lunes, 15 de febrero de 2010

nitride semiconductor laser device

lectrical engineers in Debdeep Jena's lab at the University of Notre Dame have found a way to make two nitride semiconductors conduct electricity better, which may make them useful for building more effective ultraviolet (UV) lasers and light-emitting diodes (LEDs). These devices could enable a wide range of applications such as high-density optical data storage, water treatment, sterilization of medical equipment, UV-enabled security marks on credit cards and paper money, and biological imaging. 

Nitride semiconductors such as aluminum gallium nitride and gallium nitride have the widest spectral range of band gaps--the energy required to move electrons through the material--among all semiconductors, ranging from the infrared through the visible and into the deep UV range. This makes them excellent for use in short-wavelength lasers and in LEDs for solid-state lighting, but it also makes it hard for engineers to design energy-efficient devices. 

Like all semiconductors, nitrides need to be "doped" with foreign materials to conduct electricity efficiently. This either provides the material with charge-carrying electrons, or electron vacancies--called holes--that allow electrons to move freely. But the energy barriers in gallium nitride (GaN), for instance, are so large that even devices made with magnesium (the most commonly used hole-dopant for GaN) don't work well at room temperature, making them extremely inefficient. 

In a paper published in the January 1, 2010, issue of Science, Jena and his colleagues describe growing graded layers of aluminum gallium nitride (doped with magnesium) on the nitride surface of gallium nitride crystals. This means that the proportion of aluminum to gallium in the top layer increased as its thickness grew. Experiments testing this material's conductivity showed that making the semiconductor this way efficiently activated the magnesium doping atoms at room temperature.

Jena's group also built prototype UV LEDs using both the graded aluminum gallium nitride (AlGaN) material and regular maginesium-doped GaN. The AlGaN LEDs were both more efficient and brighter than the GaN devices. Jena believes that this should make nitride semiconductors much more practical alternatives for any device requiring UV light. 

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nitride semiconductor laser device

ore Efficient UV Lasers and LEDs Possible
New advancements innovate this field of research
By Tudor Vieru, Science Editor
4th of January 2010, 09:05 GMT

Experts at the University of Notre Dame, in Paris, have recently managed to achieve new heights in nitride semiconductor research. They have been able to produce materials that are far more efficient than existing ones, thus opening the way for a completely new generation of ultraviolet (UV) lasers and light-emitting diodes (LEDs). The work was conducted by a team of electrical engineers, in scientist Debdeep Jena's laboratory at the university, Technology Review reports. 

 What the team basically accomplished was making nitride semiconductors exchange electricity much more efficiently than they used to. According to the team, the innovation could potentially be used in a very wide range of scientific fields, from high-density optical data storage to water treatment. The semiconductors could also have possible applications in medical-equipment sterilization procedures, credit-card security marks, paper money and a few biological imaging methods. At the basis of these processes lie lasers or diodes. With the new improvements, all the devices based on these light sources could function faster and more efficiently, Jena says. 

The reason why nitride semiconductors were selected for this work was the fact that they had the widest spectral range of band gaps of all similar materials. This ability refers to the energy level that is required in order to move electrons through the materials, the team explains. In the case of materials such as aluminum gallium nitride and gallium nitride, these energy ranges extend from infrared wavelengths to the deep-ultraviolet portion of the electromagnetic spectrum. The group has also managed to get past a very common problem in such materials, namely the fact that they can be very ineffective at room temperatures. 

In its experiments, the team used gallium nitride crystals. On the nitride surface, it managed to grow graded layers of magnesium-doped aluminum gallium nitride, which allows for better electric conductivity. Materials such as magnesium, which are called dopants, have to be regularly used in semiconductors, so as to make them capable of conducting electricity. Details of the new work appear in the January 1 issue of the top journal Science. The experts conclude by saying that their new growing method manages to activate the conductibility of the nitride semiconductors even at room temperature.

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nitride semiconductor laser device

Application-oriented quantum theory for infrared nitride lasers?
Recently, nitride semiconductor lasers have extended their wavelength reach into the green part of the visible spectrum (emitting at about 530nm in pulsed operation). This has been achieved by using non-standard-orientation gallium nitride (GaN) substrates. The aim in using these substrates has been to reduce or eliminate the strong polarization-induced electric fields that exist in the c-plane orientation of standard GaN substrates. The polarization fields are thought to separate the positive charge carriers (holes) and negative charge carriers (electrons) that should recombine to produce light.

