Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming
The commercial development of novel semiconductor devices requires that their properties be examined as thoroughly and rapidly as possible. These properties are investigated by obtaining numerical solutions of the highly nonlinear coupled set of equations
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E.A.B. Cole
Mathematical and Numerical Modelling of Heterostructure Semiconductor Devices: From Theory to Programming
E.A.B. Cole Department of Applied Mathematics University of Leeds Leeds LS2 9JT UK [email protected]
ISBN 978-1-84882-936-7 e-ISBN 978-1-84882-937-4 DOI 10.1007/978-1-84882-937-4 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2009941547 Mathematics Subject Classification (2000): 15A06, 15A18, 35J05, 35J10, 35J35, 35Q20, 35Q40, 65F15, 65N06, 65N22, 65N25, 65N50, 65N55, 65N75, 65Z05, 80A10, 81Q05, 81Q15, 81Q20, 82B05, 82B10, 82B30, 82D37, 82D80 © Springer-Verlag London Limited 2009 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Part of my lecturing work in the School of Mathematics at the University of Leeds involved teaching quantum mechanics and statistical mechanics to mathematics undergraduates, and also mathematical methods to undergraduate students in the School of Electronic and Electrical Engineering at the University. The subject of this book has arisen as a result of research collaboration on device modelling with members of the School of Electronic and Electrical Engineering. I wanted to write a book which would be of practical help to those wishing to learn more about the mathematical and numerical methods involved in heterojunction device modelling. I have introduced only a comparatively small number of topics, and the reader may think that other important topics should have been included. But of the topics which I have introduced, I hope that I have given the reader some practical advice concerning the implementation of the methods which are discussed. This practical advice includes demonstrating how the implementation of the methods may be tailored to the specific device being modelled, and also includes some sections of computer code to illustrate this implementa
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