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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 :

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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. **There are no graphs or diagrams in this transcription to describe.**
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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