Chapter 1 Introduction
1.2 Motivation
For heteroepitaxial systems with large mismatches in lattice parameters and thermal expansion coefficients between the deposited layer and substrate, significant strain is built up in the grown layer. When the stored strain energy exceeds certain threshold, the heterostructure becomes metastable and defects are generated to release the large strain energy. As revealed by many studies on another popular optoelectronic semiconductor - GaN thin films, which has the same wurtzite structure as ZnO, defects intimately affect the electrical and optical properties of the films, including the degradation of devices through carrier scattering [18], nonradiative recombination [19], and reverse-bias leakage current [20, 21]. However, the influence of defects on the physical properties of epi-ZnO films is still not well understood. A comprehensive knowledge of structural defects in ZnO epi-layer and their influence on the optical and electrical properties is valuable especially for the design of photoelectronic devices. In this dissertation, the growth of high quality ZnO epitaxial films by pulsed-laser deposition (PLD) on sapphire (0001) and Si(111) using various oxide buffer layers including γ-Al2O3 and Y2O3 is reported. The microstructure of ZnO epi-films were thoroughly studied by X-ray diffraction (XRD), transmission electron microscopy (TEM) and atomic force microscopy (AFM). The electrical properties of these epi-films were examined by using scanning capacitance
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microscopy (SCM) and conductive atomic force microscopy (C-AFM).
photoluminescence (PL) was employed to characterize the optical properties of the ZnO films. Based on the obtained results, the correlations between structural properties, in particular the structural defects, and electric as well as optical properties are established.
1.3 Organization of the dissertation
This dissertation is organized as follows. A brief review of epitaxial growth,
crystal structures, dislocation theory, and defect analysis using XRD and TEM is given in chapter 2. The basic theory of the techniques used to characterize the samples including XRD, scanning probe microscopy (SPM) and PL are also summarized in the same chapter. Chapter 3 contains the details of sample preparation and a description of experimental setups. In chapter 4, the defect structures of high quality ZnO epitaxial films grown on c-plane sapphire are reported;
the correlation between TDs and electrical properties, characterized by SCM and C-AFM, of these films is also discussed. Chapter 5 consists of the study on the structural and optical characteristics of ZnO epitaxial films on Si(111) substrates with a thin γ-Al2O3 buffer layer; the correlation between various types of TDs and the features in PL spectrum is described. In chapter 6, we show both high-quality
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crystalline and optical properties of ZnO epi-films grown on Si (111) substrates using a nano-thick Y2O3 buffer layer and a discussion of the role of MDs at the ZnO/Y2O3
interface in stabilizing the structure of this heteroepitaxial system is also presented.
Finally, chapter 7 contains the conclusion of the studies in the ZnO epi-films and the topics proposed for future studies.
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References
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Chapter 2 Theoretical background and characterization techniques
2.1 Epitaxy
Epitaxy refers to the growth on a crystalline substrate of a crystalline substance that mimics the orientation of the substrate. If a film is deposited on a substrate of the same compositions, the process is called homoepitaxy; otherwise it is called heteroepitaxy [1]. Depending on the degree of lattice mismatch, (af - as)/as, where af
and as, respectively, denote the lattice constants of film and substrate, the epitaxy of heterosystems can be modeled by lattice mismatch epitaxy (LME) or domain match epitaxy (DME). A brief review of the two epitaxy models and the difference between them is given in the following.
2.1.1 Lattice mismatch epitaxy (LME)
The well-established lattice-matching epitaxy is suitable for describing systems with small lattice misfit (less than 7%–8%). The deposited layer grows by one-to-one matching of lattice constants across the film–substrate interface. The film grows pseudomorphically up to a ‘‘critical thickness’’ where it becomes energetically favorable for the film to contain dislocations [2, 3]. In this case, the dislocations are generated at the film surface and glide to the interface; therefore, the Burgers vectors and planes of the dislocations are dictated by the slip vectors and glide planes of the crystal structure of the film [4]. Smaller lattice misfit leads to
smaller elastic energy and coherent epitaxy is formed. Above this misfit, it was surmised that the film will grow textured or largely polycrystalline.
2.1.2 Domain mismatch epitaxy (DME)
The DME concept represents a considerable departure from the conventional LME for hetero-systems with lattice misfit less than 7–8%. For hetero-systems with larger lattice misfit, integral multiples of lattice planes - domains, instead of lattice constants, match across the film–substrate interface. The size of the domain equals integral multiples of planar spacing in the DME. The detailed description of DME model can be consulted in Ref [5].
The hetero-system of ZnO grown on c-plane sapphire is an example of DME.
The lateral lattice constants of ZnO and sapphire are 3.249 and 4.758 Å, respectively, yielding a lattice mismatch of -31.7%. Figure 2-1(a) shows high-resolution TEM cross-section image taken with electrons incident along ZnO [1100] pole, in which an atomically sharp interface between ZnO epi-film and substrate is demonstrated.
