Semiconductors: Properties & Types | Physics for JEE Main & Advanced PDF Download

Semiconductors are the materials that have a conductivity between conductors (generally metals) and non-conductors or insulators (such as ceramics). Semiconductors can be compounds such as gallium arsenide or pure elements, such as germanium or silicon. Physics explains the theories, properties and mathematical approach governing semiconductors.

Properties of Semiconductors

• Semiconducting elements are tetra-valent i.e. there are four electrons in their outermost orbit.
• Their lattice is face centered cubic (F.C.C.)
• The number of electrons or cotters is given by
  
  i.e. on increasing temperature, the number of current carriers increases.
• There are uncharged.
• Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
• Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
• Lesser power losses.
• Semiconductors are smaller in size and possess less weight.
• Their resistivity is higher than conductors but lesser than insulators.
• The resistance of semiconductor materials decreases with the increase in temperature and vice-versa.

Example of different semi-conductors 

• Holes or cotters
  (i) The deficiency of electrons in covalent band formation in the valence band in defined as hole or cotter,
  (ii) These are positively charged. The value of positive charge on them is equal to the electron charge.
  (iii)  Their effective mass is less than that of electrons.
  (iv)  In an external electric field, holes move in a direction opposite to that of electrons i,e. they move from positive to negative terminal.
  (v)  They contribute to current flow.
  (vi)  Holes are produced when covalent bonds in valence band break.

Transfer of electrons from valence band to conduction band

Types of Semiconductor

Semiconductors can be classified as:

• Intrinsic Semiconductor
• Extrinsic Semiconductor

Intrinsic Semiconductor

• An intrinsic type of semiconductor material is made to be very pure chemically. It is made up of only a single type of element.

Conduction Mechanism in Case of Intrinsic Semiconductors (a) In absence of electric field (b) In presence of electric Field

• Germanium (Ge) and Silicon (Si) are the most common type of intrinsic semiconductor elements. They have four valence electrons (tetravalent). They are bound to the atom by covalent bond at absolute zero temperature.
• When the temperature rises, due to collisions, few electrons are unbounded and become free to move through the lattice, thus creating an absence in its original position (hole). These free electrons and holes contribute to the conduction of electricity in the semiconductor. The negative and positive charge carriers are equal in number.
• The thermal energy is capable of ionizing a few atoms in the lattice, and hence their conductivity is less.

➢ The Lattice of Pure Silicon Semiconductor at Different Temperatures

• At absolute zero Kelvin temperature: At this temperature, the covalent bonds are very strong and there are no free electrons and the semiconductor behaves as a perfect insulator.
• Above absolute temperature: With the increase in temperature few valence electrons jump into the conduction band and hence it behaves like a poor conductor.

➢ Energy Band Diagram of Intrinsic Semiconductor

• The energy band diagram of an intrinsic semiconductor is shown below:
  
  
  (a) Intrinsic Semiconductor at T = 0 Kelvin, behaves like an insulator (b) At t>0, four thermally generated electron pairs
• In intrinsic semiconductors, current flows due to the motion of free electrons as well as holes. The total current is the sum of the electron current Ie due to thermally generated electrons and the hole current Ih
  Total Current (I) = Ie + Ih
• For an intrinsic semiconductor, at finite temperature, the probability of electrons to exist in conduction band decreases exponentially with increasing bandgap (Eg)
  Where,
  E_g = Energy bandgap
  K_b = Boltzmann’s constants

Extrinsic Semiconductor

• The conductivity of semiconductors can be greatly improved by introducing a small number of suitable replacement atoms called impurities.
  
• The process of adding impurity atoms to the pure semiconductor is called doping. 
• Usually, only 1 atom in 107 is replaced by a dopant atom in the doped semiconductor. 
• An extrinsic semiconductor can be further classified into:
  (i) N-type Semiconductor
  (ii) P-type Semiconductor

Table: Difference between intrinsic and extrinsic semiconductors

➢ Properties of Extrinsic Semiconductors

• At absolute zero temperature (0 K) there are no free electrons in them.
• At room temperature, the electron-hole pair in sufficient number are produced.
• Electric conduction takes place via both electrons and holes.
• The drift velocities of electrons and holes are different.
• The drift velocity of electrons (V_dn) is greater than that of holes (V_dp).
• The total current is I = I_n + J_p.
• In connecting wires the current flows only via electrons.
• The current density is given by:
  
  Where V_dn = drift velocity of electrons
  μ_n = mobility of electrons
  V_dp = drift velocity of holes
  μp = mobility of holes
• The electric conductivity is given by s = nq(m_n + m_p).
• Mobility of electron m_n = V_dn / E.
• Mobility of holes m_p = V_dp/E.
• At room temperature s_Ge > s_Si because n_Ge > n_Si 
  where n_Ge = 2.5' 10¹³/cm³ and n_Si = 1.4' 10¹⁰ /cm³.

N-Type Semiconductor

• Mainly due to electrons
• Entirely neutral
• I = Ih and nh >> ne
• Majority – Electrons and Minority – Holes
• When a pure semiconductor (Silicon or Germanium) is doped by pentavalent impurity (P, As, Sb, Bi) then, four electrons out of five valence electrons bonds with the four electrons of Ge or Si.
• The fifth electron of the dopant is set free. Thus, the impurity atom donates a free electron for conduction in the lattice and is called “Donar“.
• Since the number of free electron increases by the addition of an impurity, the negative charge carriers increase. Hence, it is called n-type semiconductor.
• Crystal as a whole is neutral, but the donor atom becomes an immobile positive ion. As conduction is due to a large number of free electrons, the electrons in the n-type semiconductor are the majority carriers and holes are the majority carriers.

