Michael Lindeborg ‘14
University of California, Santa Barbara, Materials Department
GaN and AlGaN/GaN are group-III nitride semiconductors with outstanding opto-electronic and microelectronic application potentials. Understanding their optimal preparation techniques and final compound structures will allow for the production of more efficient semiconductors. This study focuses on GaN epilayers and AlGaN/GaN HEMT structures grown by molecular beam epitaxy (MBE). A series of different MBE growth conditions were selected to map out regions with optimum structural quality and electrical performance. These epilayers were characterized using atomic force microscopy and Hall effect measurements. Under high-temperature growth (T>760°C), GaN exhibited superior surface structure with low RMS (root-mean-square) surface roughness when the Ga/N flux ratio was close to stoichiometric conditions (Ga/N ~ 1). In addition, electron mobility decreased with thermal etching of the underlying GaN substrate and Si overdoping. For both GaN and AlGaN/GaN, decreased RMS surface roughness also improved electron mobility. Our research further defines the optimal growth conditions and characteristics of an efficient group-III nitride semiconductor. This study can ultimately aid in the development of more energy efficient technologies.
This study investigated a novel class of group–III nitride semiconductors, which have outstanding optoelectronic and microelectronic application potentials. Focus was placed on GaN epilayers and AlGaN/GaN HEMT structures grown by molecular beam epitaxy (MBE).
GaN crystals provide a promising material with which to employ their high-quality electrical properties for a number of applications. They have shown success in their use in electronic devices, such as RF power devices and amplifiers, demonstrating an ability to withstand high power loads and frequencies, breakdown voltages of 3 MV/cm and thermal conductivities of 130 W/mK [1,2]. Electron mobilities as high as 1150~1190 cm2/V·s have been achieved with films grown in plasma-assisted molecular beam epitaxy (PAMBE) systems , creating further advantages to their use in semiconductor high-speed electronics.
In this study, two separate types of investigations were performed: on bulk GaN epilayers and AlGaN/GaN HEMTs. In the first type of study, various MBE growth conditions were analyzed and several types of film growth modes were characterized, primarily dependent on the Ga/N flux ratios and growth temperature . Much of the previous work done on the study of GaN has focused on growth regions with relatively lower temperatures. Only recently have the growth modes for GaN in higher temperature regions with PAMBE begun to be characterized [3,4]. The growth regions in these temperature ranges have provided films with properties comparable to the best of those grown in lower temperature regions . Higher growth temperatures were used to further reduce the threading dislocation densities in heteroepitaxial film growth, as well as to reduce unintentional impurity incorporation, further enhancing the film quality. The major growth regions in the higher temperature range include a Ga-rich step-flow growth region, a Ga-rich layer-by-layer growth region, and an N-rich layer-by-layer growth region. Some additional growth modes, including Ga-droplets and 3D growth, are easier to obtain at temperatures lower than ~760 °C . Further study is required to fully characterize the newer growth regions and to optimize the material properties of the GaN films created within them. In this study, PAMBE GaN films were grown in the temperature range of 780-795 °C, providing insight into the characterization of the upper end of studied growth regions.
With respect to the second part of this study, high electron mobility transistors (HEMTs) have a vast potential in applications including cell-phones, direct broadcast satellites, and radar because of their direct band gaps, high voltage, and high power . HEMTs are based on various semiconductor combinations with two different band gaps, which are regions of energy between the valence band (VB) and the conduction band (CB) where electrons cannot propagate. HEMTs are made of a variety of compounds such as GaAs, InP, or SiC. However, nitrides, such as the AlGaN/GaN structures (Figure 1), make the AlGaN/GaN HEMT more effective than other kinds of HEMTs. Nitrides’ advantageous properties include a stable wurtzite crystal structure. This structure creates covalent bonds and a high thermal conductivity, both of which are necessary for heat dissipation out of a HEMT . The high thermal conductivity of the nitrides therefore allows the HEMTs to be useful in a wider range of applications . Another important property of nitrides is the high velocity of the electron-carriers, which allows for greater electron-carrier mobilities and higher voltages and further enhances the HEMTs . Nitrides also carry a larger internal electric field up to one order of magnitude greater than that of GaAs. These all contribute to making an effective HEMT. Analysis of AlGaN/GaN samples will determine specific trends in electronic properties that create a more proficient HEMT.
