a) Using the depletion approximation and C = dQs/dV, derive Eq (7.12) in the Semiconductor Device Fundamentals textbook: 2 NB(x) = qK,EgA²d(1/C})/dv Note that under the depletion approximation Qs = QANBW (assuming a one-side junction), where W is the depletion region width on the lightly doped side. Also recall that the reverse- KEQA biased capacitance C = C :
a) Using the depletion approximation and C = dQs/dV, derive Eq (7.12) in the Semiconductor Device Fundamentals textbook: 2 NB(x) = qK,EgA²d(1/C})/dv Note that under the depletion approximation Qs = QANBW (assuming a one-side junction), where W is the depletion region width on the lightly doped side. Also recall that the reverse- KEQA biased capacitance C = C :
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![**Topic:** Derivation Using Depletion Approximation in Semiconductor Devices
**Objective:** To derive Equation (7.12) using the depletion approximation and capacitance relationship from the Semiconductor Device Fundamentals textbook.
### Problem Statement:
**a)** Using the depletion approximation and \( C = dQ_s/dV \), derive Equation (7.12) from the textbook.
\[ N_B(x) = \frac{2}{qK_s \varepsilon_0 A^2 d(1/C_J^2)/dV} \]
### Key Concepts:
- **Depletion Approximation:** Assumes that charge carriers are completely depleted in a region of a semiconductor.
- **Charge and Capacitance Relationship:** \( C = dQ_s/dV \), where \( C \) is the capacitance, \( Q_s \) is the charge, and \( V \) is the voltage.
### Notes:
- Under the depletion approximation, the charge (\( Q_s \)) is expressed as:
\[ Q_s = qAN_BW \]
Where:
- \( q \) is the charge of an electron.
- \( A \) is the area of the semiconductor.
- \( N_B \) is the concentration of impurity atoms.
- \( W \) is the depletion region width on the lightly doped side, assuming a one-side junction.
- The reverse-biased capacitance is given by:
\[ C = C_J = \frac{K_s \varepsilon_0 A}{W} \]
Where:
- \( K_s \) is the relative permittivity of the semiconductor.
- \( \varepsilon_0 \) is the permittivity of free space.
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Transcribed Image Text:**Topic:** Derivation Using Depletion Approximation in Semiconductor Devices
**Objective:** To derive Equation (7.12) using the depletion approximation and capacitance relationship from the Semiconductor Device Fundamentals textbook.
### Problem Statement:
**a)** Using the depletion approximation and \( C = dQ_s/dV \), derive Equation (7.12) from the textbook.
\[ N_B(x) = \frac{2}{qK_s \varepsilon_0 A^2 d(1/C_J^2)/dV} \]
### Key Concepts:
- **Depletion Approximation:** Assumes that charge carriers are completely depleted in a region of a semiconductor.
- **Charge and Capacitance Relationship:** \( C = dQ_s/dV \), where \( C \) is the capacitance, \( Q_s \) is the charge, and \( V \) is the voltage.
### Notes:
- Under the depletion approximation, the charge (\( Q_s \)) is expressed as:
\[ Q_s = qAN_BW \]
Where:
- \( q \) is the charge of an electron.
- \( A \) is the area of the semiconductor.
- \( N_B \) is the concentration of impurity atoms.
- \( W \) is the depletion region width on the lightly doped side, assuming a one-side junction.
- The reverse-biased capacitance is given by:
\[ C = C_J = \frac{K_s \varepsilon_0 A}{W} \]
Where:
- \( K_s \) is the relative permittivity of the semiconductor.
- \( \varepsilon_0 \) is the permittivity of free space.
**There are no graphs or diagrams in this transcription to describe.**
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