Tarun Sharma and Elias Towe believe that, rather than the polarization field, it is the lattice matching between the InGaN layers and the oriented substrate that determines the longest laser wavelengths achievable in the nitride system [J. Appl. Phys., vol107, p024516, 2010]. Towe is based at Carnegie Mellon University; Sharma is visiting Carnegie Mellon from the Raja Ramanna Centre for Advanced Technology, India.

It is proposed that 'application-oriented nitride substrates' be developed using bulk indium gallium nitride (InGaN) to lattice match the laser epilayers that are needed for longer wavelengths. Sharma and Towe point out that Shuji Nakamura managed to create nitride semiconductor light-emitting diodes emitting red light of 600nm wavelength in 1996. The researchers comment: "We believe it would be possible, by using this concept, to make nitride lasers at the fiber-optic communication windows at 1.3μm and 1.55μm, thus eliminating the need to use the hazardous arsenide/phosphide materials currently used to make communication lasers."

These claims are based on a theoretical analysis of the emission capabilities of quantum wells (QWs) of various thicknesses. In existing technology using GaN templates, the layers that make up the QWs are strained, because the lattice constants of InGaN (a ~ 3.5Å, c ~ 5.7Å) are larger than those of GaN (3.2Å, 5.2Å). As the indium content increases, the strain becomes greater. At higher strains, it becomes difficult to grow high-quality layers of appreciable thickness. Beyond a critical thickness, many defects and dislocations form.

Sharma and Towe note that, from their own experience and that of others, one is limited to strains of less than 3% in constructing InGaAs/GaAs lasers. For InGaN/GaN, this corresponds to indium contents of less than 0.3.
Figure 1: Energy values corresponding to ground-state transitions in InGaN/GaN QWs and corresponding emission wavelength for different values of QW thickness/composition.

On this basis, Sharma and Towe calculate the emission wavelength of InGaN QWs of various thicknesses with GaN barriers with indium content up to 0.3 (Figure 1). The envelope approximation is used with parameters from the literature and adopting a simple formalism for taking account of the change in band structure with strain previously developed by the authors. The calculations do not include polarization fields that can give a red shift of up to 30nm in wavelength. One finds that one is limited to emissions of less than 500nm in wavelength (less than the 520–570nm range for green light).

Although one can shift the upper limit a bit using differently oriented substrates, Sharma and Towe suggest another route to longer wavelengths – using InGaN templates, which they call 'application-oriented nitride substrates' (AONS). This would shift the amount of indium that one could incorporate and hence give longer-wavelength emission. With 
In0.1Ga0.9N substrates, one could have wells with indium content up to around 0.4, giving emission up to wavelengths of almost 600nm (orange), they believe. With 
In0.45Ga0.55N substrates, infrared wavelengths of around 1000nm could be accessed.

igure 2: Proposed laser diode structure on InGaN AONS for wide wavelength range. All epilayers are expected to lattice match to AONS except compressively strained QW.

Some InGaN templates are already available, grown on sapphire using hydride vapor phase epitaxy (HVPE). Sharma and Towe believe these could be used to extend the wavelength of light-emitting diodes. For lasers, one would need bulk material. Since ternary indium gallium arsenide (InGaAs) and indium gallium antimonide InGaSb are already available, 'there seems to be no fundamental reason preventing the development of InGaN AONS'. The researchers suggest that a range of AONS to cover extended nitride semiconductor applications could consist of a few products based on 'judicious compromises'. For example, In0.15Ga0.85N substrates could cover the blue, green and red portions of the spectrum.

"Although InGaN AONS do not exist at the present time, it is reasonable to challenge the wafer manufacturers to create them in light of the envisioned numerous device applications that would be enabled by this class of substrates on various orientations," the researchers comment.

