Semiconductors
GUJCET – Physics
1. Simple Explanation
Semiconductors are materials whose electrical conductivity lies between that of conductors (e.g., copper) and insulators (e.g., glass). Their conductivity can be controlled by temperature, impurities, and electric fields, making them the backbone of modern electronics.
- Intrinsic semiconductors – pure material (e.g., Si, Ge).
- Extrinsic semiconductors – doped with impurities to increase carriers.
2. Key Concepts & Points
| Concept | What It Means | Why It Matters |
|---|---|---|
| Energy Band Structure | Electrons occupy discrete energy bands. The valence band is full; the conduction band is empty in pure semiconductors. | The band gap (E_g) determines the intrinsic carrier concentration and temperature sensitivity. |
| Band Gap ((E_g)) | Energy difference between valence and conduction bands. | Small (E_g) (Si: 1.12 eV; Ge: 0.66 eV) → high intrinsic conductivity at room temp. |
| Intrinsic Carrier Concentration ((n_i)) | Number of thermally generated electron–hole pairs per unit volume. | (n_i \propto e^{-E_g/(2kT)}). |
| Doping | Adding donor (n‑type) or acceptor (p‑type) atoms. | Controls carrier type & concentration → enables devices like diodes, transistors. |
| p‑type | Acceptors (e.g., B in Si) create “holes”. | Majority carriers = holes; minority = electrons. |
| n‑type | Donors (e.g., P in Si) provide extra electrons. | Majority carriers = electrons; minority = holes. |
| p‑n Junction | Interface between p‑ and n‑type semiconductors. | Forms depletion region, rectifying (diode) behavior. |
| Depletion Region | Zone near junction devoid of mobile carriers. | Contains built‑in electric field; controls current flow. |
| Diode I‑V Characteristics | Forward bias → exponential increase; reverse bias → limited leakage. | Fundamental for rectification, signal modulation. |
| MOSFET & BJT | Transistor types built on semiconductor junctions. | Switching, amplification in digital & analog circuits. |
| Temperature Dependence | Conductivity increases exponentially with temperature. | Important for reliability & thermal management. |
3. Worked Example – Diode Current Calculation
Problem:
A silicon PN‑junction diode has a built‑in potential (V_{bi}=0.7\ \text{V}). At room temperature (300 K), the saturation current (I_S = 10^{-12}\ \text{A}). Find the forward current when a 0.9 V bias is applied. Assume the diode follows the Shockley equation:
[ I = I_S \left( e^{\frac{qV}{kT}} - 1 \right) ]
where
(q = 1.602 \times 10^{-19}\ \text{C}),
(k = 1.381 \times 10^{-23}\ \text{J/K}),
(T = 300\ \text{K}).
Step‑by‑Step
-
Compute the thermal voltage (V_T = \frac{kT}{q}).
[ V_T = \frac{1.381\times10^{-23}\times300}{1.602\times10^{-19}} \approx 0.0259\ \text{V} ] -
Insert the applied voltage (V=0.9\ \text{V}) into the Shockley equation.
[ I = 10^{-12}\ \text{A} \left( e^{\frac{0.9}{0.0259}} - 1 \right) ] -
Evaluate the exponential term.
[ \frac{0.9}{0.0259} \approx 34.78 \ e^{34.78} \approx 1.3\times10^{15} ] -
Find the current.
[ I \approx 10^{-12}\ \text{A} \times (1.3\times10^{15} - 1) \approx 1.3\times10^{3}\ \text{A} ]
Answer: The forward current at 0.9 V is roughly 1.3 kA – a very large value, illustrating the exponential nature of diode conduction. (In real devices, series resistance limits the current.)
4. Quick Revision Summary
- Semiconductor: Material with intermediate conductivity; controllable via temperature & doping.
- Energy bands: Valence band → full, Conduction band → empty; band gap (E_g) crucial.
- Intrinsic carriers: Thermally generated electrons‑holes; (n_i \propto e^{-E_g/(2kT)}).
- Doping:
- n‑type: donors → extra electrons.
- p‑type: acceptors → holes.
- p‑n junction: Depletion region + built‑in electric field → rectification.
- Diode I‑V: Shockley equation (I = I_S(e^{qV/kT} -1)).
- Applications: Diodes, transistors (MOSFET, BJT), integrated circuits.
- Temperature effect: Conductivity rises exponentially with (T).
Use this cheat‑sheet to recall the fundamental principles before tackling GUJCET questions on semiconductors. Good luck!