1

Karmanyevaadhikaaraste maa phaleshu kadaachana;Maa karmaphalahetur bhoor maa te sango’stwakarmani.

Thy right is to work only, but never with its fruits; let not the fruits of actions be thymotive, nor let thy attachment be to inaction.

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2

BAND THEORY OF SOLIDS

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3What these terms are: Valence band Conduction band Forbidden gap

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4

FORBIDDEN GAPEn

erg

y

Valence Band

Conduction Band

5Categories of Solids

There are three categories of solids, based on their conducting properties: conductorssemiconductorsinsulators

6Electrical Resistivity and Conductivity of Selected Materials at 293 K

7Reviewing the previous table reveals that: The electrical conductivity at room

temperature is quite different for each of these three kinds of solids Metals and alloys have the highest

conductivities followed by semiconductors and then by insulators

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8Conductors

Valence Band

Conduction Band

Ener

gy

In conductors there is no forbidden gap.

The valence band and the conduction band overlap.

The electrons from valence band freely enter into the conduction band due to overlapping of bands.

Therefore very low potential difference can cause continuous flow of current.

No forbidden gap

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9Semiconductors

Valence Band

Conduction Band

FORBIDDEN GAPAround 0.7eV (Ge) and 1.1 eV (Si)

Ener

gy

In the case of semiconductors the forbidden gap is very small.

At 0K the conduction band is empty and the valence band is completely filled.

When a small amount of energy is supplied, the electrons can easily jump the forbidden gap.

The conductivity of a semiconductor is of the order of 10 2mho m-1

Filled Band

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10

Arrangement of electrons in an isolated Silicon atom

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11Electron arrangement in a silicon atom

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12

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13

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14The thermal energy at room

temperature is easily enough to do this, meaning that the electron is essentially free to move from the moment the phosphorus atom is introduced into the silicon crystal.

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15

Insulators

FORBIDDEN GAP

Ener

gy

When the temperature is increased, then, some electrons will move to go to conduction band. This is the reason why certain materials which are insulators at room temperature become conductors at high temperature.

The resistivity of an insulator lies approximately between 10 11 and 10 16 Ωm

Valence Band

Conduction Band

16

Resistivity vs. Temperature

Figure: (a) Resistivity versus temperature for a typical conductor. Notice the linear rise in resistivity with increasing temperature at all but very low temperatures. (b) Resistivity versus temperature for a typical conductor at very low temperatures. Notice that the curve flattens and approaches a nonzero resistance as T → 0. (c) Resistivity versus temperature for a typical semiconductor. The resistivity increases dramatically as T → 0.

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17Comparison of Insulator ,Semiconductor and

Conductor

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