On the basis of electrical conductivity, the materials can be divided into three categories :
(1)  Conductors (e.g., Cu, Al, Fe, etc.),
(2)  Insulators (e.g., wood, diamond, mica, etc.), and
(3)  Semiconductors (e.g., Ge, Si, GaAs, … etc.)

At room temperature (≈300 K), the conductivity of conductors is in the range 10⁶ – 10⁸ S/m, and that of insulators, 10^–8 to 10⁴ S/m.  The conductivity of semiconductors lies in between that of conductors and insulators.
Electronic devices (such as diodes, transistors, ICs) are made from silicon (Si) and germanium (Ge).  In the early days (around 1950), mostly germanium was used, because it was comparatively easier to purify germanium.  However, it was found that the devices made from silicon are more stable and their functioning is less dependent on temperature variations.  Now, we have much improved metallurgical processes to purify silicon.  So, now-a-days mostly the devices are of Si.  An integrated circuit (IC) is made from a silicon chip or wafer.

Energy Bands in Solids

The electrons in an isolated atom have discrete energy levels.  However, in a crystal an atom is surrounded by a large number of other atoms.  Due to interatomic interactions, the energy levels are modified.  This modification is more prominent for the electrons in the outermost shell.  (The electrons in the inner shells are shielded by the electrons in outer shells and are not much affected by the electric fields of the neighbouring atoms.)  Due to this modification, each energy level splits into a very large number of levels (~ 10²³) lying close to one another.  We can regard a bunch of these energy levels as a continuous energy distribution, and call it energy band.
The energy bands, which are completely filled at 0 K are called valence bands (VB).  The bands with higher energies are called conduction bands (CB).  We are generally concerned with the highest valance band and the lowest conduction band.

Note that a conduction band is either completely empty or partially filled.
The difference between the highest energy in a valence band and the lower energy in the next higher conduction band is called forbidden energy gap (E_g).
As an example, consider a specimen of sodium (Na) containing N atoms.  Its atomic number is 11 (1s², 2s², 2p⁶, 3s¹).  The details of its energy bands are shown in the table.

As temperature is raised, the electrons may collide with each other and with ions to exchange energy.  The order of energy exchanged is kT.  At room temperature (300 K), kT is 0.026 eV.  Ordinarily, the energy gaps are much larger than kT.  An electron in a completely filled band (i.e., a valence band) does not find an empty state with a slightly higher or lower energy.  Hence, it cannot accept or donate any energy of the order of kT.  However, the outermost electrons, which are in the highest occupied energy band, may take up this energy ≈kT provided some empty states are available in the same band.
Similar thing happens when a piece of sodium is connected to a battery.  The electric field can supply only a small amount of energy to the electrons.  Only the electrons in the highest occupied band can accept this energy and then move according to the field.  This gives rise to an electric current.  The electrons in the inner (valence) bands cannot accept this small amount of energy and hence cannot take part in electric conduction.

Why Materials Have Different Conductivities
There can be four broad types of energy band structures, as shown.
(A) The highest occupied energy band is only partially filled at 0 K.  (Such is the case with sodium, copper, etc.)  When electric field is applied, the electrons in the partially filled band can accept energy from the field and can drift accordingly.  Hence, such materials are good conductors of electricity.

(B) The highest occupied energy band (VB) is completely filled at 0 K and next higher band is completely empty (CB).  But the two are overlapping.  (Zinc has such energy band structure.)  Therefore, there are empty energy stats close to the occupied states.  Hence, such solids are also good conductors.

