A comparative analysis of oxidation rates for thin films of SiGeversusSi
Summary (18 min read)
6 Overview of articles 83
- The research into semiconductor devices during and in the years following the second world war that led to transistors, integrated circuits, and modern solid state electronics focused on silicon and germanium [1–4].
- These were homojunction devices, but the earliest proposals for heterojunction devices were based on abrupt junction and alloyed silicon and germanium [6, 7].
- Furthermore, even though solar cells and the photovoltaic effect were discovered using selenium crystals in the latter half of the nineteenth century, it wasn’t until 1953 that research into silicon based electronics at Bell labs lead to the discovery of the utility of silicon in producing solar cells .
- It is perhaps something of a self fulfilling prophecy that the superiority of the oxide on silicon and the subsequent industrial dominance of silicon has led to oxidation of silicon being substantially more profoundly understood than oxidation of silicon-germanium.
2 Chapter 1. Introduction
- Still, Kroemer and Shockley’s descriptions of silicon-germanium heterostructure devices [6, 7] were prescient, and the use of germanium in standard digital and analog processes is becoming common.
- The possibility to create direct bandgaps in core-shell nanowires could also have profound implications for solar cell or energy harvesting applications.
- Silicon-germanium-on-insulator (SGOI) has been suggested as a replacement for bulk silicon in deep sub-micron CMOS applications , and the fabrication of SGOI wafers using germanium condensation by thermal oxidation [63–66] as well as by thermally induced germanium dilution  has been suggested.
- Both modeling and experimental results reveal that the germanium content at the oxidation front is strongly dependent on the oxidation temperature and only weakly dependent on the germanium content in the as-grown silicon-germanium layer.
- An empiric relation for the germanium content at the oxidation interface is derived and supported by experimental data.
8 Chapter 1. Introduction
- Raty, “First-principles design of efficient solar cells using two-dimensional arrays of core-shell and layered SiGe nanowires,” Phys. Rev. B, vol. 83, no.
- Ge fraction for sub-100 nm strained silicon-on-insulator MOSFETs,” Japan.
2.1.1 Lattice constant
- Silicon-germanium (SiGe) is a miscible binary alloy that takes a diamond crystal structure .
- The random placement of silicon and germanium atoms in the alloy result in a lattice constant that varies continuously between those of silicon and germanium [1, 2].
14 Chapter 2. Materials properties
- Though, the compressive strain in pseudomorphically strained Si1−XGeX on Si will tend to reduce the bandgap from the value for relaxed Si1−XGeX .
- Figure 2.4 shows a clear tendency for higher degrees of strain, that are associated with higher Ge contents, to exaggerate the reduction in the bandgap.
2.1.5 Critical thickness
- A fundamental limitation associated with using strain to alter the bandgap is the tendency for strain energy to be relieved by formation of threading defects and misfit dislocations.
- Figure 2.5 shows the critical thickness as predicted by Matthews and Blakeslee  as well as that predicted by People and Bean .
- Defect free films grown to thicknesses greater than the critical thickness may exist in a metastable region wherein defects will develop over time.
- It has been suggested that their predictions may sit in a region of metastability .
- The development of defects over time would make such layers unsuitable for applications in electronics due to compromised reliability.
2.1.6 Diffusion of Si and Ge
- Figure 2.6(c) plots the diffusivity of Si in Si1−XGeX for several temperatures typical of thermal oxidation.
- The diffusivities in figure 2.6(c) indicate that Si diffuses between four and six orders of magnitude faster in Si than in Ge.
2.1.8 Long range order and alternative morphologies
- As stated above, SiGe forms in the diamond structure wherein the Ge and Si atoms are randomly placed in the crystal lattice.
- It has been demonstrated that long range order of the Ge and Si atoms may occur under certain conditions.
- This is significant because, although SiGe is typically described as having an indirect bandgap, strain and long range ordering may allow creation of SiGe based structures that exhibit a direct bandgap .
- Ordering has been shown in strained super-lattice structures , and although it is presumed that strain plays a critical role in establishing or stabilizing long range order, ordering has also been observed in relaxed or bulk like films .
- Long range ordering represents a phase change from the diamond structure to either a zinc-blende or a rhombohedral structure and depends on both chemical and mechanical energies [25, 26].
2.1. References 17
- Bonds, will influence the ratio of the number of Si-Ge to Si-Si and Ge-Ge bonds in a SiGe crystal, which would in turn result in the rhombohedral structure being more stable than the zinc-blende structure [24, 25].
- These more recent values are consistent with Pauling’s  estimation for the relationship between bond energies of diatomic molecules and the electronegativities of the constituent atoms (reported as 1.9 and 2.0 for Si and Ge, respectively .).
- The wide variations in reported values for diatomic bonds and the strong dependence of electronegativities on bonds with tertiary elements make it difficult to form definitive conclusions about the validity of arguments based on bond energies.
3.1 Variable angle spectroscopic ellipsometry (VASE)
- Ellipsometry is a non-destructive optical method for characterizing both thin and thick layers of either amorphous or crystalline material.
- It is well suited for measuring films with thicknesses of a few angstroms up to several microns, particularly for those materials that have well established values for the indices of refraction.
- The wavelengths of light used in this study are between 380 and 900 nm.
- Ellipsometry relies on measuring the polarization of light which has been reflected and refracted by one or more layers in a sample.
