The document provides an overview of semiconductors, covering topics such as band structure, intrinsic and extrinsic semiconductors, electrical conductivity, the Hall effect, and types of diodes including p-n junction and tunnel diodes. It also discusses optical properties including absorption and photoconductivity. The text serves as a fundamental guide for understanding semiconductor principles and applications.

1. Basic of
Semiconductors and
Optical Properties
- Kamran Ansari
CBS 6th Semester09 – May - 2018

2. Contents
• Band Structure
• Intrinsic Semiconductors
• Extrinsic Semiconductors
• Electrical conductivity and Mobility
• Hall Effect
• P-N Junction Diode
• Tunnel diode
• Optical properties of semiconductor
• Absorption
• Exciton Absorption
• Photoconductivity

3. Band Structure
The energy of the conduction band has the form:
𝐸𝑐 = 𝐸𝑔 +
ℏ2
𝑘2
2𝑚 𝑒

4. Intrinsic Semiconductors
Fig. : The electronic bonds in an intrinsic semiconductor (Si).

5. • Electron and holes (free carriers) in intrinsic semiconductor are
produced due to temperature and the carriers follow the Fermi-Dirac
distribution function,
𝑓 𝐸 =
1
𝑒
(𝐸−𝐸 𝐹)
𝑘 𝐵 𝑇 + 1
where 𝑓 𝐸 is probability density function for concentration of
electrons at temperature T.
Fig. : The Fermi-Dirac distribution function.

6. Extrinsic Semiconductors
Fig. : The electronic bonds in Si crystal doped with Boron B (p type semiconductor)
and Silicon crystal doped with Arsenic As (n type semiconductor).

7. Electrical conductivity and Mobility
• Electrical conductivity is the measure of a material's ability to allow
the transport of an electric charge.
𝜎𝑒 =
𝑛𝑒2
𝜏 𝑒
𝑚 𝑒
𝜎𝑒 ≅ 1 𝞨𝑚 −1is a typical figure in semiconductor.
• The electron mobility 𝜇 𝑒is the drift velocity electron per unit field
strength and measure of the rapidity or swiftness of the motion of
electron in the field.
𝜇 𝑒 =
𝑒𝜏 𝑒
𝑚 𝑒

8. Hall Effect
The Hall effect is the production of a voltage difference (the Hall voltage) across
an electrical conductor, transverse to an electric current in the conductor and to
an applied magnetic field perpendicular to the current.
Hall voltage 𝑉𝐻 =
𝐼 𝑥 𝐵 𝑧
𝑛𝑡𝑒
Hall coefficient 𝑅 𝐻 =
𝐸 𝐻
𝐽 𝑥 𝐵 𝑧
= −
1
𝑛𝑒

9. Applications of Hall effect:
• The sign of charge carriers,
• The number of charge carriers per unit volume,
• Mobility of charge carriers,
• The unknown magnetic field if the hall voltage (VH) is known.

10. P-N Junction Diode

11. • Shockley Diode equation,
𝐼 = 𝐼𝑠 𝑒
𝑉 𝐷
𝑛𝑉 𝑇−1
I : diode current,
𝐼𝑠: reverse bias saturation current,
𝑉𝐷:voltage across the diode,
𝑉𝑇:thermal voltage kT/q = 25.85mV at 300K and,
𝑛 : ideality factor (between 1 and 2)

12. Tunnel Diode
• A Tunnel diode is a heavily doped p-n junction diode in which the
electric current decreases as the voltage increases.
• Width of the depletion region in tunnel diode is very narrow due to
high amount of impurities in semiconductor.
• In tunnel diode, electric current is caused by “Tunneling”.

13. Fig. : Working principle of Tunnel diodes.

14. Applications of Tunnel diodes:
• Logic memory storage devices,
• Relaxation oscillator circuits,
• Ultra high-speed switch,
• FM receivers.

15. Optical properties of semiconductor: Absorption
• The Fundamental Absorption process:

16. • The Exciton absorption:
The energy of the photon involved in exciton absorption is
ℎ𝜗 = 𝐸𝑔 − 𝐸𝑒𝑥
where 𝐸𝑒𝑥 (about 0.01 eV)is the exciton binding energy.
Fig. : The exciton level and associated absorption.

17. Photoconductivity
• When an incident light having energy ℏ𝜔 > 𝐸𝑔,is incident upon a
semiconductor causes an increase in the electrical conductivity, This
phenomena is called Photoconductivity.
Fig. : Basic experimental setup for photoconductivity.

18. Thank You