Figure 3: Bandgaps of three nitride ternary alloys (AlGaN, InGaN, and InAlN) vs lattice constant, showing possible bandgaps for InAlN alloy using different bowing parameters (2.5–4.5eV). Measured band bowing can be up to 4.5eV, but 'first principles' calculations suggest its intrinsic value could be about 3eV. Band-bowing values used for AlGaN and InGaN are 1.0eV and 1.2eV, respectively. Vertical blocks show positions for development of nitride LDs at green, red, and infrared wavelengths. Linear interpolation (Vegard's Law) is used to convert from lattice constant to alloy composition.
One major roadblock to this scenario for creating longer-wavelength nitride laser diodes is the cladding that is needed (Figure 2). These layers need to be lattice matched with the underlying substrate and have energy bandgaps that are larger than that of the waveguide layer (unstrained InGaN). One possibility is indium aluminum nitride (InAlN). Unfortunately, the measured bandgaps for this material system are not much different from the corresponding lattice-matched InGaN material (Figure 3). However, it is expected that, as better-quality InAlN is developed, it will have less 'band bowing', leading to a greater difference in bandgap.

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C.I. 17862728
electronica del estado solido

nitride semiconductor laser device

Blue-violet semiconductor lasers are used to read digital signals from Blu-ray discs, and the commercial development of Blu-ray products that have enabled millions of consumers to enjoy true HD in their homes would not have been possible without this core component device. Thanks to determined efforts by its engineers racing against time, Sony was able to complete development of the laser within a very tight schedule in time to start the mass-production of millions of PLAYSTATION 3 consoles, the first product to incorporate Blu-ray technology. In this interview with Masao Ikeda of Sony Advanced Materials Labratories, we learn about the numerous failures with deadlines looming in the development of the first 3 in 1 laser (CD, DVD, and BD) for the Playstation 3, and how Masao thought it would never happen.

Masao: During my time with Sony, I have been involved in the development of semiconductor lasers for optical discs, including CD, DVD and BD systems. For me the most exciting achievement, and one that required enormous effort, was the development of the blue-violet semiconductor laser.

A semiconductor laser is to an optical disc what a needle is to an analog record. The surface of an optical disc is covered with minute pits (concave areas) and ridges (convex areas). By bouncing laser beams off these areas and reading information contained in the reflected light, we can play back the content recorded on the disc. If we reduce the wavelength of the laser beam, the spot diameter of the laser is also reduced, allowing us to use smaller pits and ridges on the disc. By recording data using a laser with a short wavelength, we can store more information within the same disc area. The development of semiconductor lasers with progressively shorter wavelengths has driven the evolution of optical discs, from CDs to DVDs, and now to BDs. The laser used when playing a music CD has a wavelength of 780nm (nm=nanometer), while a DVD requires a 650nm red laser. Because the red laser used to write DVDs has a shorter wavelength, the capacity of DVDs is correspondingly greater. To create the BD, which has around five times more recording capacity than a DVD, we needed to develop a blue-violet laser capable of producing light with an even shorter wavelength.


Masao: The development of blue lasers began in the 1980s. Despite the efforts of engineers in many countries, the development of suitable materials was a slow process. Semiconductor lasers emit light when an electrical current is passed through the semiconductor used. To discover suitable materials for semiconductor lasers, we need to find combinations of substances that will produce laser light with the desired wavelength when current passes through them.

Initially Sony tried to develop a semiconductor laser using materials based on zinc selenide, and in 1996 we succeeded in maintaining continuous oscillation for 100 hours. However, Sony changed its development strategy after Nichia Corporation succeeded in developing a gallium nitride semiconductor laser with a shorter wavelength. It was a difficult decision to abandon development of the materials that we had previously been researching. However, we wanted Sony to maintain its leading role in the advancement of optical disc technology, and we saw this as the best decision in terms of ensuring that Sony would be the first to develop next-generation products based on BD technology.