- The oscillation of the electric field will form an elliptical shape in the XY plane (hence the name ellipsometry) and the polarization can be described by the two angles, Δ and Ψ.
22 Chapter 3. Physical analysis methods
- Components of the AutoEL-II are shown in figure 3.1.
- The value of θ is manually set to one of three discreet values (65◦, 70◦, or 75◦) by rotating the primary and secondary side components and fixing their position using a pin.
- The polarizers on the primary and secondary sides are labeled “Polarizer” and “Analyzer”, respectively, and are used to condition the light prior to measurement by the photodetector.
- There are advantages and disadvantages to both methods but these are not critical to the present application [2, 4].
3.1. Variable angle spectroscopic ellipsometry (VASE) 23
- The extinction coefficient, k, is indicative of the absorptivity of the material, and is close to zero for those wavelengths where the material is transparent.
- Figure 3.2(a) shows the basic geometry for the reflection and refraction of a beam of light with wavelength λ that is incident upon a sample with a single film at an angle θ0.
- The way in which the light beam is refracted and reflected when passing between the ambient and the top layer of the sample is described by Snell’s law, N0 sin θ0 = N1 sin θ1.
- Furthermore, if the plane that contains both the incident and reflected beam is the plane of incidence, the polarization may be separated into the component that is parallel to the plane of incidence (p-polarization) and that which is perpendicular to the plane of incidence (s-polarization.).
- In the event that the sample is composed of more than one layer of different materials, each with its own N , these equations may be extended to models with multiple layers.
24 Chapter 3. Physical analysis methods
- Various layers may be determined using the method of least squares.
- For a sample with three layers wherein the thicknesses and values of n and k for the layers and substrate are unknown, there will be 12 unknowns.
- Using a 2.5 petaflop computer, this would take longer than the age of the universe to complete the calculations, and would require about 7 × 1024 TB of storage; this is clearly not a practical approach.
- The color maps demonstrate that a large number of local minima can be generated for various combinations of values for the two unknowns, without producing a unique minimum χ2 value.
- Published values of the optical constants of Si, SiO2 , and SiGe  have either been used outright or used to minimize the range in which to search for n and k.
26 Chapter 3. Physical analysis methods
- On the other hand, due to the difficulty distinguishing SiGe from Si at longer wavelengths, there will be a higher degree of uncertainty when measuring the SiGe layer thicknesses.
- This is contrasted to shorter wavelengths, where the values of n and k differ substantially between Si and SiGe, which facilitates characterization of SiGe layers but adds to the complexity of the analysis.
- It should be clear that measuring each sample with a series of wavelengths (referred to as spectroscopic ellipsometry) can add substantially to the certainty with which various sample characteristics are determined.
- This has the advantage of increasing the number of measurements for each sample, and measuring various path lengths within the sample without altering λ or N .
- VASE will act to minimize both random and systematic measurement error and to maximize the contrast in χ2 for the range of unknowns being considered.
3.2. X-ray diffraction (XRD) 27
- A number of samples of Si and SiGe that have been oxidized for various times and temperatures will have a range of oxide and SiGe film thicknesses, but, the values of N for the SiO2 and Si will be the same for all of the samples.
- Analyzing all of the samples simultaneously and using a common value for N will produce a substantial improvement in the certainty of the solutions.
- The analyses done for the present work made use such simultaneous analyses of groups of samples in combination with data produced by both spectroscopic ellipsometry and VASE.
- Use of the measured data to determine N for SiO2 and Si produced results that were essentially the same as published values [6, 7] as implemented by the CompleteEASE software .
3.2 X-ray diffraction (XRD)
- X-ray Diffraction (XRD) is an analysis method that relies on diffraction of monochromatic x-rays to characterize the structure of the crystalline material being analyzed.
- Large single crystals, or polycrystalline samples, this work uses the method exclusively for analysis of thin films.
- Figure 3.5 shows the basic components of such an instrument.
- The Göbel mirror removes the Cu-Kβ radiation and reflects the Cu-Kα x-rays as a parallel beam.
- The slit on the primary side defines the beam width, while the slit on the secondary side helps to confine the detected signal.
28 Chapter 3. Physical analysis methods
- To diffracted radiation by removing scattered radiation.
- It is also possible to use a Ge analyzer crystal on the secondary side with a scintillation detector to increase the angular resolution, however, the cost of the higher resolution is a substantially reduced detected beam intensity.
- Rotation in χ is used primarily to align the sample such that the preferred crystallographic plane (i.e. (100), (110), or (111)) is perpendicular to the plane containing the x-ray beam.
- This alignment is only done prior to measurement and will adjust for deviations between the (100), (110), or (111) planes from the sample surface (often referred to as sample offcut) or for samples that are, for some reason, tilted with respect to the chuck surface.
- The beam path and the detector sit in the xz plane with the detector and Eulerian cradle held by a goniometer.
3.2. X-ray diffraction (XRD) 29
- Crystal lattice, d, and the angle of incidence and diffraction, θ .
- Considering the wave nature of x-rays, if an incident beam of x-rays strikes a crystal structure at an angle, ω, the x-rays that are diffracted by multiple planes of the crystal will undergo constructive or destructive interference.
- Germanium, and their alloys are cubic in nature, they form crystals that have a diamond structure.