The Fourier-filtered image of Fig. 2-1 (b) is shown in Fig. 2-1 (b), in which the vertical lines above and below the interface are associated with the (2110) planes of ZnO film and the (0110) planes of sapphire substrate, respectively. The image clearly manifests the matching of 5 or 6 (2110) planes of ZnO with 6 or 7 (3030) planes of sapphire at the interface. The corresponding diffraction pattern, shown in
13
Fig. 2-1 (c), confirms the relative orientation between film and substrate. The c-plane of ZnO lies on the basal plane of sapphire with a 30° in-plane rotation, as
illustrated in Fig. 2-1(d), which leads to the alignment of the {3030} planes of sapphire with the {2110} planes, i.e. a planes, of ZnO. Thus, the domain consisted of an average 5.5 ZnO {2110} lanes with size of 8.935 Å matches nicely with the domain made of an average 6.5 sapphire
p Å. The DME of ZnO on (0001) sapphire has also been demonstrated by in-situ x-ray diffraction measurement during initial stage of film growth [5]. Narayan et al.
applies the time-resolved x-ray crystal truncation rod (CTR) measurements made after each excimer laser ablation pulse. They found the surface structure transients associated with ZnO clustering and crystallization last for about 2 sec. following the abrupt ~5 μs duration of laser deposition and discovered the rapid relaxation of ZnO films on sapphire. The relaxation process requires the creation of dislocations, which involves nucleation and propagation of dislocations. The rapid relaxation process in DME is consistent with the fact that the critical thickness under these large misfits is less than 1 monolayer [6]. As a result, dislocations can nucleate during initial stages of growth and most defects are confined to the region near the interface, leading to fewer defects in the interior of the deposited layer, the active region of the device.
plane
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Fig. 2-1 (a) High-resolution TEM cross section image with (0110) foil plane of sapphire and (2110) plane of ZnO showing domain epitaxy in ZnO/apphire system; (b) Fourier-filtered image of the region near interface manifesting the matching of ZnO (2110) and sapphire (3030) planes with a 5/6 and 6/7 ratio; (c) corresponding electron diffraction pattern showing the alignment of planes in ZnO and sapphire; and (d) schematic of atomic arrangement in the basal plane of ZnO and sapphire. [5]
epitaxy 2 .2 Structural defect in
The structural defects in epitaxial film are generally categorized as threading and misfit dislocation, stacking fault, oval defect, and etc., as illustrated in Fig. 2-2. The most important structural defect in epitaxial films is the dislocation which also named as line defect. Dislocations can be further clarified into two sections according to their location in epitaxial films. One is threading dislocations (TDs) which extends throughout the entire thickness of an epitaxial film and the other one is misfit dislocation (MDs) located mainly at the interface between the substrate and the
15
deposited layer during initial stage of epitaxy. In following section, a brief review of dislocation theory is given.
Fig. 2-2 The typical structural defect in epitaxy
2.2.1 Dislocations
2.2.1.1 The theory of dislocation
A dislocation is a crystallographic defect, or irregularity, within a crystal structure.
The presence of dislocations strongly influences the properties of materials. Some types of dislocations can be visualized as being caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the surrounding planes are not straight but bend around the edge of the terminating plane so that the crystal structure is perfectly ordered on either side. According to the relationship between Burgers vector and dislocation line, there are two primary types of dislocations, screw and edge dislocations. Mixed dislocation is a combination of the two types of
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dislocation [7-9]. Some characteristics of both screw and edge dislocations are summarized below.
1. Screw dislocations:
A screw dislocation is much harder to visualize. Imagine cutting a crystal along a plane and slipping one half across the other by a lattice vector, the halves will fit back together without leaving a defect. If the cut only goes part way through the crystal and then slipped, the boundary of the cut is a screw dislocation. It comprises a structure in which a helical path is traced around the linear defect (dislocation line) by the atomic planes in the crystal lattice, as shown in Fig.2-3 (a). For pure screw dislocations, the Burgers vector b is parallel to the dislocation line. A screw dislocation moves (in the slip plane) in a direction perpendicular to the Burger vector (slip direction) cause the strain and elastic stress field surrounding a screw dislocation, as shown in Fig. 2-4 (a) are written as
material, respectively. According to the linear elasticity theory, the strain energy density in the stress field of the screw dislocation is τ2/2μ. The strain energy per unit length of the screw dislocation can be estimated with the following integration.
0
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where Ws is the energy per unit length of the screw dislocation, r0 is the inner radius that excludes the dislocation core and r’ is an outer limiting radius for integration. It is normally assumed that linear elasticity does not hold below r0 ~ b.