Yet at this stage, we had simply selected the material that we would use. There were still many challenges to overcome before we could turn this into a semiconductor laser that could be used in commercial products. The first of these was the solution of problems surrounding Nichia Corporation's patents relating to gallium nitride. In the second half of the 1990s, there was a patent lawsuit between Nichia Corporation and Toyoda Gosei Co., Ltd. concerning a blue LED made using gallium nitride. There was extensive media coverage about the blue LED that couldn't be marketed because of the patent dispute. Urgent steps were needed to resolve this problem so that Sony could introduce its blue-violet semiconductor laser. However, Nichia Corporation took the position that it would sell products but not the technology, and that it would opt for licensing if there were complementing technologies. Fortunately, Sony had laser manufacturing patents, expertise and commercialization experience dating back to the CD era. We also had manufacturing facilities with world-class technology, including Sony Shiroishi Semiconductor Inc. (Sony Shiroishi), the Sony's Group's semiconductor laser manufacturer.

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electronica del estado solido

nitride semiconductor laser device

The successful fabrication of light emitting diodes and semiconductor lasers from gallium nitride (GaN) and related wide bandgap nitrides has prompted considerable research into the growth and development of these compounds. Currently, the most common means for deposition of GaN by chemical vapor deposition (CVD) requires large excesses of ammonia and temperatures exceeding 1000°C. Meanwhile, alternative means of deposition using other azide-containing compounds have proven to be unsuccessful because the organic groups present in these compounds incorporate undesirable carbon compounds. Still, alternative synthetic methods based on single source molecular precursors that incorporate Ga—N bonds and labile, preferably, non-organic leaving groups offer the potential of significant improvements in film quality and growth process: lower deposition temperature, elimination of the inefficient use of ammonia, reduction in nitrogen and carbon contamination, much enhanced doping capabilities, etc. Consequently, optimal precursor compounds, providing a facile decomposition pathway leading to the desirable material and offering sufficient volatility at room temperature to undergo CVD or molecular beam epitaxy (MBE), are desirable.
Invention Description
Accordingly, researchers at Arizona State University have identified novel compounds which serve as single source precursors for the deposition of gallium nitride on thin films. Likewise, these researchers have developed a means to synthesize and a method to use single source precursor compounds which allow the deposition of GaN at low temperatures and allow stoichiometric deposition of GaN onto thin films.
• Light Emitting Diode Fabrication
• Semiconductor Fabrication (e.g. Semiconductor Lasers)
• Preparation of Thin Films and Bulk Powder
• Lower Deposition Temperature – sufficiently volatile at room temperature for CVD and MBE
• Eliminates Inefficient Use of Ammonia
• Reduction in Nitrogen Vacancies and Carbon Contamination – does not contain heavy organic groups, which invariably introduce carbon contamination during film growth; does not contain N—H bonds, which promote loss of nitrogen
• Improved Decomposition Reactions – yields pure GaN heterostructures and nanostructures of unusual morphologies and microstructure
• Allows Standard Methods of Analysis

