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Structural Characterization

  • Paul D. Brown
Part of the Springer Handbooks book series (SPRINGERHAND)

Abstract

The aim of this chapter is to convey the basic principles of x-ray and electron diffraction, as used in the structural characterization of semiconductor heterostructures. A number of key concepts associated with radiation-material and particle-material interactions are introduced, with emphasis placed on the nature of the signal used for sample interrogation. Various modes of imaging and electron diffraction are then described, followed by a brief appraisal of the main techniques used to prepare electron-transparent membranes for TEM analysis. A number of case studies on electronic and photonic material systems are then presented in the context of a growth or device development program; these emphasize the need to use complementary techniques when characterizing a given heterostructure.

The functional properties of semiconductors emanate from their atomic structures; and, the interrelationship between materials processing, microstructure and functional property lies at the heart of semiconductor science and technology. Hence, if we are to elucidate how the functional properties of a semiconductor depend on processing history (the growth or device fabrication procedures used), then we must study the development of the microstructure of the semiconductor by applying an appropriate combination of analytical techniques to the given bulk crystal, heterostructure or integrated device structure.

The main aim of this chapter is to provide a general introduction to the techniques used to characterize the structures of semiconductors. Thus, we consider techniques such as x-ray diffraction (XRD ) and electron diffraction, combined with diffraction contrast imaging, alongside related techniques used for chemical microanalysis, since modern instruments such as analytical electron microscopes (AEM s) provide a variety of operational modes that allow both structure and chemistry to be investigated, in addition to functional activity. For example, chemical microanalyses of the fine-scale structures of materials can be performed within a scanning electron microscope (SEM ) and/or a transmission electron microscope (TEM ), using the techniques of energy dispersive x-ray (EDX ) analysis, wavelength dispersive x-ray (WDX ) analysis or electron energy loss spectrometry (EELS ). In addition, the electrical and optical properties of semiconductors can be investigated in situ using the techniques of electron beam induced conductivity (EBIC ) or cathodoluminescence (CL ), respectively. Techniques such as x-ray photoelectron spectrometry (XPS; also known as electron spectroscopy for chemical analysis, ESCA ), secondary ion mass spectrometry (SIMS ) or Rutherford backscattering spectrometry (RBS ), can also be used to study semiconductor chemistry. We should also mention reflection high-energy electron diffraction (RHEED ), which can be used for the rapid structural assessment of the near surface of bulk or thin film samples.

A far from exhaustive list of acronyms one might come across when assessing a given sample is incorporated into the general list of abbreviations at the start of this book. We can organize these techniques used to characterize materials into groups based on a number of viewpoints: for example, with respect to the material property being investigated; whether they are destructive or nondestructive; bulk or near-surface assessment techniques; based on radiation-material or particle-material interactions, or based on elastic or inelastic scattering processes, or whether they are diffraction-, imaging- or spectroscopic-based techniques.

In this broad introduction to the structural characterization of semiconductors, we focus on the interaction of a material with radiation and/or particles. Thus, we start by considering the interactions of photons, electrons or ions with a sample and the nature of the signals used for structural or chemical microanalysis. We then briefly focus on the techniques of x-ray and electron diffraction, and issues regarding the formation of TEM images. The aim is simply to convey an appreciation of the underlying principles, the applicability of these characterization techniques and the information content provided by them. We also briefly consider aspects of sample preparation, and the chapter closes with a variety of TEM-based case studies of semiconductor heterostructures, which are included to illustrate some of the approaches used to characterize fine-scale microstructure, as well as to emphasise the need for complementary analysis when assessing the interrelationships between processing, structure and functional property. Much literature already exists in this area, and a selection of references is provided at the end of the chapter that tackle many of the topics we cover here in more detail [17.1, 17.10, 17.11, 17.12, 17.13, 17.14, 17.15, 17.16, 17.17, 17.18, 17.19, 17.2, 17.20, 17.21, 17.22, 17.3, 17.4, 17.5, 17.6, 17.7, 17.8, 17.9].

17.1 Radiation-Material Interactions

Each part of the electromagnetic spectrum has quantum energies that can be used to elicit certain forms of excitation at the atomic or molecular level. Different parts of the electromagnetic spectrum will interact with matter in different ways, according to the energy states within the material, allowing absorption or ionization effects to occur. The salient features of these various radiation–material interaction processes are summarized in the schematics shown in Fig. 17.1.
Fig. 17.1

Schematics illustrating the various interactions of energetic radiation with a molecule or atom

As the quantum energy increases from radio waves, through microwaves, to infrared and visible light, absorption increases, whilst specific quantized ionization effects come into play upon moving further into the ultraviolet and x-ray parts of the spectrum. Microwave and infrared radiation, for example, can interact with the quantum states of molecular rotation and torsion, leading to the generation of heat. Strong absorption also occurs within metallic conductors, leading to the induction of electric currents. Visible and ultraviolet light can elevate electrons to higher energy levels in what is known as the photoelectric effect, which is essentially the liberation of electrons from matter by short-wavelength electromagnetic radiation when all of the incident radiation energy is transferred to an electron. This process can be explained in terms of the absorption of discrete photon energies, with electrons being emitted when the photon energy exceeds the material’s work function for the case of weakly bound electrons or the binding energy for more strongly bound inner shell electrons (Fig. 17.2a).
Fig. 17.2a–c

Schematics illustrating (a) the photoelectric effect; (b) characteristic x-ray emission and (c) Auger electron emission

X-ray and γ-ray quantum energies are generally too high to be completely absorbed in direct electron transitions, but they can induce ionization, with the displacement of electrons from atoms to form ions. The relaxation of a high-energy electron to the vacated state can lead to the emission of a characteristic x-ray (Fig. 17.2b) or the emission of an Auger electron (Fig. 17.2 c). During the process of ionization, some of the incident photon energy is transferred to the ejected electron in the form of kinetic energy, and the scattering of a lower energy photon (longer wavelength x-ray) occurs, termed Compton scattering. x-rays can also be scattered elastically by shell electrons, without the loss of energy, through a process of absorption and re-emission.

17.2 Particle-Material Interactions

The interaction of an energetic particle with the surface of a material is most commonly associated with the process of sputtering – the non-thermal removal of atoms from a surface under ion bombardment. Transfer of momentum to the surface atoms is followed by a chain of collision events leading to the ejection of matrix atoms. Figure 17.3 illustrates the various signals produced when a particle interacts with a material, depending on the energy available. In broad terms, processes in the range 104–105 eV are associated with ion implantation, the 10–103 eV energy range is associated with sputtering, whilst the creation of activated point defects occurs in the 1–103 eV range. At lower 0.1–100 eV energies, desorption of surface impurity atoms occurs, whilst energies in the range 0.01–1 eV are associated with the enhanced mobility of surface condensing particles, such as those required during growth. In practical terms, the process of sputtering is most efficient when the masses of the incident and ejected particles are similar, whilst it is also dependent on the sputtering gas pressure, the energy spread of the particles, the bias conditions and the sample geometry.
Fig. 17.3

Schematic illustrating the signals produced by the interaction of an energetic ion beam with a sample

In this context, we should briefly mention the technique of SIMS, which uses heavy ions, typically in the range 2–30 keV, with an ion current density of \(\approx{\mathrm{1}}\,{\mathrm{mA/cm^{2}}}\). The sputtered atoms consist of a mixture of neutrals and ions, and the latter may be mass-spectrally analyzed in order to perform elemental depth profiling. The sensitivity of the technique is very high – for example on the scale of dopant concentrations within semiconductors – but standards are required for quantitative analysis. One variant of SIMS makes use of lower energy primary ions (0.5–2 keV, \(\approx{\mathrm{1}}\,{\mathrm{nA/cm^{2}}}\)) with an almost negligible sputter rate, thus enabling surface chemical analysis. Conversely, the technique of RBS makes use of a very high energy (2–3 MeV) beam of light ions bombarding a sample normal to its surface. An ion such as helium is chosen to avoid the effects of sputtering, whilst high energy is required to overcome the problem of ion neutralization and the screening interaction potential between the ion and the nucleus associated with techniques such as low-energy ion scattering (LEIS ). As an energetic positive ion penetrates the sample it loses energy, mainly due to collisions with electrons, but occasionally (and more significantly) with nuclei. The energy of the backscattered ion depends on the depth of the collision and the mass of the target atom. By measuring the energy spectrum of the recoiling ions, information on elemental composition and depth within a sample can be obtained.

By way of comparison, Fig. 17.4 illustrates the variety of signals produced from the interaction of an energetic beam of electrons with a thin (< 1 μm) semiconductor sample. In order to make sense of the origins of the many different signals, we must consider the phenomenon of electron scattering, which underpins them all. The process of elastic (Rutherford) scattering arises from an electrostatic (Coulomb) interaction with the nucleus and surrounding electrons of an atom, leading to a change in the incident electron direction without loss of energy. Elastically scattered electrons contribute to the formation of diffraction patterns and diffraction contrast images in TEM. Conversely, inelastically scattered electrons have, by definition, lost a certain amount of energy. In this context, core–shell interaction processes produce scattered electrons whose energies depend on the atomic number of the scatterer, and an analysis of the loss of electron energy (up to ≈ 1000 eV) is the basis of the technique of electron energy loss spectroscopy (EELS). In addition, plasmon scattering (5–30 eV loss) can occur, due to the interactions of incident electrons with waves in the conduction band of a metal, or the bonding electrons of non-metals. The signatures from plasmon-scattered electrons can dominate the low-energy regimes of EEL spectra, providing information on sample thickness. Phonon scattering (≈ 1 eV loss) can also occur, which is the interaction of incident electrons with quantized atomic vibrations within a sample, leading to the production of heat. In an interaction of an electron beam with a bulk sample, nearly all of the incident energy ends up being dissipated through such phonon interactions. The probability of each type of scattering interaction is commonly expressed either as a cross-section, representing the apparent area the scattering process presents to the electron, or as a mean free path, which is the average distance the electron travels before being scattered.
Fig. 17.4

Schematic illustrating the signals produced by the interaction of an energetic electron beam with a thin sample foil

A variety of secondary events also occur as a direct consequence of these primary electron scattering processes. For example, following interactions with a high-energy beam of electrons, excited atoms may subsequently relax in a number of different ways (in a similar fashion to the processes induced by incident high-energy x-ray photons). If core-level (inner shell) electrons are displaced, the relaxation of electrons from higher energy shells to the lower energy core states can lead to the discrete emission of x-ray photons characteristic of the atomic number of the element concerned. This is referred to as the K, L, M, N, series, and Moseley’s law states that the square root of the frequency of the characteristic x-rays of this series, for certain elements, is linearly related to the atomic number. Discrimination of these characteristic x-rays, as a function of energy or wavelength, provides the basis for the EDX or the WDX techniques, respectively. Alternatively, a secondary process of Auger electron emission may occur, particularly for low atomic number materials, whereby outer shell electrons are ejected with a characteristic kinetic energy. It should be noted that characteristic x-rays may also induce the emission of lower energy x-rays within a sample, and this is the basis of x-ray fluorescence (XRF ) and the origin of background scintillation during EDX analysis.