- In addition to those reflections that are forbidden by the nature of the lattice structure, there are a number of reflections that can not be measured due to the geometry of the instrument and the sample.
30 Chapter 3. Physical analysis methods
- As shown in figure 3.8, the diffraction peaks that are permitted and that can be measured are confined within an arc in the QxQz plane.
- There are two symmetric hemispheres within this arc that represent the space in which the incident or diffracted beams are below the surface of the sample, thus preventing measurement of the peaks that fall within these two smaller hemispheres.
- Figure 3.8 is drawn for a sample with a (100) oriented surface, for which the (004) peak is the most commonly measured symmetric peak.
- For a single crystalline Si wafer with a (100) surface orientation, the primary symmetric Bragg peak is the (004) peak.
3.2. X-ray diffraction (XRD) 31
- Both the intensity of the thin film peak and the periodicity of the Kiessig fringes are indications of the layers’ thickness.
- It is frequently difficult to fully evaluate an epitaxially grown thin film using a single 2θ-ω scan.
- A reciprocal space map is a scan of an area of the QxQz space that is typically focused around one or more peaks and can be used to evaluate epitaxial layer characteristics, like layer tilt,.
32 Chapter 3. Physical analysis methods
- Strain and relaxation, lattice mismatch, and defectivity.
- A fully relaxed epitaxial layer would be indicated by the lines linking the substrate and epitaxial layer peaks being directed towards the origin in QxQz space.
- All samples were fully pseudomorphically strained prior to oxidation.
- After oxidation, the reciprocal space maps of both symmetric and asymmetric reflections showed that the substrate and SiGe layer peaks were aligned vertically along Qz.
- The oxidation process may also cause relaxation by formation of dislocations and other defects , but defectivity will contribute to broadening of the XRD peak for the layer, rather than shifting of the peak in the reciprocal space.
3.3. X-ray photo-electron spectroscopy (XPS) 33
- Intensity reductions may occur due to both thinning of layers and relaxation, layer thickness can also be estimated based on the spacing of the fringes around the main layer peak.
- Assumption of the SiGe layers as having the same lattice constant as the substrate allows measurement of the Ge content in the SiGe layers using only 2θ-ω scans of symmetric peaks, but without the confounding influence of strain or relaxation induced variations in the lattice constant.
- All samples in the present work were measured using 2θ-ω scans of one or more symmetric peaks.
- The software allows construction of multilayered models for which specific model characteristics (i.e. Ge content and layer thickness) may be set as variables.
- The 2θ-ω scan is simulated for the model and matched to the measured scan using a genetic algorithm and the MSE method.
3.3 X-ray photo-electron spectroscopy (XPS)
- X-ray photo-electron spectroscopy (XPS) is a non-destructive method for both chemical and elemental surface analysis.
- The method depends on analysis of the kinetic energy and flux of photo-electrons that are ejected from the core energy levels of chemically bound atoms in a sample that is illuminated by x-ray radiation .
- The instrument used in the present study was a Kratos Axis Ultra DLD, and figure 3.12 shows a schematic of the essential components of such a.
34 Chapter 3. Physical analysis methods
- A monochromatic x-ray source illuminates a sample within a high vacuum environment.
- The electrons emitted from the sample surface are propelled through an electrostatic lens and an electron analyzer towards a detector.
- It is this excitation of core level electrons that makes XPS unique among analysis techniques and allows for the identification of chemical states as well as elements.
- The energy from the electron transition from L1 to K is transferred to another core level electron which is ejected and becomes an Auger electron.
- The core level transitions in Auger will produce both emitted electrons and x-rays, with the electron emissions dominating for elements with low atomic numbers ( 30) and x-ray emissions dominating for elements with.
3.3. X-ray photo-electron spectroscopy (XPS) 35
- Though, as a practical matter, neither hydrogen nor helium is measurable by either AES or XPS .
- The end result is the same in both Auger and XPS, that is, electrons are emitted and subsequently collected to measure their kinetic energy and current at the detector.
- Changes in the binding energies for the various elements are indicative of the chemical states of the atoms in the sample.
- The Al Kα radiation (hν = 1486.6eV) used in the present work offers a relatively small bandwidth of x-rays leading to reduced full-width-half-max (FWHM) values for the measured peaks and thus clearer discrimination between peaks during analysis.
- The detection depth for an XPS measurement is related to the penetration depth of the incident x-rays and the inelastic mean free path of the photo-electrons, as described by the BeerLambert law.
36 Chapter 3. Physical analysis methods
- Photo-electrons are traveling through an SiO2 layer, and by using data from the Tanuma, Powell, and Penn algorithm [12, 13].
- Sample tilting or ion milling can be used in conjunction with XPS to create depth profiles for arbitrarily deep analyses .
3.4 Rutherford backscattering spectroscopy (RBS)
- Rutherford backscattering spectroscopy (RBS) is based on measuring the intensity and energy of ions with small masses that have been scattered from the larger atoms in a sample.
- The instrument used for an RBS measurement may be described as a modification of an ion implantation system, and figure 3.15 shows a schematic such an instrument.
- The ion source produces 4He+ cations (also commonly referred to as alpha particles) which are subsequently propelled towards a large magnet that acts as a beam path selector and mass separator.
