Master’s Thesis
Oxygen-related defects in Carbon-rich Solar Silicon studied by Fourier Transform Infrared
Spectroscopy
Mette Fjelltveit Rye-Larsen
A thesis submitted in partial fulfilment of the requirements for the degree of MSc
in
Materials, Energy and Nanotechnology
May, 2016
The study of point defect complexes and thermal double donors (TDDs) in Silicon, has been of great interest in the field of semiconductor physics for several decades. However, due to a growing environmental awareness and increasing demand for high-efficiency and low-cost solar cells, the research activity in this field is once again flourishing. In this work, n-type Cz-Silicon with high and low carbon concentrations have been sequentially annealed in the temperature range of 450-550°C, and investigated using FTIR spectroscopy. MeV electron irradiation has facilitated a detailed study of vacancy-oxygen (VOn) and carbon-related complexes. Their formation and evolution during thermal treatments have been studied, and their relation to TDD formation has been addressed.
TDDs were found to form at 450 and 500°C, while being unstable at 550°C. FPP resistivity measurements provided an estimate for TDD concentrations after thermal treatments. The presence of high carbon concentrations were found to strongly inhibit TDD generation. Cz-Si with carbon concentrations of 2.5×1017cm−3were found to reduce the final TDD concentration by factors of 7 and 30 when annealing at 450 and 500°C, respectively, relative to carbon-lean samples. The obtained results suggest that carbon specifically impedes the formation of TDD3. Formation kinetics confirmed a sequential formation of the larger CsO3i complexes by prolonged annealing of the carbon-rich samples at the highest temperatures, while the smaller CsOicentres became unstable. The direct involvement of VOncentres in TDD formation was ruled out. The presence of both VOnand CsOndefects were found to consume oxygen and act as traps for migrating oxygen atoms during annealing, effectively reducing TDD formation.
PL measurements have been correlated with IR measurements in terms of carbon-complexes and formation of TDDs. Zero-phonon and phonon replica luminescence lines of TDDs and irradiation induced carbon-complexes have been identified.
I would like to express my utmost gratitude to my supervisor Prof. Bengt Gunnar Svensson for introducing me to the exciting field of semiconductor physics. Thank you for sharing your endless knowledge and expertise in this field of science through fruitful discussions, invaluable advice, and revision that made this thesis possible.
I would like to thank Frank Herklortz for introducing me to FTIR spectroscopy, Alexander Hupfer for helping me with analysis in Python, Thomas Sky for a helping hand when MatLab wouldn’t cooperate and for proof-reading my thesis. Dr. Augustinas Galackas, thank you for carrying out the PL measurements, and for all your patient help and advice. A special thanks to Vegard Skiftestad Olsen for revising my thesis repeatedly, and for being a great friend through these years at LENS. A big thanks goes to Micke and Victor for always helping me with practical issues at MiNaLab, and for your wonderful humour. Micke, thank you for not giving up after endless hours of repairing the FTIR lifting-table with me.
To everyone at LENS, thank you for making these years a rewarding and fulfilling period of my life. I have highly appreciated the environment between us master students, where sharing and discussions of each others work has been encouraged amongst everyone.
Mom and dad, thank you for being the most supportive parents one could ever ask for, I would not have finished this degree without you. Mamma, thank you for always wholeheartedly car- rying all of my frustrations. And to Eric, thank you for motivating me when inspiration was low, always being there for me, and for tolerating long working hours during this year.
Mette Fjelltveit Rye-Larsen, Oslo, May 2016
1 Introduction 1
2 Background 3
2.1 Crystal structure and defects . . . 3
2.2 Fundamentals of semiconductors . . . 5
2.2.1 Electronic energy bands . . . 5
2.2.2 Charge carrier generation . . . 8
2.2.3 Charge carrier density . . . 9
2.3 Theory of vibrational spectroscopy . . . 12
2.3.1 Molecular vibrations . . . 13
2.3.2 Infrared absorption . . . 14
2.3.3 Vibrational modes in crystals . . . 14
2.3.4 Localized vibrational modes . . . 15
2.3.5 Electronic transitions . . . 15
2.3.6 Free carrier absorption . . . 16
2.3.7 Infrared transmission measurements . . . 16
3 Silicon; growth, main impurities and defects 18 3.1 Fundamentals . . . 18
3.2 Crystal growth and impurity incorporation . . . 19
3.3 Point defects and their complexes . . . 20
3.3.1 Oxygen . . . 21
3.3.2 Carbon . . . 21
3.3.3 Vacancy-oxygen complexes . . . 21
3.3.4 Carbon-related complexes . . . 22
3.4 Thermal donors . . . 22
3.4.1 Formation kinetics . . . 23
3.4.2 Structural models . . . 24
3.4.3 The effect of carbon on donor formation . . . 26
3.5 Light induced degradation . . . 27
4 Experimental techniques and procedure 28 4.1 Fourier Transform Infrared (FTIR) Spectroscopy . . . 28
4.1.1 The Michelson interferometer . . . 28
4.1.2 Generation of the interferogram . . . 29
4.1.3 Spectral treatment . . . 31
4.1.3.3 Baseline correction . . . 33
4.1.4 Advantages and limitations of FTIR spectroscopy . . . 33
4.1.5 FTIR instrumentation . . . 34
4.2 Four-point probe (FPP) . . . 36
4.3 Photoluminescence (PL) Spectroscopy . . . 37
4.4 Experimental Procedure . . . 38
5 Results and discussion 40 5.1 FTIR measurements . . . 40
5.1.1 Issues with MCT detector . . . 40
5.2 Impact of electron irradiation . . . 41
5.2.1 Simulation of VO development with irradiation . . . 44
5.3 Isothermal annealing studies . . . 45
5.3.1 Irradiation induced complexes of low thermal stability . . . 45
5.3.2 Interstitial oxygen . . . 46
5.3.3 Substitutional carbon . . . 49
5.3.4 Vacancy-oxygen complexes . . . 51
5.3.5 Carbon-related complexes . . . 56
5.3.6 Thermal Double Donors . . . 63
5.4 FPP resistivity measurements . . . 68
5.5 Photo Luminescence measurements . . . 75
5.5.1 Carbon lines . . . 75
5.5.2 TDD lines . . . 77
6 Summary 79 6.1 Conclusion . . . 79
6.2 Suggestions for further work . . . 81
Appendices 82
A Overview of IR absorption bands 83
B Overview of FPP measurements 87
C VO simulation 89
Introduction
While the global demand for energy increases rapidly, a strong reduction in the exploitation of fossil fuels is required to reduce the environmental consequences of electrical power generation.