Further, if an outer (valence) electron state is vacant, relaxation across the band-gap of a semiconductor may occur with the emission of light, and this constitutes the basis of the CL technique. Alternatively, a current may be induced within a sample and nonradiative recombination pathways in the presence of structural defects (and a collection junction) provide the contrast mechanism for the EBIC technique that profiles the electrical activity within a crystalline semiconductor. Also, incident electrons that interact with atomic nuclei may become backscattered with energies comparable to the incident energy, and used to image a sample surface with contrast that is dependent on the average local composition. Secondary (low-energy, < 50 eV) electrons (SEs), produced by a variety of mechanisms, may also be emitted and escape from the near-surface of a sample. SEs can be used to obtain topographic images of irregular surfaces since they are easily absorbed.

Table 17.1 lists the most commonly used characterization techniques based on x-ray, ion or electron beam interactions with a semiconductor, and broadly indicates their limits of applicability.
Table 17.1

Overview of characterization techniques. EDS = energy dispersive x-ray spectroscopy, BSE = backscattered electron

Technique

Primary beam

Energy

Signals detected

Assessment

Spatial

resolution

Elements detected

Detection limit

AES

Electron

0.5–10 keV

Auger electron

Surface composition

Lateral ≈ 200 nm (LaB6source)

lateral ≈ 20 nm (FE source) depth ≈ 2–20 nm

Li–U

≈ 0.1–1at % (sub-monolayer)

accuracy ≈ 30%

RBS

Ion

(He2+)

> 1 MeV

Ion (He2+)

Depth composition and thickness

Lateral ≈ 1 mm depth ≈ 5–20 nm

B–U

≈ 0.001–10 at %

SEM/EDS

Electron

0.3–30 keV

Electron (SE, BSE) x-ray (characteristic)

Surface morphology and composition

≈ 1–3 nm (SE) ≈ 2–5 nm (BSE) lateral > 0.3 μm(EDS)

depth ≈ 0.5–3 μm(EDS)

B–U

≈ 0.1–1at %

accuracy ≈ 20%(depends on matrix)

SIMS

Ion (Cs+, O 2 + , Ga+)

1–30 keV

Ion (secondary)

Depth trace composition

Lateral ≈ 60 μm (Dynamic SIMS) lateral ≈ 1 μm(Static SIMS)

depth ≈ 2–20 nm

H–U

\(\approx{\mathrm{10^{-10}}}{-}{\mathrm{10^{-5}}}\) at %

TEM/EDS/

EELS

Electron

100–400 keV

Electron (elastic, inelastic)

x-ray (characteristic)

Structure and chemistry of

thin sections (high resolution)

≈ 0.1–0.3 nm

lateral > 2 nm (EDS) lateral ≈ 1 nm(EELS)

energy resolution ≈ 1 eV(EELS)

Up to U

≈ 0.1–1at %

accuracy ≈ 20%(depends on matrix)

XPS

X-ray

1–15 keV

Photo

electron

Surface composition (chemical bonding)

Lateral \(\approx{\mathrm{10}}\,{\mathrm{\upmu{}m}}-{\mathrm{2}}\,{\mathrm{mm}}\)

depth ≈ 1–10 nm

Li–U

≈ 0.1–1at % (sub-monolayer)

accuracy ≈ 30%

XRD

X-ray

1–20 keV

X-ray

Structure

Lateral ≈ 10 μm depth ≈ 0.1–10 μm

Low Z may be difficult to detect

≈ 3 at % in a two-phase mixture (≈ 0.1at % for synchrotron)

accuracy ≈ 10%

XRF

X-ray

30 kV ∕ 20 mA

X-ray (fluorescent)

Composition

Lateral ≈ 0.1–10 mm depth ≈ 10 nm

Na–U

≈ppb–ppm,

accuracy ≈ 10%

17.3 X-ray Diffraction

The basic concepts behind radiation-material interactions and scattering link into the concept of diffraction, whereby the spatial distribution and intensity of scattered x-rays or electrons provide information on the arrangement of atoms in a periodic sample. The theory of wave-particle duality proposes that an electron may be considered to be a wave rather than a particle when discussing diffraction. Electrons are scattered by electric fields within a crystal whilst x-rays are scattered by shell electrons. Nevertheless, the geometry of diffraction is very similar in both cases, being governed by Bragg’s law.

The basic principles of diffraction (in reflection, transmission or glancing angle geometries) may be introduced with reference to x-ray scattering and interference. X-rays are a form of energetic electromagnetic radiation of wavelength \(\approx{\mathrm{10^{-10}}}{-}{\mathrm{10^{-11}}}\,{\mathrm{m}}\), of comparable size to the spacing of atoms within a solid. A crystal lattice comprises a regular array of atoms; and the electron clouds around these atoms act as point sources for spherical x-ray wavelets, through a process of absorption and re-emission, when interaction with an incident x-ray beam occurs. Constructive interference of the scattered wavelets, related to the Huygens’s principle for wave propagation (Fig. 17.5), occurs in preferred directions, depending on the Bravais lattice of the crystal and the x-ray wavelength. The positions of the resultant maxima in scattering intensity may be used to deduce crystal plane spacings and hence the structure of an unknown sample when correlated with database values. Geometrical considerations show that the scattering angles corresponding to diffracted intensity maxima can be described by the Bragg equation nλ = 2dsinθ (sometimes expressed with Miller indices notation as λ = 2d hkl sinθ hkl ). Formally, this equation describes the minimum condition for the coherent diffraction of a monochromatic x-ray beam from a set of planes of a primitive lattice. Figure 17.6 illustrates the geometrical conditions associated with Bragg diffraction from a set of { hkl }  planes spaced d hkl apart, with x-rays incident at a Bragg angle θ being diffracted through an angle 2θ. The path difference between the x-rays reflected from successive planes must be equivalent to an integer number of wavelengths n for constructive interference to occur.
Fig. 17.5

Schematic illustrating Huygens’s principle, with a reconstruction of spherically emitted x-ray wavefronts providing diffracted intensity in specific directions

Fig. 17.6

Geometric illustration of Bragg diffraction. For constructive interference, \({n}{\lambda}=AB+BC=2{d}\sin{\theta}\)

In order to interpret the information contained in the intensity of the diffracted beam, which is measured in practice, it is necessary to consider the amplitude of the elastically scattered waves. (The phase of the scattered beam is much more difficult to measure.) A useful concept to introduce at this stage is that of the atomic scattering factor f, which is a measure of the amplitude of the wave scattered by an atom, which depends on the number of electrons in the atom. Formally, the atomic scattering factor is the ratio of the amplitude of the wave scattered by an atom to the amplitude scattered in the same direction by a free classical electron. (For the purpose of such discussions, an electron orbiting an atom is considered to be a free classical electron.) The scattered amplitude (and hence \(\text{intensity}=|\text{amplitude}|^{2}\)) varies with direction, with higher angles θ being associated with lower amplitudes.

When x-rays interact with a periodic crystal lattice, it is considered that each atom scatters with an amplitude f into an hkl reflection, while there is a summation of all of the scattering amplitudes from different atoms, with phase differences that depend on hkl and the relative positions of the atoms. This leads to the concept of the structure factor, F hkl , which is the total scattering amplitude from all of the atoms in one unit cell of a lattice. Formally, the structure factor is the ratio of the amplitude scattered by a unit cell into an hkl reflection to that scattered in the same direction by a free classical electron. The phase difference between waves scattered from two different atoms depends on the Miller indices of the reflection being considered and the fractional coordinates of the atoms within the unit cell. In general terms, for a reflection from a set of { hkl }  planes, the phase difference φ between the wave scattered by an atom at the origin and that scattered by an atom with fractional coordinates \(x,y,z\) is given by \(\phi=2{\pi}(h{x}+k{y}+l{z})\). In theoretical terms, the resultant intensity of the scattered beam is denoted \({I}_{\textit{hkl}}\propto|{F}_{\textit{hkl}}|^{2}\), where \({F}_{\textit{hkl}}=\sum{f}_{\mathrm{j}}({\theta})\exp(i{\phi}_{\mathrm{j}})\), which is a summation of the individual scattered sinusoidal waves, performed over both phase and amplitude. In a practical diffraction experiment, however, the combination of photoionization and Compton scattering can act to diminish the scattered beam intensity. Consideration also needs to be given to the effects of absorption, along with the effect of multiplicity, which arises from the number of symmetrical variants of a unit cell, and the geometrical and polarization factors specific to a given experimental arrangement.

The crystallographic structure of an unknown material can, nevertheless, be analyzed via the diffraction of x-rays of known wavelength. For example, for a crystal system with orthogonal axes, the general formula which relates plane spacing, d hkl , to the plane index { hkl }  and the lattice parameters \({a},{b},{c}\) is \(1/({d}_{\textit{hkl}})^{2}=h^{2}/{a}^{2}+k^{2}/{b}^{2}+l^{2}/{c}^{2}\). For a cubic system, this simplifies to
$$d_{\textit{hkl}}=\frac{a}{\sqrt{(h^{2}+k^{2}+l^{2})}}=\frac{a}{\sqrt{N}}\;.$$
Thus, \(\lambda=2a\sin\theta/\sqrt{N}\), from which \({N}=(4{a}^{2}/{\lambda}^{2})\times\allowbreak\sin^{2}{\theta}\) and hence N ∝ sin2θ. Accordingly, the 2θ angles of scattering arising from the process of x-ray diffraction may be used to identify values for N, against which hkl indices can be assigned and the lattice identified. Information is contained within the intensities and widths of the diffracted x-ray peaks, in addition to their positions. The process of formal identification can be automated by electronically referencing crystallographic databases containing the positions and relative magnitudes of the strongest diffraction peaks from known compounds. Systematic or partial absences may also occur depending on the lattice symmetry, and the intensities of some peaks may be weak due to the motif of the crystal lattice – the number of atoms associated with each lattice point. For example, sphalerite or wurtzite lattices may show weak reflections that are absent for face-centered cubic or hexagonal close-packed structures, respectively.

Partial differentiation of the Bragg equation gives \(2(\sin{\theta})\delta d+2{d}(\cos{\theta})\delta\theta=0\), from which \(\delta d/\delta\theta=-{d}\cot{\theta}\). Thus, for a fixed error in θ, the error in d hkl will minimize as cotθ tends to zero (as θ tends to 90). Hence, diffraction techniques are more accurate when measurements are made at high 2θ angles. Similarly, it can be shown that the sensitivities and resolutions of diffraction measurements improve at high scattering angles. The sensitivity of the x-ray diffraction technique, for example, is sufficiently high to enable subtle stress measurements to be made, with elastic changes in plane spacings leading to small shifts in diffracted peak positions. Accordingly, diffraction techniques may be used to investigate temperature-dependent order–disorder transitions within alloys and preferred orientation effects. The high accuracy of lattice parameter measurement similarly enables good compositional analysis of an alloy when Vegard’s law applies, i. e., the alloy exhibits a linear dependence of lattice parameter on composition, between the extremes of composition. Brief reference should be made here to the related technique of neutron diffraction, which is able to sample over a much larger range of d hkl spacings, which makes it particularly useful for the ab initio determination of very complex structures. The very rigorous approach of Rietveld refinement can also be used to model a complete diffraction profile, deducing the structure from first principles using atom positions as fitted parameters.

