CHAPTER 1 INTRODUCTION
1.4 R EFERENCES
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Figure 1.01. Self-consistent solutions to the Schrödinger-Poisson solutions for the band profile for GaN/ InxGa1-xN/GaN quantum well in polar and nonpolar orientation.
Chapter 2
Experimental Apparatus
2.1 Sapphire Substrate
The crystal lattice of crystalline sapphire is formed by Al3+ and O2− ions. If the O2− anions are depicted as balls, the crystal lattice takes the form of their closest hexagonal packing in figure 2.01. The Al3+ cations are located in a crystalline field that has no symmetry center (due to crystal lattice distortions). These cations lie in the octahedral hollows between the closely packed O2− ions, filling two thirds of these hollows. The octahedron hollow is surrounded by six balls. If the radius of each is taken as a unit, then the hollow contains a ball with a relative radius of 0.41. Due to the ratio of the ionic radii of O2− and Al3+ (equal to 1.40 and 0.57 Å, respectively), the cations are located within the hollows of the anion packing. They slightly distort the lattice, but do not fall outside the stability limits of the octahedron position.
Lattice parameters, or hexagonal lattice constants of crystalline sapphire are a = b and c, and the interplanar distances are given by the equation 2.01
dhkl =1 / [(4/3α2)(h2+k2+hk) + (1+1/c2)l2]1/2 (2.01)
The values of the interplanar distances are presented in Table 2.01. The lattice parameters increase with increasing temperature. At 295.65K a=4.759213Å, c=12.991586 Å [2.01], and the ratio c/a=2.729776 far exceeds that of a crystal with ideal hexagonal packing (8/3)0.5=1.633. Precise measurements of the temperature
dependence of the lattice parameters within 4.5~374K temperature range in figure 2.02 were carried out using 57Fe Mössbauer radiation [2.02].
Cleavage in sapphire arises at the intersections of a pair of parallel nets formed by anions. Nets with like charges reduce attractive forces. The larger the distance between the nets, the more vividly the cleavage manifests itself. In a perfect crystal the plane of chipping must pass between these nets. In the basal plane with interchanging O–Al–Al–O–Al–O layers there are no conditions for cleavage, whereas in the plane (10-11) with interchanging O–O–Al–O–Al–O–O—O–Al–O–Al–O layers the bonds between the layers O–O located at a distance of 1.06 Å are weakened.
Sapphire does not have such a vivid cleavage as diamond and other crystals. For a long period of time, sapphire was considered to exhibit no cleavage at all.
Theoretically, it has nine cleavage planes. Six planes are parallel to the facets {11-20}and {10-11}, and to the c-axis; three planes are parallel to the facets {10-11}
and inclined to the c-axis at an angle of 33°, the normal vectors to them make an angle of 57° with the C-axis. Crystals with a small quantity of dislocations and which do not contain blocks may have perfect cleavage in the plane of the morphological rhombohedron {10-11}. However, when block-containing and stressed crystals grown by the Verneuil method are chipped along the prismatic planes, mirror chips with steps of several atomic parameters are often observed as in figure 2.03. To achieve more desirable chipping of these crystals, the direction of the c-axis is set at an angle 57° to the crystal growth axis at the location of the prism and rhombohedron planes, as shown in figure 2.03 [2.03].
The energy required for destruction along the plane {10-11} is 6 J/m2, whereas for the basal plane the corresponding value is more than 40 J/m2 [2.04]. Shown by the
estimation of the surface energy of the planes, considered to be defined by the quantity of free bonds per unit of surface, the minimum quantity of such bonds corresponds to the plane (10-11) [2.05].