The International Energy Association (IEA) predicts a growth in energy demand by nearly one third between 2013 and 2040, in which the global electricity demand is predicted to increase by a staggering 70% [1]. At the same time, the Intergovernmental Panel on Climate Change (IPPC) reports that the human influence on the climate system is clear, and recent anthropogenic emission of green-house gases is the highest in history [2].
A growing awareness for the need to secure sources of electricity, alternative to fossil fuels, has expanded the interest in harvesting solar energy by the use of Photovoltaics (PV). Since 2010, the world has added more solar PV capacity than the previous four decades, and the total global capacity overtook 150 GW in early 2014 [3]. The IEAs technological roadmap envisions PVs share of global electricity to reach 16% by 2050, corresponding to a total of 4600 GW of installed PV capacity. If this roadmap is reached, the emission of up to 4 Giga-tonnes (Gt) of CO2 would be avoided annually [3].
Despite the promising development in installed PV capacity, most European consumers are still depending on government incentives to achieve grid parity, in terms of electricity cost [4].
This calls for further development of the technologies in terms of reduced production cost and higher module efficiency. Silicon (Si) is the "work horse" of the PV industry, and constitutes the greater majority of all commercial solar cells. A vast abundance of the precursor material quartz, and a relatively low production cost are essential reasons for this predominance. While the theoretical efficiency limit for a single-crystal, homo-junction Si solar cell is approximately 30%, the commercial solar cells today are normally limited to only 16-18%. Therefore, to make PVs a competitive source of electricity, further progress must be made in both processing technology and material quality. Point defects and point defect complexes which form during crystal growth and subsequent thermal processing, are decisive for the materials structural and electrical quality.
The present work reports on a study of various oxygen and carbon related defects which de- velop in Czochralski (Cz) grown Si during thermal treatment. Oxygen together with carbon are the two most abundant, unintentionally introduced impurities in Cz-Si. When oxygen and carbon atoms are present in their usual interstitial and substitutional positions in the
Si lattice, respectively, they are rather stable, immobile and electrically inactive. However, heating of Cz-Si to temperatures typical for solar cell processing steps, leads to the formation of electrically active, detrimental defect complexes in the material. In this work, the develop- ment of defect complexes in Cz-Si after sequential isothermal heat treatments (annealings) in the temperature range of 450-550°C has been investigated using Fourier Transform Infrared (FTIR) Spectroscopy. A particular focus has been devoted to the development of Thermal double donors (TDDs), a series of electrically active defect species caused by the agglomer- ation of oxygen atoms into specific structural formations. Furthermore, the effect of a high carbon concentration on the development of these species has been investigated.
To facilitate the investigation of different reaction paths for the oxygen and carbon atoms in the material, defects have been intentionally generated by MeV electron irradiation. An objective of the present work has been to determine if a direct involvement of VOn (n≤6) centres or their dissociation to form fast diffusing oxygen species, contributes to TDD formation. Four point probe (FPP) resistivity measurements have been used to estimate the concentration of donor species. Photoluminescence (PL) spectroscopy has been utilized in correlation with IR bands to study the development of carbon related species.
The contents of this thesis are divided into five chapters, excluding the current introduc- tory one. Chapter 2 presents fundamental theory on semiconductor physics and vibrational spectroscopy. In chapter 3, theory on Silicon; growth, main impurities and defects will be presented to lay a foundation for the experimental work performed in this thesis. Chapter 4 outlines the experimental methods utilized, with a particular focus on the main technique, Fourier Transform Infrared Spectroscopy. In chapter 5 the obtained results are presented and discussed consecutively. A summary and conclusion on the established results are then given in chapter 6.
Background
In this chapter some fundamental concepts of crystals and electronic properties of semicon- ductors will be given. Further, relevant theory of vibrational motion in molecules and solids are presented. This is applied to explain the main principles of infrared (IR) spectroscopy, with a particular focus on the absorption mechanisms in silicon.
2.1 Crystal structure and defects
This section is based on the references by Tilley [5] and Campbell [6].
A solid can be classified with respect to the periodicity of the atoms constituting the material.
Crystalline solids consist of one single crystal,polycrystalline solids are composed of several small crystallites and amorphous solids have no long range order. In a crystalline solid the atoms or ions are joined together in a periodical network in three dimensions. The periodicity is defined in terms of a symmetric array of points in space, having the same spatial surroundings, called thelattice. At each lattice point an arrangement of one or more atoms, termed thebasis, is added, making up the crystal. The lattice is therefore a mathematical concept, and can be defined by three translational vectorsa,bandc. If an arbitrary lattice point is chosen as the origin, the positionPof any other lattice point is defined by,
P(uvw) =ua+vb+wc, (2.1)
where u,v and w are positive or negative integers. The parallelepiped formed by the three translational vectors defines theunit cell. The lattice will for all crystals contain a smallest volume, or cell, that represents the entire lattice and is regularly repeated throughout the crystal. Thus, when a, b and c represent the smallest distance between two lattice points,
|a|=a0, |b|=b0and |c|=c0, they are defined as primitive vectors, and the cell they span is called the primitive cell. A perfect crystal can therefore be constructed by an infinite repetition of the basis, attached to the lattice, illustrated in figure 2.1.
A perfect crystal is an idealization, and is only theoretically possible at absolute zero tem- perature (0 K). At finite temperatures (T>0 K) defects are inevitable as disorder increases the entropy of the system. Deviations from a perfect crystal structure may exist as a single point defect or extend in one-, two- or three dimensions. A point defect disturbs the crystal
(a) Lattice points (b) Basis (c) Crystal structure
a b
Figure 2.1: At each lattice point (a) a basis (b) of one or more atoms is added to obtain the total crystal structure (c). The translational vectorsaandb are illustrated.
pattern at an isolated site and the simplest type is avacancy, in which an atom is absent from a normally occupied site, as can be seen from the illustration in figure 2.2. A closely related point defect is an atom residing in the space between lattice positions, and is referred to as aninterstitial atom. If the atom that resides on an interstitial site is of the same element as the atoms in the lattice, it is termed aself-interstitial. Both vacancies and self-interstitials are intrinsic defects. Another type of one dimensional defect is anextrinsic point defect, which occurs when an impurity atom substitutes a lattice site or occupies an interstitial site. In the former case it is referred to as a substitutional impurity. Furthermore, an accumulation of point defects extending in only one dimension would result in a line defect, where the most common example is a dislocation. Defects extending in two dimensions are termed area de- fects, in which the most obvious type is a grain boundary. Controlling grain boundaries is important for polycrystalline materials, as they tend to decrease the electrical and thermal conductivity. Furthermore, if the concentration of a defect exceeds its solubility upon cooling, it tends to precipitate from the crystal, leading to three-dimensional precipitation defect com- plexes. Subsequent heat treatments of a material may also lead to the formation of precipitate defects.