The principle behind the generation of x-rays from characteristic transitions, used when performing chemical microanalyses of unknown samples by EDX or WDX, also provides the route to defining an x-ray source from a known target sample for the purpose of XRD. In practical terms, the x-ray tube of a diffractometer is an evacuated vessel in which electrons from a hot filament are focused onto a cooled metal target, such as Cu or Ni. The x-ray spectrum generated consists of x-rays characteristic of the target material, along with a background emission of x-rays of continuous wavelengths, termed Bremsstrahlung (braking radiation), which are caused by the acceleration of electrons in the vicinity of nuclei. The x-rays emerging from the tube, through a window made from a material of low atomic number, can be filtered and collimated to define a beam of specific wavelength.

The precise geometry used in a diffraction experiment will depend on the form of the sample and the information content required. For example, crystalline samples such as semiconductor heterostructures can be rotated within a cylindrical geometrical framework that enables successive sets of crystal planes to be brought into play for detection. Figure 17.7 illustrates the basic geometrical arrangements for a four-circle diffractometer that allows diffraction data to be acquired. Computer-controlled rotation of the sample around ω, χ and φ axes, as the detector is rotated about the 2θ axis, enables the positions and intensities of hkl reflections to be recorded. By way of example, Fig. 17.8 shows a 2θ ∕ ω plot recorded from a heteroepitaxial GaN/GaAs(001) sample, with reflections attributable to both epilayer and substrate, whilst the full width at half maximum (FWHM ) values for the diffraction peaks provide a measure of the mosaic spread of the subgrains within the sample.
Fig. 17.7

X-ray four-circle diffractometer

Fig. 17.8

Example of a 2θ ∕ ω plot for cubic GaN/GaAs(001)

Since amorphous materials do not exhibit long-range order, their diffraction profiles show diffuse intensities rather than well-defined maxima. Partially crystalline materials may show broad diffraction peaks, from which it is possible to approximate the crystal size from the λ–peak-width relationship. Other x-ray diffraction techniques include Laue back reflection, that can be used conveniently to orient bulk single crystals, for example for sectioning prior to use as substrates for heteroepitaxial growth. Alternatively, the Debye–Scherrer method can be used for powder samples, since a significant number of crystal grains will always be in an orientation that satisfies the Bragg equation for each set of { hkl }  planes. In this scattering arrangement, the diffracted rays form cones coaxial with the incident x-ray beam, with each cone of diffracted rays corresponding to a Bragg reflection from a specific set of lattice planes in the sample.

To reiterate, it is the combination of Bragg’s law and the structure factor equation that enables the directions and intensities of beams scattered from a crystal to be predicted. In this context, it is instructive to briefly compare XRD with electron diffraction. Electrons are scattered by the periodic potential – the electric field – within a crystal lattice, whilst x-rays are scattered by outer shell electrons. Since x-rays and electrons exhibit comparable and comparatively small wavelengths, respectively, on the scale of the plane spacings of a crystal lattice, this equates to large and small angles of scattering, respectively, for the diffracted beams. Accordingly, XRD offers greater accuracy than electron diffraction for the measurement of lattice parameters. It should also be noted that XRD is essentially a kinematic process based on single scattering events, whilst electron diffraction is potentially more complex due to the possibility of dynamic (or plural) scattering processes which can affect the generated intensities. Also, electrons are more strongly absorbed than x-rays, so there is need for very thin sample foils, typically < 1 μm, for the purposes of transmission electron diffraction (TED ) experiments. However, electrons are more easily scattered by a crystal lattice than x-rays, albeit through small angles, so an electron-transparent sample foil is capable of producing intense diffracted beams. X-rays require a much greater interaction volume to achieve a considerable diffraction intensity. The effectiveness of the technique of electron diffraction becomes most apparent when combined with TEM-based chemical microanalysis and imaging techniques. This enables features such as small grains and embedded phases, or linear or planar defect structures such as dislocations and domain boundaries, to be investigated in detail.

Before describing some variants of the electron diffraction technique, a few concepts related to imaging and modes of operation of the TEM need to be introduced.

17.4 Optics, Imaging and Electron Diffraction

The aim of a microscope-based system is to image an object at high magnification, with optimum resolution and without distortion. The concepts of magnification and resolution associated with imaging in electron microscopy are usually introduced via light ray diagrams for optical microscopy. The constraints on achieving optimum resolution in TEM are generally considered to be lens aberration and astigmatism. The concepts of depth of field and depth of focus must also be considered.

If we consider the objective lens shown in Fig. 17.9, a single lens is characterized by a focal length f and a magnification M. The expression \(1/{f}=1/{u}+1/{v}\) relates the focal length to the object distance u and the image distance v for a thin convex lens. The magnification of this lens is then given by \({M}={v}/{u}={f}/({u}-{f})=({v}-{f})/{f}\), from which it is apparent that u − f must be small and positive for a large magnification to be obtained. In practice, a series of lenses are used to achieve a high magnification overall whilst minimizing distortion effects. For the combined projection optical microscope system shown in Fig. 17.9, magnification scales as \({M}^{\prime}=({v}-{f})({v}^{\prime}-{f}^{\prime})/{ff}^{\prime}\).
Fig. 17.9

Schematic ray diagram for a transmission projection optical microscope

Resolution may be defined as the smallest separation of two points on an object that can be reproduced distinctly within an image. The resolution of an optical lens system is diffraction-limited since light must pass through a series of apertures, and so a point source is imaged as a set of Airy rings. Formally, the minimum resolvable separation of two point sources, imaged as two overlapping sets of Airy rings, is given by the Rayleigh criterion, whereby the center of one set of Airy rings overlaps the first minimum of the second set of Airy rings. The defining equation for resolution is given by \({r}=0.61{\lambda}/{n}\sin{\alpha}\), where λ is the wavelength of the imaging radiation, n is the refractive index of the lens, and α is the semiangle subtended at the lens. The combined term nsinα is the numerical aperture of the lens. Thus, resolution can be improved by decreasing λ or by increasing n or α. It is noted that magnification beyond the resolution limit of the system is possible, but there is no benefit to achieving this, and so it is termed empty magnification.

The performance of a TEM can be described in analogous terms, comprising an electron gun and a series of electromagnetic lenses for sample illumination, image formation and magnification: the condenser, objective and projector systems, respectively (Fig. 17.10). The electron source can be either a hot filament (e. g., W or LaB6) for thermionic emission, or a hot or cold cathode (e. g., ZrO2 coated W) for field emission. The gun and lenses are traditionally assembled in a column with a viewing screen and camera at the bottom to record images or diffraction patterns from an electron-transparent sample placed within the objective pole piece. A range of differently sized apertures are located in the condenser system to help collimate the electron probe, in the projector system to select a region of sample from which a diffraction pattern may be formed, and in the objective lens just below the sample to select the transmitted beam(s) used to form an image. The path of travel of the electron beam through the entire electron-optic column must be under conditions of high vacuum, considering the ease of absorption of electrons in air. The electrons are accelerated by high voltage, typically 100 or 200 kV, although there are TEMs that operate at MV conditions, depending on the intended application. An accelerated, high-energy electron acquires significant kinetic energy and momentum. It can also be represented by a wavelength (corrected to take into account relativity) that can be approximated in nanometers by \({\lambda}=[1.5/({V}+{\mathrm{10^{-6}}}{V}^{2})]^{0.5}\). By way of example, an electron beam within a conventional TEM operating at 200 kV has a relativistically corrected wavelength of 0.0025 nm, as compared with the range of ≈ 400–700 nm for visible light. Since resolution is wavelength-limited, the technique of TEM is, in principle, able to provide a vast improvement in resolution over conventional optical systems. The equation for resolution becomes approximated by \({r}\approx 0.61{\lambda}/{\alpha}\) since n = 1 for electromagnetic lenses and sinα ≈ α in view of the small angles associated with electron diffraction. A value of α ≈ 150 mrad would suggest a resolution approaching ≈ 0.01 nm. However, this level of resolution for TEM is generally not achievable in practice due to the effect of lens aberration, which degrades the resolution of an image to a disc of least confusion above the theoretical wavelength-limited resolution of the electron-optic system. Resolution values of ≈ 0.2–0.3 nm are associated with the best conventional instruments. (When charting the historical development of TEM, improvements in resolution have depended on the construction of microscopes operating at higher voltages, in order to capitalize on the benefits from the reduced electron wavelength. However, it should be noted that recent improvements in techniques of compensating for spherical and chromatic aberration have now enabled a resolution of ≲ 0.1 nm to be achieved for intermediate-voltage, field emission gun instruments.)
Fig. 17.10

Simplified lens configuration of a TEM

The variation in focal length of a lens as a function of the distance of a beam from the center of the lens results in rays traveling further from the optic axis being brought to focus closer to the lens (Fig. 17.11a-ca). This spread in path lengths of rays traveling from an object to the image plane is termed spherical aberration. In this case, the radius of the disc of least confusion is given by rs = Csα3, when referred back to the object, where Cs is termed the spherical aberration coefficient and α is again the semiangle, in radians, subtended at the lens. Spherical aberration can be limited by reducing α; in other words by stopping down the lens by using smaller apertures (in this case, the term α corresponds to the aperture collection angle). However, this conflicts with the large value of α needed to optimize resolution, so a balance is required for optimum resolution, which is achieved when \({\alpha}_{\text{opt}}\sim({\lambda}/{C}_{\mathrm{s}})^{1/4}\), corresponding to an effective resolution of \({r}_{\text{opt}}\sim{\lambda}^{3/4}{C}_{\mathrm{s}}^{1/4}\). Lenses also exhibit different focal lengths for electrons with different wavelengths; such a spread of wavelengths can arise from slight fluctuations in the accelerating voltage or from inelastic scattering (energy loss) processes within the specimen, and this effect is termed chromatic aberration (Fig. 17.11a-cb). The radius of the disc of least confusion in this instance is given by \(r_{\mathrm{c}}={C}_{\mathrm{c}}{\alpha}(\Updelta E/{E}_{0})\), where Cc is the chromatic aberration coefficient, E0 the accelerating voltage and ΔE the spread in electron energy.
Fig. 17.11a–c

Schematic illustration of (a) spherical aberration; (b) chromatic aberration and (c) astigmatism

An additional aberration, termed astigmatism, arises from the asymmetry of a lens about the optic axis. The different focal lengths of a lens for different orientations leads to a loss of sharpness of the image at focus. One measure of the astigmatism is the distance between the two foci formed at right angles along the optic axis (Fig. 17.11a-cc), in contrast to a single point of focus. Astigmatism may be compensated for by using electromagnetic stigmators that generate a compensating field to bring the rays back into common focus. Distortion of an image can also occur due to slight variations in magnification with radial distance from the optic axis, leading to so-called pin-cushion or barrel distortion. This effect can become particularly noticeable at very low magnification.

