The process of adding impurities to a pure semiconductor is called doping. The doped material is referred as extrinsic semiconductor. Doping is done to generate either a surplus or a deficiency in valence electrons.

Suppose a ‘ n ’ -type wafer is created by doping Si crystal having 5 × 10 28 atoms / m 3 with 1 ppm concentration of A s . On the surface 200 ppm Boron is added to create ‘ P ’ region in this wafer.Considering n i = 1 . 5 × 10 16 m – 3 , (i) Calculate the densities of the charge carriers in the n & p regions. (ii) Comment which charge carriers would contribute largely for the reverse saturation current when diode is reverse biased.

When A s (pentavalent) is added to S i the n -type wafer is created. So, the number of majority carriers in n - type wafer, N e = N D and D Si = 1 10 6 × 5 × 10 28 = 5 × 10 22 / m 3 For number of minority carriers n h n e × n h = n i 2 n h = n i 2 n e = 1 . 5 × 10 15 × 1 . 5 × 10 16 5 × 10 22 ( n i = 1 . 5 × 10 16 / m 3 ) (Given) = 0 . 3 × 1 . 5 × 10 32 - 22 = 0 . 45 × 10 + 10 electrons per m 3 When boron(trivalent) is implanted in S i crystal, p - type wafer is formed with number of holes, n h = ( N D × n of S i ) = 200 10 6 × 5 × 10 28 = 1000 × 10 28 - 6 n h = 1 × 10 25 per m 3 Minority carrier in p - type water n e × n h = n i 2 n e = n i 2 n h = 1 . 5 × 10 16 × 1 . 5 × 10 16 10 25 = 2 . 25 × 10 7 = 2 . 25 × 10 7 electrons per m 3 When reversed bias is applied on p - n junction then the minority charge carrier moves towards depletion layer i . e . , holes n h = ( 0 . 45 × 10 10 per m 3 ) from n side and n e = 2 . 25 × 10 7 / m 3 from p side moves towards junction and make the depletion layer thicker.

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Important Questions on Electrostatic Potential and Capacitance

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

A

is a matrix of order

3 \times 2

, and order of the matrix

A^{'}

m \times n

, then

m + n =

_____

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

The trace of the matrix

A = [\begin{matrix} 1 & - 5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{matrix}]

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

Two cells of emf

E_{1}

and

E_{2}

have their internal resistance

r_{1}

and

r_{2}

respectively. Deduce an expression for the equivalent emf and internal resistance of their parallel combination when connected across an external resistance

R

assume that the two cells are supporting each other.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

FInd the number of all possible matrices of order

$3 \times 3$ with each entry $0$ or $1$ .

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

The number of possible matrices of order

3 \times 3

with each entry

0

1

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

In case two cells are identical, each of emf $E = 5 V$ and internal resistance $r = 2 Ω$ , calculate the voltage across the external resistance $R = 10 Ω$

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

A donor impurity results in

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

What is doping?

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

A semiconductor has the electron concentration of

8 \times 10^{13} c m^{- 3}

and hole concentration of

4 \times 10^{13} c m^{- 3} .

Is the semiconductor p-type or n-type? Also, calculate the resistivity of this semiconductor. Given electron mobility

= 24,000 c m^{2} V^{- 1} s^{- 1}

and hole mobility

= 200 c m^{2} V^{- 1} s^{- 1}

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

Why are elemental dopants for Silicon or Germanium usually chosen from group

XIII

or group

XV

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

Suppose a

‘ n ’

-type wafer is created by doping

Si

crystal having

5 \times 10^{28} atoms / m^{3}

with

1 ppm

concentration of

A s

. On the surface

200 ppm

Boron is added to create

‘ P ’

region in this wafer.Considering

n_{i} = 1.5 \times 10^{16} m^{- 3}

, (i) Calculate the densities of the charge carriers in the

n & p

regions. (ii) Comment which charge carriers would contribute largely for the reverse saturation current when diode is reverse biased.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

In a n-type silicon, which of the following statement is true:

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

Mobilities of electrons and holes in a sample of intrinsic germanium at room temperature are

0.54 m^{2} v^{- 1} s^{- 1}

and

0.18 m^{2} v^{- 1} s^{- 1}

respectively. If the electron and hole densities are equal to

3.6 \times 10^{19} m^{- 3}

, calculate the germanium conductivity. Take,

e = 1.6 \times 10^{- 19} C

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

A semiconductor is known to have an electron concentration of

8 \times 10^{13} {cm}^{- 3}

and a hole concentration of

5 \times 10^{12} {cm}^{- 3}

. The semiconductor is

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

What type of charge carriers are there in an

n

-type semiconductor?

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

Pure silicon at

300 K

has equal electron and hole concentrations of

1.5 \times 10^{16} m^{- 3} .

Doping by indium increases the hole concentration to

4.5 \times 10^{22} m^{- 3} .

Calculate the new electron concentration in the doped silicon.

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

What type of impurity is added to obtain

n

-type semiconductor?

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

A semiconductor has the electron concentration

4 \times 10^{12} c m^{- 3}

and the hole concentration

7 \times 10^{13} c m^{- 3}

. Is the substance n-type or p-type? Also, calculate the conductivity of this semiconductor. Given electron mobility

= 22,000 c m^{2} V^{- 1} s^{- 1}

and hole mobility

= 150 c m V^{- 1} s^{- 1} .

Take,

e = 1 .6 \times 10^{- 19} C

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

Germanium is doped one part per million with indium at room temperature. Calculate the conductivity of doped germanium. Given, concentration of

G e

atoms

= 4.4 \times 10^{28} m^{- 3},

intrinsic carrier concentration

(n_{i}) = 2.4 \times 10^{19} m^{- 3},

μ_{e} = 0.39 m^{2} V^{- 1} s^{- 1}

and

μ_{h} = 0.19 m^{2} V^{1} s^{- 1} .

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Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Electrostatics of Conductors

A silicon specimen is made into a

p

-type semiconductor by doping, on an average, one indium atom per

{5 \times 10}^{7}

silicon atoms. If the number density of atoms in the silicon specimen is

{5 \times 10}^{28}

atoms

m^{- 3}

, then the number of acceptor atoms in silicon per cubic centimeter will be

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Important Questions on Electrostatic Potential and Capacitance

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