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 = 300°K): EG = 1.12eV -3 n₁ = 1 × 10¹0 cm- € Si Ksio (11.8) (8.85 × 10-¹4)F/cm = Hp 384.62cm²/V - sec, Dp = 10cm²/sec = 1230.77cm²/V – sec, - = fln Dn = 32cm²/sec Tn 1 2.0 × 10-¹sec, Tp = 9.0 × 10-5sec = 8.0 × 10-2cm, Ep = 3.0 × 10-²cm En - A sample of silicon at room temperature and in thermal equilibrium is doped with donor atoms such that ND = 4 x 10¹5 cm-³. Determine the concentration of electrons and holes. ND

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### Parameters to Use for the Following Problems

#### Fundamental Constants:
- \( K = 1.38 \times 10^{-23} \, \text{J/K} \)
- \( q = 1.6 \times 10^{-19} \, \text{coulombs} \)

#### For Silicon at Room Temperature (\( T = 300^\circ K \)):
- Energy Gap (\( E_G \)) = 1.12 eV
- Intrinsic Carrier Concentration (\( n_i \)) = \( 1 \times 10^{10} \, \text{cm}^{-3} \)
- Permittivity of Silicon (\( \epsilon_{Si} = K_{Si}\epsilon_0 \))
  - \( K_{Si} = 11.8 \)
  - \( \epsilon_0 = 8.85 \times 10^{-14} \, \text{F/cm} \)

#### Carrier Mobilities and Diffusion Constants:
- Hole Mobility (\( \mu_p \)) = \( 384.62 \, \text{cm}^2/\text{V-sec} \)
- Electron Mobility (\( \mu_n \)) = \( 1230.77 \, \text{cm}^2/\text{V-sec} \)
- Hole Diffusion Constant (\( D_p \)) = \( 10 \, \text{cm}^2/\sec \)
- Electron Diffusion Constant (\( D_n \)) = \( 32 \, \text{cm}^2/\sec \)

#### Carrier Lifetimes:
- Electron Lifetime (\( \tau_n \)) = \( 2.0 \times 10^{-4} \, \sec \)
- Hole Lifetime (\( \tau_p \)) = \( 9.0 \times 10^{-5} \, \sec \)

#### Carrier Diffusion Lengths:
- Electron Diffusion Length (\( L_n \)) = \( 8.0 \times 10^{-2} \, \text{cm} \)
- Hole Diffusion Length (\( L_p \)) = \( 3.0 \times 10^{-2} \, \text{cm} \)

### Problem 1:
A sample of silicon at room temperature and in thermal equilibrium is doped with donor atoms such that \( N_D = 4 \times
Transcribed Image Text:### Parameters to Use for the Following Problems #### Fundamental Constants: - \( K = 1.38 \times 10^{-23} \, \text{J/K} \) - \( q = 1.6 \times 10^{-19} \, \text{coulombs} \) #### For Silicon at Room Temperature (\( T = 300^\circ K \)): - Energy Gap (\( E_G \)) = 1.12 eV - Intrinsic Carrier Concentration (\( n_i \)) = \( 1 \times 10^{10} \, \text{cm}^{-3} \) - Permittivity of Silicon (\( \epsilon_{Si} = K_{Si}\epsilon_0 \)) - \( K_{Si} = 11.8 \) - \( \epsilon_0 = 8.85 \times 10^{-14} \, \text{F/cm} \) #### Carrier Mobilities and Diffusion Constants: - Hole Mobility (\( \mu_p \)) = \( 384.62 \, \text{cm}^2/\text{V-sec} \) - Electron Mobility (\( \mu_n \)) = \( 1230.77 \, \text{cm}^2/\text{V-sec} \) - Hole Diffusion Constant (\( D_p \)) = \( 10 \, \text{cm}^2/\sec \) - Electron Diffusion Constant (\( D_n \)) = \( 32 \, \text{cm}^2/\sec \) #### Carrier Lifetimes: - Electron Lifetime (\( \tau_n \)) = \( 2.0 \times 10^{-4} \, \sec \) - Hole Lifetime (\( \tau_p \)) = \( 9.0 \times 10^{-5} \, \sec \) #### Carrier Diffusion Lengths: - Electron Diffusion Length (\( L_n \)) = \( 8.0 \times 10^{-2} \, \text{cm} \) - Hole Diffusion Length (\( L_p \)) = \( 3.0 \times 10^{-2} \, \text{cm} \) ### Problem 1: A sample of silicon at room temperature and in thermal equilibrium is doped with donor atoms such that \( N_D = 4 \times
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