The term depth of field is defined as the distance along the optic axis that an object can be moved without noticeably reducing the resolution. This effect is again dependent on the radius of the disc of least confusion that can be tolerated and α. The depth of field approximates to λ ∕ α2, and a typical value of a few tens of nm for electron microscopy means that every point within the thickness of a typical electron-transparent foil can be imaged at focus. Conversely, the depth of focus corresponds to the maximum permissible spacing between the imaging screen and the photographic plate or CCD used to record an image. The depth of focus approximates to λM2 ∕ α2, and since this works out at many meters, the viewing screen and recording system of an electron microscope need not coincide.

Following on from these general considerations affecting the process of imaging, we now move on to briefly describe the conventional modes of operation of a TEM. The accelerating stack and condenser system of the microscope defines the high-energy electron probe incident at a thin sample, within which many complex interactions occur and various signals are produced, as detailed earlier. A diffraction pattern is initially formed in the back focal plane of the objective lens and the recombination of diffracted beams allows the reconstruction of an inverted image in the first image plane. Changing the strengths of the intermediate lenses allows the back focal plane (corresponding to a projection of reciprocal space) or image plane (corresponding to a projection of real space) to be observed on the viewing screen (Fig. 17.12a,ba,b). Placing an aperture with selected area in an intermediate image plane, around a feature of interest within a projected image, ensures that only beams from that particular area of the sample contribute to the diffraction pattern viewed on the screen.
Fig. 17.12a,b

Schematic ray diagrams showing the projection of (a) a diffraction pattern and (b) an image onto a TEM viewing screen

It is sometimes convenient to think of the intersection of an Ewald sphere with a reciprocal lattice when describing the construction and projection of a diffraction pattern. A reciprocal lattice is constructed from a crystal lattice such that any vector from the origin to a diffracted spot is normal to a particular plane in the real lattice, with a reciprocal length given by the plane spacing. Thus, a three-dimensional crystal lattice can be transformed into a three-dimensional reciprocal lattice (mathematically, the process is a Fourier transform). The Ewald sphere can be thought of as a geometrical construction of radius 1 ∕ λ intersecting the reciprocal lattice. Figure 17.13a-ca illustrates the construction of an Ewald sphere for the case of large-angle scattering (x-ray diffraction). The direction of the incident beam at the sample corresponds to the direction of the vertical radius of the Ewald sphere, and the point of emergence of this vector at the sphere surface, coincident with a reciprocal lattice point, is taken as the origin 000 of the diffraction pattern. The same construction applies for a beam of electrons, but the sphere surface has very shallow curvature relative to the reciprocal lattice spacings, due to the very small value of λ relative to d hkl (Fig. 17.13a-cb). Further, diffraction from a thin crystal is associated with a lengthening of the reciprocal lattice spots into rods in a direction parallel to the electron beam. Consequently, if the electron beam is incident along a low index zone axis, the Ewald sphere approximates to a plane and intersects a layer of reciprocal lattice points, and a two-dimensional array of diffraction spots is projected. In very general terms, it is considered that a set of { hkl }  planes is at the Bragg condition when the reciprocal lattice point corresponding to hkl falls on the surface of the Ewald sphere. For the case of larger angles of electron diffraction, an outer ring of diffraction spots may be observed, termed a high-order Laue zone (HOLZ ), since the Ewald sphere has sufficient curvature to intersect with a neighboring layer of points within the reciprocal lattice (Fig. 17.13a-cc).
Fig. 17.13a–c

Ewald sphere construction for (a) x-ray diffraction (large angle scattering); (b) electron diffraction (zone axis projection) and (c) electron diffraction (tilted projection)

We should also mention the Kikuchi lines that arise in diffraction patterns due to the elastic scattering of incoherently scattered electrons. The intensities of these Kikuchi lines increase with increasing thickness of sample foil, and the line spacings are the same as the spacings of the diffraction spots from the associated crystal planes. Kikuchi lines move as the sample is tilted and hence can be used to establish very precise crystal orientations for the purpose of image contrast or convergent beam electron diffraction (CBED ) experiments.

Referring back to Fig. 17.12a,b, a diffracted beam may be selected using an aperture inserted into the back focal plane of the objective lens and used to form an image. If the undeviated, transmitted beam is used, then a bright field image is formed where the areas that diffract strongly appear dark. Image contrast also arises from a mass-thickness effect, whereby thicker or high-density regions of material scatter more strongly and hence appear dark. Alternatively, a centered dark field image may be created by tilting the illumination to center the diffracted beam, termed a g hkl reflection, down the optic axis of the microscope (in contrast to moving the aperture over the diffraction spot, which would increase aberrations and degrade resolution). Areas where the { hkl }  planes diffract strongly appear bright in such cases. Weak beam images can also be produced under dark field imaging conditions, with the sample tilted slightly away from a strong Bragg condition. The trade-off, in this instance, is reduced image contrast for the improved resolution, which allows fine detailed features, such as partial dislocations bounding dissociated dislocations, to be delineated.

By way of example, Fig. 17.14 shows the different contrasts obtained from a plan-view Si/Si0.96Ge0.04/Si(001) sample foil imaged under bright-field and weak-beam diffraction conditions, respectively. The sample foil contains orthogonal arrays of interfacial misfit dislocations that are generated as a consequence of the relaxation of the strain arising from the different lattice parameters of Si and Si0.96Ge0.04 [17.23]. The strain fields around the dislocations lead to a local deviation away from the exact Bragg condition, which can be used to delineate the (approximate) positions of the dislocation cores. The weak beam technique allows for complex dislocation tangle to be resolved more clearly. Imaging such sample foils using different diffraction vectors produces different contrasts that allow the nature of the dislocations to be precisely determined. Hence, the dislocation reaction mechanisms responsible for microstructure development can, in principle, be identified.
Fig. 17.14

(a) Bright-field and (b) weak-beam plan-view TEM images of Si/SiGe/Si(001)

Some examples are now presented that illustrate how electron diffraction can contribute to the structural characterization of semiconductors. The use of conventional TED combined with image contrast analysis to assess the defect microstructure of a semiconductor heterostructure is initially considered. The application of the CBED technique, sometimes termed microdiffraction, in order to determine the polarities of noncentrosymmetric crystals is then described. We also focus on the RHEED technique, which may be used for rapidly assessing the near-surface microstructures of semiconductor thin films.

17.4.1 Electron Diffraction and Image Contrast Analysis

Figure 17.15 shows a TED pattern corresponding to a highly symmetric, low-index, zone axis projection, acquired from an electron-transparent foil of epitaxial GaN grown on the {0001} basal plane of sapphire, viewed in cross-section under spread beam conditions, i. e., near-parallel illumination.
Fig. 17.15

TED pattern acquired from epitaxial GaN/sapphire{0001} viewed in cross-section, corresponding to the \(\left\langle 11\overline{2}0\right\rangle_{\text{nitride}}||\left\langle 1\overline{1}00\right\rangle_{\text{sapphire}}\) axis projection

It is generally instructive to view such diffraction patterns alongside direct images of the sample. Figure 17.16 compares high-resolution electron microscopy (HREM ) and conventional TEM (CTEM ) images of heteroepitaxial GaN–sapphire sample acquired for this projection. The HREM mode of imaging, otherwise termed phase contrast or lattice imaging, makes use of several diffracted beams selected by a large objective aperture; the resulting interference patterns can be used to elucidate the locations of atomic columns (Fig. 17.16a). Careful simulation is required to precisely assign atomic positions within such images, since the contrast is strongly dependent on defocus, foil thickness and sample orientation. However, the structural integrity of the interface between GaN and sapphire can be appraised, along with the presence of nanometer-scale, three-dimensional growth islands formed during the initial stages of epitaxy, prior to layer coverage. Conversely, the conventional many-beam, bright-field image of heteroepitaxial GaN–sapphire (Fig. 17.16b) was created using a small objective aperture placed over the directly transmitted beam, and recorded at lower magnification. The image contrast is again complicated because there are many excited diffracted beams operating for this low-index crystal orientation combined with strain fields associated with the large number of threading defects (\(\approx{\mathrm{10^{10}}}\,{\mathrm{cm^{-2}}}\)) within this sample. Despite this level of defect content, the diffraction pattern of Fig. 17.15 still reflects a high level of crystallographic perfection of the matrix. Also, rotation of this sample foil by 30 about the growth axis enabled a \(\left\langle 1\overline{1}00\right\rangle_{\text{nitride}}||\left\langle 11\overline{2}0\right\rangle_{\text{sapphire}}\) projection to be established, consistent with the hexagonal symmetry of this GaN–sapphire system. Indeed, establishing different diffraction patterns for different sample projections, for known angles of sample tilt, enables the phase and structural relationship of an epilayer and substrate to be clarified.
Fig. 17.16

(a) HREM and (b) many-beam CTEM images of GaN/sapphire{0001}

There is a need to characterize the precise nature of the fine-scale defect content within such samples. Dislocations, for example, generally act as nonradiative recombination centers, which can deleteriously affect the charge transport properties of a semiconductor [17.24]. Gaining an improved understanding of how dislocations are created and how they interact enables us to identify mechanisms that could be used to control their development, thereby improving the growth of a semiconductor and the resultant properties of devices made from it.

Dislocations are one-dimensional defects that can be pure edge, pure screw or mixed edge-screw in character. In certain circumstances, a dislocation can dissociate to form a pair of partial dislocations bounding a stacking fault ribbon, the separation of which depends on the material stacking fault energy. Dislocations can be described with reference to their line direction u and Burgers vector b, representing the closure failure of a loop of equal atomic spacings around the defect core. Dislocations can move through a crystal lattice by glide or climb mechanisms; for example, when under deformation or as part of a strain relaxation mechanism during heteroepitaxial growth. Also, dislocations can interact to either self-annihilate or multiply to generate more dislocations depending on their respective type, habit plane and the slip system of the matrix.

The technique of diffraction contrast analysis allows the nature of dislocations to be ascertained. The approach used is to tilt the sample away from a highly symmetrical, low-index zone axis orientation in order to establish diffraction contrast images under selected two-beam conditions, with one strong diffraction spot excited (g) in addition to the central transmitted beam, corresponding to one set of crystal planes at the Bragg condition. When \(\boldsymbol{g}\cdot\boldsymbol{b}=0\), the displacement associated with a dislocation does not affect the diffracting planes used to form the image and so the defect appears invisible. In practice, two examples of this invisibility condition are generally required to determine the precise displacement associated with a given defect. The dislocation will appear visible when \(\boldsymbol{g}\cdot\boldsymbol{b}=1\) and might show a more complex double image for the case of \(\boldsymbol{g}\cdot\boldsymbol{b}\geq 2\). For example, since a screw dislocation is characterized by a Burgers vector b parallel to the line direction u, the defect is invisible if a diffraction vector perpendicular to the line direction is chosen. In the case of an edge or mixed dislocation where b is not parallel to u, there is a stricter requirement for both \(\boldsymbol{g}\cdot\boldsymbol{b}=0\) and \(\boldsymbol{g}\cdot(\boldsymbol{b}\times\boldsymbol{u})=0\) for true invisibility, otherwise residual contrast might be present that acts to confuse image interpretation. We should also mention the deviation parameter s when establishing a diffracting condition, which represents a short distance in reciprocal space from the exact Bragg condition, since this is associated with imaging artefacts such as extinction contours and thickness fringes that may act to further complicate an image.