An electric field existing between a heterojunction of two different materials with a high and low band gap creates an effective HEMT. In this case, the two materials are AlGaN and GaN. As a result of the heterojunction, internal strain is created at the AlGaN/GaN crystal interface (the active region), which results in a larger piezoelectric polarization. In addition to the piezoelectric component, the nitrides also contain a large internal spontaneous polarization due to the polar direction of the crystals. The polarization-induced electric field affects the two different materials, causing the conduction and valence bands to bend. At the heterojunction, the different band gaps of the materials create a quantum well where the 2-dimensional electron gas (2DEG) resides (Figure 1) . Without bending bands, the electrons would normally be equally distributed along the conduction band on GaN; however, the quantum well creates a “sea of electrons” restricted to flowing along the heterojunction. HEMTs can be enhanced by improving the 2-DEG mobility and density, making a high-speed channel for electrons (Figure 1) . By analyzing specific properties of AlGaN/GaN, such as its surface morphology and the electronic properties, the effectiveness of a HEMT can be determined.
Materials and methods
Gallium nitride thin-film crystals and AlGaN/GaN HEMT’s were grown in a Veeco Gen II plasma-assisted molecular beam epitaxy (PAMBE) system. Growth took place in a highly-controlled ultra-high vacuum (UHV) environment, where the background pressure of the chamber was on the scale of 10-9 torr . The reacting gallium and aluminum were held in quasi-Knudsen cells, where they were sublimated into a vapor phase by the maintenance of a sufficiently high melting temperature . The gallium and aluminum beams were directed from the cell to a substrate material in the growth chamber, where film growth occurred as the gallium reacted with nitrogen that was generated by an rf-plasma from an external source . Iron-doped, semi-insulating GaN templates (manufacturer: Lumilog), with dislocation densities of 5×108/cm2, served as the substrate material. The beam flow rates and substrate temperature were varied widely to produce a wide range of growth conditions. In addition, thermal etching, by which GaN-template substrates were heated to remove varying amounts of impure surface material, and silicon doping were also applied to some samples. Ga-flux ranged from 2-14 nm/min, and the N-flux was held constant at 5 nm/min for all samples. Growth temperatures ranged from 780-795 °C, and thermal etching thickness ranged from 0-50 nm. Silicon doping on samples, when applied, ranged from cell temperatures of 1140-1300 °C, corresponding to concentrations of ~1016-1018 cm-2. Such variations resulted in significant changes of film properties and surface morphology, which were categorized in one of several growth regions based on these conditions [3,10]. The relatively slow growth rates when using MBE allowed for precise control of the film thickness. Real-time, in situ, monitoring of crystal growth was accomplished through the use of Reflection High Energy Electron Diffraction (RHEED) [8,9]. The diffraction pattern was indicative of the current surface condition of the sample. Combined, slow growth rates and RHEED monitoring allowed for very precise control of crystal growth. Once wafers of the crystal film were grown, they were cut with diamond scribes into approximately 1 cm2 square samples to be further analyzed.
Electrical properties analysis
The carrier density and carrier mobility of the GaN and AlGaN/GaN films were determined by the use of a Hall effect measurement set-up and the Van der Pauw method. The four ohmic contacts required by the Van der Pauw method were made of indium metal soldered onto the corners of the sample. Placement of the indium contacts as close to the edge as possible, as well as a regular square geometry, were required for ideal measurements . The sample was then placed onto a contact card, which was inserted into the Hall set-up. In the apparatus, the sample card was placed between two strong electromagnets that provided the magnetic field in which the Hall effect could be observed. Computer software measured and recorded all data. Current and voltage measurements were taken along each side of the sample. From Ohm’s Law, the resistivity values were calculated. The Hall setup then applied the magnetic field, and the computer software calculated the carrier density and carrier mobility of the sample as determined by standard Hall effect theory .
