Carrier Transport MCQ Quiz in मल्याळम - Objective Question with Answer for Carrier Transport - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

In diffusion, the current is given by:

\({J_{diff}} = q{D_n}\frac{{dn}}{{dx}}\)

In drift, the current expression is:

J_drift = qnμE

Analysis:

If we double the electron concentration:

In diffusion \( = q{D_n}\frac{{2dn}}{{dx}}\) (doubles)

In drift = q2nμ_nE (doubles)

∴ Both the Diffusion and drift current will double.

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:

\(μ=\frac{V_d}{E}\) cm²/Vs     ------(1)

Where,

V_d = Drift velocity

E =  field intensity

Calculation:

E = 10 V/cm

V_d = 70 m/s = 7000 cm/s

From equation (1):

\(μ=\frac{7000}{10}\)

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.

Given:

Drift velocity (V_d) = 40 m/sec

Length (L) = 10 μm

Time taken to travel 10 μm distance can be calculated as;

\(T = \frac{L}{V_d}\)

\(T = \frac{10}{40}\)

T = 0.25 μs

Given: Gradient of electron coefficient \(\frac{{dn}}{{dx}}\) is

\(\frac{{dn}}{{dx}} = - 1.4 \times {10^{15}} \times {10^6} \times {10^3}{e^{ - {{10}^3}x}}\) (changing from cm^-3 to m^-3 )

At x = 0.5 mm

\(\frac{{dn}}{{dx}} = - 1.4 \times {10^{24}}{e^{ - \left( {{{10}^3} \times \frac{1}{2} \times {{10}^{ - 3}}} \right)}}\)

\( = - 0.85 \times {10^{24}}~{m^{ - 4}}\)

Electron diffusion current density,

 \({J_n} = e\;{D_n}\frac{{dn}}{{dx}}\) 

\( = - 1.6 \times {10^{ - 19}} \times {D_n} \times 0.85 \times {10^{24}}\)

D_n = diffusion co-efficient = μ_nV_T

= 3800 × 10^-4 × 26 × 10^-3

= 9.88 × 10^-3 m²/s

⇒ J_n = 1.6 × 10^-19 × 9.88 × 10^-3 ×(- 0.85 × 10²⁴ A/m²)

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.

Important PointsCurrent flow in a semiconductor depends on the phenomenon of drift, diffusion, and recombination.

Additional InformationDoping: The process by which an impurity is added to a semiconductor is known as Doping. 

Concept: 

The hall voltage VA is given by:

\( {V_H} = \frac{{BI}}{{ρ_cW}} = \frac{R_HBI}{W}\)

ρc: Charge density

RH: Hall coefficient

\(R_H = \frac{1}{- nq} = \frac{1}{pq}\)

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

Calculation:

W = Thickness = 2.5 mm, I = 4A, RH = 5 x 10^-7, B = 0.8 Wb/m2  

\( {V_H} = \frac{R_HBI}{W}\)

\(V_H=\frac{5\times10^{-7}\times0.8\times4}{2.5\times10^{-3}}\)

V_H =  6.4 × 10-4 V

The Hall Effect describes the phenomena, if a specimen (semiconductor or metal) carrying current I is placed in transverse magnetic field B, an electric field E is induced in direction perpendicular to both I and B. The induced potential due to induced electric field is called Hall voltage V_H, it is given by

\({V_H} = \frac{{BJd}}{\rho } = \frac{{BI}}{{\rho w}}\)

Here d = width of specimen and w = breadth of specimen

In the question given breadth (w) = d and width (d) = w, hence

\({V_H} = \frac{{BJw}}{\rho } = \frac{{BI}}{{\rho d}}\)

So the Hall voltage is not proportional to 1/w

Concept:

The number of minority carriers generated because of light is given by the generation rate as:

\(G = \frac{{excess\;minority\;carrier\;generated}}{{minority\;carrier\;life\;time}} \)

\(G= \frac{{{\rm{\Delta }}p}}{{\tau_p}} = \frac{{{\rm{\Delta }}n}}{{\tau_n}}\)

Analysis:

N_A = 10¹⁶ / cm³

G = 10²⁰ / cm³ – sec

τ = 100 μsec

ni = 10¹⁰ / cm³

before shining light:

Hole concertration (p) ≃ N_A = 10¹⁶ / cm³

Electron concentration (n) \(= \frac{{n{i^2}}}{p} = \frac{{{{10}^{20}}}}{{{{10}^{16}}}} = {10^4}/c{m^3}\) 

After illumination of light minority carrier will be generated.

So after light illumination hole conc. (p’) = p + Δp

p’ = 10¹⁶ + 10²⁰ × 10^-6 × 100

= 2 × 10¹⁶ / cm³

After illumination e^- conc. (n’) = n + Δn

= 10⁴ + 10²⁰ × 10^-6 × 100

≃ 10¹⁶ / cm³

Product of e^- and hole concertration = n’ × p’

= 2 × 10³² / cm^-6

Hall Effect:

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

Hall Voltage is given by:

\({V_H} = Ed = \frac{{BI}}{{ρ W}}\)

The hall coefficient is given as:

\({{\rm{R}}_{\rm{H}}} = \frac{1}{{\rm{ρ }}} = \frac{1}{{{\rm{ne}}}}\)

Where,

ρ = charge density = σ / μ 

n = charge concentration

σ = conductivity

μ = mobility constant

Hence Hall coefficient becomes

\({{\rm{R}}_{\rm{H}}} = \frac{1}{{\rm{ne }}} = \frac{\mu}{{{\rm{\sigma }}}}\)

• 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 semiconductor is P-type.
• A negative sign for the Hall coefficient indicates that the majority carriers are electrons and 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 HALL Experiment, perpendicular MAGNETIC field and electric field are applied on the material and other parameters are measured.

Concept:

The mobility of a carrier is related to the diffusion coefficient through Einstein’s relation as:

\(\frac{{{{\rm{D}}_p}}}{{{\mu _p}}} = \frac{{KT}}{q}\) 

D_p = Hole diffusion density

μ_p = Mobility of holes

Calculation:

With μ_p = 500 cm² / V-S and \(\frac{{KT}}{q} = 26\;mV,\) we can write:

\(\frac{{{D_p}}}{{500}} = 26\;m\) 

D_p = 500 × 26 m

D_p = 13000 m cm² / s