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C.I. 17862728

electronica del estado solido

nitride semiconductor laser device

Managing Director of the Board (R&D Center, Optoelectronics Sales Div.), TOYODA GOSEI CO., LTD.
Nitride semiconductor LEDs
Blue LEDs were not considered to be developed during the 20th Century.
Prof. Akasaki aggressively spent his life for developing GaN which is a material suitable for Blue LEDs.
As a result, the following all fundamental technologies for Blue LEDs (used for White converted LEDs) were established first in the world.
1) Crystallization of high quality GaN
2) n-type GaN
3) p-type GaN
These LEDs are used for large size full screen displays, backlights of cell phones and notebook PCs, and recently penetrating into LCD TVs and light sources of general lighting. Its market size is huge and unpredictable.
Toyoda Gosei started the R and D of Blue LEDs in 1986 under Prof. Akasaki's supervision and commercialized Blue LEDs.
In this report, the history of Blue LED development is reviewed, and its technologies progress and applications including the future technologies are introduced.
Masao Ikeda
R&D Director and Chief Distinguished Engineer, Advanced Materials Laboratories, Sony Corporation
Nitride semiconductor LDs
Stimulated by the fact that the GaN-based laser diode (LD) was successfully realized using breakthroughs brought by Prof. Akasaki et al., we changed our direction of developing short-wavelength LD based on II-VI materials for use in next-generation optical disk systems, toward development based on nitride materials. Thanks to the rigid nature of GaN-based materials, such as stable threading dislocations in the active layers which are never multiplied by current injection, and a high critical optical power density for catastrophic optical damage of laser facets, the development of reliable and high-power LDs progressed quite satisfactorily, resulting in the successful commercialization in Blu-ray Disc, PS3, and so on. Recently in collaboration with Tohoku University, we started to investigate pico-second super high-power lasers as an attempt to pursue the potential performance of GaN-based LD and expand applications. The superior potential of GaN-based materials has already been demonstrated by 12 W peak-power under gain-switching operation, which was one order of magnitude higher than the power reported for other material systems. In this talk therefore, I would like to present our recent results of pico-second super high-power LDs based on GaN-based materials.
Fumio Hasegawa
Professor Emeritus, University of Tsukuba
Nitride semiconductor high-speed and power devices
--- Present status and future prospect of AlGaN/GaN HFETs ---
Compound semiconductor electron devices have to always compete with Si devices in cost as well as in performance, differently from light emitting devices. Even if output power and efficiency (performance) is 1.5 times better than those of Si devices, compound semiconductor electron devices can not be sold in twice price.
There are two applications for nitride electron devices; microwave devices and power switching devices. The former is already used for power amplifiers of meteorological radars and satellite communications as replacement of klystrons and traveling wave tubes. They are expensive, lower reliable than semiconductor devices and need a high voltage power supply, therefore, expensive nitride devices can be used. The biggest potential market of the power switching device is those for hybrid and electric vehicles. Normally off operation is inevitable for the switching device for vehicles. Several structures have been proposed and demonstrated, but the performance is not enough yet. A structure with an essential normally off mechanism should be developed even if it needs a complicated structure with a difficult fabrication process.
Yasuhiko Arakawa
Professor, Institute of Industrial Science, The University of Tokyo
Nitride semiconductor nanostructures
The nitride semiconductor science established by the pioneering achievement of Dr. Isamu Akasaki has emerged in the last decade as innovative technologies for blue light-emitting diodes, lasers and FETs which are indispensable in future IT societies. On the other hand, the concept of quantum dots proposed in 1982 has brought up unique features of artificial atoms, leading to a wide variety of experimental investigations into semiconductor physics and device applications. In particular, a remarkable progress of InAs-based quantum dot technology has resulted in commercialization of the quantum dot lasers in the quite near future. In this presentation, we overview recent advances in GaN-based nanostructures with emphasis on physics, growth, and device applications of quantum dots and nanowires. Outlook and issues of research fields of GaN-based nanostructures are also addressed.
Akira Usui
Executive Officer, R&D Division, Furukawa Co., Ltd.
Reduction of defects in nitride semiconductors
The first report on semiconductor GaN crystal growth was published in 1969, where the growth was carried out by HVPE (hydride vapor phase epitaxy) method on a sapphire substrate. However, the crystallinity was insufficient because the large island growth was dominant on the substrate. Important breakthrough was in a low-temperature buffer layer technique proposed by Dr. Akasaki et al, which becomes a standard process to grow nitrides materials on foreign substrates. However, in order to improve device performances, further reduction of dislocation density was needed. The lateral overgrowth method was proposed to satisfy with such requirement. In this technique, the generation of dislocations in the overgrown layer on the mask was suppressed and threading dislocations were largely reduced by the bending effect due to facet planes appeared on the side walls of selective-area growth clusters. In this talk, the reduction of defects in nitride semiconductors using above techniques will be discussed by focusing on the preparation of GaN crystal by HVPE.