- The 100◦ angle between the incident ion beam path and the detector is referred to as a glancing-angle detector geometry, and is used to provide enhanced depth resolution for accurate analysis of films near the sample surface; a typical detector geometry would use an angle closer to 170◦.
- The 2 MeV energy of the incident ion beam should result in detection depth.
3.4. Rutherford backscattering spectroscopy (RBS) 37
- Given that the thicknesses of the SiGe and oxide films on the samples in the present study are frequently smaller than 20 nm, it is critical to use the instrument configuration that will give the highest possible resolution.
- The measured spectrum will show a count rate or yield versus backscattering energy; the backscattering energy may be binned into discrete channels.
- There will also be a width to the feature for each element that is characteristic of the distribution of the element in the sample; the broader the distribution of an element, the wider the feature will be.
- The germanium signal starts wide and becomes much thinner after oxidation, which is consistent with the increased concentration of germanium in the SiGe layer after oxidation of the sample.
3.4. References 39
-  M. Birkholz, Thin Film Analysis by x-ray scattering.
- Evaluation of calculated IMFPs and of the predictive IMFP formula TPP-2 for electron energies between 50 and 2000 eV,” Surf.
- This chapter reviews the modeling and experimental results that are detailed in the attached articles.
- Additionally, supporting data is presented and discussed with an emphasis on the physical mechanisms and materials characteristics that are important for designing and constructing nanostructures by thermal oxidation of silicon-germanium.
4.1 Oxidation rate modeling
- Early literature on the oxidation of metals was reviewed and explained by diffusion of ions and electrons in a space charge induced field in an oft-cited work by Cabrera and Mott .
- In their analysis, they made a critical distinction between very thin oxides with high growth rates and thicker films characterized by slower growth rates.
- At, or cubic, z3ox = 3At, models and that A may take on various definitions.
- Oxidation of silicon has been explained by both linear [2, 3] and parabolic  models.
- Azox = B(t + τ), where B is the parabolic rate constant, B/A is the linear rate constant, and τ is a factor which adjusts the oxidation time to account for any pre-existing oxide.
42 Chapter 4. Results and discussion
- Where C1, L1, C2, and L2 are additional oxidation constants.
- The values used for any given model’s coefficients depend critically on such variables as the oxidant partial pressure [3, 6, 9], crystalline orientation [2, 7, 9–12], water content in the ambient [4–6, 9, 11], and impurities in both the ambient and the material being oxidized .
- A simple Arrhenius model is adequate for describing the growth of oxides with thicknesses between a few tens of angstroms and about a hundred nanometers.
4.3. Modeling of the pile-up region 43
- The width of the pile-up region may be considered to be very small such that the flux of silicon exiting the initial silicon-germanium layer, Jpu, is exactly equal to the flux of Si entering the oxide, Jox, i.e. Jpu = Jox.
- The flux of silicon atoms into the oxide, Jox, is defined by the rate at which silicon atoms are removed from the surface of the crystalline silicon-germanium and bonded to oxygen atoms to form the growing oxide, i.e. the oxidation rate.
- Jox is then equivalent to requiring that the dose from silicon diffusion through the pile-up is equal to the dose of silicon incorporated into the oxide, Qpu = Qox.
- The dose of silicon incorporated into the oxide, Qox, can be determined directly from the oxidation rate and the atomic density of silicon in silicon dioxide.
4.4 Layer thicknesses: measurement and calculation
- The measurement methods used in the present work each rely on different physical phenomena but are capable of measuring some of the same sample characteristics.
- Its estimation of zpu is less robust due to uncertainty in the values for Xpu and X , as well as, the high degree of sensitivity of the complex index of refraction to Ge content at short wavelengths .
- These figures also show several statistics 4.4.
48 Chapter 4. Results and discussion
- The intensity of the pile-up layer’s XRD peak will be determined by the thickness of the pile-up layer, and so, the uncertainty in the measurement of Xpu increases as the thickness of the pile-up layer approaches zero.
- For pile-up layers thicker than 10 nm, the standard error in the Xpu measurement is less than ∼1%.
- Figure 4.6(a) compares the oxide thickness as measured by VASE to that determined by equation 4.5 with XRD measurements of zpu, Xpu, and X .
- Si atoms/cm3 which is consistent with the density of thermally grown silicon oxide as is commonly reported in the literature [9, 14, 20–22].
- So, even though the mismatch between measured and calculated values in figure 4.6 can be reduced by altering Nox to 2.95×.
50 Chapter 4. Results and discussion
- From the substrate into the initial SiGe layer that is inevitable during oxidation.
- The deviation between X measured post oxidation and the actual pre-oxidation value will be aggravated by longer oxidations (i.e. thicker oxides) and variation in X between samples.
- Critical thickness is of fundamental importance to nanostructure design for opto-electronic applications.
- So, it is useful to have an appreciation for the relative magnitudes of the pile-up thickness and critical thickness.
- The data for zpu in the figure is limited to temperatures above 700 ◦C because all of the oxidations in the present study were done at temperatures above this and because lower temperatures may lead to oxidation of Ge as well as Si.
4.5. Ge content in the pile-up: measurement and calculation 51
- By starting with a sufficiently low initial.
- Ge content, thin pile-up layers may be grown without adverse effects from variations in the oxidation rate.
- This is particularly important when oxidizing SiGe, where the oxidation rate is relatively poorly characterized and strongly dependent on the oxidizing ambient.
