?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F398%2F&rft.title=A+Mathematical+Model+for+Epitaxial+Semiconductor+Crystal+Growth+from+the+Vapor+Phase+on+a+Masked+Substrate&rft.creator=French%2C+D.A.&rft.creator=Pelesko%2C+J.A.&rft.creator=Braun%2C+R.&rft.subject=Materials&rft.description=Certain+materials+used+in+lasers+are+made+by+a+process+called+epitaxial+semiconductor+crystal+growth.+In+this+report+a+mathematical+model+is+developed+for+this+growth+process+which+occurs+on+a+substrate+at+the+junction+between+a+masked+region+and+exposed+substrate+in+a+vapor.+This+new+model+consists+of+two+partial+differential+equations%3B+one+for+the+surface+dynamics+and+one+for+the+crystal+growth+on+the+exposed+substrate.+An+analysis+of+the+steady+state+solutions+is+furnished.+Approximate+solutions+for+time-dependent+cases+are+found+using+two+numerical+methods.+An+asymptotic+analysis+is+also+carried+out+to+determine+transient+solution+behavior.+The+undesireable+%22bump%22+structure+at+the+mask%2Fsubstrate+junction+which+has+been+observed+experimentally+is+present+in+the+solutions+found+by+each+method.&rft.date=1999&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F398%2F1%2FEpitaxial-semiconductor-crystal-growth.pdf&rft.identifier=++French%2C+D.A.+and+Pelesko%2C+J.A.+and+Braun%2C+R.++(1999)+A+Mathematical+Model+for+Epitaxial+Semiconductor+Crystal+Growth+from+the+Vapor+Phase+on+a+Masked+Substrate.++%5BStudy+Group+Report%5D+++++