In this thesis the main focus will be on the development of point defect complexes. The nomenclature commonly used for describing a point defect is:
Xpq. (2.2)
Here, X corresponds to the defect species, which may be a host atom or impurity atom/- molecule or a vacancy (V). p indicates the lattice site in which the species occupy. This can be at an interstitial position (i) or at a substitutional position (s). q denotes the electronic charge of the species relative to the site it occupies. Defects in semiconductors may have more than one possible charge state, so the charge is not always specified. In the case of an elemental crystal (e.g. Si), self-interstitials are commonly denoted I.
I
X
V
s
Xi
Figure 2.2: Two-dimensional illustration of point defects in a crystal structure. A vacancy (V), a self-interstitial (I), and an impurity element X occupying substitutional (Xs) and interstitial (Xi) lattice sites.
2.2 Fundamentals of semiconductors
This section is based on the references by Streetman [7], Nelson [8], Kittel [9] and Hemmer [10].
Semiconductor materials have characteristic electrical properties, with conductivities ranging between those of metals and insulators. The conductivity of semiconductors can further be varied as a function of temperature, optical excitation or by doping. These materials can hence be tailored to meet the specific needs of a desired application. The electronic characteristics of solids are understood by examining the band structure and associated electronic occupancy of the respective materials.
2.2.1 Electronic energy bands
The electrons in an isolated atom are restricted to discrete energy levels. The allowed energy levels, the eigenvalues, are found by solving the Schrödinger equation for the atom’svalence electrons1. In a solid material the number of atoms, and thus electrons, is very large and a simplification of this many-body problem is necessary. An approximation of the electronic nature of electrons in solids is found by the nearly free electron model. Here the valence electrons are modelled as a free electron gas distributed over the material, only perturbed by a positive potential set up by the fixed ion cores at the lattice points. The periodic potential has the same periodicity as the lattice, i.e., U(r)=U(r+R), whereRis a translational vector.
The time-independent Schrödinger equation for an electron in such a potential is, Hψ(r) =ˆ
−~2
2m∇2+U(r)
ψ(r) =Eψ(r), (2.3) where Hˆ is the Hamiltonian operator, ψ(r) is the wave function of the electron, ~ = h/2π is the reduced Planck’s constant, m the electron mass and E the energy eigenvalue for the
1The valence electrons of an atom is the outermost electrons that can participate in forming bonds.
given potential. Felix Bloch proved in 1928 that the wave functions,ψ(r), for such a periodic potential must be on the form of aBloch function [11], that is,
ψ(r) =eikruk(r) (2.4)
wherekis an arbitrary wave vector,eikris a plane wave anduk(r)inherits the same periodicity as the potential:
uk(r+R) =uk(r). (2.5)
The energy eigenvalue in eq.(2.3) depends on the wave vector,k, and gives the energy states that an electron is allowed to occupy. For a givenkseveral discrete levelsEn(k) exists, where the band index, n, can take positive integer values. The energy eigenvalues will further vary withk, as illustrated in figure 2.3. The range that the function En(k) sweeps over when k varies is termed anenergy band. Two consecutive bands can overlap or be separated by gaps of forbidden states, calledband gaps(Eg). These forbidden regions are a result of the interactions between the valence electrons and the ion cores of the crystal. Electrons will further seek to minimize their energy, and in the ground state electrons will occupy the lowest possible energy configuration. The highest occupied band at absolute zero temperature (0 K) is called the valence band (VB), while the lowest unoccupied band is termed the conduction band (CB).
The energy of the corresponding bands edges are termed Ev and Ec, respectively.
E
k E (k)3
E (k)1 E (k)2
E E
E
c
v g
Figure 2.3: An arbitrary (E, k) relationship. The energy ranges that the electron eigenvalues span correspond to energy bands. Here band 2 and 3 overlap, while an area of forbidden states, i.e. the band gap, exists between band 1 and 2. The figure is adapted from Hemmer [10].
An analogous approach for deriving the band gaps in solids, is to consider the crystal as a linear combination of atomic orbitals (LCAO). This is done by envisioning a stepwise combination of atoms to form the solid. If two atomic orbitals (AOs) (with one electron each) are joined together to form a molecular orbital (MO) the discrete energy levels will split into a bonding (symmetric) and antibonding (antisymmetric) level, slightly lower and higher in energy than the initial energy levels, respectively. The number of MOs is thus equivalent to the initial AOs. When a larger number of atoms are joined together the discrete energy levels multiply as more and more atoms are added to the crystal. Eventually, the energy levels will be so closely spaced that they can be considered as continuous bands of energy that the electrons can occupy, separated by ranges of no MOs.
Depending on the energy landscape and the occupancy of the bands, a material can be cate- gorized as a metal, semiconductor or insulator. For conduction of current to occur, electrons must be able to experience acceleration in an applied electric field, which implies that allowed energy states, not already occupied, must be available. If the VB is not completely filled, or overlaps with the CB, electrons will be free to move and can easily conduct current. Such a material is ametal. At 0K a semiconductor and an insulator inherit essentially the same structure, a filled VB separated from an empty CB by a band gap. What distinguishes a semi- conductor from an insulator is the magnitude of this gap. The relatively small band gap (Eg. 3-5 eV [8]) of semiconductors allows for excitation across the gap at reasonable2 amounts of energy. An insulator will in contrast have a negligible number of excitations for the same conditions. The important difference between an insulator and semiconductor is thus that the number of electrons available for conduction can be increased vastly in semiconductors by optical or thermal excitation. The described characteristics are illustrated in figure 2.4.
Filled states
Insulator
Filled states
Semiconductor
Filled states Partially filled states
Overlap
Metal Eg
Empty states
Empty states
Eg Ec
Ev
Ec
Ev
Ec
Ev
Ec
Ev
Figure 2.4: Energy diagram for an insulator, a semiconductor and a metal at 0K. In metals, free states are always available for electrons, and the material conducts current. In an insulator the band gap is of such magnitude that negligible amounts of charge carriers will be generated by thermal or optical excitation. For semiconductors the band gap is small and charge carriers can be generated. Figure adapted from Streetman [7].
Semiconductors can further be divided into two categories, depending on the position of the VB maximum with respect to the CB minimum, as illustrated in figure 2.5. In a direct band gap semiconductor the extreme band values occur at the same wavevector,k. In this case an electron can be excited directly across the band gap by the absorption of a photon with energy corresponding to the band gap (Eg). If the extremes exist at differentk, the smallest possible transition from VB to CB requires a change in the electron momentum, p=~k. As photons carry virtually no momentum, the transition must be assisted by the absorption of a lattice vibration, a phonon, of the correct energy. In the latter case the material is consequently termed anindirect band gap semiconductor.