Bright-field, dark-field or weak-beam diffraction contrast imaging techniques can be used for defect analysis, depending on the resolution required. By way of example, epitaxial GaN–\(\left\{\overline{1}\overline{1}\overline{1}\right\}\)B GaAs grown by molecular-beam epitaxy (MBE ) at 700C exhibits a mosaic cell structure with subgrain boundaries delineated by predominantly mixed-type threading dislocations (typically \(> {\mathrm{10^{11}}}\,{\mathrm{cm^{-2}}}\)) [17.25]. The epitaxial relationship is given by \([000\overline{1}]_{\text{GaN}}||[\overline{1}\overline{1}\overline{1}]_{\text{GaAs}}\), \([1\overline{1}00]_{\text{GaN}}||[2\overline{1}\overline{1}]_{\text{GaAs}}\) and \([11\overline{2}0]_{\text{GaN}}||[01\overline{1}]_{\text{GaAs}}\), and the mismatch between GaN and GaAs is 38.2% between \(\left\{1\overline{1}00\right\}_{\text{GaN}}\) and \(\left\{2\overline{2}0\right\}_{\text{GaAs}}\), with the epilayer in tensile strain. Figure 17.17a-ca,b are weak-beam images of the epilayer viewed in cross-section near the \([11\overline{2}0]\) zone axis, using \(\boldsymbol{g}=000\overline{2}\) and \(\boldsymbol{g}=1\overline{1}00\), respectively. Most of the dislocations have a line direction of ⟨ 0001 ⟩ . Examples of perfect edge, \(\boldsymbol{b}=1/3\left\langle 11\overline{2}0\right\rangle\), and screw-type dislocations, b =  ⟨ 0001 ⟩ , are apparent, but mostly dislocations (typically ≈ 70%) can be seen in both images, hence they are mixed-type, with Burger’s vector components of a and c, i. e., \(1/3\left\langle 11\overline{2}3\right\rangle\).
Fig. 17.17a–c

Weak-beam images of the same regions of a GaN epilayer viewed in cross-section using (a\(\boldsymbol{g}=000\overline{2}\) and (b\(\boldsymbol{g}=1\overline{1}00\). (c) Schematic diagram summarizing Ishida’s rule for determining b for \({n}={-2}\) and n = 2

It is possible to move this analysis forwards by applying Ishida’s rule, which allows the magnitude and sense of a Burgers vector to be determined if there are terminating thickness fringes at the exit of a dislocation from a wedge-shaped sample foil [17.26]. If there are n fringes terminating at one end of a dislocation, then \(\boldsymbol{g}\cdot\boldsymbol{b}={n}\) and the sign of n ( n > 0 or n < 0 )  is defined according to Fig. 17.16c. For example, the screw dislocation S (Fig. 17.17a-ca) imaged using \(\boldsymbol{g}=000\overline{2}\) has two thickness fringes terminating on the right-hand side of the dislocation, with the dislocation line pointing towards the \([000\overline{1}]\) growth direction. Hence, \(\boldsymbol{g}\cdot\boldsymbol{b}=-2{L}=2\), so b is \([000\overline{1}]\) for this screw-type dislocation. For dislocations of mixed type, Fig. 17.17a-ca,b show that some have strong contrast in both images, while others have strong contrast when imaged using \(\boldsymbol{g}=000\overline{2}\) and weak contrast when \(\boldsymbol{g}=1\overline{1}00\). For the former, for example the dislocation denoted as Ms in Fig. 17.17a-ca, thickness fringes terminate at the left-hand side of the dislocation with reference to the dislocation line pointing downwards along [0001]. Hence, \(\boldsymbol{g}\cdot\boldsymbol{b}=-2L=-2\) for \(\boldsymbol{g}=000\overline{2}\) and \(\boldsymbol{g}\cdot\boldsymbol{b}=-1\) for \(\boldsymbol{g}=1\overline{1}00\), so its Burgers vector is either \(1/3[\overline{2}113]\) or \(1/3[\overline{1}2\overline{1}3]\). For the cases of strong contrast by \(\boldsymbol{g}=000\overline{2}\) and weak contrast by \(\boldsymbol{g}=1\overline{1}00\), such as the dislocation labeled Mw in Fig. 17.17a-ca, such dislocations have b of \(\pm 1/3[11\overline{2}3]\) or \(\pm 1/3[11\overline{2}\overline{3}]\), and the weak contrast is due to \(\boldsymbol{g}\cdot(\boldsymbol{b}\times\boldsymbol{u})\neq 0\). Because the thickness fringes connected with this defect type are not clear in the images, a more precise value for b cannot be determined. It is also noted that some dislocations have opposite values of b to others, such as those denoted as M and N in Fig. 17.17a-ca. These two opposite types of dislocations delineate a subgrain, and the region showing bright contrast when imaged with \(\boldsymbol{g}=1\overline{1}00\) in Fig. 17.17a-cb is a misoriented subgrain, tilted close to the Bragg condition.

17.4.2 Microdiffraction and Polarity

If an electron beam is converged to form a focused probe at the sample, then there will be a range of beam directions within the incident probe and within the transmitted and diffracted beams. This leads to the formation of diffraction patterns comprising discs rather than spots. The fine detail within such microdiffraction or CBED patterns contains space and point group information. Such patterns also provide a sensitive measure of lattice parameters and strain within a sample, and can be used also to assess defect type.

Two examples showing how focused probe diffraction patterns can be used to determine the absolute polarities of sphalerite and wurtzite noncentrosymmetric crystals, in situ in the TEM, are now illustrated. It is often important to know the polar orientation of a heterostructure since this can strongly influence the mode and rate of growth, the incorporation of dopants or impurities, and the development of extended defects, and hence the functional performance of the resulting device structure. The opposite polar faces of noncentrosymmetric crystals [17.27] may be distinguished in practice using appropriate chemical etchants. However, such reagents are discriminatory in their action and need to be correlated with some other experimental technique for the purpose of absolute polarity determination. For most cases of diffraction, there is no difference between the intensities of beams scattered by hkl and \(\overline{h}\overline{k}\overline{l}\) diffracting planes. This indeterminacy is known as Friedel’s law. However, the technique of microdiffraction coupled with a breakdown in Friedel’s law allows the absolute polarities of sphalerite crystals to be determined when the anion and cation sizes are very similar (as with GaAs, ZnSe and CdTe) [17.28]. The diffraction condition shown in Fig. 17.18a corresponds to a projection tilted \(\approx{\mathrm{10}}^{\circ}\) off a GaAs [110] zone axis, arrived at following an \(\approx 00\overline{4}\) Kikuchi band. The interaction of the doubly diffracted high-order, odd-index \(1\overline{1}9\) and \(1\,\overline{1}\,\overline{11}\) beams with directly scattered \(00\overline{2}\) reflection gives rise to destructive interference through the \(00\overline{2}\) disc when all of the reflections are close to the Bragg position. Figure 17.18c, corresponding to a more highly converged incident electron beam, emphasizes the formation of the dark cross through the \(00\overline{2}\) diffraction disc. Similarly, Fig. 17.18b shows the bright cross formed through the opposite 002 diffraction disc, by constructive interference following interaction with the corresponding 1 \(\overline{1}\) 11 and \(1\overline{1}\overline{9}\) high-order, odd-index reflections. Figure 17.18d,e, showing the [110] and \([1\overline{1}0]\) projections of the sphalerite space lattice and reciprocal lattice, respectively, are given, to clarify this particular sample geometry. Establishing such microdiffraction patterns requires carefully balancing crystal orientation, probe convergence and layer thickness, and the technique is found to work best with freshly plasma-cleaned sample foils to minimize the effect of extraneous hydrocarbon contamination (which diffuses out fine-scale contrast under the imaging electron beam).
Fig. 17.18

(ac) Microdiffraction patterns from [110] GaAs. (a) Destructive interference through an \(00\overline{2}\) diffraction disc due to the interaction of doubly diffracted \(1\overline{1}9\) and \(1\overline{1}\,\overline{11}\) beams. (b,c) Constructive and destructive interference through 002 and \(00\overline{2}\) diffraction discs. (d,e) Sphalerite space lattice and reciprocal lattice projections for [110] and \([1\overline{1}0]\), indexed for an electron beam traveling down into the page

The dynamical equations of electron diffraction demonstrate that the 002 reflection, which exhibits constructive interference effects (bright cross), always occurs in the sense of the cation to anion bond (Fig. 17.18d), and hence is always associated with the sense of advancing \(\{\overline{1}\overline{1}\overline{1}\}_{b}\) planes. To emphasise this, defining [001] as the growth direction of an epilayer on an (001) oriented GaAs substrate, and establishing a bright cross through an 002 diffraction disc, for example through the interaction of \(1\overline{1}9\) and \(1\overline{1}\,\overline{11}\) reflections, corresponds to the sense of advancing \((\overline{1}11)_{b}\) and \((1\overline{1}1)_{b}\) planes in the growth direction, which corresponds to the absolute [110] projection of the sample foil. Conversely, a dark cross through an 002 diffraction disc, such as that obtained through the interaction of \(11\overline{9}\) and 1 1 11 reflections, corresponds to the sense of advancing (111) a and \((\overline{1}\overline{1}1)_{a}\) planes in the growth direction, which corresponds to the \([1\overline{1}0]\) projection of the sample foil. Since microdiffraction patterns are directly sensitive to crystallographic polarity, a qualitative interpretation of such results allows the crystal orientation to be determined unambiguously, in situ within the TEM, without reference to any other technique.

Contrast reversals within diffraction discs of systematic row CBED patterns can similarly be used to determine absolute crystal polarity, since Friedel’s law again breaks down due to dynamical scattering. In practice, this approach is found to be most effective when used with noncentrosymmetric crystals that have much larger differences in anion and cation sizes, such as wurtzite GaN [17.29]. Figure 17.19 presents a thin section through a columnar defect, imaged within homoepitaxial GaN grown on an N-polar \((000\overline{1})\) GaN substrate, with two associated CBED patterns inset, recorded either side of the boundary plane corresponding to matrix and core material, respectively. Simulation of the contrast within the 0002 diffraction discs, for a known sample foil thickness, demonstrates that the central bright and dark bands correspond to N and Ga-polar growth directions, respectively. The reversal of contrast within the 0002 diffraction discs across the boundary plane therefore indicates an inversion in crystal polarity, confirming the defect to be an inversion domain in this instance.
Fig. 17.19

Inversion domain within GaN with CBED patterns recorded across the boundary plane (inset)

17.4.3 Reflection High-Energy Electron Diffraction

Electron-transparent samples are required for TED investigations. For the case of semiconductor heterostructures, sample preparation requires sequential mechanical polishing and ion beam thinning, which can be very time-consuming, but the advantage of this approach is that diffraction data can be directly correlated with projected images of the internal structure of the sample. A complementary approach is to use glancing angle electron diffraction techniques to characterize the near-surface microstructure of a bulk sample or an as-grown heterostructure. Coupling of the electron beam directly with the wafer surface at low angle allows scattering of the electrons to occur, producing a diffraction pattern that may be viewed or recorded directly. This provides valuable information on the near-surface crystallography of the sample, which can be correlated with the growth conditions used or surface modifications applied, without the need for time-consuming sample preparation.

