physics-class-12-unit-14-chapter-02-doping-in-semiconductors-l-2-8-lb2iinnipr4

Doping in Semiconductors

Semiconductor

For an isolated atom, the possible energies $\rightarrow 3p$

Of quantum states are discrete. We talk of $\rightarrow 3s$

Is 2s, 3s, 3p etc orbitals having different $\rightarrow 2p$

Energies. $\rightarrow 2s$

$\rightarrow 1s$

Doping in Semiconductors Semiconductor

For a gas/vapour of that material, the same energies are available. Number of quantum states increases according to the number of atoms.
Electrons fill the orbitals from lowest energy states, one per quantum state. The last non empty level may be completely or partially filled.

Doping in Semiconductors Semiconductor

As the atoms are brought closer to form the solid crystalline state, outer electrons also start interacting through bonding and the energies are split to form almost continuous energy bands
The lower energy levels are populated by inner electrons and are not affected by the inter atomic electron interactions but the higher ones spread more
The highest completely filled energy band is called valence band and the next higher band is called conduction band.

Doping in Semiconductors

Semiconductor

In good conductors, the conduction band is partially filled, there are enough electrons and enough empty state even at very low temperatures
In insulators the conduction band is completely empty and the energy gap between the valance band and conduction band is large, say 3-6 eV. At usual temperatures no electrons populate the quantum states in conduction band

Doping in Semiconductors

Semiconductors

In Semiconductors, the conduction band is completely empty at very low temperatures. The energy gap between the (CB) valance band and conduction band is (VB) relatively small, say around or less than 3 $\mathrm{eV}$ . For Silicon it is $1.12 \mathrm{eV}$
At higher temperatures (say at room temperature), some of the electrons in the valance band get sufficient energy from thermal interactions to cross over the gap and occupy quantum states in the conduction band. This leaves behind vacant quantum states in the valence band

Doping in Semiconductors

Intrinsic and Extrinsic Semiconductors

$\text{Creation of e-h pair}$

$\text{Destruction of e-h pair}$

Doping in Semiconductors

Example

RT Si $5\times 10^{22} \text{atoms} /cm^3$

e-h pairs $1.5 \times 10^{10} cm^3$

Doping in Semiconductors

Example

RT Si - $5 \times 10^{22} \text{atoms} /cm^3$

e-h pairs $1.5\times 10^{10}/cm^3$ Instrisic Semi Conductors

$kT \simeq 0.02 eV$

$E, =1.12 eV$

$\text{Copper}.~8.4\times 10^{22} \text{atoms}/cm^3$

Doping in Semiconductors

Instrinsic Semi Conductors

$n_e = n_h = n_i$

Extrinsic Semiconductor

Doped Semi Conductor

Doping in Semiconductors

Instrisic Semi Conductors

$n_e = n_h =n_i$

Extrinsic Semiconductor

Doped Semi Conductor

$z = 14$

$s^2 p^2$

$s^2 p^3$

(Phosphorus Arsenic)

Doping in Semiconductors

Impurity Levels / Donor Levels

$hhh$ V.B.

$n_e » n_h$

$n_e> n_i$

$n_h < n_i$

$n_e n_h = n_i^2$

Doping in Semiconductors

Numercial Problems

Silicon $-$ at Room Temprature.

No. of atoms per unit volume $=5 \times 10^{28}/m^3$

$n_e = n_h = n_i$ $= 1.5\times 10^{16}/m^3$ Pentavalent Arsenic $1ppm$

$ppm \rightarrow$ Parts Per Million:1 in $10^6.$

Electron density $n_e =?$

Hole density $n_h = ?$

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

Doping in Semiconductors

Solution

1 ppm of $A_s$ $n_i = 1.5\times 10^{16} ~/m^3$

1 ppm of $A_s$

$n_i = 1.5\times 10^{16} ~/m^3$

No. of electrons = ?
No. of holes =?

$n_e = 5\times 10^{22}$

$n_e. n_h = n_i^2 = 2.25\times10^{32}$

$n_h = \frac{2.25\times 10^{32}}{5\times 10^{22}} = 0.45\times 10^{10} = 4.5 \times 10^9 /m^3$

Doping in Semiconductors

Solution

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

1 ppm of $A_s$ , $n_i = 1.5\times 10^{16} ~/m^3$

$n_e = 5\times 10^{22}$ , $n_e. n_h = n_i^2 = 2.25\times10^{32}$ , $n_h = \frac{2.25\times 10^{32}}{5\times 10^{22}}$ , $=0.45\times 10^{10}$ , $= 4.5 \times 10^9 /m^3$ , $n_e » n_h$

$\text{n-type Semi Conductors}$ , $n_h » n_e$

$\text{p-type Semi Conductors}$

Doping in Semiconductors

Summary

Impurity level

Acceptor level, $n_e n_h = n_i^2$

Doping in Semiconductors

Intrinsic Semiconductor

$n_e = n_h = n_i$

$n_e =$ Number of Conduction electrons

$n_h =$ Number of holes

Doping Control on Conductivity

Pentavalent impurities

$n_e »n.$

Doping in Semiconductors

Charge Density

Pentavalent Impurity $n_e>n_h$

$\text{n-type semiconductor}$

Negative: $\text{majority charge carrier electrons}$

$n = \text{Negative}$

$\text{Charge Density = 0}$

Dope Neutrals

$I = I_e + I_h$

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