2. Edge dislocations:
An edge dislocation is a line defect where an extra half-plane of atoms is introduced mid way through the crystal, distorting nearby planes of atoms. When enough force is applied from one side of the crystal structure, this extra plane passes through planes of atoms breaking and joining bonds with them until it reaches the grain boundary.
The "extra half-plane" concept of an edge dislocation can be used to illustrate lattice defects such as dislocations, as shown in Fig. 2-3(b). An edge lies perpendicular to its Burgers vector and moves in the direction of the Burgers vector. The stress field surrounding an edge orientation is more complicated than that surrounding a screw dislocation. It is generally assumed that an edge dislocation lies in an infinitely large and elastically isotropic material. Assuming the dislocation line coincides with the z-direction, the stress at a point with polar coordinates r and θ, as shown in Fig. 2-4 (b), can be calculated based on the elasticity theory and has the following component:
.(sin )
σrr are tensile stress components in the r and θ direction,
where the τrθ
is the shear force, an ν denotes the Possion’s ratio. The strain energy per unit d
length of edge dislocation, WE is given as
he combination of edge and screw dislocation.
) Fig. 2-3 Three types of dislocation are screw (a), edge (b), and mixed (c) types,
respectively.
(a) (b)
Fig. 2-4 The stress and strain associated with screw (a) and edge (b) dislocation.
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2.2.1.2 The influence of dislocation on electrical and optical properties
Dislocations are known to exhibit a wide variety of effects that can have a significant impact on the mechanical, electrical, and optical properties of materials [8, 10]. As reported in a large number of studies in GaN, dislocations indeed influence the optical properties and device performance through nonradiative recombination.
Table 2-1 summarizes the influence of threading dislocations (TDs) on electrical and optical properties for GaN epitaxial film.
Table 2-1. The influence of TDs on electrical and optical properties of GaN epitaxial film
TDs type Electrical property Optical property
Screw TDs
Leakage current under reverse bias voltage
[11, 12]
Degradation of PL intensity at NBE
[13, 14]
Edge TDs
Extra negative charge [15], nonconductive
[16]
Enhancement of PL intensity at DLE
[17, 18]
2.3 Characterization techniques
2.3.1 X-ray diffraction (XRD)
The reciprocal lattice plays a fundamental role in most analytic studies of periodic structures, particularly in the theory of diffraction. Using the information collected in reciprocal space, one can infer the atomic arrangement of a crystal in real space.
The following sections give an introduction of crystal structure and corresponding reciprocal space, the basic theory of diffraction, a description of both the Laue and Bragg condition for diffraction, and the formula for defect analysis based on XRD data [19, 20].
2.3.1.1 The equivalence of Bragg law and reciprocal lattice
For three-dimensional (3D) lattice, the lattice is given by a set of vectors Rn of the form ; where a1, a2, and a3 are the lattice vectors, and n1, n2, and n3 are integers. These vectors a1, a2, and a3 define the unit cell. To describe a crystal structure completely, we need to associate a basis, consisting of atoms or molecules, with each lattice point. The construction of a 2D crystal from a “lattice+basis” is illustrated schematically in Fig. 2-5. The position of each atom in the crystal can be written as Rn+rj , where Rn specifies the origin of the nth unit cell and rj denotes the position of the jth atom within the unit cell. The scattering amplitude for a crystal can be factorized into two parts and written as
1 1 2 2 3 3
Rn = n a +n a +n a
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( ) ( ) j n
unit cell structure factor lattice sum
iq r iq R
crystal
j
j n
F q =
∑
f q e ⋅∑
e ⋅ (2-5)The first part is the scattering amplitude from the single unit cell and is know as
the structure factor
. .( ) ( ) iq rj
u c
j j
F q =
∑
f q e ⋅ (2-6)where fj denotes the scattering cross section of atom j. It is a linear combinational of
atomic form factor f, weighted by the corresponding phase factor eiq r⋅j to taken into account the path difference of scattered x-rays. The structure factor is a function of scattering vector.
Lattice Basis
Crystal
Fig. 2-5 The construction of a 2D crystal structure from ‘lattice+basis”.
The second term is the lattice sum to add up the contribution of all the unit cells.
The sum of phase factors is negligible except when the phases associated with all the unit cells are different by 2π or its multiple, i.e.