Surface morphology analysis
The surfaces of the GaN and AlGaN/GaN samples were imaged using atomic force microscopy (AFM). Veeco models D3100 and D3000 were used to conduct the AFM scans. AFM creates images of the surface of the sample by measuring the deflection of a micrometer-long silicon cantilever and tip mechanism . Tip deflections are a result of Van der Waals forces, electrostatic forces, and other intermolecular forces between the tip and sample surface. Our scans were completed in AFM tapping mode, in which a piezoelectric actuator vibrates the tip at its resonant frequency, which was approximately 300-350 kHz. Tip-surface interactions affect the tip’s oscillation amplitude, from which the surface contour maps can be made. The actual deflection of the tip is measured by a laser aimed at the cantilever. Tip deflections move the reflected image of the laser, which is measured by a photo-detector .
Real-time modifications of tip parameters were used to optimize measurement noise. Image scan sizes ranged from 1-100 μm2. After raw images were taken, they were processed with Nanoscope image software to acquire image height ranges (Z-range), roughness (RMS-roughness), feature dimensions, and three-dimensional maps
After all GaN and AlGaN/GaN samples were grown via PAMBE, they were characterized with AFM imaging and Hall effect measurements. The sixteen different sets of growth conditions of GaN films covered much of the N-rich layer-by-layer (l-b-l) growth region, though there were samples from the Ga-intermediate region, with both l-b-l growth and step-flow growth (Figure 2). There were fifteen samples of aluminum gallium nitride (AlGaN/GaN) that were tested. By characterizing certain sets of samples, trends in electrical properties and surface morphologies were deduced from growth conditions.
Ga-flux variations and RMS roughness
Samples grown at 780 °C with varying Ga-fluxes showed a distinct trend in surface morphology. Ga-fluxes of 14, 7.5 and 4 nm/min resulted in root-mean-square (RMS) roughness of 1.8, 1.0, and 0.5 nm respectively (Figure 3a). Image a demonstrates a stepped surface with clear ridges as well as pits. The surface in image b has a flatter and smoother overall morphology; however, it still exhibits pits, which is indicative of the termination of lattice dislocations within the crystal. Image c lacks any clearly defined pits and has much more homogenous surface features.
The RMS roughness values sharply decreased as the Ga-flux was lowered, transitioning through the growth regions from Ga-rich step-flow, to Ga-rich l-b-l, to N-rich l-b-l. Moving from high to more equal Ga/N ratios resulted in empirically smoother samples. The growth mode diagram shows that the high Ga/N ratios result in step-flow, where more equal ratios result in l-b-l growth. Therefore, there is a correlation between l-b-l and smoother surfaces. This trend appears closely linear at constant temperature (Figure 3b). Samples grown at 770 °C also showed a clear trend in RMS roughness with variation in Ga-flux. Films grown with 4, 3, and 2 nm/min Ga-fluxes showed RMS roughness values of 3.9, 7.1, and 19.4 nm, respectively on 10 µm × 10 µm images (Figure 4a). These samples were all in the N-rich region and showed a RMS roughness trend opposite to the previous set of films. Image a is mildly smooth, but clearly shows surface features that indicate suppressed gallium and nitrogen diffusion along the surface. Image b shows a similar case, but to a rougher extent. Image c contains scale-like, jagged features which make it the roughest of all images in this series. In this set of conditions, RMS roughness varied inversely with Ga-flux. This demonstrates that when Ga/N flux ratios are too low, as in sample c, there is not enough gallium to facilitate surface diffusion, resulting in rougher films. Thus, as the Ga-flux approaches the fixed N-flux, RMS roughness is lowered (Figure 4b).