There are three variants of reflection electron diffraction (RED ) depending on the accelerating voltage available:
  • Low (< 1 kV)

  • Medium (1–20 kV)

  • High (20–200 kV) energy.

Medium–energy electron diffraction (MEED ) systems are commonly associated with UHV growth chambers, whilst a variant of RHEED can be performed using a conventional TEM. In general terms, the coupling of an electron beam with a flat single crystal tends to be associated with the formation of diffraction streaks normal to the surface, providing information on the reconstruction of atomic layers at the surface. More precisely, streaky RED patterns are indicative of a surface that is not quite perfectly flat, but has slight local misorientations combined with some degree of surface disorder [17.30]. When electrons are coupled with a slightly rougher surface, there is a tendency for more three-dimensional information to be obtained from interactions with the near-surface microstructure. This leads to the production of spotty diffraction patterns from crystalline materials (half-obscured by the sample shadow edge), in an analogous fashion to TED. It is noted that UHV-MEED systems allow for intensity fluctuations within the central beam to be monitored in real time, providing a way to monitor and control layer-by-layer growth.

In practice, RHEED is used most effectively for rapid comparative studies of samples sets; for appraising the effect of changing the growth parameters on the structural integrity of deposited thin films [17.31]. This approach to process mapping provides a convenient way to identify appropriate samples for more detailed TEM investigation prior to sample foil preparation. There are two variants of the RHEED technique that may be used in a TEM: one where small samples are mounted vertically in the objective lens pole piece, and the other where larger samples are mounted vertically below the projector lens; we focus on the latter variant here.

A schematic illustration of the diffraction geometry for a RHEED experiment is shown in Fig. 17.20a. The diffraction spacing R hkl can be measured and the associated crystal plane spacing d hkl determined using the equation, λL = R hkl d hkl , where λL is known as the camera constant. Figure 17.20b,c shows a RHEED stage made to interface with a TEM through an existing camera port at the base of the projector lens. The vacuum system of the TEM vents the space below the projector lens upon opening the camera chamber, and so the only waiting time is for the chamber to pump down upon changing a specimen. The RHEED stage is able to support centimeter-square sections of a crystalline specimen, whilst full tilt, twist and lateral movements enable any zone axis within the growth plane of the sample to be accessed. A shadow image of a sample, as projected onto the microscope phosphor screen, is shown in Fig. 17.20d. The area sampled by the glancing electron beam is typically ≈ 1 mm2, and so this experimental arrangement is closely associated with glancing angle XRD, although the acquisition time for RHEED data is extremely short, with photographic plate exposure times of ≈ 1 s. Three or four samples can typically be examined within 1 h.
Fig. 17.20

(a) Schematic illustration of the RHEED diffraction geometry; (b) RHEED stage; (c) magnified view of the sample holder; and (d) projected shadow image of a specimen on TEM phosphor screen

The 100 kV RHEED patterns shown in Fig. 17.21a-ca,b were acquired from a highly Si-doped GaN/GaAs(001) heterostructure, grown by MBE at 700C, before and after plasma cleaning. Surface hydrocarbon deposits arising from specimen handling can generate an amorphous background glow that can hinder RHEED pattern acquisition (Fig. 17.21a-ca). The oxygen-argon plasma acts to remove such contaminants, allowing high-contrast RHEED patterns to be obtained (Fig. 17.21a-cb). In this instance, the generated RHEED pattern remained effectively constant as the sample was rotated, indicating a random distribution of columnar grains. This predicted microstructure was subsequently confirmed by means of conventional plan-view TEM imaging (Fig. 17.21a-cc, with TED pattern inset), which revealed a fine-scale distribution of rotated columnar grains (\(\approx{\mathrm{20}}^{\circ}\) of arc).
Fig. 17.21a–c

RHEED patterns from Si-doped GaN/GaAs(001) (a) before and (b) after plasma cleaning. (c) Plan-view TEM image confirming the presence of rotated columnar grains (TED pattern inset)

The RHEED patterns shown in Fig. 17.22a-fa–f, acquired from a variety of III–V heterostructures grown by MBE, are presented to illustrate the variety of microstructures that can be readily distinguished. In the first instance, variations in spot, arc or ring spacings from the central beam provide evidence of the different phases present within a sample and show the general nature of the structural integrity of the near-surface layer (presumed to be representative of the bulk or thin film). Thus, polycrystalline, preferred orientation or single-crystal growth (Fig. 17.22a-fa–c) can be rapidly distinguished, whilst embedded phases (Fig. 17.22a-fd) and anisotropic defect distributions within zinc blende thin films (Fig. 17.22a-fe,f) are also revealed.
Fig. 17.22a–f

RHEED patterns from (a) GaAs/AlN(As)/GaP(001) indicating polycrystalline growth; (b) GaN(As)/GaP(001) grown under low As flux at 620C showing disordered growth with some degree of preferred orientation; (c) Mg-doped GaN/GaAs \(\{\overline{1}\overline{1}\overline{1}\}\)B showing α-GaN single-crystal growth (\(\langle 11\overline{2}0\rangle\) projection); (d) GaN(As)/GaP (001) grown under high As flux at 650C showing spots due to single-crystal GaAs and β-GaN; (e,f) Be-doped GaN/GaAs (001) grown at 700C showing orthogonal ⟨ 110 ⟩  and \(\left\langle 1\overline{1}0\right\rangle\) projections. Extra spots indicate a high degree of anisotropy for the distribution of microtwin defects within this sample

17.5 Characterizing Functional Activity

There are many solid state analytical techniques that employ x-ray or electron probes, generating a variety of signals for chemical microanalysis. However, techniques for performing correlated assessment of the structural and functional performance of a material are perhaps less well-covered in mainstream texts. Accordingly, we introduce briefly the techniques of scanning transmission electron beam induced conductivity (STEBIC ) and TEM-cathodoluminescence (TEM-CL ), since these allow us to make correlated structure-property investigations of electrical and optical activity within a semiconductor, respectively.

When an electron beam is incident on a semiconductor specimen, electron-hole pairs are created by excitation of crystal electrons across the band-gap. These electron-hole pairs can, for example, recombine to emit light that may be detected by a photomultiplier providing, e. g., information on the semiconductor band-gap. A CL image can then be obtained by displaying the detected photomultiplier signal as a function of the position of the incident electron beam as it is scanned across the specimen. CL spectra can also be acquired in spot mode, which show features attributable to excitons, donor–acceptor pairs or impurities. The information content of CL images and spectra includes the location of recombination sites such as dislocations and precipitates, and the presence of doping-level inhomogeneities. Similarly, if the sample is configured to incorporate a collection junction, such as a Schottky-contacted semiconductor or an ohmic-contacted p–n junction, electron-hole pairs that sweep across the built-in electric field constitute a current flow. This can be amplified and an image of the recombination activity displayed as the electron beam is rastered across the sample. If the dislocations within a semiconductor act as nonradiative recombination centers, then they appear as dark lines in both CL and EBIC images because of the reduced specimen luminescence or reduced current that is able to flow through the collection junction when the beam is incident at a defect.

The techniques of CL and EBIC are most commonly performed in an SEM, but this precludes the direct identification of features responsible for a given optical or electronic signature. The resolution of extended defects achieved using EBIC and CL techniques is limited by the penetration depth of the electron beam, the effect of beam spreading and the diffusion length of minority carriers. Conversely, the resolutions of the STEBIC and TEM-CL techniques, as applied to electron-transparent sample foils, are essentially limited by specimen geometry. The constraint of minority carrier diffusion length is removed due to the close proximity of the sample foil surfaces, and resolution depends on the incident probe size, the width of the electron hole pair generation zone and recombination velocity at the free surface. For the case of STEBIC, resolution also depends on defect position relative to the collecting junction. The trade-off is low electrical signal and a degraded signal-to-noise ratio due to the small generation volume and surface recombination effects, in addition to the practicality of contacting and handling thin foils.

Before presenting some material characterization case studies based on electron beam techniques, we now discuss the preparation of electron transparent foils that are free from artefacts and suitable for TEM investigation.

17.6 Sample Preparation

We should initially consider whether destructive or nondestructive preparative techniques need to be applied. Some characterization techniques allow samples to be examined with a minimal amount of preparation, provided they are of a form and size that will fit within the apparatus. For example, the crystallography of bulk or powder samples may be investigated directly by XRD, since the penetration depth of energetic x-rays within a sample is on the scale of ≈ 100 μm. The surface morphology and near-surface bulk chemistry of a sample may be investigated directlywithin the SEM, noting the interaction volume of electrons [on the scale of ≈ 1  ( μm)3] associated with the EDX and WDX techniques. It might, however, be necessary to coat insulating samples with a thin layer of carbon or gold prior to SEM investigation to avoid charging effects. Similarly, minimal preparation might be required before surface assessment using XPS or RHEED, such as cleaning using a degreasing protocol or plasma cleaning. Accordingly, the focus of this section is to introduce techniques used to prepare samples for TEM investigation, since the requirement is for specimens that are typically submicrometer in thickness and free of preparation artefacts. For example, a complex sequence of sequential mechanical polishing, dimpling, ion beam thinning and plasma cleaning may be required to produce a pristine semiconductor heterostructure sample, with each stage of the process being designed to minimize artefacts from the previous stage of the preparation process. The idea being to minimize or eliminate artefacts from the preparation process, to ensure that the sample being investigated is representative of the starting bulk material. Care is also needed to avoid artefacts that might be introduced through interaction of the high-energy electron beam with the sample.

In this context, it is interesting to note how TEM sample preparation techniques have developed over the years. Small particles of MgO, produced by igniting the metal and drifting a specimen grid through the smoke, were typical of samples investigated in the 1940s, along with sample replicas made by a dry stripping technique using formvar films. Biological samples fashioned by enzymatic digestion, staining and microincineration were also possible by 1945. Glass and diamond knife microtomes were introduced in the 1950s and used to section soft biological materials. Advances in the controlled preparation of inorganic materials were made upon the introduction of argon ion beam thinning in the late 1960s, which allowed for cross-sectional observation of semiconductor heterostructures when combined with sequential mechanical polishing and dimpling. Significant development work in this area appears throughout the literature from the 1970s. The problem of surface amorphization, introduced by the argon sputtering process, was minimized by adopting low-voltage milling techniques to define the final electron-transparent sample foil. Low stacking fault energy semiconductors, such as II–VI compounds which are easily damaged or InP-based compounds that suffer from In droplet formation with conventional milling techniques, were also successfully prepared for TEM observation using the technique of iodine reactive ion beam etching (RIBE ), otherwise known as chemically assisted ion beam etching (CAIBE ), developed in the 1980s. The 1990s, however, saw the development of the most effective raft of sample preparation techniques for functional materials and complex semiconductor device structures in particular: i. e., tripod polishing, focused ion beam (FIB ) milling and plasma cleaning.

The fine adjustment of micrometer supports is the key to tripod polishing that allows for direct mechanical polishing of specimens down to < 10 μm thickness, using diamond-impregnated polishing cloths on a stable, high-torque, low-speed polishing wheel. A brief final stage of low-voltage argon ion beam thinning (with liquid nitrogen cooling) then enables electron-transparent sample foils to be defined, free of differential mechanical polishing and shadowing artefacts, whilst minimizing remnant surface amorphization.