4.5 Ge content in the pile-up: measurement and calculation
- This is illustrated by figure 4.9, wherein the calculated values of Xpu are plotted against T .
- Figure 4.9 also shows linear fits to the data for each orientation.
- Qualitative confirmation of the relationship between temperature and Ge content at the oxidation interface is presented in figure 4.10, which shows.
- It is important to note the negative slope of Xpu(T ); the fact that the melting point of SiGe decreases as Ge content increases might seem to suggest that conducting high temperature oxidations to increase the Ge content at the oxidation interface might result in melting of the pile-up layer.
4.6 Manipulating the Ge content in the pile-up region
- The factors that contribute to establishing Xpu(T ) become apparent by considering equation 4.2.
- The logarithmic dependence on time is consistent with the observation that, for any given temperature and orientation, the values of Xpu remain nearly constant for a variety of oxide thicknesses; this is shown in figure 4.12.
- Aside from T , the variables that have the largest potential for modifying Xpu, by manipulation of the oxidation conditions, are A0 and Eox.
- Their values are primarily a function of factors that are determined by the oxidant partial pressure, oxidant chemistry, crystalline orientation, and the presence of Ge at the oxidation front.
- This is consistent with experimental observations and.
4.7. Oxidation rate ratios 55
- Associated modeling showing the tendency of high pressures to incite formation of mixed oxides [28–30].
- The manipulation of oxidant pressure as a means of controlling Xpu is only applicable for those oxidations that are substantially controlled by the oxidant pressure, an exception being oxides with zox less than about 20 nm (where oxidation is faster than the linear oxidation rate model would predict).
- Modifications to the chemistry of the oxidizing ambient can be used to increase or decrease the oxidation rate; an obvious example being dry versus wet oxidations.
- Other modifications of the oxidation environment will alter both the oxidation rate and the diffusivity of Si in SiGe.
- These observations are consistent with equation 4.2, where a drastic reduction in Eox would lead to Xpu values greater than one, and thus formation of GeO2, unless it is accompanied by a commensurate reduction in ESi.
4.7 Oxidation rate ratios
- Figure 4.13 shows the oxide thickness versus time for both Si and SiGe samples of three different crystalline orientations that were oxidized at different temperatures.
- It is evident that both crystalline orientation and Ge have the potential to influence the oxidation rate; considering these.
56 Chapter 4. Results and discussion
- Factors separately will be useful in identifying the physical mechanisms involved in the oxidation of SiGe.
- The oxidation rate ratio is defined here as ρa/b = νa/νb, where νa and νb are the oxidation rates for two samples with identical oxidation conditions and a single differentiating characteristic that is indicated by the subscript.
- As the oxidations conducted in this study are in the linear or linear-parabolic regime, the oxidation rate can reasonably be described by an Arrhenius relation, A0exp[−Eox/(kT )].
58 Chapter 4. Results and discussion
- Ous influences of point defects, strain, steric hindrance, and Ge induced growth rate enhancement will be absorbed into the values of A0 and Eox and can be eliminated by considering the ratio of the oxidation rates of similar samples.
- By way of example, consider that the pre-exponential constant for Si(100) is A0 while the pre-exponential for SiGe(111) is A0 ∗ AGe ∗ A111, where AGe and A111 are factors to accommodate for the influence of Ge and orientation on the oxidation rate.
- Using such oxidation rate ratios to compare oxidation rates is far more effective than making qualitative judgments based on viewing plots of oxide thickness versus oxidation time, as it is done in figure 4.13.
4.8 Ambient chemistry
- The oxidation kinetics for Si and SiGe are similar in the sense that, the ambient chemistry will have an integral role in determining the oxidation rate.
- Comparison of dry and wet oxidations is perhaps the most obvious demonstration of the role of the oxidation ambient chemistry in determining the oxidation rate.
- It has been established that “dry” oxidations are typically not completely free of H2O due to contamination from the room ambient by diffusion through the wall of a single walled furnace or by back-flow from the end of the furnace [9, 11, 35].
- The introduction of H2O to an oxidizing ambient will also accelerate the oxidation rate of SiGe (i.e. ρwet/dry > 1 for both SiGe and Si).
4.8. Ambient chemistry 59
- While wet ambients induce growth rate enhancement (ρSiGe/Si > 1), both wet ambients diluted with N2 and dry ambients result in equivalent oxidation rates for SiGe and Si (ρSiGe/Si ≈ 1) .
- Ambients composed of plasma generated atomic oxygen have also resulted in ρSiGe/Si > 1 .
- Each oxidation run in the present study consisted of a single time and temperature and involved oxidizing SiGe and Si samples of each of the three orientations simultaneously and side by side in the oven to ensure identical oxidation conditions for all samples in a given oxidation run.
- The flow rate may not have been high enough or stable enough to eliminate contamination by H2O or N2 from the room air.
4.9 Bond energies and electronegativity
- One of the more popular explanations for how Ge acts as a catalyst in oxidizing SiGe is that the dissociation energy for a Si-Ge bond is lower than for a Si-Si bond [36, 45, 56–58].
- Such a simplistic explanation for the observed growth rate enhancement is clearly insufficient.
