Transmission Electron Microscopy of Semiconductor Nanostructures: An Analysis of Composition and Strain State

by Rosenauer, Andreas

• ISBN13: 9783540004141
• ISBN10: 3540004149
• Format: Hardcover
• Copyright: 2003-05-01
• Publisher: Springer Verlag

Summary

This book provides tools well suited for the quantitative investigation of semiconductor electron microscopy. These tools allow for the accurate determination of the composition of ternary semiconductor nanostructures with a spatial resolution at near atomic scales. The book focuses on new methods including strain state analysis as well as evaluation of the composition via the lattice fringe analysis (CELFA) technique. The basics of these procedures as well as their advantages, drawbacks and sources of error are all discussed. The techniques are applied to quantum wells and dots in order to give insight into kinetic growth effects such as segregation and migration. In the first part of the book the fundamentals of transmission electron microscopy are provided. These are needed for an understanding of the digital image analysis techniques described in the second part of the book. There the reader will find information on different methods of composition determination. The third part of the book focuses on applications such as composition determination in InGaAs Stranski--Krastanov quantum dots. Finally it is shown how an improvement in the precision of the composition evaluation can be obtained by combining CELFA with electron holography. This is demonstrated for an AlAs/GaAs superlattice.

Table of Contents

Introduction	1	(12)
Strain State Analysis [7, 8, 9, 10]	2	(1)
CELFA [7, 25, 26, 27, 28]	3	(1)
Organization of the Book	4	(9)
References	6	(7)
Part I Theoretical Fundamentals of Transmission Electron Microscopy
Electron Diffraction	13	(20)
Single-Atom Electron Scattering	13	(4)
The Integral Form of the Schrodinger Equation	13	(2)
The Atomic Scattering Amplitude for Electrons	15	(2)
Kinematical Approximation	17	(7)
The Structure Amplitude	17	(1)
The Lattice Amplitude	18	(1)
The Thin-Foil Specimen	19	(2)
Chemical Sensitivity	21	(3)
The Block Wave Approach	24	(5)
Channeling Theory	29	(4)
References	31	(2)
Image Formation	33	(24)
Nonlinear Coherent Imaging	33	(5)
Influence of Aberrations and Defocus of the Objective Lens	34	(2)
Nonlinear Imaging Theory	36	(2)
Effects of Incoherence	38	(8)
Spatial Incoherence	38	(2)
Temporal Incoherence	40	(2)
The Transmission Cross-Coefficients	42	(1)
Delocalization	42	(4)
Reconstruction of the Electron Wave Function	46	(11)
Focal-Variation Reconstruction	47	(2)
Off-Axis Electron Holography	49	(4)
References	53	(4)
Part II Digital Image Analysis
Strain State Analysis	57	(30)
Displacements and Lattice Spacings	57	(12)
Noise Reduction	58	(2)
Detection of Lattice Sites and Gridding	60	(4)
Calculation of Lattice Base Vectors	64	(1)
Local Displacements and Lattice Spacings	65	(2)
Averaged Displacements and Lattice Spacings	67	(2)
Determination of the Specimen Thickness	69	(8)
Cell Transformation	69	(2)
Determination of Relative Thickness Values	71	(4)
Determination of Absolute Thickness Values	75	(2)
Elastic Relaxation and Finite-Element Calculation	77	(10)
The Analytical Solution of the Thin- and Thick-Sample Limits	77	(3)
Finite-Element Calculations	80	(4)
References	84	(3)
Lattice Fringe Analysis	87	(52)
On the Basic Ideas Behind CELFA	87	(7)
General Aspects and Definitions	87	(3)
Discussion of Optimum Imaging Conditions	90	(3)
Fringe Images	93	(1)
Theoretical Considerations	94	(8)
Calculation of Reflection Amplitudes	94	(5)
Determination of Sample Thickness and Phase φ	99	(3)
Practical Considerations	102	(22)
Measurement Procedure	102	(3)
Example of an Evaluation	105	(3)
Alternative Methods and Noise Reduction	108	(8)
Errors Due to Objective Lens Aberrations	116	(3)
Errors Due to Specimen Thickness Uncertainties	119	(5)
Strain Effects	124	(9)
Variation of Lattice Parameter	126	(2)
Method for Simulation of Strain Effects	128	(4)
Beam Amplitudes and the Effect of Strain	132	(1)
Nonrandom Distribution of Elements	133	(6)
References	136	(3)
Part III Applications
Introduction	139	(8)
Stranski--Krastanov Growth Mode	139	(2)
Segregation in III--V Ternary Alloys	141	(6)
References	144	(3)
In0.6Ga0.4As/GaAs(001) SK Layers	147	(22)
Experimental Setup	147	(1)
Experimental Results	148	(11)
Uncapped Samples	148	(4)
Capped Samples	152	(7)
Discussion and Conclusions	159	(7)
Strain-Induced Migration of Ga	160	(1)
Bulk Interdiffusion	161	(1)
Segregation	162	(1)
Growth Model	163	(2)
Correlation with PL Results	165	(1)
Composition Distribution in Free-Standing Islands	165	(1)
Summary	166	(3)
References	167	(2)
InAs Quantum Dots	169	(24)
Experimental Setup	169	(2)
Experimental Results	171	(13)
Conventional Transmission Electron Microscopy	171	(1)
Investigation of Uncapped Islands	172	(7)
Investigation of Capped Samples	179	(4)
Combination of the Results	183	(1)
Discussion	184	(7)
Correlation Between TEM and PL Data	184	(1)
Segregation Efficiency	185	(1)
Segregation Models	185	(4)
Modeling	189	(1)
Segregation and Mass Transport of Ga	190	(1)
Conclusion	191	(2)
References	191	(2)
Electron Holography: AlAs/GaAs Superlattices	193	(16)
Experimental Setup	193	(1)
Description of the Method	194	(9)
Imaging Condition	194	(2)
Experimental Details	196	(3)
Delocalization	199	(1)
Iterative Computation of the Composition	200	(3)
Discussion	203	(4)
Conclusion	207	(2)
References	207	(2)
Outlook	209	(2)
Appendices	211	(6)
A List of Acronyms Used	213	(2)
References	214	(1)
B Fourier Transform, Convolutions and δ-``Function''	215	(2)
B.1 Fourier Transform	215	(1)
B.2 Convolution	215	(1)
B.3 δ-``Function''	216	(1)
References	216	(1)
Color Plates	217	(18)
Index	235