At T-300 K, for Ge semiconductor, Nc =1.03x1019 cm3, Ny = 5.35x1018 cm3, calculate the intrinsic carrier density. Eg = 0.66 eV. Comparing to Si, the intrinsic carrier density is larger or smaller? What is the dominant factor that caused the difference? (Show details, not just an answer.)
At T-300 K, for Ge semiconductor, Nc =1.03x1019 cm3, Ny = 5.35x1018 cm3, calculate the intrinsic carrier density. Eg = 0.66 eV. Comparing to Si, the intrinsic carrier density is larger or smaller? What is the dominant factor that caused the difference? (Show details, not just an answer.)
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![**Title: Calculating Intrinsic Carrier Density for Ge Semiconductor**
**Introduction:**
Explore the intrinsic carrier density of a Germanium (Ge) semiconductor at room temperature (300 K) and compare it to Silicon (Si). Understand the factors influencing the intrinsic carrier densities through calculations and comparisons.
**Problem Statement:**
At T = 300 K for a Ge semiconductor, we have:
- Effective density of states in the conduction band, \( N_c = 1.03 \times 10^{19} \, \text{cm}^{-3} \)
- Effective density of states in the valence band, \( N_v = 5.35 \times 10^{18} \, \text{cm}^{-3} \)
- Energy band gap, \( E_g = 0.66 \, \text{eV} \)
**Tasks:**
1. Calculate the intrinsic carrier density of Ge.
2. Compare it with the intrinsic carrier density of Si.
3. Determine whether the intrinsic carrier density for Ge is larger or smaller than that for Si.
4. Identify the dominant factor causing the difference in intrinsic carrier densities between Ge and Si.
**Instructions:**
1. Use the formula for intrinsic carrier density:
\[ n_i = \sqrt{N_c \times N_v} \times e^{\left(-\frac{E_g}{2kT}\right)} \]
Where \( k \) is Boltzmann's constant \( (8.617 \times 10^{-5} \, \text{eV/K}) \) and \( T \) is temperature in Kelvin.
2. Compare the calculated \( n_i \) for Ge with known values for Si.
3. Highlight the role of the energy band gap \( (E_g) \) and its influence on carrier density.
**End Note:**
Ensure to show detailed calculations and comparisons, beyond providing just an answer, to understand the impacts of material properties on semiconductor behavior.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e3992ca-2280-40ba-b65a-68dc98c03d5d%2F589c53e7-c17f-4441-83c2-fc4bbdec2f18%2F6kuxj6c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Intrinsic Carrier Density for Ge Semiconductor**
**Introduction:**
Explore the intrinsic carrier density of a Germanium (Ge) semiconductor at room temperature (300 K) and compare it to Silicon (Si). Understand the factors influencing the intrinsic carrier densities through calculations and comparisons.
**Problem Statement:**
At T = 300 K for a Ge semiconductor, we have:
- Effective density of states in the conduction band, \( N_c = 1.03 \times 10^{19} \, \text{cm}^{-3} \)
- Effective density of states in the valence band, \( N_v = 5.35 \times 10^{18} \, \text{cm}^{-3} \)
- Energy band gap, \( E_g = 0.66 \, \text{eV} \)
**Tasks:**
1. Calculate the intrinsic carrier density of Ge.
2. Compare it with the intrinsic carrier density of Si.
3. Determine whether the intrinsic carrier density for Ge is larger or smaller than that for Si.
4. Identify the dominant factor causing the difference in intrinsic carrier densities between Ge and Si.
**Instructions:**
1. Use the formula for intrinsic carrier density:
\[ n_i = \sqrt{N_c \times N_v} \times e^{\left(-\frac{E_g}{2kT}\right)} \]
Where \( k \) is Boltzmann's constant \( (8.617 \times 10^{-5} \, \text{eV/K}) \) and \( T \) is temperature in Kelvin.
2. Compare the calculated \( n_i \) for Ge with known values for Si.
3. Highlight the role of the energy band gap \( (E_g) \) and its influence on carrier density.
**End Note:**
Ensure to show detailed calculations and comparisons, beyond providing just an answer, to understand the impacts of material properties on semiconductor behavior.
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