2Reasonable amounts is referring to thermal energy in the room temperature range or photon energies corresponding to the wavelengths of visible light.
E E
Eg Eg
Ec Ec
Ev Ev
Direct Indirect
Photon Photon
Phonon assisted
k k
Figure 2.5: A simple illustration of a direct and indirect band gap. In a direct band gap semicon- ductor an electron can be excited from the VB maximum to the CB minimum by the absorption of a photon of energy Eg. The indirect transition requres a change in momentum (p=~k), generally supplied by the absorption of a phonon.
2.2.2 Charge carrier generation
A perfect semiconductor crystal, free of defects and impurities, is calledintrinsic. At 0 K an intrinsic semiconductor will have a completely filled VB separated from an empty CB and no charge carriers exists. When an electron is thermally or optically excited from the VB to the CB, an accompanying hole remains in the VB, and an electron-hole-pair (EHP) is created.
Both electrons and holes conduct current, where the hole can be considered as a positive charge carrier, moving in the opposite direction as electrons in an applied electric field. In intrinsic semiconductors EHPs are the only charge carriers and the concentration of electrons (n) in the CB and holes (p) in the VB must be equal. The concentration is called the intrinsic carrier concentrationni,
p=n=ni. (2.6)
A semiconductors ability to conduct current depends primarily on the number of available charge carriers. By introducing impurity elements by a process called doping, the number of charge carriers and therefore the conductivity can be increased. When impurities or lattice defects are incorporated into the crystal, additional levels are created in the energy band structure. Generally, heterovalent atoms containing more valence electrons than the host material will generate an energy level close below the CB edge. This level is filled with electrons at 0 K, meaning that the valence electrons of the impurity element are bound to their ion core. At relatively low thermal energies these electrons will ionize, and be donated to the CB. The dopant is termed donor and the energy level is accordingly termed donor level.
Similarly, impurities with fewer electrons than the host atom generate energy levels close above the VB. At 0 K this band is empty, i.e. filled with holes. An increase in temperature leads to electrons being accepted from the VB to this level. The dopants thus contribute holes to the VB by accepting electrons. Such a dopant is termedacceptor and its energy level is an acceptor
level. When a material is doped with a significant number of donor atoms, the equilibrium concentration of electrons, n0, greatly exceeds the equilibrium concentration of both holes p0 and intrinsic carriers ni, n0 p0,ni, and the material is called n-type. The material is termed p-type when the same is true for acceptors, p0 n0,ni. Donors and acceptors with the characteristics described above are termedshallow impurities, referring to the position of the impurity level with respect to the CB and VB edges. Shallow impurities are easily ionized and thus contribute with free charge carriers to the semiconductor. The positioning of shallow donor- and acceptor energy levels are illustrated in figure 2.6. Impurities may also produce deep energy levels, positioned further from the band edges, these are termeddeep impurities. Deep impurities are less likely to ionize, due to a higher requirement of thermal energy and may instead act as traps and/or recombination centres, where charge carriers can be trapped and/or annihilate. When a crystal is doped such that the equilibrium carrier concentrations n0 and p0 are different from the intrinsic carrier concentration ni the material is said to be extrinsic.
Figure 2.6: Illustration of N-type and P-type semiconductors, at low temperature. Shown is a filled donor level (ED), acceptor level (EA) and Fermi level (EF) for the respective materials.
The effect of doping is easily understood by the covalent binding model. For instance, Si has four valence electrons that all participate in covalent bonding with four neighbouring Si atoms, as illustrated in figure 2.7. If a Phosphorous (P) atom is introduced to the crystal, substituting Si, four of the P valence electrons will participate in bonding, while the fifth will be held by Coulomb interactions to the ion core. Only a small amount of energy is required to excite this electron and it will thus be available to conduct current. P is therefore a donor, with a donor level just below the CB of Si. Similarly, if a Boron (B) atom, containing only three valence electrons is introduced, an electron is missing to complete the covalent bonding to all four Si neighbours. B is an acceptor, and by accepting a valence electron from Si it contributes conducting holes to the VB.
2.2.3 Charge carrier density
To understand the electronic properties of semiconductors, the distribution of carriers over available energy states must be evaluated. The electrons and holes in solids obey Fermi- Dirac3 statistics. The Fermi-Dirac distribution function,f(E), gives the probability of finding
3Fermi-Dirac statistics describes a distribution of particles (fermions) over energy states in systems consist- ing of many identical particles that obey the Pauli exclusion principle.
h+
e-
B
P Si
-
+
Figure 2.7: When a phosphorous (P) atom substitutes a silicon (Si) atom it donates an electron to the lattice. When boron (B) is the substituent, a hole is created. These processes are known as donor- and acceptor doping, respectively.
an electron at an available energy state, E, at an absolute temperature, T:
f(E) = 1
1 +e(E−EF)/kBT, (2.7)
wherekB is the Boltzmann constant and EF is known as the Fermi level. EF represents an energy state at which the probability of occupancy is exactly 1/2. At T=0 K all allowed states below EF will be filled and all above will be empty. Hence, for an intrinsic semiconductor at absolute zero temperature where the VB is completely filled and CB is empty, the Fermi level lies approximately in the middle of the band gap. When the temperature is increased, there exists a finite probability of finding electrons above and holes below the Fermi level, however the Fermi function is symmetrical aboutEF for all temperatures, making it a natural reference point for calculations. The probability of finding a hole in an available energy state is equivalent to the probability ofnot finding an electron, hence the function[1−f(E)]represents the probability of finding a hole.
