1) A sample of silicon at room temperature and in thermal equilibrium is doped with acceptor atoms such that NA = 10¹5 cm-³. Determine the concentration of electrons and holes. ΝΑ 21 A complo of silicon at room tompor thermal equilibrium is dar por atoms

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### Parameters to Use for the Problems that Follow

- **K** = 1.38 × 10⁻²³ J/K
- **q** = 1.6 × 10⁻¹⁹ coulombs

### For Silicon at Room Temperature (T = 300K)

- **E_G** = 1.12 eV
- **n_i** = 1 × 10¹⁰ cm⁻³
- **ε_Si** = **K_Siε_0** = (11.8)(8.85 × 10⁻¹⁴) F/cm
- **μ_p** = 384.62 cm²/V·sec,  **D_p** = 10 cm²/sec
- **μ_n** = 1230.77 cm²/V·sec, **D_n** = 32 cm²/sec
- **τ_n** = 2.0 × 10⁻⁴ sec, **τ_p** = 9.0 × 10⁻⁵ sec
- **L_n** = 8.0 × 10⁻² cm, **L_p** = 3.0 × 10⁻² cm

### Problems

1. **Problem 1:**
   A sample of silicon at room temperature and in thermal equilibrium is doped with acceptor atoms such that \(N_A = 10^{15} \text{cm}^{-3} \). Determine the concentration of electrons and holes.

   ![Acceptor Atoms](attachment:acceptor_atoms.png)

2. **Problem 2:**
   A sample of silicon at room temperature and in thermal equilibrium is doped with donor atoms such that \(N_D = 4 \times 10^{15} \text{cm}^{-3} \). Determine the concentration of electrons and holes.

   ![Donor Atoms](attachment:donor_atoms.png)

3. **Problem 3:**
   A silicon-based pn-junction at room temperature is doped such that \(N_A = 10^{15} \text{cm}^{-3} \) and \(N_D = 4 \times 10^{15} \text{cm}^{-3}\). A voltage of -2V is applied. Determine the junction capacitance per unit area.

   ![PN Junction](attachment:pn_junction
Transcribed Image Text:### Parameters to Use for the Problems that Follow - **K** = 1.38 × 10⁻²³ J/K - **q** = 1.6 × 10⁻¹⁹ coulombs ### For Silicon at Room Temperature (T = 300K) - **E_G** = 1.12 eV - **n_i** = 1 × 10¹⁰ cm⁻³ - **ε_Si** = **K_Siε_0** = (11.8)(8.85 × 10⁻¹⁴) F/cm - **μ_p** = 384.62 cm²/V·sec, **D_p** = 10 cm²/sec - **μ_n** = 1230.77 cm²/V·sec, **D_n** = 32 cm²/sec - **τ_n** = 2.0 × 10⁻⁴ sec, **τ_p** = 9.0 × 10⁻⁵ sec - **L_n** = 8.0 × 10⁻² cm, **L_p** = 3.0 × 10⁻² cm ### Problems 1. **Problem 1:** A sample of silicon at room temperature and in thermal equilibrium is doped with acceptor atoms such that \(N_A = 10^{15} \text{cm}^{-3} \). Determine the concentration of electrons and holes. ![Acceptor Atoms](attachment:acceptor_atoms.png) 2. **Problem 2:** A sample of silicon at room temperature and in thermal equilibrium is doped with donor atoms such that \(N_D = 4 \times 10^{15} \text{cm}^{-3} \). Determine the concentration of electrons and holes. ![Donor Atoms](attachment:donor_atoms.png) 3. **Problem 3:** A silicon-based pn-junction at room temperature is doped such that \(N_A = 10^{15} \text{cm}^{-3} \) and \(N_D = 4 \times 10^{15} \text{cm}^{-3}\). A voltage of -2V is applied. Determine the junction capacitance per unit area. ![PN Junction](attachment:pn_junction
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