2-1 The laser-MBE system and principle of laser-MBE deposition
Figure 2-1 illustrates the schematic of a laser-MBE deposition system. Laser beam is shined on the target material. The high heating power leads to the evaporation of the target material, forming a high-temperature plasma plume that expands away from the target surface. The ablated target material is deposited on a substrate and forms a thin film. Depending on the types of interaction of the laser beam with target, the laser deposition process can be classified into three parts:
i. Interaction of laser beam with the target
Upon being struck by a high power density nanosecond excimer-laser pulse, heating and vaporizing the material will occur at the beginning of the pulse. The amount of evaporated flux varies linearly with the pulse energy.
ii. Interaction of the laser beam with the evaporated material
As the evaporated material is heated by the laser beam, it results in the formation of high-temperature plasma plume consisting of ions, atoms, molecules, electrons, etc. The temperature attained by the plasma depends on the power density, frequency, pulse duration of the laser beam, and the optical and thermo physical properties of the
material. During the incidence of the laser pulse, the isothermal expanding plasma is constantly increased at its inner surface with evaporated particle from the target. The acceleration and expansion velocities in this regime are found to depend on the initial velocities of the plasma. The plasma expands preferentially normal to the irradiated surface due to the large lateral dimensions of the plasma.
iii. Adiabatic plasma expansion and deposition of thin films
After the termination of the laser pulse, the plasma expands adiabatically with the expansion velocities controlled by its initial dimensions. The plasma cools rapidly during the expansion process, with the edge velocities reaching asymptotic values.
The particles from the expanding plasma strike the substrate and form a thin film with characteristic spatial thickness.
KrF
Focusing lence
KrF excimer laser 248 nm
high purity ZnO (5N) ceramic disk vacuum chamber 3x10-8torr
Fig. 2-1 Schematic of a laser-MBE growth system
2-2 X-ray diffraction
X-ray scattering techniques are a family of non-destructive analytical techniques which reveal information about the crystallographic structure, chemical composition, and physical properties of materials and thin films. These techniques are based on observing the scattered intensity of an x-ray beam hitting a sample as a function of incident and scattered angle, polarization, and wavelength or energy.
2-2-1 Theory of x-ray diffraction
X-ray diffraction finds the geometry or shape of a molecular. X-ray diffraction techniques are based on the elastic scattering of x-rays from structures that have long range order. A crystal consists of a regular array of atoms, each of which can scatter electromagnetic waves. A monochromatic beam of X-ray that falls on a crystal will be scattered in all directions, in certain direction the scattered waves will constructively interfere with one another while others will destructively interfere. The analysis was developed in 1913 by W. L. Bragg. The condition which must be fulfilled for radiation scattered by crystal atoms to undergo constructive interference can be obtained from a diagram like that in Fig. 2-2. In the plane wave description, a beam containing X-rays of wavelength λ impinges on a crystal at an angle θ with a family of Bragg planes, whose space is d. The beam goes past atom A in the first plane and atom B in the next, and each of them scatters part of the beam in random directions. Constructive
interference occurs only between those scattered rays whose paths differ by exactly λ, 2λ, 3λ, and so on. That is, the path difference must be nλ, where n is an integer. The only rays scattered by A and B for which this is true are those labeled I and II in Fig. 2-2.
The first condition on I and II is that their common scattering angle is equal to the angle of incidence θ of the original beam. The second condition is that
2dsinθ = nλ, n = 1,2,3,…, (2-1)
since ray II must travel the distance 2dsinθ farther than ray I. The integer n is the order of the scattered beam. Then considering a hexagonal unit cell as shown in Fig.
2-3 which is characterized by lattice parameters a and c. The interplanar spacing d for the hexagonal structure is given as:
. (2-2)
Combining Bragg’s law with (2-2):
. (2-3)
Rearranging (2-3) g ves i
. (2-4)
The lattice parameter a or c can be determined by simultaneously fitting the diffraction angles of different reflections using Eq. 2-4.
Fig. 2-2 X-ray sscattering ffrom a cubic crystal
Fig. 2-3 TThe hexagoonal unit ceell
2-2-22 Rocking ccurve
4 Illustratioon of phi sccan
2-2-4 Analysis of threading dislocation density
Figure 2-5 depicts different types of dislocations and the corresponding Burgers vectors. Before characterizing the threading dislocations (TDs), the Burgers vectors should be defined. The Burgers vector, denoted by b, is a vector that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice [20].
