% protection against crystal burn-out due to excessive current. The supply is a highly regulated and practically ripple free dc source.
Specifications
Current : 0-20mA
Resolution : 10μA
Accuracy : ±0.2% of the reading ±1 digit Load regulated : 0.03% for 0 to full load Line regulation : 0.05% for 10% variation

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