Variations in growth temperature in the N-rich growth regime
Samples grown at the same Ga-fluxes as above, but with varying growth temperatures, exhibit a similar RMS roughness trend. Morphologies of GaN films were grown with Ga-fluxes of 2, 3, and 4 nm/min, and at temperatures of 785, 788, and 795 °C, respectively. Images at 2 nm/min showed a very rough surface, with hexagonally shaped, tower-like 3D structures. These towers had a height of at least 38.0 nm. Consistent with the GaN films grown at 770 °C, the RMS roughness decreased as the Ga-flux approached the fixed N-flux of 5 nm/min: films grown with Ga-fluxes of 2, 3, and 4 nm/min had RMS roughness values of 10.4, 9.2, and 1.4 nm, respectively on 10 µm × 10 µm images (Figure 5). Other scan sizes showed the same general trend; however, only the 1 µm × 1 µm scan demonstrated a clear linearity. As shown in Figure 4a and b, surface roughness increased due to the very low Ga/N ratios. Without enough gallium, surface diffusion could not occur and rough features, such as towers, accumulated.
GaN sub-layer and surface morphology
Surface morphology was also affected by the addition of a 100-nm-thick, Ga-rich, GaN sub-layer below the N-rich GaN epilayer. The buffer layer was grown at 700 °C with a Ga-flux of 8 nm/min and N-flux of 3.5 nm/min. Two samples with and without this GaN buffer layer were grown at 785 °C with a Ga-flux of 4 nm/min and an N-flux of 5 nm/min. Each was approximately 0.4 µm thick. The film with the GaN buffer layer showed a RMS roughness of 2.3 nm for the 10 µm × 10 µm scan and 0.9 nm for the 1 µm × 1 µm scan. The largest single peak/valley was 29.8 nm in the sample without the buffer layer, but only 7.5 nm in the buffer layer sample. This value was significantly lower in the sample with the buffer layer, which had a RMS of 6.2 nm for the 10 µm × 10 µm scan and 3.4 nm for the 1 µm × 1 µm scan. Clearly, the GaN sub-layer positively affected the surface smoothness of the film.
Thermal etching thickness and electron mobility
Etching of GaN templates was performed in situ within a vacuum in the MBE chamber at elevated temperatures (780°C) in order to remove any potential surface impurities (typically Si, O, H and C). The heat caused the surface of the film to effectively bake off, therefore reducing the thickness of the film. The purpose was to try and remove impurities on the surface, but at the same time, the heating could introduce structural imperfections into the crystal. This could lead to electron traps and scattering centers, which reduce mobility. Similar to RMS roughness, determination of the electron mobility of the GaN films prepared with this etching step was critical to proper understanding of the overall material quality. As with surface morphology, several trends in electron mobility exist. Figure 6 shows the effect of thermally etched GaN-template substrates before growth on electron mobility. As etching was increased at 10, 25, and 50 nm, the mean electron mobility decreased to 310.7, 285.1, 156.1 cm2/V·s, respectively. This suggests that larger etching thicknesses most likely promoted the development of defects, yielding electron traps within the film, and thus restricting the free movement of carriers. Typically, thermal etching reduces impurities at the GaN/GaN-template interface. Unlike etching, RMS roughness appeared to have no direct effect on electron mobility; however, such an expected trend could be obscured by the interference of other growth parameters, including thermal etching and Si-doping.