P-Type Semiconductor

• Mainly due to holes
• Entirely neutral
• I = Ih and nh >> ne
• Majority – Holes and Minority – Electrons
• When a pure semiconductor is doped with a trivalent impurity (B, Al, In, Ga ) then, the three valence electrons of the impurity bonds with three of the four valence electrons of the semiconductor.
• This leaves an absence of electron (hole) in the impurity. These impurity atoms which are ready to accept bonded electrons are called “Acceptors“.
• With the increase in the number of impurities, holes (the positive charge carriers) are increased. Hence, it is called p-type semiconductor.
• Crystal as a whole is neutral, but the acceptors become an immobile negative ion. As conduction is due to a large number of holes, the holes in the p-type semiconductor are majority carriers and electrons are majority carriers.

Table: Difference between N-type and P-type semiconductors

P N Junction Formation 

(a) The device formed by joining atomically a wafer of P-type semiconductor to the wafer of N-type semiconductor is known as P-N junction.

(b)There are three processes of making junctions

(i) Diffusion

(ii) Alloying

(iii) Growth

In majority of cases P-N junction is formed by diffusion process. The impurity concentration is maximum at surface and decreases gradually inside the semiconductor.

(c) Conduction of current in P-N Junction:

(i) In P-N junction the majority cotters in P-region and majority electrons in N-region start diffusing due to concentration gradient and thermal disturbance towards N-region and P-region respectively and combine respectively with electrons and cotters and become neutral.

(ii) In this process of neutralization there occurs deficiency of free current carriers near the junction and layers of positive ions in N-region and negative ions in P-region are formed. These ions are immobile. Due to this an imaginary battery or internal electric field is formed at the junction which is directed from N to P.

(a) The region on both sides of P-N junction in which there is deficiency of free current carriers, is known as the depletion layer.

(b) Its thickness is of the order of 1 micro m (= 10^–6)

(c) On two sides of it, there are ions of opposite nature. i.e. donor ion (+ve) on N-side and acceptor ions (–ve) on P-side.

(d) This stops the free current carriers to crossover the junction and consequently a potential barrier is formed at the junction.

(e) The potential difference between the ends of this layer is defined as the contact potential or potential barrier (V_B).

(f) The value of V_B is from 0.1 to 0.7 volt which depends on the temperature of the junction. It also depends on the nature of semiconductor and the doping concentration. For germanium and silicon its values are 0.3 V and 0.7 V respectively.

(h) Symbolic representation of diode:

(ii) The direction of current flow is represented by the arrow head.

(iii) In equilibrium state current does not flow in the junction diode.

(iv) In can be presumed to be equivalent to a condenser in which the depletion layer acts as a dielectric.

(v) Potential distance curve at P-N Junction

(vi) Charge density curve at P-N Junction

(vii) Curve between electric field and distance near P-N junction

p-n Junction Diode

• A semiconductor diode is a p-n junction with metallic contacts provided at the ends for the application of an external voltage
• Thus p-n junction diode is a two terminal device represented as
  
• The equilibrium potential barrier can be altered by applying an external voltage V across the diode

There are two methods of biasing a p-n unction – Forward bias and reverse bias

Forward biasing

• If the positive terminal of the external battery is connected to the p-side and the negative terminal of the external battery is connected to the n-side, then the p-n junction is said to be forward biased
  
• The direction of the applied voltage V is in a direction opposite to that of the potential barrier setup at the junction
  
• As a result of this, the depletion layer width decreases and the barrier height is reduced. The effective barrier height under forward bias is V_B – V
• If the applied voltage V is small, the barrier potential will be reduced only slightly below the equilibrium value. Hence, only small number carriers will possess energy to cross the junction. Thus, the current is small
• If the applied voltage V is large, the barrier potential will be reduced significantly. Hence, the current is significant
• Due to the applied voltage, the electrons from the n-side cross the depletion region and reach the p-side. Similarly, the holes from the p-side reach the n-side
• As electrons reach the p-side and electrons are minority carriers in p-region, the forward bias is also known as minority carrier injection
• At the junction, the minority carrier concentration increases significantly
• Due to concentration gradient, the injected electrons on p-side diffuse from the junction edge of p-side to the other end of the p-side
• Similarly, the injected holes on the n-side diffuse from the junction edge of n-side to the other end of n-side
• The motion of charged carriers on either side gives rise to current and is usually measured in mA
• The total diode forward current is sum of hole diffusion current and conventional current due to electron diffusion

Reverse biasing

• If the positive terminal of the external battery is connected to the n-side and the negative terminal of the external battery is connected to the p-side, then the p-n junction is said to be reverse biased
  
• The direction of the applied voltage is same as that of the barrier potential.
• As a result, the barrier height increases and the depletion region widens due to change in electric field.
• The effective barrier height is V_B + V.
• This suppresses the flow of electrons from n region to p region and holes from the p region to n region. Hence, diffusion current decreases.
• The electric field direction of the junction is such that if electrons on p-side or holes on n-side in their random motion come close to the junction, they will be swept to its majority zone. This gives rise to drift current of order of few µA.
• The diode reverse current is not much dependent on the applied voltage. Even a small voltage is sufficient to sweep the minority carriers from one side of the junction to the other side of the junction.
• The current under reverse bias is essentially voltage independent up to a critical reverse bias voltage, known as breakdown voltage V_BE.
• When V = V_BE, the diode reverse current increases sharply. If the current is not limited, the p-n junction will get destroyed.