The shape of natural crystals usually has the following facets (denoted by the most often used literal symbols): c(0001), a{11-20},
γ
{10-11}, n{22-43}, m{10-10}, s{02-21}, s{22-43}, R{01-12}, p{11-23}(figure 2.04) and others. The symbols of crystallographic planes in the morphological and the structural classification systems, the stereographic projections of sapphire for some planes are given in Tables 2.02 and 2.03. Besides the main crystallographic planes, tens of others exist which have their own symbols. The main forms with their spherical coordinates are presented in Table 2.04. The planes that are most often encountered in the practice of sapphire usage are shown in Fig. 2.05. The plane (1012) is inclined to (0001) plane at an angle of 57°36’, while with the plane (1120) it makes an angle of 32°24’. The angles between the normals to the facets of sapphire are given in Table 2.05.2.2 Metalorganic Chemical Vapor Deposition (MOCVD)
Metalorganic Chemical Vapor Deposition (MOCVD) is the most common epitaxial technique used in both industry and research. It has the benefit of high growth rate on large area wafers. One problem with MOCVD is that it requires complicated and sometimes vary hazardous gases in order to produce the epitaxial layer. Compound semiconductors are grown from the surface reaction of organic compounds or metalorganics and hydrides containing the required species. In growing
GaN hydride mixture containing ammonia and trimethyl-gallium (TMGa), highly diluted by hydrogen or nitrogen, is led into the reactor separately. Figure 2.06 shows a schematic drawing of the MOCVD subsystem. The vapor pressure of the MO source is a function of temperature. By placing the MO bottle in a bath containing a mixture of water and glycol, the vapor pressure can be controlled over a wide range of temperature. The carrier gas is “bubbled” through the MO liquid and transport into the line. The amount of vapor transported into the line depends on the flow rate of the carrier gas (
Φ
c), the pressure in the bottle (Pb) and the vapor pressure Pvap of the MO (Φ
MO). When growing epitaxial films in the reactor, it is of great importance to know how much source material is introduced. Since the volume and the temperature of the source bottle is constant, the perfect gas law can be used to determine the flow rate of MO (Φ
MO). During a time interval Δt, ΦMO．Δt α n moles of source material is defined from the bottle. According to the perfect gas law(2.02)
where Pc is the partial pressure of the carrier gas in the bottle. In the gas panel configuration shown in figure 2.06, the pressure in the bottle is controlled from the following line. The partial pressure of the source gas can be expressed as Pc= Pb
－
Pvap. Inserting into equation 2.02 the flow rate of the MO (in cm3/min) can be evaluated.The precursor molecules NH3 and TMGa are fed in separately into the reactor chamber. In the reactor reactions take place both on the wafer and before the molecules reach the wafer. Formation of the epitaxial layer occurs by the reaction
Ga(CH3)3 + NH3 → GaN + CH4 (2.03)
Figure 2.07 illustrate the growth process with impinging precursors and rest products. Due to the low cracking efficiency of ammonia and adatom mobility the growth of GaN is carried out at very high temperature around 1000°C ~1100°C to high crystalline quality. Many of the difficulties involving the growth of GaN are due to the high volatility of nitrogen. The pressure of nitrogen in the vapor must not be below a certain value to produce the solid without other phases. If the pressure is too low, a Ga liquid phase is formed resulting in droplet formation on the surface of crystal (GaN + 3/2H2 → Ga + NH3). An alternative precursor to NH3 for atomic nitrogen is dimethyl-hydrazine [2.06]. It has successively been used for growth of GaN [2.07]. Dimethyl-hydrazine has a relatively low decomposition temperature compared to NH3. At 420°C it decompose up to 50% [2.08], while NH3 only 15% at 950°C [2.09].
One thing to be mentioned is that MOCVD is a diffusion controlled process, as the region II in figure 2.08. This regime appears at moderate temperatures. Compared with the chemical reaction regime the mass transport rate of the reactant gaseous species is much lower than that of the chemical reaction, i.e. hG << kS. The coating growth is limited by the mass transport from the bulk gas to the substrate surface. In this case a steep concentration gradient within the boundary layer is generated and the reactant gaseous species are nearly consumed on the substrate surface.
In this regime, the temperature dependence of the growth rate becomes mild, which is attributed to the gaseous species diffusivity. The growth rate of the coating increases linearly with the partial pressure increasing of the reactant gaseous species (preact), which is confirmed through experimental work as shown in figure 2.08. The growth rate is inversely proportional to the total pressure in the system. The mass transport rate can be considerably enhanced through a decrease in the total pressure.
This is the main reason that most CVD processes are operated at reduced pressures.
An increase in the gas velocity in the bulk is useful to reduce the thickness of the boundary layer and, hence, results in a more rapid growth rate of coatings.
For the growth of monolithic materials the high growth rate is much more important than the thickness uniformity from an economical view. The MOCVD processes are often performed in the mass transport regime. The higher processing temperatures are used for thermal gradient CVI and forced CVI processes in which fast growth rates are needed to ensure the rapid densification of the composites.