Silicon doping and electron mobility
The concentration of the silicon dopant added to GaN films affected electron mobility as well. The addition of charge carriers increased carrier density, although the dopant atoms generally did not fit into the existing crystal lattice, causing crystal defects which reduce mobility. Therefore, increased doping increased carrier density but also decreased mobility. Figure 7 shows the relationship between the concentration of silicon dopant and electron mobility in the GaN films. The graph plots Si-doping in terms of the cell temperature at which it was deposited into the film. Cell temperature is directly related to the concentration of the Si-dopant, which can be used as a means of comparison. The graph demonstrates that a maximum electron mobility of 718.0 cm2/V·s was achieved at a Si-cell temperature of 1140 °C. As silicon concentration was increased with cell temperatures of 1200, 1260, and 1300 °C, electron mobility diminished to 147.4, 179.0, and 66.9 cm2/V·s. Thus, over-doping the GaN film causes excessively high levels of silicon impurities, which trap electrons and significantly reduces mobility.
In silicon-doped samples, a distinct relationship between electron concentration and electron mobility was apparent, as shown in Figure 8. As electron concentration was increased, electron mobility was significantly affected. Concentration values of 6.8 1016 cm-3, 1.0 × 1017 cm-3, 1.3 × 1018 cm-3, 1.5 × 1018 cm-3, and 8.9 × 1018 cm-3 had decreasing electron mobilities of 718.0, 453.2, 179.0, 147.4, and 66.9 cm2/V·s. This relationship is nearly inverse proportional where nµ = k, n is electron concentration, and µ is electron mobility. The actual curve yields n0.46 as opposed to n1; k was approximately 10 V-1s-1.
AlGaN thickness in AlGaN/GaN structures and 2DEG Hall Mobility
The samples measured were grown at similar conditions (same Ga/N and (Al+Ga)/N ratio) with varying temperature between 770-790°C and all contained a gallium-rich buffer. Thermal etching of the underlying GaN substrates was also performed among some samples, with etching thicknesses ranging between 0-200 nm. When comparing the Hall mobility to aluminum thickness of the AlGaN/GaN layer in Figure 9, a distinct parabolic trend could be identified. Hall mobility increased as AlGaN thickness increased, and a maximum Hall mobility was achieved at an AlGaN thickness of 33 nanometers, after which larger thicknesses negatively affected mobility. When analyzing the surface morphology of the various AlGaN layers, a distinct trend was also observed with AlGaN thickness. According to the AFM images shown in Figure 9, larger AlGaN thicknesses created higher root mean squared (RMS) roughness values as compared to lower thicknesses. This discrepancy was most likely due to the typical statistical roughening, which occurs at increased layer thicknesses. The increased RMS roughness is correlated with decreased Hall mobility and, hence, a less effective AlGaN/GaN HEMT could be expected. For AlGaN thicknesses greater or smaller than 33 nm, RMS roughness is higher and Hall mobility is lower.
Al composition in AlGaN/GaN structures and 2DEG Hall mobility
The samples measured were grown at similar conditions with temperatures varying between 770-790 °C. However, these samples were prepared utilizing a carbon-doped buffer. The carbon-doped buffer was used to generate a semi-insulating GaN buffer, isolating the 2DEG active region from the regrowth interface, where a parasitic conductive channel might preside due to residual impurities not sufficiently etched. Most of the underlying GaN substrates were thermally etched by 25 nm except for sample 021208A, which was significantly smaller when etched at 25 nm than at 200 nm. The relationship between aluminum composition and Hall mobility can be seen in Figure 10, which is similar to the trend for the AlGaN thickness study. Aluminum composition and aluminum thickness are closely related. Parabolic shaped Hall mobility curves were present for both experiments. As a result, an optimum Al composition and AlGaN thickness was found at which Hall mobility was at a maximum. In this set of data, the Al composition at which Hall mobility was highest occurred at 25%. This result may be explained by postulating that too much Al composition creates an overabundance of electron scattering centers in the layer, which has adverse effects on the mobility. Also, the data indicated that the Hall mobility was affected by the surface RMS roughness. As shown in the AFM images in Figure 10, higher RMS roughness yielded a lower Hall mobility.