- Defining this factor as, Γ = [(1 − Xpu) HSi−Si + XpuHSi−Ge] /HSi−Si, where HSi−Si and HSi−Ge are the dissociation energies for Si-Si and Si-Ge bonds, respectively, will increase the oxidation rate by a factor of about one to three which is approximately what has been observed empirically.
- It is known that, despite it’s position on the periodic table, Ge has a higher electronegativity than Si , and it follows from Pauling’s definition of electroneg-.
4.10. Electric potential 61
- Ativity  that an atom’s tendency to attract electrons depends on which other atoms it is bound to.
- So, although the dissociation energy of Si-Ge may tend to be lower than for Si-Si, these bond energies, and the difference between them, will vary due to tertiary bonds with elements like hydrogen, fluorine, or chlorine.
- This may help explain how ρSiGe/Si can be both larger than and smaller than one, depending on the mix of atoms and bonds present at the oxidation interface.
4.10 Electric potential
- These observations indicate that oxidations that involve ionized oxidants and that have fast enough oxidation rates (relative to the diffusivity of Si in SiGe) to form a mixed oxide may show higher ρSiGe/Si values than would be expected were the oxide to be composed entirely of SiO2.
- There is, however, some debate about how these results should be interpreted, and thus about the role of ions in dry thermal oxidations .
- On the other hand, if one accepts that increasing values of Xpu will lead to weakened Si bonds, increased ion diffusion, or higher electron injection rates, then the qualitative observation that lower oxidation temperatures lead to higher values of Xpu should lead to the conclusion that lower oxidation temperatures also lead to larger values of ρSiGe/Si.
- This is not supported by the data in table 4.3.
4.11 Point defects
- A number of studies have speculated that the generation of vacancies and interstitials in the SiGe layers plays a critical role in explaining Ge’s role as a catalyst for oxidation [30, 37, 38, 48, 59, 60, 75].
- The authors propose that this mechanism is reversed and replaced by injection of vacancies which enhances rapid diffusion of Si through the Ge enriched layer.”.
- The notion that point defects play an important role in the oxidation kinetics of SiGe is evi-.
4.11. Point defects 63
- It has been established that oxidation enhanced diffusion of dopants in Si is tied to both point defects and crystallographic orientation [78–80].
- This is consistent with the orientation dependent shifts in Xpu in figure 4.9 and with the variation in the values for the diffusivity of Si in SiGe for various orientations listed in table 4.1.
- As seen in figure 4.15, the data in this study does indicate that ρSiGe/Si is reduced as oxide thickness increases towards the parabolic regime, but, this effect is small and it is not clear if this is related to point defects or some other effect.
- Also, figure 4.12 shows that Xpu is nearly constant or slightly increasing as zox increases; a slight increase in Xpu with increasing zox is also supported by simulations .
4.12 Strain and crystallographic orientation
- Both crystallographic orientation and strain between the oxide and the underlying SiGe have the potential to influence the oxidation of SiGe.
- Given that strain in the oxide is due to the change in volume between Si and SiO2, the influence of strain on the oxidation of multi-dimensional structures will vary for purely geometric reasons; planar, cylindrical, spherical, and fin shaped structures all show different volume changes due to an increase in oxide thickness.
- They also found that, for both tensile and compressive strain, the strain induced growth rate reduction increases as oxidation temperature is decreased.
- Explanations of this temperature dependence rely on the notion that there is a viscous flow in the oxide at high temperatures [83–87, 89].
4.12. Strain and crystallographic orientation 65
- The values for the surface energies, ε, are not the same for Si and Ge, but the ratio between Si and Ge is the same for the three orientations considered.
- So, oxidation rates for (110) oriented material may be either faster or slower than for (111) oriented material.
- Figure 4.16 shows data that supports the notion that a coupling.
66 Chapter 4. Results and discussion
- Between oxide strain and steric hindrance creates a crossover point.
- The value of ρ111/110 decreases towards one as zox decreases and is below one for the two points with zox < 23 nm.
- The additional strain due to the SiGe layer should shift the data to the left and result in a smaller crossover thickness for SiGe in figure 4.16.
- It is conceivable that, if electronegativities and bond energies only allow for the oxidation rate of SiGe to be greater than or the same as that of Si, the additional strain in the SiGe layers act to retard the oxidation of the SiGe samples enough to cause ρSiGe/Si < 1, which would help to explain the data in figure 4.15.
- Recognizing that strain is a function of oxide thickness, and that, for a given oxidation time and temperature, zox for SiGe may be larger or smaller than for Si, oxide strain will have some influence on ρSiGe/Si.
4.12. Strain and crystallographic orientation 67
- That is, the tendency of strain to slow the oxidation rate for thicker oxides more than for thinner oxides will tend to reduce the difference between the oxide thicknesses on SiGe and Si from what they would be in the absence of oxide strain.
- Furthermore, by inducing strain in Si substrates using stripes of oxide and measuring the oxidation rate adjacent to these stripes, Pliskin  showed that the influence of strain on the oxidation rate is not strictly due to changes in the diffusivity of oxidant in the oxide.
- LeGoues et al  recognized the possibility that variation in the lattice constant of relaxed SiGe could influence the oxidation rate of SiGe and suggested that Ge may induce vacancies in favor of the interstitials that would be expected in the case of Si oxidation; a surplus of vacancies should create misfit dislocations which would act to relieve oxide strain.