The magnitude and direction of vector is best understood when the dislocation-bearing crystal structure is first visualized without the dislocation, that is, the perfect crystal structure. In this perfect crystal structure, a rectangle whose lengths and widths are integer multiples of "a" (the unit cell length) is drawn encompassing the site of the original dislocation's origin. Once this encompassing rectangle is drawn, the dislocation can be introduced. Said rectangle could have one of its sides disjoined from the perpendicular side, severing the connection of the length and width line segments of the rectangle at one of the rectangle's corners, and displacing each line segment from each other. What was once a rectangle before the dislocation was introduced is now an open geometric figure, whose opening defines the direction and magnitude of the Burgers vector. Specifically, the breadth of the opening defines the magnitude of the Burgers vector, and, when a set of fixed coordinates is introduced, an angle between the termini of the dislocated rectangle's length line segment and width line segment may be specified. The direction of the vector depends on the plane of
dislocation, which is usually on the closest-packed plane of unit cell. The magnitude is usually represented by equation:
| | √ , for a cubic system, (2-5) where a is the unit cell length of the crystal, |b| is the magnitude of Burgers vector and h, k, and l are the components of Burgers vector, b = <h k l>.
TDs in a film produce crystalline plane distortions and the associated lattice deformation depends on the geometry of the TDs [21]. For a (0001) oriented thin film with wurtzite structure, the TDs are classified into three different types according to the direction of the corresponding Burgers vector (b) relative to the [0001] line direction.
They are edge dislocation with bE = 1/3⋅<1120>, screw dislocation with bC = <0001>, and mixed dislocation with bM = 1/3⋅<1123>, which is a combination of bE and bC. For edge dislocation, the Burgers vector and dislocation line are at right angles to one another. For screw dislocation, they are parallel. Pure edge TDs twist surrounding hexagonal lattice about [0001], leading to the formation of vertical grain boundaries [22]. Under this circumstance, the (hkil) crystalline planes with nonzero in-plane component, i.e. either h or k is not zero, are distorted. On the other hand, the pure screw TDs result in the tilting of the lattice, generating a pure shear strain field [23], and the crystalline planes with nonzero l are deformed. Therefore, to investigate the influence of edge TDs, measuring the profiles of ( 0 0)h h surface reflections is
necessary, which are not sensitive to lattice distortion caused by pure screw TDs. On the other hand, measuring the line widths of the (000l) normal reflections, which are not affected by the pure edge TDs is a good method to characterize the screw TDs.
The broadening of radial scan line width would come from crystallite size, strain and instrument effects. The experimentally measured FWHM, Bexp, is a convolution of the instrumental broadening, Binstr., and the broadening coming from the sample, of which strain induced broadening, Bstrain, and finite crystal size induced broadening , Bsize, are the major contributions.
As compared with the measured line width of ZnO, the instrumentation induced broadening is much smaller and thus can be safely neglected in our results. To obtain meaningful quantitative results, Williamson-Hall plot [24] is employed to analyze the quantity of domain size and strain. We make a Δqr vs. q plot with q = 4πsinθ/λ denoting the scattering vector and Δqr standing for the line width in q along the radial direction to separate the broadening due to finite structural coherence length from strain induced broadening. The equation of the line in Williamson-Hall plot can be expressed as:
∆ ∆ ∆ , (2-6) where L and ε represent the coherent length and inhomogeneous strain, respectively.
Thus, the inverse of ordinate intercept yields the coherence length (L), i.e., the effective
domain size, and the slope yields the root-mean-square (RMS) inhomogeneous strain (ε) averaged over the effective domains [24]. The Δqt vs. q plot, where Δqt = Δθ × q denoting the line width in q along the transverse direction, for θ-scans across the (000l)
and in-plane (h0h0) reflections, of which the slopes yield the spreads of tilt and twist angles, respectively. The density of TDs can be evaluated from the corresponding Burgers vectors and the tilt/twist angles. For screw TDs, the density NS is calculated
according to
of corresponding Burgers vector. For edge TDs, the formula employed to calculate the density, NE, depends on the spatial arrangement of the TDs [26]. Assuming a random
distribution, we can apply
case of TDs accumulating at a small-angle boundary, we should adopt the formula:
2.1 αΦ
E =
E
N b L, where L denotes the correlation length along the in-plane direction. In
both formulae of NE, bE is the length of associated Burgers vector bE = 1/3< 1120 >. The real edge TDs density falls between that of random and piled up distribution.