Sheet Carrier Density and Hall Mobility
A relationship was identified between the 2DEG Hall density and the Hall mobility for the same samples of AlGaN/GaN prepared with a buffer doped with carbon. In Figure 11, 2DEG Hall density ranges between the values of -1.06 × 1013 to -2.94 × 1013 cm-2, which is relatively higher than the typical values obtained from samples with merely the gallium-rich buffer samples. The graph shows that with increasing 2DEG Hall density causes a decrease in the Hall mobility. As shown by the samples 052008A-051508A, the 2DEG density increased from -1.06 × 1013 to -1.82 × 1013 cm-2, and the Hall mobility decreased dramatically. However, from 051508A to 060208A, the curve became more constant and tapered off between densities of -1.82 × 1013 and -2.94 × 1013 cm-2. Thus, an inverse relationship exists between Hall density and Hall mobility—as Hall density increases, Hall mobility decreases. As observed previously, an increase in RMS roughness leads to a decrease in Hall mobility. This observation holds true for all samples grown under similar growth conditions.
2DEG characteristics between carbon-doped and Ga–rich buffers
Another analysis investigated the effects of the gallium-rich buffer, the carbon-doped buffer, or no buffer on the 2DEG characteristics, which function to bury the impurities caused by crystal mismatch with the substrate during wafer growth. In this comparison, the purpose was to determine which buffers allow for a greater mobility among these samples prepared under similar growth conditions. These conditions were growth temperatures in the range between 770-795°C and an even distribution of aluminum composition between the types of samples. A significant trend appeared between the gallium-rich buffer and the carbon-doped buffer samples. They both had parabolic curves which followed the same paths. However, the carbon-doped buffer samples had higher Hall mobility. Higher Hall mobility was also positively affected by the RMS roughness of the samples. Two different samples (031708A and 032608A) with similar aluminum composition (27%, 28%) but different buffers were analyzed. Sample 031708A contained a gallium-rich buffer and sample 032608A had a carbon-doped buffer. Measured at a 10 µm × 10 µm window, the sample with the buffer doped with carbon had a RMS roughness of 8.0 nm while the gallium-rich buffer had a RMS roughness of 10.3 nm. Therefore, RMS roughness decreases as the Hall mobility increases. These factors indicate the ideal conditions sought after when creating a HEMT.
GaN film RMS roughness values show a clear relation to Ga-flux (Ga/N ratio) for GaN films grown at high temperatures. In Ga-rich conditions, decreasing the Ga/N results in smoother surfaces, whereas in N-rich conditions, increasing Ga/N results in smoother surfaces. Both of these trends have linear properties and show the smoothest surfaces close to flux stoichiometry when Ga/N~1. The reason for the increase in RMS roughness when deviating from the Ga/N ratio of 1 lies in the enhanced thermal decomposition under Ga-rich conditions (Ga/N >> 1) and the lack of sufficient surface diffusion under N-rich conditions (Ga/N << 1). Ga-rich buffer layers appear to improve surface morphology of the top N-rich grown GaN films. Increased thermal etching thickness, as well as silicon over-doping, negatively affects electron mobility. Silicon-doping appears to create maximum electron mobility at low concentrations. Electron density and electron mobility in silicon-doped GaN films have a clear inverse proportionality.
Systematic studies have also shown how to increase the Hall mobility. Increasing Hall mobility is one of the important variables, which can be modified to affect the electronic properties of the structure. All of the trends identified in the study included a relation to Hall mobility through aluminum composition, thickness, or 2DEG hall density. Trends were identified most clearly with the aluminum composition in the AlGaN of the AlGaN/GaN sample. The most effective HEMTs are created when the aluminum composition is at 25% or the thickness of the aluminum in the sample is at 33 nm. Therefore, too large an Al composition and AlGaN thickness would cause both enhanced alloy scattering and roughness scattering. Depending on the type of doping of the GaN buffer, mobilities or RMS roughness values were affected. Using carbon-doped buffers resulted in higher mobilities with lower Hall densities in comparison to the gallium-rich buffers. A final observation was determined concerning carbon-doped samples in which mobility increased as the Hall density decreased, creating a much more effective HEMT.