(C) The highest occupied energy band (VB) is completely filled and the next higher band is completely empty (CB).  There is a large gap (E_g > 5 eV) between these two bands.  (Diamond is of this type.)  The electrons in VB refuse to accept any energy from electric field, because there is no empty state nearby.  Only when the energy supplied (either by applied field or by raising the temperature) is more that E_g (~ 5 eV), an electron from VB can jump to CB, after which it can take part in electrical conduction.  Therefore, at ordinary temperatures, these materials behave as insulators.
(D) The VB and CB are separated by small gap at 0 K (E_g ~ 1 eV).  [For Ge, E_g = 0.72 eV ; and for Si,  E_g = 1.12 eV.]  At 0 K, an ordinary battery cannot supply even this much energy.  Hence electrical conduction cannot take place.  That is, at 0 K, these materials behave as perfect insulators.  However, at room temperature, thermal energy pushes some of these electrons in VB to CB.  Thus, small conduction becomes possible.  Such solids are therefore called semiconductors.

INTRINSIC SEMICONDUCTORS

To make a diode or a transistor, the first step is to obtain a sample of semiconductor in its purest form.  This is called intrinsic semiconductor.  The impurity content is less than one part impurity in 100 million parts of semiconductor.

Crystal Structure of Semiconductors

Each atom of an intrinsic semiconductor (Ge or Si) has four valence electrons.  These four electrons of each atom form covalent bonds with the four neighbouring atoms.  Thus, the semiconductor has tetrahedral lattice structure.  A simplified two-dimensional representation of this crystalline structure is shown in figure.  The core represents the nucleus and all the orbiting electrons except the four valence electrons.  Therefore the core has +4 charge.  A covalent bond consists of two electrons, one from each adjacent atom.  At 0 K, all the valence electrons are tightly bound to the parent atoms.  No free electrons are available for electrical conduction.  Hence, the semiconductor behaves as a perfect insulator at 0 K.

Charge Carriers in Intrinsic Semiconductors

At room temperature, thermal energy is sufficient to make a valence electron jump to the conduction band.  It starts orbiting the nucleus at a larger radius, and frequently it jumps from one nucleus to the other.  It has become  free electron.When an electron breaks a covalent bond and moves away, a vacancy is created in the bond.  A positive charge is associated with this vacancy.  This vacancy is called a hole.  Free electrons and holes are always generated in pairs.  At any time, the concentration of free electrons is same as the concentration of holes in an intrinsic semiconductor,

ni=pi

Just as free electrons move randomly in the crystal, so do the holes.  An electron from the neighbouring bond can make a jump to fill the vacancy, thereby shifting the vacancy (or the holes) to new location.  Much energy is not needed to induce such a transfer, as all the electrons in the valence band have roughly the same energy.  A free electron carries negative charge (–1.6 x 10^–19 C) with it.  A hole carries a positive charge (+1.6 x 10^–19 C) with it.
A metal (such as Cu, Al, etc.) has only one type of charge carriers, namely, free electrons.  But a semiconductor has two types of charge carriers ¾ free electrons and holes.
When an electric field is applied, the free electrons (in the conduction band) drift opposite to the field and the holes drift along the field.  Thus, both types of carriers contribute to electric conduction.

In a semiconductor, not only the thermal generation of electron-hole pairs takes place, but also there is simultaneous pair recombination.  When a free electron encounters a hole, during their random motion, the electron occupies the vacancy, re-establishing the covalent bond.  The individual identity of both is lost.  In this recombination process, same amount of energy is given out as was taken to generate electron-hole pair.  At equilibrium the rate of pair recombination is equal to the rate of pair generation.  If temperature increases, more bonds are broken, that is, the rate of generation increases.  This increases the concentration of free electrons and holes, which in turn increases the rate of recombination.  Equilibrium is again established.
Note that E_g is more in silicon (E_g = 1.12 eV) than in germanium (E_g = 0.72 eV).  Therefore, at a given temperature, less number of electron-hole pairs will be generated in silicon than in germanium.  Hence, the conductivity of silicon is less than that of germanium. 

Conduction in Intrinsic Semiconductor

When a battery is connected across a semiconductor, the free electrons drift towards +ve terminal and holes drift towards –ve terminal.  The total current I is summation of the current due to electron flow I_n and the current due to hole flow.  The current in the connecting wire is due to electron flow.

