A semiconductor is a material which is neither a good conductor of electricity nor a good insulator. Its conductivity lies midway between a conductor and an insulator. The resistivity of semiconductors varies from $10^{-5}$ to $10^{-4} \ \Omega$-m as compared to values ranging from $10^{-8}$ to $10^{-6} \ \Omega$-m for a conductor and $10^7$ to $10^8 \ \Omega$-m for insulators.
Examples of such substances are the crystalline forms of the fourth group of the Periodic Table. Germanium (Ge) and Silicon (Si) are two very typical substances showing this behaviour. In addition, there are certain compound semiconductors such as gallium arsenide (GaAs), indium phosphide (InP), cadmium sulphide (CdS) etc., which are formed from the combination of elements of group (III) and (V) or group (II) and (VI).
The band gap of semiconductors varies from 0.2 to 2.5 eV which is quite small as compared to that of insulators. For example, the band gap of diamond (a typical insulator) is 6 eV. The valence and conduction bands of metals may even overlap.
Intrinsic Semiconductor
The intrinsic semiconductors like Si and Ge are pure (undoped) semiconductors. The electrical conductivity of an intrinsic semiconductor is solely determined by thermally generated charge carriers as explained below.
Consider the case of Ge. The atomic number of germanium is 32 and it contains 2 electrons in the K-shell, 8 in the L-shell, 18 in the M-shell and 4 in the outermost N-shell. In germanium, which has a tetrahedral (cubical) structure, no free electrons exist at very low temperatures. Each atom of germanium shares one electron each with four neighbouring atoms by covalent bonds that involve all the valency electrons. The outermost shell becomes saturated with eight electrons, four of its own and four shared between four other atoms as shown in Fig. 7.1(a). At very low temperatures, germanium is, therefore, not a conductor of electricity.
The energy gap i.e., the energy required to take an electron from the valence band to the conduction band, is only 0.7 eV. Hence at room temperature, an electron, here and there, may break away from its valence band due to thermal agitation and move into the conduction band and become free. This electron drifts under the effect of electric field in a random manner.
Hole
The atom from which the electron breaks away is left with a Hole and has a tendency to catch an electron due to its electro-positive character. An electron from the covalent bond of a neighbouring atom shifts to fill this hole, thereby creating a new hole in the atom from which it shifts and so on. Thus the hole shifts from atom to atom and behaves like a free positive electronic charge. It means the conduction band electron and the valence band hole are created simultaneously and are known as electron hole pair (EHP). An electron hole pair is shown in Fig. 7.1(b).
Electrons and Holes Contribute to Conductivity
In the absence of an electric field, the negative electrons and the positive holes move randomly at thermal velocities. When an electric field is applied, the positive carriers (holes) drift in the direction of the field from positive to negative and the negative carriers (electrons) in the opposite direction. Thus the material behaves as an intrinsic semiconductor. In an intrinsic semiconductor, both the electrons and the holes contribute towards electrical conductivity as explained below:
In a filled band, all available energy states are occupied. For every electron moving with a given velocity $v$, there is some other electron moving with the same velocity in the opposite direction. When we apply an electric field, the net current is zero, because for every electron moving with a velocity $+v$ there is some other electron moving with a velocity $-v$.
Mathematically, if there are $N$ electrons per cm³ in the band, the current density $J = 0$ and is given by
$J=(−q)∑i=1Nvi=0J = (-q) \sum_{i=1}^N v_i = 0$
where $(-q)$ is the charge on each electron.
Now, if we create a hole by removing one electron, say $j$th, then the current density is given by
$J=∑i=1Nvi−qvj=−q∑i≠jvi−(−q)vjJ$ $= \sum_{i=1}^N v_i – q v_j = -q \sum_{i \neq j} v_i – (-q) v_j$
As the first term is zero, the net current is given by $+q v_j$. Although the charge transport is due to the uncompensated electron corresponding to the $j$th, the current contribution $+q v_j$ is equivalent to that of a positively charged particle of charge $+q$ moving with a velocity $v_j$. It is, therefore, customary to treat the empty space or the hole in a valence band as a charge carrier with a positive charge.
Thus the current in a semiconductor is due to both the type of charge carriers—the electrons moving in the conduction band and the holes moving in the valence band.
Recombination
In addition to the generation of free electron-hole pairs, there is another process called recombination of carriers in the semiconductor. A free electron moving at random in a semiconductor may encounter a hole and combine with it to reconstruct a broken bond. Thus the electron-hole pair is destroyed, and the free electron is converted into the bound electron.
This recombination process is equivalent to the electron jumping from the conduction band to the valence band with the release of energy in the form of electromagnetic waves equivalent to the band gap energy.
In an intrinsic semiconductor, the rate of generation of electron-hole pairs gg is equal to their rate of recombination RR when equilibrium state is reached, i.e.,
g=Rg = R
The Figure below illustrates the generation and recombination of an electron-hole pair.
What is doping?
The electrical conductivity of a crystal like germanium (or silicon) can be very much increased by adding a suitable impurity in a very small proportion, say one in ten million parts, during crystal growth. This process is known as doping. When a crystal is doped, the semiconductor is said to be an extrinsic semiconductor.
What are extrinsic semiconductors?
The intrinsic semiconductors are not of much use due to their small and fixed conductivity. The conductivity of a semiconductor can be considerably improved by adding a small amount of impurity. Such semiconductors are known as impurity semi-conductors or extrinsic semi-conductors or doped semi-conductors.
As the intrinsic semiconductors are generally elements of group (IV), i.e., they have 4 electrons in the outermost electronic orbit, the impurity element chosen has 5 electrons in the outermost orbit, group (V), i.e., one more than that required to completely fill the outermost shell of the intrinsic semiconductor, or it may have 3 electrons, group (III), i.e., one less than the required number.
- The impurity atoms of group (V) are known as donor or n-type and give rise to n-type semiconductors.
- The impurity atoms of group (III) are known as acceptor or p-type and give rise to p-type semiconductors.
The dopants are added in the ratio of about 1 in 10610^6 to 10810^8 atoms of the semiconductor material. Such a small quantity of dopant does not bring about any structural changes in the semiconductor because the impurity atoms replace the regular atoms in the crystal.
Donor or n-type Semiconductor
If a small quantity of a pentavalent impurity (having 5 electrons in the outermost orbit) like arsenic (As), antimony or phosphorus is introduced in germanium, it replaces an equal number of germanium atoms without changing the physical state of the conductor.
Each of the four out of five valence electrons of impurity (say of arsenic) enters into covalent bonds with germanium, while the fifth valence electron is set free to move from one atom to the other, as shown in Fig. 7.3(a). The impurity is called donor impurity, as it donates electrons, and the crystal is called n-type semiconductor.
A small but definite amount of energy is required to detach the fifth electron from its nucleus and make it free to conduct. The energy required is, however, really small as compared to the energy required to break a covalent bond and can be easily provided by thermal agitation inside the crystal.