- The fact that point defect generation, oxide strain, SiGe layer strain, oxidant ambient, diffusivity of Si in SiGe, and other factors are so closely tied to one another makes it difficult to quantitatively differentiate between the various effects and their influence on Ge induced growth.
68 Chapter 4. Results and discussion
- It is the Ge content in the pile-up region that will determine the degree to which strain, oxidant and impurity chemistry, et cetera, interact to increase or decrease the oxidation rate.
- Furthermore, the combination of temperature, oxidant partial pressure, oxidant and impurity chemistry, and UV illumination should provide a large degree of flexibility in determining both the Ge content at the oxidation interface and the oxidation rate.
4.13 Summary of results
- It has been recognized that oxidizing crystalline SiGe will have the effect of leaching Si from the surface of the SiGe to form an oxide composed of SiO2 and concentrating the remaining Ge at the interface between the oxide and the underlying SiGe.
- The modeling leads to equations describing the thickness of the pile-up region, zpu, and the Ge concentration in the pile-up region, Xpu.
- Data from a series of experiments using XRD, VASE, and RBS are used to observe the redistribution of Ge and to support modeling predictions.
- Both the oxidation rate and the diffusivity of Si in SiGe vary with crystallographic orientation, however, they vary in such a way that Xpu(T ) is similar for the three orientations studied, (111), (110), and (100).
- The presence of Ge at the oxidation interface may have either a catalytic or inhibitive effect on the oxidation rate of SiGe, but, any such.
70 Chapter 4. Results and discussion
- N. Nagasima, “Structure analysis of thermal oxide films of silicon by electron diffraction and infrared absorption,” Japan.
- H. Stöhr and W. Klemm, “Über zweistoffsysteme mit germanium.
4.13. References 75
- K. E. Bean and P. S. Gleim, “The influence of crystal orientation on silicon semiconductor processing,” Proc. IEEE, vol. 57, no.
- Chapter 5 Future work and potential applications.
5.1 Benefits of using low Ge contents in as-grown layers
- Over the course of the research presented here, it has become evident that there are a number of advantages to using Si1−XGeX with a small X as a starting material for experimenting with oxidation induced Ge condensation.
- The most trivial of these is that many of the physical properties of SiGe vary between those of Si and those of Ge (see chapter 2), and after more than half a century of intense research and industrial use, Si is much better understood than Ge.
- Using smaller values of X will likely lead to less uncertainty in the results obtained by the empiricist and will minimize the temptation to explain away various phenomena by attributing them to the poorly characterized properties of Ge or high values of X in the starting material.
- Relatively thick initial SiGe layers can be grown epitaxially without reaching the critical thickness.
5.2 Variable temperature, vacuum-UV, pressure, and ambi-
- The relationship between the Ge content in the pile-up and the oxidation temperature has been explored in some depth in the present work and is expressed by equation 4.2.
- Still, the oxidation conditions may be manipulated in a number of ways in order to change the oxidation rate, and hence the Ge content in the pile-up layer.
- Ambient chemistry, oxidant partial pressure, and illumination by vacuum-ultra-violet (VUV) radiation are all oxidation conditions that could be used to manipulate the Ge content at the oxidation interface, but which haven’t been investigated.
- It would be advantageous to limit the thermal budget for processing by using pressure as a process control, but, pressure will only alter the oxidation rate, and may result in unacceptably long processing times.
- Illumination of the sample with UV light may allow for.
5.3 SiSn and SiGeSn oxidation
- The Gibbs free energies for formation of SiO2, GeO2, and SnO2 from their constituent elements are shown in figure 5.1.
- This is supported by XPS measurements in multiple studies indicating a thermodynamic preference for SiO2 over SnO2 [2, 3].
- A proposal for tin based confinement modulated gap transistors (CMGT) relies on using the orientation and diameter of a nanowire to manipulate the bandgap of the transistor channel material (Sn) between ∼2.7 and 0 eV .
- It is possible that ohmic contacts to source and drain regions of transistors could be improved and that contact implants could be eliminated by using Sn condensation.
5.4 Dopant and alloy gradients by differential diffusion
- They demonstrated that the n-type dopants (phosphorus, arsenic, and antimony) tend to become depleted at the oxidation interface, while the p-type dopants (boron, gallium, and indium) tend to pile-up at the oxidation interface.
- Phosphorus , arsenic , and antimony  have been shown to diffuse faster as the Ge content is increased, while results for boron and gallium diffusion are mixed; boron and gallium diffusion are reported either to be independent of Ge content, or to decrease as Ge content increases [12–15].
- The tendency of Ge to pile up at the oxidation interface during thermal oxidation should exaggerate the accumulation or depletion of dopants at the same interface, and could be used to build opto-electronic devices.
- Another application could be in formation of ohmic contacts for the source and drain of transistors.
- Contact implants have been used in integrated circuit fabrication to create a highly doped region where the metal contacts meet the source and drain of a transistor in order to minimize the contact resistance.
6.1 Article I
- New data for the dry O2 oxidation of MBE grown thin films of Si0.80Ge0.20 and Si0.85Ge0.15 is presented along with data for Si control samples.
- The new data is compared to data for dry O2 oxidation of SiGe from the literature as well as common models for oxidation of Si.
- This is coupled with the observation that there is wide variation in the oxidation rates for SiGe between studies and in the models for Si oxidation.
