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Semiconductors and Superconductivity: Foundations of Modern Technology
Semiconductor Physics
Band Structure
- Silicon Bandgap: 1.12 eV at 300K
- GaAs Bandgap: 1.42 eV (direct bandgap)
- Carrier Concentration: \( n_i = 1.5 \times 10^{10} \, \text{cm}^{-3} \) (Si, 300K)
Doping Techniques
| Type | Dopant | Carriers | Concentration Range |
|---|---|---|---|
| n-type | Phosphorus (Si) | Electrons | 10¹⁴-10²⁰ cm⁻³ |
| p-type | Boron (Si) | Holes | 10¹⁴-10²⁰ cm⁻³ |
Superconductivity Fundamentals
BCS Theory
- Cooper pairs form below Tc
- Critical temperature equation: \( T_c \approx 1.13\theta_D e^{-1/N(0)V} \)
Type I vs Type II
| Property | Type I | Type II |
|---|---|---|
| Materials | Pure metals | Alloys/Compounds |
| Tc Range | < 10K | Up to 138K (HgBaCaCuO) |
Cutting-Edge Applications
Quantum Computing
- Superconducting qubits operate at ~15 mK
- Coherence times: 50-100 μs (2023)
Power Grid Innovations
- REBCO tapes carry 500 A/mm² at 77K
- Superconducting fault current limiters respond in <5 ms
Neuromorphic Chips
- Memristors emulate synapses (10¹² ops/J)
- Phase-change materials for analog computing
Worked Example
Solar Cell Parameters:
- Current: 5 A
- Voltage: 10 V
- Efficiency: 22%
\[
P_{out} = IV = 50 \, \text{W}
\]
\[
P_{in} = \frac{P_{out}}{\eta} = \frac{50}{0.22} \approx 227 \, \text{W solar input}
\]
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