By combining the probability distribution of carriers, f(E), with the density of states in the relevant energy range, N(E)dE, the equilibrium concentration of electrons,n0, and holes,p0, in the CB and VB, respectively, can be found:
n0 = Z ∞
EC
f(E)N(E)dE, (2.8)
p0= Z Ev
−∞
[1−f(E)]N(E)dE. (2.9)
The product f(E)N(E) decreases rapidly above Ec, as f(E) in eq.(2.7) becomes extremely small for large energies. For that reason, very few electrons occupy energy states far above the CB edge. Similarly, few holes are found far below the VB edge, as [1−f(E)]accordingly decreases rapidly below the VB edge. The distributed electron states in the CB can further be represented by an effective density of states Nc, located at the Ec:
Nc= 2
2πm∗nkT h2
3/2
(2.10)
and for holes in the VB at Ev:
Nv = 2
2πm∗pkT h2
3/2
(2.11) Herem∗nandm∗p represent the effective mass of electrons and holes, respectively. As described in section 2.2.1, the electrons and holes are not completely free to move since they interact with the periodic potential of the lattice. The influence from the potential is contained in the curvature of the energy bands, ddk2E2. This modification of charge carrier mass allows for the use of electrodynamic equations. The representations of effective density of states in eq.(2.10) and (2.11) gives the same results as obtained by performing the integration over the states in eq.(2.8) and (2.9). If the Fermi level is assumed to lie at least several kT from the band edges,f(E) can be approximated by the Maxwell Boltzmann function. This approximation simplifies the electron and hole concentration to:
n0=Ncf(Ec) (2.12)
p0=Nv[1−f(Ev)], (2.13)
where the aforementioned distribution function for electrons and holes are approximated to:
f(Ec) = [1 +e(Ec−EF)/kT]−1'e−(Ec−EF)/kT (2.14) 1−f(Ev) = 1−[1 +e(Ev−EF)/kT]−1 'e−(EF−Ev)/kT. (2.15) Hence, the electron and hole concentrations in the CB and VB, respectively, can now be expressed as:
n0 =Nce−(Ec−EF)/kT (2.16)
p0 =Nve−(EF−Ev)/kT. (2.17)
For an intrinsic semiconductor, the Fermi level lies at some intrinsic level, Ei, near the middle of the band gap. By combining eq.(2.16) and the corresponding equation for the intrinsic charge carrier concentration, ni in which EF = Ei, the electron concentration can be given by:
n0=nie(−(Ec−EF)+(Ec−Ei))/kT =nie(EF−Ei)/kT. (2.18) By applying the same approach for holes in eq.2.17, and realizing that ni=pi, since intrinsic carriers are generated in pairs:
p0 =nie(−(EF−Ev)+(Ei−Ev))/kT =nie(Ei−EF)/kT. (2.19) The charge carrier concentration in an intrinsic semiconductor depends only on temperature and the inherent properties of the material. The only charge carriers in such material are EHPs. For an extrinsic material, donors or acceptors are added to increase the charge carrier density. By evaluating eq.(2.16) and (2.17) it is evident that the Fermi level will move closer to the CB edge as the number of electrons is increased by the addition of donor species. The same is true for holes, where the Fermi level is positioned closer to the VB as the number of acceptors are increased. When a semiconductor is doped with a significant number of donor atoms, i.e. the number of donors is several orders of magnitude larger than the number of intrinsic carriers, the charge carrier concentrations can be approximated by the doping concentration.
If a semiconductor is doped withNdsingle donor species4 the electron concentration is simply equal to the donor concentration. The hole concentration can be calculated utilizing the law of mass action (np=n2i):
n0 ≈Nd (2.20)
p0≈ n2i
Nd. (2.21)
Similarly, for a p-type semiconductor the hole concentration is equal to the acceptor doping concentration,Na, and the electron concentration is found:
p0≈Na (2.22)
n0 ≈ n2i
Na. (2.23)
When a semiconductor contains both donors and acceptors, one can not expect a concentration of holes in the VB corresponding to the number of acceptors, or a concentration of electrons in the CB equal to the number of donors. The excess carriers provided by the dopants may instead compensate each other by recombining. The relationship between electron, hole, donor and acceptor concentrations can be found by considering the requirement for space charge neutrality:
p0+Nd+=n0+Na− (2.24)
2.3 Theory of vibrational spectroscopy
This section is based the on references by Griffiths [12], Kittel [9] and Schroder [13].
Vibrational spectroscopy is the study of the interaction between electromagnetic radiation and matter, where the particular interaction depends on the radiation wavelength. When a material is exposed to electromagnetic radiation in form of infrared (IR) light the chemical bonds in the material may absorb this radiation at specific frequencies, characteristic of their nature and chemical environment. The IR region corresponds approximately to wavelengths spanning from 700 nm to 1 mm, or an energy in the range 1.24 meV - 1.7 eV. This is in the range of energies separating the quantum states of molecular vibrations, which makes IR spec- troscopy an efficient method for investigating the chemical composition of semi-transparent solid-state materials.
In silicon there are four main origins of radiation absorption: lattice vibrations (phonons), localized vibrations (due to defects perturbing the lattice symmetry), electronic transitions in impurities and free charge carriers. To understand the principles of vibrational spectroscopy, some knowledge of the vibrational motion of atoms is necessary, before proceeding to the fundamentals of specific absorption mechanisms.
4Single donor species contribute one electron each to the CB when ionized.
2.3.1 Molecular vibrations
In the simple case of a diatomic molecule, vibrational motion can be described using Newtonian mechanics, where the atoms are modelled as masses connected by a massless spring. A simple harmonic oscillator is a system that when displaced from its equilibrium position, experiences a restoring forceF proportional to the displacementx. A diatomic molecule can be modelled as such a system, where the displacement represents the change in bond length from its equilibrium value. The motion is governed byHooke’s law:
F =−kx=µd2x
dt2, (2.25)
wherek is the force constant in units N/m, µ =m1m2/(m1+m2) is the reduced mass of a heteronuclear molecule, and Newton’s second law is applied. The solution to this differential equation is a simple harmonic motion describing the vibrationx(t):
x(t) =Asin(ωt), (2.26)
whereA is the amplitude, t is the time and ω is the angular frequency of oscillation, given by:
ω= s
k µ =
rm1+m2 m1m2
k. (2.27)
This simple classical model gives an accurate description of the vibration in a molecule, vir- tually any oscillatory motion is approximately simple harmonic as long as the amplitude is small [14]. However, when describing the interaction with electromagnetic radiation, a quan- tum mechanical approach is required.
The spring force in eq.(2.25) gives rise to the one-dimensional potential:
U(x) = 1
2µω2x2, (2.28)
where the spring constant is eliminated in favour of the classical frequency in eq.(2.27). The quantum mechanical equivalent of the derivation in the previous section is to solve the time- independent Schrödinger equation for a molecule moving in such a potential, i.e.:
− ~ 2m
d2 dx2 + 1
2mω2x2
ψ(x) =Eψ(x). (2.29)
By solving the differential equation the vibrational energies in a quantum mechanical harmonic oscillator is found to be:
En=~ω
n+1 2
. (2.30)
The quantum number n in eq.(2.30) characterizes the different eigenstates of the harmonic oscillator, and can take non-negative integer values (n=0,1,2,..). The equation shows that the energies of vibrational motion is quantized, and the only transitions allowed are from one eigenstate to another. Under certain conditions molecules may participate in allowed energy transitions, and this can be observed in IR spectroscopy.