Effect of Temperature on Conductivity of a Semiconductor

When temperature is raised, more electron-hole pairs are generated.  The higher the temperature, the higher is the concentration of charge carriers.  Because of this, the conductivity increases with temperature.  In other words, the resistivity (ρ=1/σ) decreases with rise in temperature.  That is, the semiconductors have negative temperature coefficient of resistance.

EXTRINSIC SEMICONDUCTORS     

Intrinsic (pure) semiconductors are of little use.  For making a semiconductor device, we deliberately add a tiny and controlled amount of desired impurity to the highly purified semiconductor.  This process is called doping.  A doped semiconductor is called extrinsic semiconductor.  The proportion of impurity added is about 1 in 10⁶.

N-type, or Donor Type

Pentavalent impurity (from group V, such as phosphorous, arsenic, or antimony) is added so that an impurity atom substitutes for a silicon atom in the crystalline structure.  Four of its valence electrons make four covalent bonds with neighbouring atoms.  The fifth electron remains unpaired, and is quite loosely bound to the nucleus.  It needs very little energy (0.01 eV in Ge, 0.05 eV in Si) to free itself from the attractive force of the nucleus.  At room temperature, the thermal energy is enough to do this job for all the impurity atoms added.  Since each impurity atom donates one electron to the conduction band, this type of impurity is called donor type.

After donating an electron, the impurity atom becomes +ve ion.  However, this +ve charge is immobile as the ion is held in its place by covalent bonds.  In addition to the free electrons donated by impurity atoms, there are some more due to breaking of covalent bonds.  Thus, a few holes are also produced.  If N_D is the concentration of donor (impurity) atoms, n that of free electrons and p that of hole, we have

N_D           +           p           =              n

(+ve ions)            (holes)               (electrons)

As a whole, the N-type semiconductor is neutral.  It has electrons in majority and holes in minority (n>>p).

P– type, or Acceptor Type

Here, trivalent impurity (from group III, such as boron, aluminium, gallium and indium) is added.  The three valence electrons make only three covalent bonds with neighbours.  The fourth bond remains incomplete.  There exists a vacancy of an electron in this bond.

Note that this vacancy is not a hole, as no charge is associated with it.  However, the single electron in the incomplete bond has a great tendency to snatch an electron from neighbouring  bonds.  Only a little (about 0.01 eV) additional energy is needed by the electron in adjacent bond to jump and occupy the vacancy around the impurity atom.  When this happens, a hole is now formed in the adjacent bond.  This hole goes on moving around randomly in the crystal carrying +ve charge with it.
When impurity atom accepts an electron to complete fourth bond, it becomes –ve ion (immobile).  At room temperature, all impurity atoms (concentration N_A) convert into –ve ions.  In addition to the holes created due acceptor impurity atoms, there will be some covalent bonds broken due to thermal energy.

N_A           +             n              =            p

(–ve ions)            (electrons)               (holes)

The holes are in majority (p>>n).

Doping Level

If the doping level (i.e., the impurity concentration) is increased in an extrinsic semiconductor, the concentration of majority carriers increases.  As a result, the chances of their recombining with minority carriers increase; and hence the concentration of minority carriers decreases.  In fact, in an extrinsic semiconductor, we have

np=n2i
where n_i is the intrinsic concentration of free electrons (or of holes).

Effect of Temperature on Extrinsic Semiconductor

The number of charge carriers in an extrinsic semiconductor is much larger than that in intrinsic semiconductor.  Hence, its conductivity is also many times that of an intrinsic semiconductor.
Consider an N-type semiconductor.  All the donors have already donated the electrons to the crystal at room temperature.  If the temperature is raised further, more covalent bonds are broken.  As a result, the concentration of minority carriers increases.  Eventually a temperature is reached when the concentration of minority carriers becomes almost same as that of majority carriers.  It will then behave like an intrinsic semiconductors (with higher conductivity).  Any device made of P- and N-type semiconductor will fail at such a temperature.  This critical temperature is about 85 °C for Ge and 200 °C for Si.