Fig. 2-5 Illustration of Burgers circuits, Burgers vectors, types of edge and screw dislocations
2-3 Transmission electron microscopy
The transmission electron microscope (TEM) has become the premier tool for the micro-structural characterization of materials. In practice, the diffraction patterns measured by x-ray methods are more quantitative than electron diffraction patterns, but electrons have an important advantage over x-ray- electrons can be focused easily [27].
The optics of electron microscopes can be used to make images of the electron intensity emerging from the sample. Several different techniques of TEM often employed for
2-3-1 Selected area electron diffraction (SAED)
SAED is a crystallographic experimental technique that can be performed inside a TEM. A thin crystalline specimen is subjected to a parallel beam of high-energy electrons. The specimens are typically ~100 nm thick, and the electrons typically possess energy of 100 - 400 keV. Thus, electrons can pass through the sample easily.
Electrons can be treated as wave-like, rather than particle-like. Because the wavelength of high-energy electrons is a fraction of a nanometer, and the spacing between atoms in a solid is only slightly larger, the atoms act as a diffraction grating to the electrons, which are diffracted. That is, some fraction of them will be scattered to particular angles, determined by the crystal structure of the sample, while others continue to pass through the sample without deflection. As a result, the image on the screen of the TEM will be a series of spots – the selected area diffraction pattern, SADP, each spot corresponding to a satisfied diffraction condition of the sample's crystal structure. If the sample is moved under the beam, bringing different sections of it under illumination, the arrangement of the spots in the diffraction pattern will change. It is useful to select a single crystal for analysis at a time. It may also be useful to select two crystals at a time, in order to examine the crystallographic orientation between them. As a diffraction technique, SADP can be used to identify crystal structures and examine crystal defects. It is similar to x-ray diffraction, but what is unique in that is area as
small as several hundred nanometers in size can be examined, whereas x-ray diffraction typically sample area several centimeters in size.
2-3-2 Analysis of threading dislocation density
The dislocation density D can be obtained by the following equation:
, (2-7) where n is obtain by counting the number n of dislocations and measuring the foil length l and foil thickness h in a cross sectional TEM image. The number of dislocations and foil length could be numbered and measured easily from the picture;
however, the foil thickness has to be derived from thickness fringe in TEM image.
From the Howie-Whelan equations, the intensity of Bragg diffracted beam can be written as [28]:
| | 1 , (2-8) where t is the z axial distance of intensity at the bottom of the specimen, Ig is the dark field image intensity, φg is the amplitude of the diffracted beam for reflection G, seff is the effective excitation error
, (2-9) with s being a measure of how far deviating from the exact Bragg condition, and the excitation being the characteristic length distance for the diffraction vector g and also named as extinction distance. The extinction distance can be described as:
, (2-10)
where λ is the wavelength of electrons, Fg is the structure factor for the diffraction vector g, Vc is the volume of a unit cell and θB is Bragg angle. If we neglect the relativistic effects:
, , (2-11)
2 , (2-12) , (2-13)
If take relativistic effects into account:
, 2 , (2-14)
, 1 , . (2-15)
Combining (2-12) into (2-15) gives:
, ; (2-16) Combining (2-14) into (2-16) gives:
2 , 2 ; (2-17)
And combining (2-17) into (2-13) gives:
, (2-18)
where h is the Plank’s constant equal to 6.626 x 10-34 Nms, p is the momentum of electron, charge e equals to -1.602 x 10-19 C, rest mass m0 = 9.109 x 10-31 kg, speed of light in vacuum c = 2.998 x 109 m/sec.
For acceleration voltage 200 kV, the relativistic wavelength is 0.0251 Å. For hexagonal ZnO operated at 200 keV, g = (0002), a = 3.2438 Å and c = 5.2036 Å, Eq.
(2-4) gives θB=0.27689o, where θB is Bragg angle. The structure factor Fg of ZnO with
diffraction vector g = (0002) is F0002=11.564 Å and the volume of a unit cell
√ 47.6199 Å3. Substituting these parameters into Eq. (2-10) gives
515.4 Å. Considering Eq. (2-8) for only one diffraction beam g, the
two-beam approximation is applied. The two-beam condition means that we tilt the crystal so that there are only two strong beams exist. One is the direct beam and the other is the diffraction beam with s = 0. The rest of the diffracted beams are very weak (s >> 0 or << 0) and the contribution to is ignored. Then, Eq. (2-9) becomes
. Simplify Eq. (2-8), we have | | 1 , for t = 0 or t
= n , Ig = 0 and for t = , Ig = 1. The oscillatory intensity variations with t are illustrated in Fig. 2-6.