2.3 Inductively Coupled Plasma Reactive Ion Etching (ICP-RIE)
It has been demonstrated that conventional RIE is perfectly capable of etching sub-100 nm structures. The only limitation is its relatively low etch rate, which is normally less than 200 nm min–1 for Si. The etching rate in RIE directly depends on plasma density. For the conventional RIE system as shown in Figure 2.09, plasma density increases with increase of RF power. However, increasing RF power will also increase the self-biasing voltage on the cathode where the etching sample is situated.
The consequence is the increase of ion bombardment energy, hence deterioration of etching selectivity. This becomes a particularly serious problem in sub-100 nm RIE, because the masking layer is always thin to enable photon or e-beam patterning of polymer resist at sub-100 nm feature dimension.
Inductively coupled plasma (ICP) system has cleverly solved the problem. In an ICP source, the plasma generation is separated from etching chamber, as shown in Figure 2.10. Radio frequency power is coupled into plasma chamber by an induction coil from outside. The sample stage is connected to a second RF power source as an auxiliary RF source to enhance the production of plasma. Electromagnetic field generated by inductive coupling coil can sustain electron cycling movement in plasma for a long period, which has greatly increased ionization probability while keeping the pressure low in the etching chamber. As the sample stage has an independent input of RF power, the self-biasing voltage can be independently controlled. Therefore, an ICP system can produce very high plasma density (>5×1011 cm–3) compared to conventional RIE (108~1010 cm–3), as well as maintain low ion bombardment energy.
The conflict between high plasma density and high etch selectivity encountered in conventional RIE systems has been resolved. With such high plasma density and high etching selectivity, high etching rate and deep RIE (DRIE) become possible.
ICP-RIE has been widely used for etching other materials, especially the III-nitride semiconductors. The ICP with high plasma density offers much higher etch rate and selectivity than it is possible by conventional RIE. For example, GaN or sapphire is known to be difficult to etch. With a conventional RIE, the etch rate is less than 5nm min–1. Using an ICP-RIE the etch rate is nearly 10 times enhanced.
Inductively coupled plasma systems are widely used to etch III–V semiconductor materials which are of great importance in high frequency and optoelectronic applications currently.
2.4 Potassium Hydroxide (KOH)-Ethylene Glycol Solution
Potassium hydroxide is an inorganic compound with the formula KOH. Along with sodium hydroxide (NaOH), this colorless solid is a prototypical "strong base". It has many industrial and niche applications. Most applications exploit its reactivity toward acids and its corrosive and etching nature to many materials including the GaN semiconductors. Potassium hydroxide can be found in pure form by reacting sodium hydroxide with impure potassium. Potassium hydroxide is usually sold as translucent pellets, which will become tacky in air because KOH is hygroscopic. Consequently, KOH typically contains varying amounts of water (as well as carbonates). Its dissolution in water is strongly exothermic, meaning the process gives off significant heat. Concentrated aqueous solutions are sometimes called potassium lyes. Even at high temperatures, solid KOH does not dehydrate readily [2.10].
Approximately 121g of KOH will dissolve in 100 ml of water at room temperature (compared with 100 g of NaOH in the same volume). Lower alcohols such as methanol, ethanol, ethylene glycol and propanol are also excellent solvents.
The solubility in ethanol is about 40 g KOH/100 ml.
In the experiments for the thesis, the solvent chosen for KOH is ethylene glycol.
Ethylene glycol, with molecular formula C2H6O2, density 1.1132g/cm3, melting point 240K (-12.9°C) and most important of all, boiling point 470K (197.3°C), is perfectly suitable to make the KOH- ethylene glycol solution to the concentration of >30% and heat up to >140°C. At the same time, the high boiling temperature protects the solution from evaporation seriously at high temperature and maintains the concentration of KOH at a relatively stable level. The properties of viscosity of
ethylene glycol is 1.61×10−2N．s/m2, which do not hinder the solution from flowing into the specifically designed structure in the experiment.
One more thing to note is that the ethylene glycol enhances the etching rate of GaN, excepting the higher boiling point, by the higher solubility of Ga2O3 in it. The faster the product during GaN etching process is dissolved, the faster the etching rate performed. The easily-prepared, low-temperature KOH-ethylene glycol solution provides a relatively higher etching rate to GaN than that of extremely high-temperature molten KOH.
2.5 Scanning Electron Microscopy (SEM)
It is worthwhile to understand the technique and type of instrument of SEM.
