Energy gap on an intrinsic semiconductor

Introduction

Semiconductors are thermally very sensitive resistors which are a two-terminal device. Semiconductors usually exhibit negative temperature co-efficient of resistance, i.e. the resistance decreases with increase of temperature.

Aim

To determine the energy gap of a given intrinsic semiconductor.

Apparatus

An intrinsic semiconductor, an oven, a voltmeter, an ammeter, a digital thermometer, a constant current source and a few patch cords.

Theory and formulae

In semiconductors there is a small energy gap between the balance and conduction bands. At absolute zero of temperature, semiconductors act as perfect insulators. However, with increase of temperature, more and more electrons from the valence band get excited to the conduction band resulting in the decrease of resistance with increase of temperature.

The equation governing the variation of resistance, R, of a semiconductor with the temperature may be written as,

(1)

where a and Eg are constants characteristic of the material, and Eg refers to the energy gap of the semiconductor. Eg is expressed in eV.

Procedure

The semiconductor is kept in an oven which is attached with a temperature controller and a thermocouple. The two leads of the semiconductor (in the form of a single crystal) are connected to the terminals of the unit used to study the characteristics of a p-n diode.

R = aexpEg

2KT⎛⎝⎜

⎞⎠⎟

of 1 3

Here, the voltage is set at a certain value which is less than 5V and the corresponding current is noted (in mA) at room temperature. The temperature reading is selected with a selector switch given in the p-n study kit, then the temperature is set with a knob again given in the kit. The green light switches on until the set temperature is attained. After this, the voltage and the current are read from the p-n kit using the selector switch. The resistance is calculated using the following equation:

(2)

These are tabulated.

A graph of versus is plotted. The slope of this graph gives the value of the

Eg, the energy gap, i.e.,

(3)

Using appropriate units for K, Eg in eV can be calculated.

Precautions

1. The semiconductor should not be heated beyond 85oC.2. Do not drop the specimen holder as the crystal is mounted for pressure

contact.3. Typically, the value of Eg is of the order of 0.6eV. However, a tolerance of 20%

in the value of Eg is stated by the manufacturer.4. The given semiconductor is a Germanium single crystal.

Results

The variation of resistance of an intrinsic semiconductor with temperature is studied. It is found that the resistance varies inversely with temperature. That is, the intrinsic semiconductors have negative temperature coefficient of resistance.

The energy gap of the given semiconductor is determined graphically. It is found that, Eg = ____________ (from the graph) Eg = ______________ (from least square fit)

R = VoltageCurrent

logR 1T

slope =Eg

K log10 2

of 2 3

Circuit:

Nature of the graph:

Observations: I = 0.05mATemperature

T(K)

VoltageV

(V) (kΩ) log R

of 3 3

V

Semiconductor

Ammeter

+ –

– +

Oven

Voltmeter

DC power supply

A

C B

log R

1/T (in K-1)

Slope = ABBC

R = VI

1T×10−3K −1