FIB instrumentation (now commonly integrated with SEM) was originally developed for the semiconductor industry as a diagnostic tool for silicon chip fabrication. The application of a focused beam of gallium ions enables sample material to be sputtered away in a controlled fashion to produce an electron-transparent membrane, for example through a specific device within a complex microprocessor. Samples may be periodically observed using SEs generated by gallium ion/material interactions in order to maintain control over and the precision of the sputtering process. In particular, the ability of FIB instruments to prepare site-specific TEM membranes provides a unique opportunity to access the subsurface microstructure of complex device structures or specific regions within a heterostructure identified as being particularly interesting from observations of the surface. By way of example, Fig. 17.23a-d shows a TEM membrane sectioned through the apex of a hillock identified within a sample of heteroepitaxial GaN–sapphire. Prior to sectioning, the sample was coated with a thin layer of gold and a platinum alkyl decomposed under the rastered Ga beam to define protective metallic stripes. Sequential sputtering and reduction of the incident Ga beam current density allowed a supported thin membrane to be defined (Fig. 17.23a-dd). Care is required to minimize amorphization artefacts at the surfaces of such membranes, arising from the sputtering action of the glancing, high-energy Ga ion beam. Further, charging effects associated with insulating samples can act to compromise the fine-scale control of the ion milling procedure. However, this particular problem can be addressed by using low ion dose and shadowing techniques, combined with charge neutralization procedures to inhibit the deflection of the incident ion beam.
Fig. 17.23a–d

SE images showing the application of FIB milling to target a source of defects buried beneath the emergent core of a growth hillock. (a) An etched CVD -grown GaN/sapphire hillock (≈ 5 μm in size; CVD – chemical vapor deposition). (b) Platimum stripes deposited along the hillock facet edges in order to retain sight of the defect core (≈ 100 nm in size). (c) A high Ga flux is used to create an access trench to the defect. (d) Decreasing the Ga flux enables an electron-transparent membrane (arrowed) to be defined at the position of the defect core

Plasma cleaning using oxygen-argon gas, commonly used for the final stage of TEM sample preparation, enables pristine electron-transparent membranes to be obtained, suitable for detailed chemical microanalysis. The disassociated oxygen component of the plasma reacts with organic surface contaminants to produce CO, CO2 and H2O reaction products that can be pumped away conveniently. To illustrate the effectiveness of this procedure, it was found that the quality of EELS data from GaN electron transparent foils was significantly improved following plasma cleaning. Figure 17.24a,b shows the removal of the artefact carbon K-edge and enhancement of the sample nitrogen K-edge after a few minutes of exposure to the plasma. It is worth noting that in principle the argon component of the plasma permits gentle sputtering of the sample to occur if low-pressure conditions are used due to the larger mean free path and hence increased energy of the ions. However, this can be problematic due to the possibility of sample cross-contamination with material sputtered from the supporting sample stage. Another cautionary note on plasma cleaning relates to semi-insulating samples that can become too clean and consequently more susceptible to charging effects under the imaging electron beam.
Fig. 17.24a,b

EELS spectra from GaN (a) before and (b) after plasma cleaning

17.7 Case Studies – Complementary Characterization of Electronic and Optoelectronic Materials

There are four general levels of interest when characterizing a given sample:
  • What is it made of?

  • What additional imperfections does it contain?

  • How did it get to be that way?

  • How does the microstructure influence the functional properties of the material/device?

For example, one might wish to identify the chemical constituents and crystal structure of a sample to start with, such as whether it is a compound or an alloy, and whether it is single-crystal, polycrystalline, exhibits preferred orientation, or is amorphous. One might then wish to characterize the additional fine-scale defect microstructure within the sample, including precipitates or extended structural defects such as dislocations, stacking faults or domain boundaries, since these could deleteriously affect the functional properties of the material. The next level of understanding focuses on how the material has formed via growth, processing or device usage, and seeks to make sense of the process of dynamic evolution, since this potentially enables us to find ways to improve the material in a controlled manner. A clear record of sample history is generally helpful in this context, particularly when trying to identify defect sources. The final level of understanding is possibly the most challenging, since it seeks to associate microstructure with the functional properties exhibited by the material, and thereby to make sense of its process–structure–property interrelationship at the fundamental level.
In this context, the structural characterization of semiconductor heterostructures tends to focus on the following issues:
  • The integrity of the layer growth and the orientation relationship with the substrate.

  • The nature of the structural defects within the epilayer, arising, e. g., from lattice mismatch or from differential thermal contraction following cool-down from the growth temperature.

  • The structural integrities of critical interfaces within the device’s active region, such as multiple quantum wells, and the chemical homogeneity of the associated alloy layers.

  • Modification of the microstructure due to subsequent processing, such as contact formation and device usage.

XRD techniques are well-suited to assessments of the structural integrities of bulk and epitaxial thin film semiconductors. However, we should note the inherent averaging over a large number of microscopic features, such as dislocation distributions responsible for the twist and tilt of mosaic grains, associated with such techniques. Conversely, TEM and related techniques are more suited to assessing the fine-scale defect microstructure of heterostructures. For example, conventional weak-beam, HREM or CBED analysis can be used for fine-scale defect structural analysis, whilst EELS and EDX analysis can be used to profile composition. However, the ability to perform atomic-level structural characterization and chemical analysis on the nanometer scale is offset by concerns about statistical significance and whether the small volume of material analyzed is truly representative of the larger object. Hence, electron microscopy-based techniques combined with FIB procedures for site-specific sample preparation tend to be favored when investigating integrated device structures.

The examples provided so far illustrate how various diffraction and imaging techniques can provide information on the structural integrity of a given sample. The following examples emphasize the need to apply complementary material characterization techniques in support of the development of semiconductor science and technology.

17.7.1 Identifying Defect Sources Within Homoepitaxial GaN

The emergence of the (In,Ga,Al)N system for short-wavelength light-emitting diodes, laser diodes and high-power field effect transistors has been the semiconductor success story of recent years. In parallel with the rapid commercialization of this technology, nitride-based semiconductors continue to provide fascinating problems to be solved for future technological development. In this context, a study of homoepitaxial GaN, at one time of potential interest for high-power blue–UV lasers, is presented.

The reduction in extended microstructural defects permitted by homoepitaxial growth was considered to be beneficial in the development of nitride-based technology, particularly in view of evidence confirming that dislocations do indeed exhibit nonradiative recombinative properties. However, in the case of metal organic chemical vapor deposition (MOCVD )-grown homoepitaxial GaN on chemomechanically polished \((000\overline{1})\), N-polar substrates, gross hexagonally shaped surface hillocks were found to develop, considered problematic for subsequent device processing [17.32]. The homoepitaxial GaN samples examined in this case study were grown at 1050C. The bulk GaN substrate material was grown under a high hydrostatic pressure of nitrogen (15–20 kbar) from liquid Ga at 1600C. Prior to growth, the \((000\overline{1})\) surfaces were mechanically polished using 0.1 μm diamond paste and then chemomechanically polished in aqueous KOH solution. Epitaxial growth was performed using trimethylgallium and NH3 precursors with H2 as the carrier gas, under a total pressure of 50 mbar. Figure 17.25 shows an optical micrograph of the resultant homoepitaxial GaN/GaN\((000\overline{1})\) growth hillocks, typically 5–50 μm in size depending on the layer thickness (and therefore the time of growth).
Fig. 17.25

(a) Optical micrograph of MOCVD-grown GaN on a KOH chemomechanically polished, N-polar, bulk GaN substrate showing a high density of hillocks. (b) Slightly tilted plan-view TEM image through a growth hillock revealing a central defect core (arrowed). An enlarged ⟨ 0001 ⟩  projected image of the hillock core is shown in the inset. (c) Cross-sectional, weak-beam TEM image through a hillock core. CBED analysis confirmed the feature to be an inversion domain. (dHAADF image indicating the presence of a low atomic number material at the inversion domain source. (e) HREM image indicating the presence of a narrow band of amorphous material at the inversion domain source. (f) EEL second difference spectrum indicating the presence of oxygen at the nucleating event

Electron-transparent samples were prepared in plan view using conventional sequential mechanical polishing and argon ion beam thinning procedures applied from the substrate side, whilst cross-sectional samples were prepared using a Ga-source FIB workstation. As shown earlier, the selectivity of the FIB technique enables cross-sections through emergent cores of the hillocks to be obtained, thereby allowing nucleation events associated with these features to be isolated and characterized. When prepared in plan-view geometry for TEM observation, each hillock exhibited a small faceted core structure at the center (Fig. 17.25b), but otherwise the layers were generally found to be defect-free. Low-magnification cross-sectional TEM imaging also revealed the presence of faceted column-shaped defects beneath the apices of these growth hillocks (Fig. 17.25c). It was presumed that these features originated at the original epilayer-substrate interface since no other contrast delineating the region of this homoepitaxial interface could be discerned. A reversal of contrast within 0002 diffraction discs from CBED patterns acquired across the boundary walls of such features (Fig. 17.19) confirmed that they were inversion domains. Thus, the defect cores were identified as having Ga-polar growth surfaces embedded within an N-polar GaN matrix. Once nucleated, the inversion domains exhibited a much higher growth rate than the surrounding matrix, being directly responsible for the development of the circus tent hillock structures around them. Competition between growth and desorption rates of Ga and N-polar surfaces allowed the gross hexagonal pyramids to evolve.

This initial approach of applying electron diffraction and imaging techniques thus enabled the nature of the inversion domains to be identified and their propagation mechanism established in order to explain the development of the hillocks. However, more detailed chemical analysis was required to ascertain the nature of the source of the inversion domains and how this related to substrate preparation and the growth process. A high-angle annular dark field (HAADF) image of the inversion domain nucleation event is shown in Fig. 17.25d. HAADF is a scanned electron probe imaging technique with a resolution defined by the size of the incident probe, with the scattering (and hence contrast) governed by local average atomic number. In this instance, the sample, tilted slightly to minimize the effects of diffraction contrast, showed dark contrast at the position of the inversion domain source, confirming the presence of a low atomic number material associated with the nucleation event. HREM subsequently confirmed that such nucleation events were due to narrow bands of amorphous material, 2–5 nm in thickness (Fig. 17.25e), whilst EELS confirmed the presence of oxygen (Fig. 17.25f) within these narrow amorphous bands. Accordingly, these defect sources were attributed to remnant contamination from the chemomechanical polishing technique used to prepare the substrates prior to growth. The oxygen-containing residue was presumed to be gallium oxide or hydroxide – being products of the reaction of the KOH etchant with GaN. An improved surface preparation method incorporating a short, final deoxidizing polishing procedure in an aqueous solution of NaCl led to a dramatic reduction in these nucleation sources and thus allowed N-polar homoepitaxial GaN films to be grown virtually free of these hillock structures.