2.3.2 Infrared absorption
In order for IR radiation to be absorbed by matter, two conditions must be fulfilled. First, the resonance condition requires that the oscillating frequency of the incoming photon matches the natural frequency of a particular vibrational mode. Second, in order for energy to be transferred from the incoming photon to the molecule, the vibration must cause a change in the molecules dipole moment5. The reason for this is that the absorption of a photon follows from the interaction between a mode and the time-varying electrical field of the incoming light. These requirements are the selection rules governing IR spectroscopy [15]. In vibrational spectroscopy it is common to usewavenumber,˜v, rather than frequency to describe vibrational modes. The wavenumber is the spatial frequency of a wave in cycles per unit distance:
˜ v= 1
λ = ω
2πc, (2.31)
whereλis the wavelength and c is the speed of light. Transitions between the ground state (n=0) and first excited state (n=1), in eq.(2.30), of most vibrational modes has an energy dif- ference corresponding to the frequency of electromagnetic radiation in the mid IR spectrum6. This makes IR spectroscopy a powerful tool for investigating the structure of a wide variety of substances.
The requirement for a change in dipole moment as described above, means that not all vibra- tions will be detectable by IR spectroscopy. One example is that of the heteroatomic molecule N2, that do not hold a time-varying dipole moment. However, in the absence of a changing dipole moment, a change in polarizability7 will make a vibration visible in a complementary technique called Raman spectroscopy, which is based on the detection of inelastic scattering of monochromatic light. Raman-active vibrations are thus governed by different selection rules than IR absorbing vibrations and will provide complementary information. Only IR spectroscopy will be considered in the following.
2.3.3 Vibrational modes in crystals
Like molecules, crystals can also vibrate as a whole. In a crystal, a large number of atoms (or ions) are bonded together in a three-dimensional periodic array, as described in section 2.1.
In this system, each atom will experience forces from all surrounding atoms, such that every atom is held near its equilibrium position. A potential energy function characterizes the force acting between a pair of atoms, depending on the distance between such a pair. The potential energy of the entire lattice,Vlattice, is thus the sum of all pairwise potential energies:
Vlattice=X
i6=j
V(ri−rj), (2.32)
whereri is the position of the ith atom, and V is the potential energy between two atoms.
However, the number of atoms in a crystal is extremely large, on the order of Avogadro’s
5The electric dipole moment is a measure of net molecular polarity, which is the magnitude of the charge at either side of the molecular dipole times the distance between the charges.
6The mid IR spectrum spans from 400 to 4000 cm−1 or a wavelength of 2,5 to 25µm.
7The ease with which the charge distribution in a molecule can be distorted by an external electric field is called its polarizability.
number (∼ 1023), and such calculations would be extremely complex. Two important ap- proximations are therefore applied; only nearest neighbour interactions are considered and harmonic potentials are assumed. In analogy to the harmonic oscillator described in the pre- vious sections, the lattice can now be modelled as a grid of N masses connected with springs, giving a total of 3N independent harmonic oscillators. Thus, the energy of a lattice vibration is also quantized and the quantum of energy is called a phonon. Phonons are quasi particles that carry the lattice vibrations through the crystal.
The atoms in a solid can vibrate normal to- or in the same direction as the propagating wave, representing transversally- and longitudinally polarized phonons, respectively. For crystals with more than one atom in their primitive unit cell, there are two types of phonons,optical andacoustic. Acoustic phonons carry vibrations like sound waves, where neighbouring atoms vibrate coherently. When the neighbouring atoms vibrate out of phase, i.e with alternating opposite velocities, the phonons are termed optical. In compound crystals like Zinc Oxide, where the two types of atoms carry different charges, the optical phonons create a time- varying dipole moment and can therefore interact with IR light. For elemental crystals, neighbouring atoms are the same and there is no first-order dipole moment, hence no one- phonon absorption is observed. Pure Si is therefore said to be transparent in the infrared range. However, multi-phonon coupling, where a photon couples with more than one phonon, can lead to an asymmetry in the electronic charge distribution and a varying dipole moment.
Hence, the lattice itself will absorb some IR radiation. When studying defects in silicon the intrinsic contribution from the lattice is usually undesirable. To circumvent this, a semi- intrinsic reference spectrum is measured, and the ratio of the two spectra is free from the intrinsic contribution.
2.3.4 Localized vibrational modes
The vibrational properties of crystals are significantly altered by the presence of defects and impurities. Phonons in a perfect lattice have well-defined frequencies. When an impurity is introduced the translational symmetry is broken and one or more vibrational modes may appear. If an impurity atom replaces a heavier host atom, its vibrational frequency will lie above the phonon frequency range [16]. Conversely to a phonon, the vibrational mode of the defect is localized in real space and frequency space, and is referred to as a localized vibra- tional mode (LVM). The LVMs of impurities are affected by the symmetry of the surrounding environment and gives rise to sharp peaks in IR absorption spectra.
2.3.5 Electronic transitions
When a semiconductor is intentionally doped or has energy states in the band gap due to defects, IR radiation can be absorbed by these defects under certain conditions. Shallow donor or acceptor states in silicon are located meVs below the CB edge and above the VB edge, respectively. At room temperature these states are ionized and will thus not be available for absorption. However, at cryogenic temperatures donor states are filled with electrons and acceptor states are empty, i.e., filled with holes. In the case of an n-type semiconductor at low temperature, electrons will be "frozen" at the donors, and the free carrier density in the conduction band (Ec) is low. In this condition the electrons are mainly located at the lowest
energy level or donor ground state (ED). With incident photons of energyhν≤(Ec- ED), two optical absorption processes can occur. The excitation of electrons from the ground state (ED) to the conduction band (Ec) leads to a broad absorption continuum. However, electrons can also be excited from the ground state to one of several excited (donor level) states. The latter produces sharp absorption lines in a transmission spectrum, characteristic of the shallow-level impurities [13]. Thermal donors are an example of shallow-level impurities in Si which give rise to such characteristic electronic transition bands. Thus, when the thermal donor levels are filled, these can readily be observed in low temperature (LT) measurements. The detection limit for electronic transitions in impurities are lower than for the LVM’s, discussed in the previous section, but are in contrast dependent on the Fermi level position and therefore more challenging to quantify.