22
2 integer
q R⋅ n = π × for all n’s (2-7)
In such a case, all the atoms interfere constructively and the lattice sum will be equal to a huge number. To express the periodic atomic arrangement of a crystal, we can construct a corresponding lattice in the reciprocal space (which has dimensions of reciprocal length) spanned by basis vectors (a1*, a2*, a3*) which fulfill a ai⋅ ∗j =2πδij, where δij
= a +
is the Kronecker delta function which equals to 1 if i=j and is zero otherwise. Similarly, a lattice point in the reciprocal lattice can be specified by , where h, k, l are all integers. It is now apparent that any reciprocal lattice vector g satisfies Eq. (2-7) since the scalar product of g and Rn
1 2 coincides with a reciprocal lattice vector will the scattered amplitude of a crystallite be non-vanishing. This is known as the Laue condition for X-ray diffraction: . To satisfy the requirement of
= q g 2π
⋅ n =
g R n , the reciprocal lattice basis vectors can be expressed by reciprocal lattice corresponds to a set of lattice planes with the miller indices of (hkl) in the
1 ( 2 3
Vc = ⋅a a ×a
real space lattice. The direction of the reciprocal lattice vector corresponds to the normal of the real space planes, and the magnitude of the reciprocal lattice vector
23
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is equal to 2π times of the reciprocal of the interplanar spacing of the real space planes. The Laue condition can be equivalently expressed by the Bragg’s Law. In Fig. 2-6 (a) the proof of this equivalence is illustrated for the case of a 2D square lattice. X-rays are reflected from atomic planes with a spacing of d. The requirement that the path length difference between x-rays reflected by the adjacent planes is a multiple of the wavelength leads to the well-known statement of Bragg’s law: λ = 2dsinθ, where θ is the angle between incident x-rays and reflecting planes.
Replot the Bragg diffraction condition in reciprocal space using the outgoing wave vector k´ and incoming x-ray wave vector k, both of which have magnitude of 2π/λ in the elastic scattering process, and scattering vector q ≡ k´ – k = 2ksinθ, we can obtain the same diffraction condition q = g, the Laue condition [19]. The reciprocal lattice in this case is also a square lattice with a lattice spacing of 2π/d as shown in Fig. 2-6 (b) and the corresponding scattering vector q equals to g = 2π/d (01). Hence, each set of parallel planes (hkl) in real space can be expressed by a corresponding reciprocal lattice vector ghkl. The relationship between the reciprocal lattice point and the planes in real space are concluded by two points:
1. ghkl is perpendicular to the planes with Miller indices (hkl).
2. |ghkl|=2π/dhkl, where dhkl is the interplanar spacing of the (hkl) planes.
Bragg
Fig. 2-6 The equivalence of Bragg’s Law and the Laue condition for a 2D square lattice
Considering a 3D cubic crystal with lattice parameters a, Fig. 2-7 shows the lattice points in real and corresponding reciprocal space, respectively. As for a hexagonal symmetric crystal, including ZnO studied in this work, with lattice parameters a0 and c0 (a = b = a0 ≠ c0, α = β = 90ο, γ = 120ο, 3 02 0
c 2
V = a c ) we also plot the real and corresponding reciprocal space, as shown in Fig. 2-8.
3D
Fig. 2-7 The diagram of direct and the reciprocal lattice of a cubic symmetric crystal.
25
aG
Fig. 2-8 The diagram of direct and the reciprocal lattice for a hexagonal symmetric crystal.
Derived from Eq. (2-8) reciprocal lattice vector ghkl of a cubic lattice and ghkil of a
hexagonal lattice can be expressed by
2 2 2
Here the (hkl) is the three-axis Miller indices. Conventionally, for crystals with hexagonal and rhombohedral symmetry, crystallographic planes are denoted using the four indices based on a four-axis Miller-Bravias coordinate system, consisting of three basal plane axes (a1, a2, a3) at 120° angles to each other and a fourth axis (c) perpendicular to the basal plane. The Miller-Bravias indices (hkil) satisfy the
26
27
conditions i = -(h+k). When using the Miller-Bravias indices one may clearly see the equivalence of the respective directions and planes in the crystal. In this thesis, 4-digit Miller-Bravias indices are used for materials with hexagonal and rhombohedral symmetries including ZnO and sapphire to distinguish them from those with cubic symmetry, e.g. Si, Y2O3 and γ-Al2O3 where 3-digit Miller indices are employed.
2.3.1.2XRD technique
X-ray diffraction is a well established technique for structure determination of three-dimensional crystals. The diffracted intensity from crystal is collected by proper arrangement of diffractometer to match the Laue condition in sample reciprocal lattice. The four-circle diffractometer utilized consist of four rotatable circles, which are θ, 2θ, χ and φ circle; the 2θ circle is the detector axis controlling the magnitude of scattering vector q. The φ, χ, and θ circles control the sample orientation. When the q vector coincides with the specific reciprocal lattice vector g,
X-ray diffraction is a well established technique for structure determination of three-dimensional crystals. The diffracted intensity from crystal is collected by proper arrangement of diffractometer to match the Laue condition in sample reciprocal lattice. The four-circle diffractometer utilized consist of four rotatable circles, which are θ, 2θ, χ and φ circle; the 2θ circle is the detector axis controlling the magnitude of scattering vector q. The φ, χ, and θ circles control the sample orientation. When the q vector coincides with the specific reciprocal lattice vector g,