17.7.2 Cathodoluminescence/Correlated TEM Investigation of Epitaxial GaN

The CL technique is ideally suited to studies of luminescence uniformity and spectral purity. The following case study illustrates how the defect microstructure of mixed-phase epitaxial GaN/GaAs\((\overline{1}\overline{1}\overline{1})\)B can be correlated with the layer of luminescent properties [17.33].

Even though the majority of developments in GaN technology to date have come from material grown by MOCVD on sapphire and SiC substrates, there is much interest in exploring alternative growth techniques. The MBE technique offers a lower growth temperature than MOCVD and hence enables a greater range of candidate substrate materials to be investigated. One general issue for the MBE growth of heteroepitaxial GaN is the need for direct control of the process of nucleation, since this impacts on the phase and polarity of the deposit and the resultant structural integrity of the film. Epitaxial GaN preferentially adopts the wurtzite phase, with a band-gap of 3.4 eVhex, although zincblende inclusions, with a band-gap of 3.2 eVcubic, are sometimes associated with MBE-grown material (for conditions of high Ga flux); Fig. 17.26. The CL spectrum shown in Fig. 17.26a was recorded from a plan-view, electron-transparent foil of nominally single-crystal wurtzite GaN, cooled to liquid nitrogen temperature. The peak in the CL spectrum at 386 nm (3.21 eV) was used to create the image in Fig. 17.26b indicating the distribution of cubic phase inclusions throughout the hexagonal GaN matrix. The complementary conventional TEM image of this plan-view sample foil (Fig. 17.26c) allowed the nature of the fine-scale microstructure to be characterized, with diffraction patterns confirming the presence of embedded sphalerite GaN growth. The size and distribution of these inclusions correlated nicely with the distribution of bright spots in the CL image of Fig. 17.26b. A subsequent cross-sectional investigation of this GaN/GaAs\((\overline{1}\overline{1}\overline{1})\)B specimen confirmed that cubic inclusions nucleated at the epilayer/substrate interface (Fig. 17.26d).
Fig. 17.26

(a) CL spectrum acquired from an electron-transparent foil showing peaks at 357.8 nm and 386 nm, corresponding to wurtzite and zinc blende GaN, respectively; (b) CL image formed at 386 nm and (c) complementary TEM image confirming a distribution of cubic GaN inclusions (arrowed) embedded within the hexagonal GaN matrix; (d) HREM image of epitaxial GaN/GaAs \((\overline{1}\overline{1}\overline{1})\)B viewed in cross-section, indicating the nucleation of cubic phase inclusions at the epilayer-substrate interface

17.7.3 Scanning Transmission Electron Beam Induced Conductivity of Si/Si1−xGe x /Si(001)

The STEBIC technique was originally demonstrated in the late 1970s, using dedicated STEM instrumentation to obtain information on the electrical properties of dislocation core structures within (Ga,Al)(As,P), thereby providing the first evidence that nonradiative recombination processes at dislocations are related to jogs and kink sites. Dissociated 60 dislocations showed the highest electrical activity, while sessile Lomer–Cottrell edge dislocations were found to be electrically neutral, indicative of reconstructed core structures. STEBIC imaging of an electron-transparent foil allows the electrical and structural properties of defects to be observed simultaneously. The availability of electron sources with high brightness in modern scanning TEM instruments compensates for the main problem of small generation volume and provides an accessible way to perform STEBIC experiments.

The next case study illustrates how the electrical nonradiative recombination properties of MBE-grown Si/Si1−xGe x /Si(001) heterostructures correlate with the distribution of interfacial misfit dislocations [17.34]. The Si1−xGe x system has potential application in devices with high electron and hole mobilities. However, the introduction of dislocation networks, or the multiplication of existing dislocations, driven by the 4% misfit strain between Ge and Si, is generally regarded as being detrimental to device operation. With a view to gaining an improved understanding of the relationship between fine-scale structural defects and electron transport properties, the structures of capped MBE-grown Si/Si1−xGe x /Si(001) were investigated using STEBIC and a range of complementary microscopies. The samples incorporated buried p–n junctions to assist with charge collection and surmount the problem of surface recombination effects.

To prepare for the STEBIC investigation of the Si/Si1−xGe x /Si(001), evaporated Al contacts were attached to the top surface prior to preparing electron-transparent foils in plan-view by sequential mechanical polishing and argon ion milling of the substrate (Fig. 17.27a). Ohmic contact to the lower surface was made using an InGa eutectic. Electrical activity images were acquired using an electrical contact stage and a scanning TEM. Signal amplification was performed using an amplifier with low noise current. By controlling the STEM scan rate, the beam could be rastered at a rate compatible with the low bandwidth constraint of the amplifier. STEBIC signals were typically ≈ 100 pA for an electron-transparent Si/Si1−xGe x /Si foil imaged at a magnification of × 1000.
Fig. 17.27

(a) Schematic of the Al/Si/Si1−xGe x /Si(001)/InGa sample configuration used for STEBIC investigation

Figure 17.27a illustrates the physical parameters relevant to this STEBIC experiment. The silicon substrate was n-type 1018 cm−3, whilst the epilayer was p-type boron-doped to a level of 1016 cm−3. These values of sample doping were chosen to create a depletion region of ≈ 30 nm width to assist with charge collection, away from the misfit dislocations delineating the Si/Si1−xGe x and Si1−xGe x /Si interfaces. The low-magnification STEBIC image shown in Fig. 17.28b illustrates the recombination activity within a relaxed Si/Si0.96Ge0.04/Si(001) sample imaged in plan view. Submicron resolution of the recombination activity is readily achievable using this technique (Fig. 17.28c), with line scans from digitized images indicating a resolution of ≈ 0.3 μm in this case. The spacing of ≈ 1 μm striations in the STEBIC image is much greater than the spacing of individual misfit dislocations shown in the associated TEM image (Fig. 17.28d), and is more closely associated with the spacing of dislocation bundles. Thus, correlation with structural images shows that bunched arrays of orthogonal ⟨ 110 ⟩  misfit dislocations are primarily responsible for the enhanced recombination. For this particular sample, detailed g ⋅ b analysis confirmed the presence of bands of predominantly 60 misfit dislocations with a few 90 segments arising from dislocation interactions.
Fig. 17.28

(b) STEBIC image showing recombination activity due to ⟨ 110 ⟩  orthogonal arrays of misfit dislocations within relaxed Si/Si0.96Ge0.04/Si (001). (c) Higher magnification STEBIC image illustrating sub-μm resolution of the electrical activity. (d) Bright-field TEM image demonstrating the presence of bundles of misfit dislocations (g = 220 ) 

Supporting evidence for these dislocations being dissociated and probably decorated by transition metal impurities was obtained from complementary HREM and EDX investigations of metastable and relaxed Si/Si1−xGe x /Si(001) samples from the same growth trial. As the relaxation of a low Ge content, metastable Si/Si1−xGe x /Si structure proceeds, extensive arrays of orthogonal ⟨ 110 ⟩  dislocations form and interact, with dislocations generated in the strained Si1−xGe x layer being pushed by repulsive dislocation forces into the Si substrate and cap on {111} glide planes. HREM observations of relaxed Si/Si1−xGe x /Si samples in cross-section confirmed that the misfit dislocations were dissociated, with tails associated with each of the partials, indicative of impurity decoration (Fig. 17.29e). This particular image was acquired before the development of electron beam-induced damage artefact structures within this sample foil and so is considered representative of the as-grown material. A distribution of small precipitates, of typical size 5 nm, was also identified within metastable samples prior to strain relaxation. These precipitates showed strong scattering in HREM (Fig. 17.29f) and revealed the presence of Fe when analyzed using EDX within a dedicated STEM (1 nm probe size), as shown in Fig. 17.30g. No Fe was present in spectra acquired immediately to the side of the precipitates. (The Ni signal was considered to be an artefact of EDX acquisition and attributed to fluorescence from x-rays and electrons interacting with the specimen’s Ni support ring.) Hence, the suggestion is that enhanced transition metal impurity segregation at dissociated dislocations is responsible for the STEBIC contrast observed. This emphasizes the need to control dopants or impurity sources in the vicinity of heterostructure interfaces during the development of functional device structures.
Fig. 17.29

(e) HREM image of a decorated dissociated dislocation viewed in cross-section at the Si/Si1−xGe x interface following sample annealing and relaxation. (f) HREM image of a precipitate within as-grown, metastable Si/Si1−xGe x /Si

Fig. 17.30

(g) EDX spectra confirming the presence of Fe transition metal impurities

17.8 Concluding Remarks

The above commentary has attempted to convey the framework underpinning a variety of analytical techniques used to investigate the structures of semiconductors. It is emphasized that an appropriate combination of assessment techniques should be applied generally, since no single technique of assessment will provide information on the morphology, composition, microstructure and (opto)electronic properties of a given functional material or processed device structure.

This type of considered approach to materials characterization is required in order to break free of the black-box mentality that can develop if one is too trusting of the output generated by automated or computerized instrumentation systems. One should always bear in mind the process of signal generation that provides the information content. This in turn helps us to develop an appreciation of performance parameters such as spatial or spectral resolution, in addition to sensitivity, precision and detection limits. One should consider technique calibration and the appropriate use of standards in order to ensure that the data acquired is appropriate (and reproducible) to the problem being addressed. Consideration should also be given to the form and structure of the data being acquired and how the data sets are analyzed. In this context, distinction should be made between the processing of analog and digital information and the consequences of data conversion. Issues regarding the interpretation (or misinterpretation) of results often stem from the handling of experimental errors. On a practical level, rigorous experimental techniques should be applied to ensure that the data generated is both meaningful and representative of the sample being investigated, free from artefacts from the preparation and investigation processes. There are clearly differences between qualitative assessment and the more rigorous demands of quantitative analysis. The level of effort invested often reflects the nature of the problem that is being addressed. A comparative assessment of a number of samples may simply require a qualitative investigation (for example, in order to solve a specific materials science problem within a growth or device fabrication process). Alternatively, quantitative analysis may be required to gain a more complete understanding of the nature of a given sample, such as the precise composition. To summarize, an awareness of the methodology used in any investigation is required to establish confidence in the relevance of the results obtained. A range of complementary analysis techniques should ideally be applied to gain a more considered view of a given sample structure.

Notes

Acknowledgements

As ever, there are many people one wishes to acknowledge for their involvement in the growth, processing and underpinning characterisation research programmes drawn from to illustrate this chapter. University of Nottingham: with thanks to Tom Foxon, T.S. Cheng, Sergei Novikov and Chris Statton for the provision of MBE GaN samples and supporting XRD analysis; and to Mike Fay for GaAs CBED patterns. University of Cambridge: with thanks to Colin Humphreys for provision of instrumentation; Chris Boothroyd for STEM data on the SiGe and GaN samples; Michael Natusch for GaN EELS data; Robin Taylor for RHEED stage development; David Tricker for the Si-doped GaN micrograph; and Yan Xin for the GaN images used for dislocation analysis. University of Warwick: with thanks to Richard Kubiak and E.H.C. Parker for supplying SiGe/Si samples. Polish academy of Sciences, Warsaw: with thanks to Jan Weyher for homoepitaxial GaN samples. With thanks also to the EPSRC for funding support.

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dept. of Mechanical, Materials and Manufacturing EngineeringUniversity of NottinghamNottinghamUK

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