2.3.6 Free carrier absorption
At high temperatures, donors and acceptors are ionized and therefore contributing to a high carrier concentration in the CB and VB, respectively (see section 2.2.2). Free carrier absorption occurs when the material absorbs a photon due to the excitation of a charge carrier from an already excited state to another unoccupied state in the same band. Electrons in the CB can thus absorb incoming photons and be excited to a higher, unoccupied state in the CB. The lowest energy state for holes is at the top of the VB. Thus, when free holes absorb radiation they are excited to a lower, unoccupied state in the VB. Free carriers in the semiconductor VB or CB, arising from electrically active defects and impurities in the crystal, may give a significant contribution to the IR absorption by the sample. In the intrinsic regime, absorption by free carriers can generally be neglected, but it can become significant in heavier doped materials, having high carrier concentrations. Free carrier absorption does not generally result in any useful photo-response in IR spectroscopy measurements and is often regarded as a performance degrading mechanism [17]. In crystals with high carrier concentration, and thus low resistivity, the free carrier absorption can eventually limit the transmission to an extent that the method is no longer useful [18].
2.3.7 Infrared transmission measurements
Infrared spectroscopy measurements of solid state samples are performed by measuring the transmitted beam after interaction with the sample. A spectrum is then obtained by plot- ting the intensity (absorbance or transmittance) versus the wavenumber. The transmitted intensity,I(˜v), will decrease exponentially with sample thickness (penetration depth):
I(˜v) =I0(˜v)e−α(˜v)d. (2.33) HereI0(˜v)is the intensity of the incident beam andI(˜v)of the transmitted beam as a function of wavenumber,α(˜v) is thelinear absorption coefficient in units of cm−1 and d is the sample thickness. This equation is known as the Bouguer-Lambert-Beer law, usually simplified to Beer’s Law, and it is the fundamental law of quantitative spectroscopy. Eq.(2.33) neglects losses in intensity due to reflectance of the beam from the sample surfaces. The fraction of the incident radiation which is reflected from a surface is called the reflectanceR, and is given
by [13]:
Rv˜= (nv˜−1)2+k2˜v
(nv˜+ 1)2+k2˜v. (2.34) Herekv˜ is the extinction coefficient andn˜v is the refractive index of the material. For a solid sample the beam may be reflected from both the front and rear surface, which can give rise to multiple internal reflections. The transmittance of a sample is defined as the ratio between the transmitted and incident beam, and by including reflectance this gives:
T(˜v) = I(˜v)
I0(˜v) = (1−R)2e−α(˜v)d
1−R2e−2α(˜v)d (2.35) The refractive index of Si is approximatelyn˜v ≈3.42for infrared radiation [19]. The extinction coefficientk˜v which is related to the absorption coefficient by the relationα= 4πk/λis small compared to unity for the wavenumber region spanned by the mid infrared range [13]. By using these values in eq.(2.34), a constant reflectance of R≈0.3 is found for Si. The denominator in eq.(2.35) can therefore be taken as 1 without introducing any significant error. The absorption coefficient can further be divided into two parts, α = α1 +α2, where the first corresponds to absorption from the lattice and free electrons, while the second corresponds to absorption from defects.
T = I
I0 = (1−R)2e−(α1(˜v)+α2(˜v))d)≡C(˜v)e−α2(˜v)d. (2.36) The factorC(˜v) = (1−R2e−α1(˜v)d)in this expression varies only slowly with the wavenumber
˜
v, while the impurity absorption fromα2 can be detected as sharp peaks.
The absorbance, A(˜v), of the sample is defined as the negative natural logarithm of the transmittance:
A(˜v) =−ln(T(˜v)) =−ln(I I0
) =α(˜v)d. (2.37)
Furthermore, the absorbance of any component i is proportional to its concentration in the sample. The concentration of a defect species, [N] (where square brackets denotes concentra- tion) can therefore be determined as the product of the absorption coefficientαi(˜v), i.e., the amplitude of the absorption peak, and a calibration factor a,
[N] =a×αi(˜v) =a×Ai(˜v)
d (2.38)
Since IR absorption is a relative measurement, absolute methods are required to establish the calibration factor that relates the absorption to the impurity content [18]. Calibration factors can for example be established by a micro-sectioning technique as Secondary Ion Mass Spectrometry (SIMS). When calibration factors are established, the total concentration can be deducted from integrated peak area or peak amplitudes of the associated absorption bands, depending on which the calibration factors are developed for.
Silicon; growth, main impurities and defects
Oxygen (O) and carbon (C) strongly contribute to, and influence major defects in Si during crystallization and temperature processing. Thermal double donors (TDDs), O precipitates and defects causing light induced degradation (LID) are all related to O and affect the per- formance of photovoltaic cells. C is found to inhibit the formation of TDDs [20], however, the mechanisms involved in the suppression is still not clear. In the first two sections, brief theory on the Si structure and impurity incorporation during crystal growth will be given.
Further, the characteristics of important defects in Si will be discussed with a focus on O- and C-related complexes in n-type Czochralski (Cz) grown Si. The subsequent sections will present established results regarding the generation and electrical activity of TDDs in Si. In more recent years, two structural models of TDDs have been proposed.
3.1 Fundamentals
Si is a group IV element, and like C and Germanium (Ge), it crystallizes in the diamond crystal structure, where each Si atom is bound to four neighbouring Si atoms [7]. The diamond structure, illustrated in figure 3.1, consists of two inter-penetrating face-centred cubic (fcc) sublattices, or alternatively a fcc lattice with an extra atom placed ata/4 +b/4 +c/4 from each of the fcc atoms. The structure belongs to the Fd3m space-group. In Si, the lattice parameters are given by a =b = c = 543.09 pm [7]. The presence of defects may however affect this value, by causing strain in the lattice, as will be discussed later.
Si is an indirect band gap semiconductor with a band gap of Eg=1.11 eV at 300 K [7]. As mentioned in section 2.2.1, the excitation of an electron from the VB to the CB must be accompanied by a momentum conserving phonon. This means that Si, due to the indirect band gap, would not be the optimal choice as a single PV cell, when considering only the efficiency. However, due to its great abundance, band gap fit for the visible spectrum and low production cost, Si is the dominant PV material today.
Figure 3.1: Si crystallizes in the diamond structure, in which each Si atom is bound to four neighbouring Si atoms. Figure adapted from [21].
3.2 Crystal growth and impurity incorporation
Most of the mono-crystalline Si used in the integrated circuit (IC) and PV industry, is pro- duced by the Cz pulling method. The technique was first invented and named by the Polish metallurgist Jan Czochralski in 1918 [22], while the method used in today’s ingot production was developed by Teal and Little in the 1950s [23].
Several refining procedures, beyond the scope of this text, are performed to produce extremely pure, electronic grade polycrystalline Si from raw material, i.e. quartz. After refining, the Si does not become more purified, but subsequent processing is required to produce mono- crystals. In the Cz method, polycrystalline Si is melted in a crucible in an inert gas ambiance at reduced pressure, at approximately 1500°C. A chemically etched crystal seed is then lowered into the melt and pulled at controlled rates to produce a mono-crystalline Si ingot. The crystal seed serves as a template for the crystal growth, and must therefore be oriented carefully. Prior to the crystal growth, a short necking procedure is performed, to ensure a dislocation free crystal structure. During the growth process dissolution of and reactions with the environment will lead to the incorporation of significant amounts of impurities in the crystal structure, including O and C.
