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For GaAs: &= 10.9 (dielectric constant) meffective, e = 0.068 bare 4.42 x 1022 n me atomic 3 cm nintrinsic Pintrinsic = 1 x 107/cm³ (lower than Si because the bandgap is larger) Say we have a piece of GaAs doped N-type with ND = 5 x 10¹6/cm³ (typical for devices) a) Calculate the donor binding energy Eb. b) Calculate the hydrogenic radius (call it rGaAs). c) Calculate the “freeze-out” temperature (KBT freeze-out = Eb), below which most of the donor atoms do not give up their electrons to be promoted thermally to the conduction band. d) Calculate the donor concentration at which nearby orbits would just touch. (Assume the donors are arranged in a simple cubic lattice.) Call this noverlap. (Note: When ND > noverlap, es can ‘junp' from one donor to another, forming "impurity bands" which contributesd to conduction.) e) Calculate the electric field strength (dielectrically screened) at a distance rGaAs from a net (+1e) charge. (Remember, the screened field is just the bare Coulomb field divided by ε.)

For GaAs: &= 10.9 (dielectric constant) meffective, e = 0.068 bare 4.42 x 1022 n me atomic 3 cm nintrinsic Pintrinsic = 1 x 107/cm³ (lower than Si because the bandgap is larger) Say we have a piece of GaAs doped N-type with ND = 5 x 10¹6/cm³ (typical for devices) a) Calculate the donor binding energy Eb. b) Calculate the hydrogenic radius (call it rGaAs). c) Calculate the “freeze-out” temperature (KBT freeze-out = Eb), below which most of the donor atoms do not give up their electrons to be promoted thermally to the conduction band. d) Calculate the donor concentration at which nearby orbits would just touch. (Assume the donors are arranged in a simple cubic lattice.) Call this noverlap. (Note: When ND > noverlap, es can ‘junp' from one donor to another, forming "impurity bands" which contributesd to conduction.) e) Calculate the electric field strength (dielectrically screened) at a distance rGaAs from a net (+1e) charge. (Remember, the screened field is just the bare Coulomb field divided by ε.)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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For GaAs: &= 10.9 (dielectric constant) meffective, e = 0.068 bare 4.42 x 1022 n me atomic 3 cm nintrinsic Pintrinsic = 1 x 107/cm³ (lower than Si because the bandgap is larger) Say we have a piece of GaAs doped N-type with ND = 5 x 10¹6/cm³ (typical for devices) a) Calculate the donor binding energy Eb. b) Calculate the hydrogenic radius (call it rGaAs). c) Calculate the “freeze-out” temperature (KBT freeze-out = Eb), below which most of the donor atoms do not give up their electrons to be promoted thermally to the conduction band. d) Calculate the donor concentration at which nearby orbits would just touch. (Assume the donors are arranged in a simple cubic lattice.) Call this noverlap. (Note: When ND > noverlap, es can ‘junp' from one donor to another, forming "impurity bands" which contributesd to conduction.) e) Calculate the electric field strength (dielectrically screened) at a distance rGaAs from a net (+1e) charge. (Remember, the screened field is just the bare Coulomb field divided by ε.)
Transcribed Image Text:For GaAs: &= 10.9 (dielectric constant) meffective, e = 0.068 bare 4.42 x 1022 n me atomic 3 cm nintrinsic Pintrinsic = 1 x 107/cm³ (lower than Si because the bandgap is larger) Say we have a piece of GaAs doped N-type with ND = 5 x 10¹6/cm³ (typical for devices) a) Calculate the donor binding energy Eb. b) Calculate the hydrogenic radius (call it rGaAs). c) Calculate the “freeze-out” temperature (KBT freeze-out = Eb), below which most of the donor atoms do not give up their electrons to be promoted thermally to the conduction band. d) Calculate the donor concentration at which nearby orbits would just touch. (Assume the donors are arranged in a simple cubic lattice.) Call this noverlap. (Note: When ND > noverlap, es can ‘junp' from one donor to another, forming "impurity bands" which contributesd to conduction.) e) Calculate the electric field strength (dielectrically screened) at a distance rGaAs from a net (+1e) charge. (Remember, the screened field is just the bare Coulomb field divided by ε.)
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