Test: Carrier Transport - 1 - Electronics and Communication Engineering (ECE) MCQ

Drift:

• Directed motion of charge carriers in semiconductors occurs through two mechanisms:
• Charge drift under the influence of applied electric field and
• Diffusion of charge from a region of high charge density to one of low charge density.

Phenomenon:

• When no electric field is applied to the semiconductor which is above 0º K, the conduction electrons move within the crystal with random motion and repeatedly collide with each other and the fixed ions.
• Due to the randomness of their motion, the net average velocity of these charge carriers in any given direction is zero. Hence, no current exists in the crystal under this condition of no field.
• Now, consider the case when an electric field is applied to the crystal. Under the influence of this field, the charge carriers attain a directed motion which is superimposed on their random thermal motion.
• This results in a net average velocity called drift velocity in the direction of the applied electric field.
• Electrons and holes move in opposite directions but because of their opposite charges, both produce current in the same direction.
• In extrinsic semiconductors, this current is essentially a majority carrier flow.
• The drift velocity is proportional to electric field strength E, the constant of proportionality being called mobility µ.

Diffusion:

• It is the gradual flow of charge from a region of high density to a region of low density.
• It is a force-free process based on the non-uniform distribution of charge carriers in a semiconductor crystal.
• It leads to an electric current without the benefit of an applied field.
• This flow or diffusion of carriers is proportional to the carrier density gradient, the constant of proportionality being called diffusion constant or diffusion coefficient (D) which has a unit of m2/s.

Recombination:

• It is the collision of an electron with a hole.
• The process is essentially the return of a free conduction electron to the valence band and is accompanied by the emission of energy.
• The recombination rate is directly proportional to the carrier concentration for the simple reason that the larger the number of carriers, the more likely is the occurrence of electron-hole recombination.
• This phenomenon is important in describing minority carrier flow.
• In a semiconductor, the thermal generation of electron-hole pairs also takes place continuously.
• Hence, there is a net recombination rate given by the difference between the recombination and generation rates.

Concept:

The conductivity of the silicon sample is given by σ 

⇒ σ = n q μ_n,

Here,

• n is the impurity concentration
• μ is the mobility of electrons
• q is the electronic charge in coulomb

The resistance of the silicon sample is given by

⇒ R = ρL/A   

Here, 

• L is the length of the sample
• A is the cross-sectional area of the sample
• ρ is the resistivity of the sample

Calculation

Given:

n = 5 × 10²⁰ atom/m³, μ_n = 0.125 m²/v-sec, q = 1.6 × 10^-19 C

⇒ σ = ( 5 × 10²⁰) × (1.6 × 10^-19) × (0.125)

⇒ σ = 10 

Therefore Resistivity (ρ) = 1/σ = 0.1

Also given: L = 10^–3 m, A = 10^–10 m²

⇒ R = 10⁶ Ω = 1MΩ 

Hence the resistance of the silicon sample is 1MΩ 

Therefore the correct answer is option b. 

Concept: 

The hall voltage V_A is given by:

ρ_c: Charge density = ne

R_H: Hall coefficient

W is the side across which the magnetic field is applied.

n is the carrier concentration

e is the electron charge

Calculation:

W = Thickness = 5 m, I = 4 A, B =  8 A/m, n = 100000

ρ_c = ne

ρ_c = 100000 × 1.6 × 10^-19

ρ_c = 1.6 × 10^-14

Drift Current:

• Drift current in the diode is the combined effect of movement of the minority charge carrier and majority charge carriers and also on the electric field applied to the diode.
• Drift current is due to the motion of charge carriers when a force exerted on them by an electric field.
• In the p-n junction diode, electrons are the majority charge carriers in the n-region and holes are the majority charge carriers in the p-region.
• When an electric field is applied to the diode there is more number of covalent bonds break and the concentration of charge carriers also increases in both region (p-type, n-type), and hence they affect the drift current in the diode.

Drift current I_drift = J_drift × A

Where, J_drift = Drift current density

A = Area of semiconductor

Now, J_drift = σ ⋅ E

= (nqμ_n + p.qμ_p)

σ = Conductivity

E = Electric field

⇒ I_dr = (nq.μ_n + p.qμ_p) ⋅ E A,

n = Number of electrons in n region

p = Number of holes in p-region

q = Charge on electrons and holes

μ_p = Mobility of holes

μ_n = Mobility of electrons

Additional Information

Diffusion

1) Diffusion is a natural phenomenon.

