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A Si wafer has been doped n-type with 10¹7 As atoms cm³. (1) Where is the Fermi level in this sample at room temperature (27 °C) with respect to the Fermi level (EFi) in intrinsic Si? (2) Draw a schematic energy band diagram of the above systems (Indicate the valence band, conduction band, vacuum energy level, Fermi energy level, electron affinity, and work function in the diagram). Locate the Fermi energy level for n-type with As atoms 1017 cm-3 in your drawing. What is the ionization energy of an As atom?

A Si wafer has been doped n-type with 10¹7 As atoms cm³. (1) Where is the Fermi level in this sample at room temperature (27 °C) with respect to the Fermi level (EFi) in intrinsic Si? (2) Draw a schematic energy band diagram of the above systems (Indicate the valence band, conduction band, vacuum energy level, Fermi energy level, electron affinity, and work function in the diagram). Locate the Fermi energy level for n-type with As atoms 1017 cm-3 in your drawing. What is the ionization energy of an As atom?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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A Si wafer has been doped n-type with 10¹⁷ As atoms cm⁻³. 1. **Question:** Where is the Fermi level in this sample at room temperature (27 °C) with respect to the Fermi level (\(E_{Fi}\)) in intrinsic Si? 2. **Task:** Draw a schematic energy band diagram of the above systems. Indicate the valence band, conduction band, vacuum energy level, Fermi energy level, electron affinity, and work function in the diagram. Locate the Fermi energy level for n-type with As atoms 10¹⁷ cm⁻³ in your drawing. What is the ionization energy of an As atom? **Diagram Explanation:** - **Valence Band:** The energy band in a semiconductor where electrons are present at absolute zero temperature. - **Conduction Band:** The energy band where free electrons can exist, allowing electrical conduction. - **Vacuum Energy Level:** The energy reference level outside the material where electrons are free of the solid. - **Fermi Energy Level (\(E_F\)):** The energy difference between the highest and lowest occupied single-particle states at absolute zero. - **Electron Affinity:** The energy released when an electron is added to the conduction band. - **Work Function:** The energy required to remove an electron from the Fermi level to the vacuum level. The Fermi level in n-type Si doped with 10¹⁷ As atoms is closer to the conduction band compared to intrinsic Si, indicating increased electron concentration. The exact ionization energy of an As atom in the context of Si doping must be considered for precise calculations in practical applications.
Transcribed Image Text:A Si wafer has been doped n-type with 10¹⁷ As atoms cm⁻³. 1. **Question:** Where is the Fermi level in this sample at room temperature (27 °C) with respect to the Fermi level (\(E_{Fi}\)) in intrinsic Si? 2. **Task:** Draw a schematic energy band diagram of the above systems. Indicate the valence band, conduction band, vacuum energy level, Fermi energy level, electron affinity, and work function in the diagram. Locate the Fermi energy level for n-type with As atoms 10¹⁷ cm⁻³ in your drawing. What is the ionization energy of an As atom? **Diagram Explanation:** - **Valence Band:** The energy band in a semiconductor where electrons are present at absolute zero temperature. - **Conduction Band:** The energy band where free electrons can exist, allowing electrical conduction. - **Vacuum Energy Level:** The energy reference level outside the material where electrons are free of the solid. - **Fermi Energy Level (\(E_F\)):** The energy difference between the highest and lowest occupied single-particle states at absolute zero. - **Electron Affinity:** The energy released when an electron is added to the conduction band. - **Work Function:** The energy required to remove an electron from the Fermi level to the vacuum level. The Fermi level in n-type Si doped with 10¹⁷ As atoms is closer to the conduction band compared to intrinsic Si, indicating increased electron concentration. The exact ionization energy of an As atom in the context of Si doping must be considered for precise calculations in practical applications.
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