Very simply; the SEM scans a sample with a beam of electrons that interact with the sample. Some of those electrons and other electrons generated during this process escape from the sample and reach a detector. The number of electrons that reach the detector at each point on the sample depends on the topology of the sample and the atomic weight of the atoms at the surface, and these variations in signal strength lead to image formation.
A SEM column consists of an electron gun, one or two condenser lenses, an objective aperture, and an objective lens [2.11]. The electron gun produces a source of electrons and accelerates the electrons to energy of 1~30 keV. This occurs in a vacuum environment ranging from 10-4 to 10-10 Torr. The electron lenses in the column are used to demagnify the image of the gun crossover and focus a final spot on the specimen on the order of 1 nm~1 μm with a beam current in the range of
1pA~1μA. The condenser lens controls the amount of demagnification and the probe forming or objective lens focuses the final probe on the specimen. A schematic of a typical SEM is shown in Figure 2.11.
The lens and aperture system in the column provide control of the beam through manipulation of the probe diameter, probe current, and convergence angle. These three parameters can be controlled and used to achieve high depth-of-field, high-resolution, or high beam current for x-ray microanalysis. A small convergence angle is needed for high depth-of-field imaging and can be obtained with a small objective aperture and a long working distance. High resolution imaging requires a small probe size which can be obtained with a strong condenser lens, an objective aperture, and a short working distance. Finally, x-ray microanalysis may require higher beam currents which can be obtained by weakening the condenser lens and removing the objective aperture.
The interactions between the electron beam and the specimen in a SEM are the source for a wide variety of signals that can be collected and used to characterize the sample as in figure 2.12. The electron beam-specimen interactions are a result of elastic and inelastic scattering processes that occur simultaneously within the sample.
The region in which the electrons interact with the specimen is called the interaction volume. The interaction volume can extend from a few nanometers to a few microns below the surface depending on the beam and sample parameters. Elastic scattering events produce large angular changes in the trajectory of the beam electrons inside the sample, but result in little or no change to the energy of the electron, thus giving rise to the overall shape of the interaction volume. Elastic scattering primarily gives rise to backscattered electrons (BSE). Inelastic scattering events result in the transfer of
energy from the beam electrons to the tightly bound inner-shell electrons and loosely bound outer-shell electrons of the atoms in the specimen with very little angular change in the trajectory of the beam electron. During a single inelastic scattering event the beam electron can transfer an amount of energy ranging from less than 1 eV to the full energy carried by the beam electron. Inelastic scattering limits the range of the electrons within the specimen by eventually reducing the electron energy to zero.
Inelastic scattering gives rise to phonons (lattice vibrations), plasmons (electron oscillations), auger electrons, characteristic x-rays, continuum x-rays, secondary electrons (SE), and electron hole pair (EHP) generation. EHP generation in a material with a bandgap is the basis for the EBIC and CL signals.
The incident electrons interact with a certain volume of the sample called the interaction volume. There are numerous analytical expressions that have been used to model the size and shape of this interaction volume, which will not be covered here.
The interaction volume depends on a number of factors, including the beam energy, the atomic number of the specimen, and the angle the incoming probe beam makes with the sample surface. The number of backscattered and secondary electrons (BSE and SE) produced will depend on these parameters and others such as the topology of the sample, and will result in the image contrast observed. Several detection systems are depicted in figure 2.13 and 2.14.
2.6 Scanning Transmission Electron Microscopy (STEM)
High-resolution STEM capabilities are needed in order to overcome the SEM
resolution limits created by the interaction volume in bulk samples. Originally, STEM capabilities were achieved by using convergent-beam TEM in spot mode. In the traditional TEM mode, two condenser lenses are adjusted to illuminate the specimen with a nearly parallel beam of electrons. The transmitted electrons are then focused by the objective lens to form a real image. Convergent-beam TEM in spot mode uses a series of condenser lenses to demagnify the original gun crossover to a spot on the specimen [2.12]. Scan coils can then be used to move the spot across the specimen. A TEM with scanning capabilities is often referred to as a STEM in the literature [2.13].
In a dedicated STEM, the optical design is more closely related to a SEM than a TEM. A source of electrons is produced by an electron gun and accelerated to an
In a dedicated STEM, the optical design is more closely related to a SEM than a TEM. A source of electrons is produced by an electron gun and accelerated to an