2) The migration of charge carriers from higher concentration to lower concentration or from higher density to lower density is called diffusion.

3) Diffusion is mainly due to the concentration gradient and is always negative.

It is given by:

dp/dx for holes and

dn/dx for electrons.

Diffusion current is calculated by:

where,

D_p is hole diffusion constant in cm²/sec

and q is charge in Coulomb.

According to Einstein's relation, the ratio of Diffusion constant to mobility remains constant, at fixed

Temperature, i.e.

V_T – Temperature equivalent

K – Boltzman’s constant

T – Temperature in Kelvin

Concept:

For a semiconductor slab doped with excess carriers and placed in an electric field, the current equation is given by:-

J = σ E

Where J = Current Density

σ = Conductivity of the semiconductor defined as:

σ = qnμ_n + qpμ_p

n = excess electrons contributing to the current conduction.

p = excess holes contributing to the current conduction.

Also, the Resistivity is defined as the reciprocal of conductivity.

Calculation:

The given Si semiconductor is doped with Boron impurity.

So, N_a = 10¹⁶ /cm³ (p-type)

q = 1.6 × 10^-19 C

μ_n = 1300 cm²/V-s and μ_p = 500 cm²/V-s

The excess electrons is given by; 

Since, N_a ≫ n_i, we can assume that the conduction current exists only because of acceptor impunities, i.e. because of N_a.

So, σ = q N_a μ_p

ρ = Resistivity of the given Slab
Putting on the respective values, we get:

Analysis:

Drift velocity is directly proportional to the electric field, i.e.

V_d ∝ E

V_d = μE

The proportionality constant 'μ' is called as the mobility and is given by:

Substituting the respective units, we get:

Explanation:

Current in a material can be expressed as:

I = NqAv_d

Where

N = Carrier concentration

q = electrons charge (magnitude)

A = cross-section area

The current density (J) will be:

Also, J = σ E     ----(2)

σ = conductivity

E = Electric field

J = Current density

v_d = μ E    ----(3)

μ = mobility of carriers

E = Electric field

Analysis:

On using equation (1), (2) & (3) we get,

J = NqV_d = NqμE = σE

⇒ σ = Nqμ  

So as conductivity is directly proportional to the mobility of ions and the number of EH pair ions.

The conductivity of an intrinsic semiconductor depends upon the number of hole electron pairs and mobility. The number of hole electron pairs increases with an increase in temperature, while its mobility decreases. However, the increase in hole electron pairs is greater than the decrease in their mobility.

So with an increase in temperature, conductivity in semiconductors also increases.

Hence option (d) is the correct answer.

Hall Voltage states that if a specimen (metal or semiconductor) carrying a current I is placed in transverse magnetic field B, an electric field is induced in the direction perpendicular to both I and B.

Hall Voltage is given by:

ρ = Charge density

Hall coefficient can be written as:

Where,

ρ = charge density = σ / μ 

n = charge concentration

σ = conductivity

μ = mobility constant

Hence, the Hall coefficient becomes

The Hall effect provides information on the sign, concentration, and mobility of charge carriers in the normal state.

A positive sign for the Hall coefficient indicates that the majority carriers are holes and the semiconductor is P-type.

A negative sign for the Hall coefficient indicates that the majority carriers are electrons and the semiconductor is N-type.

Applications of Hall-effect:

Hall effect can be used to find:

1. Carrier concentration

2. Type of semiconductor

3. Conductivity

4. Mobility

It cannot be used to find a magnetic field.

Common Confusion Point:

Looking at the formula one can think that the magnetic field can be calculated but in the HALL Experiment, perpendicular MAGNETIC field and electric field are applied on the material and other parameters are measured.

Concept:

Mobility: It denotes how fast is the charge carrier is moving from one place to another.

It is demoted by μ.

Mobility is also defined as:

Where,

V_d = Drift velocity

E =  field intensity

Calculation:

E = 10 V/cm

V_d = 70 m/s = 7000 cm/s

From equation (1):

μ = 7000/10

μ = 700 cm²/Vs

Note: 

Electron mobility is always greater than hole mobility, 

Hence electron can travel faster and contributes more current than a hole.