Group-III nitride semiconductors have been shown to have outstanding optoelectronic and microelectronic application potentials. These investigations identified various growth conditions that positively and negatively affect the performance of both GaN epilayers and AlGaN/GaN HEMTs. It was found that under high–temperature growth (T > 760°C), superior surface structure with low RMS (root-mean-square) surface roughness was achieved when the Ga/N flux ratio was close to stoichiometric conditions (Ga/N ~ 1). Higher roughness resulted from higher (Ga/N > 1) and lower (Ga/N < 1) flux ratios. This was reflected by differences in electron mobility within GaN layers, with adverse effects also found by thermal etching of the underlying GaN substrate and Si-overdoping. For AlGaN/GaN HEMTs, similar trends were observed, i.e. an increase in electron mobility of the two–dimensional electron gas with decreasing RMS roughness. Carbon-doped GaN buffers in AlGaN/GaN samples showed higher electron mobilities than samples grown without buffers. Finally, a parabolic relationship between electron mobility and aluminum concentration and AlGaN thickness was determined for layers grown at constant Ga/N flux ratio. Future research in this area can better define the optimal growth conditions, which may result in the most efficient nitride-based semiconductors and HEMTs.
Mishra, Umesh K., Likun Shen, Thomas E. Kazior, and Yi-Feng Wu. “GaN-Based RF Power Devices and Amplifiers.” Proceedings of the IEEE 96 (2008): 287-305. 21 July 2008.
Levinshtein, M. E., S. L. Rumyantsev, and M. S. Shur, Properties of Advanced Semiconductor Materials GaN, AlN, InN, SiC, SiGe. Wiley, New York, 2001.
Heying, B., I. Smorchkova, C. Poblenz, C. Elsass, P. Fini, and S. Den Baars. “Optimization of the Surface Morphologies and Electron Mobilities in GaN Grown by Plasma-Assisted Molecular Beam Epitaxy.” Applied Physics Letters 77 (2000): 2885-2887. 21 July 2008.
Shur, Michael. “Heterostructure Field Effect Transistors.” 2007. 23 July 2008 <http://nina.ecse.rpi.edu/shur/sdm2/Notes/Notespdf/18HFET.pdf>.
Koblmüller, G., S. Fernández-Garrido, and E. Calleja. “High Electron Mobility GaN Grown Under N-Rich Conditions by Plasma-Assisted Molecular Beam Epitaxy.” Applied Physics Letters 91 (2007). 21 July 2008.
Neamen, Donald A. Semiconductor Physics and Devices. 3rd Ed. New York: McGraw Hill, 2003.
Wilson, J., and M. N. Rudden. Elements of Solid State Physics. Chichester: John Wiley and Sons Ltd., 1980.
Kosiel, Kamil. “MBE- Technology for Nanoelectronics.” Vacuum 82 (2008): 951-955. Science Direct. 23 July 2008.
Feick, Henning. “MBE Growth of GaN.” 18 Dec. 2001. Berkeley U. 17 July 2008 <http://www.mse.berkeley.edu/groups/weber/research/ganmbe.html>.
Koblmüller, G., S. Fernández-Garrido, E. Calleja, and J. S. Speck. “In Situ Investigation of Growth Modes During Plasma-Assisted Molecular Beam Epitaxy of (0001) GaN.” Applied Physics Letters 91 (2007). 21 July 2008.
Van Der Pauw, L. J. “A Method of Measuring Specific Resistivity and Hall effect of Discs of Arbitrary Shape.” Philips Research Reports 13 (1958). 23 July 2008.
Serway, Raymond A. Physics for Scientists and Engineers. 4th ed. Philadelphia: Saunders College, 1996.
Carpick, Robert W. “Scratching the Surface: Fundamental Investigations of Tribology with Atomic Force Microscopy.” Chemical Reviews 97 (1997): 1163-1194.