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In a microelectronics fabrication operation, boron (a p-type dopant) is to be doped into a silicon. Consider a long cylindrical rod (radius R) of silicon that has an impermeable coating on its curved surface which restricts transport of boron to occur only in the z-direction. Initially, the concentration of boron in the silicon is C³ = 0. At some instant in time, a constant molar flux of boron № is applied to the face at z = 0. Determine the concentration of boron CB (t, z) within the silicon rod. You may assume that the rod extends to infinity. Hint: Simplify the species balance for this situation. Then convert the simplified species balance to an equation for the z-direction flux NR.:(t, z) by taking the z partial derivate of both sides and recalling that from Fick's Law, NB,z=-DB CB Then try a similarity transform approach for NB(t, z).

In a microelectronics fabrication operation, boron (a p-type dopant) is to be doped into a silicon. Consider a long cylindrical rod (radius R) of silicon that has an impermeable coating on its curved surface which restricts transport of boron to occur only in the z-direction. Initially, the concentration of boron in the silicon is C³ = 0. At some instant in time, a constant molar flux of boron № is applied to the face at z = 0. Determine the concentration of boron CB (t, z) within the silicon rod. You may assume that the rod extends to infinity. Hint: Simplify the species balance for this situation. Then convert the simplified species balance to an equation for the z-direction flux NR.:(t, z) by taking the z partial derivate of both sides and recalling that from Fick's Law, NB,z=-DB CB Then try a similarity transform approach for NB(t, z).

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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In a microelectronics fabrication operation, boron (a p-type dopant) is to be doped into a silicon. Consider a long cylindrical rod (radius R) of silicon that has an impermeable coating on its curved surface which restricts transport of boron to occur only in the z-direction. Initially, the concentration of boron in the silicon is C3 = 0. At some instant in time, a constant molar flux of boron N3 is applied to the face at z = 0. Determine the concentration of boron C3 (t, 2) within the silicon rod. You may assume that the rod extends to infinity. Hint: Simplify the species balance for this situation. Then convert the simplified species balance to an equation for the z-direction flux Ng-(t, 2) by taking the z partial derivate of both sides and recalling that from Fick's Law, Ng2 = -Dg' Then try a similarity transform approach for Na(t, z). az
Transcribed Image Text:In a microelectronics fabrication operation, boron (a p-type dopant) is to be doped into a silicon. Consider a long cylindrical rod (radius R) of silicon that has an impermeable coating on its curved surface which restricts transport of boron to occur only in the z-direction. Initially, the concentration of boron in the silicon is C3 = 0. At some instant in time, a constant molar flux of boron N3 is applied to the face at z = 0. Determine the concentration of boron C3 (t, 2) within the silicon rod. You may assume that the rod extends to infinity. Hint: Simplify the species balance for this situation. Then convert the simplified species balance to an equation for the z-direction flux Ng-(t, 2) by taking the z partial derivate of both sides and recalling that from Fick's Law, Ng2 = -Dg' Then try a similarity transform approach for Na(t, z). az
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