The crucible containing the molten silicon is made of amorphous silica (SiO2), during the crystallization process it partly dissolves and enriches the Si melt with O, according to the reaction:
SiO2+Si→2SiO. (3.1)
Over 95% of the dissolved O escapes from the surface of the melt as volatile silicon monoxide (SiO) [24], however, a small fraction will be incorporated into the Si crystal through the crystal- melt interface. During growth, the O is constantly replenished, while the surface area of the melt that is in contact with the crucible decreases as the melt solidifies. The O concentration is therefore expected to be higher in the seed (top) part of the ingot compared to the tail (bottom). The solid solubility of oxygen can be found fromCs= 4.0×1023e−2×104/T(K)cm−3 [25], which corresponds to a value of 2.8×1018cm−3 at the melting point of Si (1412°C). An O concentration, [Oi], of approximately 1018 cm−3 is common in Cz-Si [18]. These O atoms can have an adverse effect on the electrical, chemical and physical properties of the crystal.
However, the incorporation of oxygen is also beneficial, as it increases the crystals mechanical strength.
The source of C impurities is from the graphite material making up the hot zone of the grower system, in addition to the C impurities which may have been present in the starting polycrystalline material. The SiO, originating from the dissolving crucible described above, may interact with the hot graphite components and reduce to carbon monoxide (CO), before re-entering the melt:
SiO+ 2C→SiC+CO. (3.2)
C is expected to follow normal solidification behaviour, expressed by [6]:
Ns(x) =N0k(1−x)k−1 (3.3)
whereNs,k andx are the crystal impurity concentration, the impurity segregation coefficient and the fraction of melt solidified, respectively. Since the constant N0 represents the initial impurity concentration in the melt, the equation will not reflect the system precisely. However, it gives an indication of the C distribution in the growing crystal. Since the C is constantly replenished (N0 constant or increasing) and the dopant segregation coefficient k0 is small (k0 = 0.07 [18]), the concentration of C in the grown crystal will increase towards the tail of the ingot. C concentrations of1016cm−3is commonly observed in Cz grown crystals [18].
3.3 Point defects and their complexes
Point defects are present in all crystalline solids and affect many fundamental as well as technologically important phenomena. Intrinsic elementary point defects (i.e., interstitials and vacancies) formed during crystal growth and processing interact strongly with common residual impurities such as O, C, and various transition metals, as well as intentional dopants.
Many of the point defect complexes are electrically active, with deep states in the band gap.
In addition, they may act as vehicles for diffusion. Moreover, they can be strongly harmful for semiconductor devices by acting as nucleation sites for extended crystalline defects, such as clusters, stacking faults or dislocations. In Si, point defect complexes manifest themselves by affecting the electrical, optical, structural and mechanical properties of the material [26].
Understanding and controlling point defect complexes are thus of decisive importance for the present and future use of Si in electronics and photovoltaics.
IR spectroscopy enables the identification and quantification of defect species, and is a highly suited method to study the evolution of defects after sequential thermal treatments. However, IR absorption spectroscopy is a technique of relatively low sensitivity and the concentration of a species must, at least, be on the order of ∼1014cm−3 to be detectable with this method.
The concentration of point defect complexes in current, as-grown, mono-crystalline Si wafers is typically below 1013cm−3, except for the more abundant impurities such as interstitial O and substitutional C [26]. Therefore, in order to study point defects with IR spectroscopy the number of defects must be increased, as compared to the amounts generated during crys- tal growth. This can be achieved by irradiating the Si crystal with high energy particles (e.g. electrons, neutrons or protons) in order to produce vacancies and self-interstitials which subsequently may interact with other defects, producing defect complexes in detectable con- centrations.
3.3.1 Oxygen
In its usual configuration O occupies an interstitial site, Oi, in Si. This was determined on the basis of IR measurements [27], where O was found to occupy a position midway between two neighbouring Si atoms, along the four equivalent <111> bond directions. In this configuration the two neighbouring Si atoms give up their covalent bond and engage with the O atom instead, making the O impurity electrically inactive [18]. The interstitial oxygen concentration can be determined by measuring the absorption band at 1107 cm−1 (RT), which is due to the asymmetric stretching vibration of the Si-O-Si bond [27].
The disadvantages or complications of O in Si will be elaborated in the following. However, the incorporation of O also has several important advantages, which partially is the reason why Cz-Si is used to such an extent. O impurities improve the mechanical strength of Si wafers, which increase the wafers resistance to warpage and generation of dislocations during thermal cycling in device production processing [18]. This advantage, in addition to the lower production cost compared to other crystallization techniques (e.g. Float zone growth), makes Cz wafers the most used in both electronics and PV industry [26].
3.3.2 Carbon
C is an isovalent impurity in Si and predominantly occupies a substitutional site, denoted Cs, in the crystal structure, where it is electrically inactive. In Si, Cs gives rise to absorption in a LVM at 605 cm−1 at RT [28] and 607 cm−1 at low temperature1 (LT) [29], in which the RT peak is commonly used for quantitative determination. The amount of C in a Si crystal is assumed to be limited by the lattice shrinking due to the small atomic radius of C compared to Si. However, in Cz-grown crystals, large C solubilities can be achieved as C compensates the lattice expansion due to the presence of the relatively large O atoms [28].
3.3.3 Vacancy-oxygen complexes
Mono-vacancies generated during crystal growth and irradiation are highly mobile defects, with a diffusivity of DV ≈10−9cm2s−1 at RT [30]. Oi acts as a dominant trap for the migrating mono-vacancies, forming the vacancy-oxygen (VO) centre. The VO-centre is the primary oxygen-related defect in irradiation damaged Cz-Si. The neutral VO-centre gives rise to an IR- absorption band at 835 cm−1 at LT and 830 cm−1 at RT [26]. In VO complexes the O resides slightly off-centre from the substitutional site and binds preferentially to two neighbouring Si atoms, while the other two Si neighbours form a bond [16]. The VO complex is electrically active, with a deep acceptor level Ec - 0.17 eV [26]. The complex is stable up to temperatures in excess of approximately 300°C. Annealing at higher temperatures can lead to the formation of VO2 complexes via the reaction,
V O+Oi→V O2. (3.4)
1In this text low temperature (LT) referrers to 18 K. This is the measurement temperature used for cold IR measurements.