- The point is made that since Both VASE and XRD are used to characterized the oxide thicknesses and pile-up.
- Ge concentrations for the samples from the present study.
6.2 Article II
- XPS is used to characterize the chemical composition of oxides formed on SiGe by thermal oxidation and to confirm the preferential formation of SiO2.
- XPS and RBS are used to confirm that Ge piles up at the oxidation interface.
- The theoretical foundation for the modeling that lead to the equations describing the thickness of the pile-up region (equation 4.5) and the Ge content in the pile-up region (equation 4.4) is established and explained.
- This includes a detailed discussion of the requirement that the flux of Si into the oxide be balanced by the flux of Si through the pile-up layer.
- The modeling is also used to evaluate the influences of oxide thickness and oxidation temperature on the Ge content in the pile-up layer.
6.3 Article III
- XRD and VASE are used to fully characterize the Ge content in the pile-up region for a variety of oxidation times and temperatures.
- Both simulation and empiric results are used to show that the Ge content in the pile-up is linearly dependent on oxidation temperature and to support equation 4.4.
- Measurements are presented that help confirm that Ge content in the pile-up is largely independent of oxide thickness but highly dependent on oxidation temperature; this includes measurements showing the correlation between oxide thickness and pile-up layer thickness.
- The relative influence of oxidation temperature and the Ge content in the as-grown SiGe layer on the oxidation rate is addressed and oxidation rates of SiGe samples are compared to results from an established model for the oxidation of Si.
6.4 Article IV
- The diffusivity of Si in (111), (110), and (100) oriented oxidizing SiGe is determined by combining VASE measurements of oxide thickness, XRD measurements of the Ge content in the pile-up region, and equation 4.4.
- The Ge content in the pile-up region is shown to be dependent on orientation, though, the temperature dependence is nearly identical for the three orientations.
- The linear relationship between oxidation temperature and the Ge content in the pile-up layer is explained by assumption of Arrhenius relations to describe both diffusion of Si in the pile-up layer and the oxidation rate of SiGe, resulting in equation 4.2.
- Oxidation rate ratios between SiGe and Si samples and between samples of different orientations are used to evaluate the relative importance of orientation and Ge content on the oxidation rate of SiGe.
- The ability to reduce the Ge content at the oxidation interface is consistent with the predictions made by equations 4.2 and 4.4.
Ge redistribution in SiO2/SiGe structures under thermal oxidation: Dynamics and predictions
- Experimental data from the present work shows longer oxidation times leading to an increase of Ge content in the pile-up region and eventually creating a single high.
- The proposed models may be used in nanostructuring of thin films of SiGe by oxidation and in the design of core-shell structures and transistors.
- A)Author to whom correspondence should be addressed.
- The proposed relations describe the pile-up layer thickness as a function of oxide thickness and allow prediction of the initial SiGe layer thickness required to avoid oxidation of Ge.
III. RESULTS AND DISCUSSION
- In the case of multiple oxidations at progressively lower temperatures, the Ge content at the oxidation interface, Xpu, is primarily determined by the temperature of the last oxidation performed, despite the progressively increasing Xpu.
- Most of the oxidation runs performed at 900 and 1000 C result in SiGe oxidizing faster than Si, but the longer oxidations at 950 C and the 360min oxidation at 900 C show Si oxidizing faster than SiGe.
- Figure 4 shows typical results of XRD measurements performed to quantify Xpu for the samples described in Fig.
- There are three distinct peak positions: the substrate peak at 95 , the peaks at 93:8 from the primary SiGe layers, and the leftmost peaks corresponding to the pile-up layers.
IV. SUMMARYAND CONCLUSIONS
- The present work adds to the general understanding of SiGe oxidation by measuring the Ge content in the pile-up region and the oxide thickness that result from simple and nonexotic oxidation conditions (dry O2 at 1 atm.).
- Data is presented, showing that the Ge content in the pile-up layer is primarily determined by the oxidation temperature, while it is largely independent of oxide thickness and the Ge content in the initial SiGe layer.
- Ge content at the oxidation front where oxidation occurs, the weight of the evidence indicates that Ge content does not influence the oxidation rate of SiGe for sub-100-nm thin films.
- Use of the established models and parameters for Si give very reasonable and practical estimations for the oxidation of thin films of SiGe.
- A model that allows for the explicit determination of the Ge concentration in the pile-up layer based on other known or measured values is presented.
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Frequently Asked Questions (2)
Q1. What have the authors contributed in "Nanostructuring and ge redistribution in thin films of silicon-germanium by thermal oxidation" ?
Despite the fact that germanium played a significant role in the advent of modern electronics, silicon-germanium alloys have not been used or studied nearly as extensively as silicon. Evidence is presented showing that a decrease, rather than an increase, in the germanium content at the oxidation front may be achieved under certain conditions. The germanium content at the oxidation interface is used to discuss the potential for germanium to act as a catalyst or inhibitor for oxidation of silicon-germanium alloys.
Q2. What are the future works mentioned in the paper "Nanostructuring and ge redistribution in thin films of silicon-germanium by thermal oxidation" ?
Furthermore, the possibility to increase, maintain unaffected, or to decrease Ge induced oxidation rate enhancement or retardation will be subject to a number of factors, including point defect generation, bond strengths, steric hindrance, oxide strain, oxidant ambient, and the diffusivity of Si in SiGe.