For hexagonal ZnO with two-beam condition g = (0002), t = = 257.7 Å for the first dark fringe. With given foil thickness, the dislocation density can be evaluated from the Eq. (2-7).
Fig.
2-4 Photoluminescence characterization
PL is a very useful and powerful optical characterization tool in the semiconductor industry, with its sensitive ability to reveal the emission mechanism and band structure of semiconductors. From PL spectra the defects or impurities can also be identified in the compound semiconductors, which affect material quality and device performance.
A given impurity produces a set of characteristic spectral features. The fingerprint can be used to identify the impurity type. Often several different impurities can be found in a single PL spectrum. In addition, the line width of each PL peak is an indication of sample’s quality, although such analysis has not yet become highly quantitative.
PL is the optical radiation emitted by a physical system (in excess the thermal equilibrium blackbody radiation) resulting from excitation to a non-equilibrium state by irradiation with light. Three processes can be distinguished: (i) creation of electron-hole pairs by absorption of the incoming light, (ii) radiative recombination of electron-hole pairs, and (iii) escape of the recombination radiation from the sample.
Since the incoming light is absorbed to create electron-pair pairs, the greatest excitation of the sample occurs near the surface; the resulting carrier distribution is both inhomogeneous and non-equilibrium. In attempting to regain homogeneity and equilibrium, the excess carriers will diffuse away from the surface while being depleted by both radiative and nonradiative recombination processes. Most of the excitation of
the crystal is thereby restricted to a region within a diffusion length (or absorption length) of the illuminated surface. Consequently, the vast majority of PL experiments are arranged to examine the light emitted from the irradiated side of the samples. This is often called front surface PL.
2-4-1 Fundamental Transitions
Since emission requires the system being in a non-equilibrium condition, some means of exciting energy is acting on the semiconductor to produce hole-electron pairs. We summarize the fundamental transitions, those occurring at or near the band edges as below.
1. Free excitons
A free hole and a free electron as a pair of opposite charges experience a coulomb attraction. Hence the electron can orbit about the hole as a hydrogen-like atom. If the material is sufficiently pure, the electrons and holes pair into excitons which then recombine, emitting a narrow spectral line. In a direct-gap semiconductor, where momentum is conserved in a simple radiative transition, the energy of the emitted
photon is simply hν = E
g – E
x , where E
g and E
x are the band gap and the exciton binding energy.
2. Bound excitons
Similar to the way that free carriers can be bound to (point-) defects, it is found that excitons can also be bound to defects. A free hole can combine with a neutral donor to form a positively charged excitonic ion. In this case, the electron bound to the donor still travels in a wide orbit about the donor. The associated hole, which moves in the electrostatic field of the “fixed” dipole, determined by the instantaneous position of the electron, also travels about this donor; for this reason, this complex is called a “bound exciton”. An electron associated with a neutral acceptor is also a bound exciton. The binding energy of an exciton to a neutral donor (acceptor) is usually much smaller than the binding energy of an electron (hole) to the donor (acceptor).
3. Donor-Acceptor Pairs
Donors and acceptors can form pairs and act as stationary molecules imbedded in the host crystal. The coulomb interaction between a donor and an acceptor results in a lowering of their binding energies. In the donor-acceptor pair case it is convenient to consider only the separation between the donor and the acceptor level:
,
where r is the separation of donor-acceptor pair, E
D and E
A are the respective ionization energies of the donor and the acceptor as isolated impurities.
4. Deep transitions
By deep transition we shall mean either the transition of an electron from the
conduction band to an acceptor state or a transition from a donor to the valence band in Fig. 2-7. Such a transition emit a photon hν = E
g – E
i (Ei stands for ED or EA) for direct transitions and hν = E
g – E
i - E
p if the transition is indirect and involves a phonon of energy E
p. Hence the deep transitions can be distinguished as (1) conduction-band-to-acceptor transition which produces an emission peak at hν = E
g –
EA, and (2) donor-to-valence-band transition which produces an emission peak at the higher photon energy hν = E
g – E
D.
Fig. 2-7 Radiative transitions between a band and an impurity state
5. Transitions to deep levels
Some impurities have large ionization energies; therefore, they form deep levels in
the energy gap. Radiative transitions between these states and the band edge emit at hν = E
g – E
i. Some defects not only (or a few) levels close to one band, but have
several of levels partly around the middle of the gap. They give rise to the green, orange and red emission bands of wide-gap semiconductor such as ZnO and ZnS.