Katsumi Kishino
Professor, Faculty of Science and Engineering, Sophia University
Nitride Semiconductor Nanocolumns
Nanodevices have attracted considerable attention from researchers. Nitride semiconductor nanocolumns are one-dimensional nanocrystals of typically 20-300nm diameter and 2m height. Using their dislocation-free property and high light extraction efficiency, the fabrication of high-efficiency nano-emitters producing green to red emission is highly expected. Initially, GaInN-based nanocolumns were grown through the self-assembling technique, but this introduced fluctuations in the size and position of nanocolumns, bringing about multicolor emissions. Thus we have developed a selective-area-growth technique to control the nanocolumn size and position, and a uniform array of nanocolumns was successfully fabricated. The photoluminescence emission from the InGaN quantum well was then evaluated, and we observed that the emission color changed monotonically from blue, green to red. This phenomenon indicates the possibility of realizing full-color nanodevices, such as three-primary-color nanoemitters, nanopixel devices and so forth, using GaInN-based nanocolumns. A two-dimensional periodic arrangement of nanocolumns generates strong light confinement at a specific wavelength, by which the first stimulated emission from GaInN-based nanocolumns was observed.
Yoichi Kawakami
Professor, Graduate School of Engineering, Kyoto University
Optical processes in nonpolar and semipolar nitride semiconductors
Twenty years has passed since the first achievement of the pn-conductivity-control in GaN. Thereafter, the development of light emitting diodes (LEDs) and laser diodes (LDs) has been made day by day, reaching to the realization of highly efficient light emitting devices based on InGaN, covering from near ultraviolet to blue spectral region. However, the problem still exists, where the sufficient efficiency cannot be obtained in the wavelength longer than blue-green range if In compositions are further increased. This mechanism is now understood as a result of huge internal electric fields induced by piezo-electric polarization in In-rich InGaN quantum wells grown on polar GaN (c-plane in hexagonal phase). Accordingly, this problem has led to the intensive research, where the fabrication and basic study have been performed in the InGaN/GaN hetero-structures grown on nonpolar substrates (tilted 90° with respect to c-plane), and on semipolar ones (tilted in the range of 0° to 90° with respect to c-plane). I will introduce the key developments and the future prospects in nonpolar and semipolar nitride materials and devices.
Hiroshi Amano
Professor, Faculty of Science and Engineering, Meijo University
Development of group III nitride semiconductors for light emitting, photodetector and solar cells covering infrared to UV region
High performance UV to green LEDs, white LED composed of blue LED and yellow phosphors, and violet laser diode have been commercialized using GaN-based AlGaInN semiconductors. UV and green laser diodes have also been developed by this material system. Potential of this material should not be limited from UV to green region. It is theoretically possible to fabricate infrared devices using InN and VUV devices using AlN. The highest efficiency solar cell is also possible by using tandem structure of this material system. However, due to the lack of suitable growth technique for In-rich GaInN and Al-rich AlGaN, we are unable to fabricate such novel devices. Recently, we developed new growth technology for In-rich GaInN and Al-rich AlGaN, by which we can grow high quality GaInN and AlGaN. In this presentation, new growth technology for group III nitride semiconductors having the whole compositional range will be shown.
Yasushi Nanishi
Professor, College of Science and Engineering, Ritsumeikan University
Professor, Department of Materials Science and Engineering, Seoul National University
Advancement of Indium Nitride Based Semiconductors
Bandgap energy of Indium Nitride (InN) has believed to be 1.9 eV for more than 30 years. Seven years have passed since narrow bandgap energy of around 0.7 eV was reported and this new value is well recognized these days after extensive discussions on this subject. Not only band gap energy, many physical parameters like effective mass, mobility and peak velocity are all revised. Owing to these new findings, new potential applications of nitride semiconductors and alloys like very high efficiency solar cells, wide spectrum range light emitters and sensors from deep UV to IR, high frequency electronic devices up to Terahertz operation are opened up. Several serious issues like reproducible and high quality crystal growth, high density residual carries, p-type doping and high density surface accumulated carriers should be resolved, however, before InN and related alloys are successfully applied to actual devices. Review on these recent advancements of InN and related alloys will be presented in this talk.

Marcos Pinto

Electronica del estado solido

Transición electrónica fundamental en pozos cuánticos GaN/InGaN/GaN con estructura
de zincblenda

Los compuestos GaN, AlN, InN y sus aleaciones,
también llamados nitruros, han despertado gran interés en
los últimos años debido a su potencial aplicación en
dispositivos optoelectrónicos. Particularmente, los
semiconductores basados en la aleación InGaN han sido
utilizados en el diseño de dispositivos comerciales tales
como diodos emisores de luz (LED´s) y diodos láser
(LD´s) con longitudes de onda 320-405 nm [1,2]. La
importancia de los dispositivos optoelectrónicos basados en
nitruros es debida a que presentan una alta eficiencia y un
tiempo de vida grandes. Es por esto que tienen enormes
aplicaciones en la vida cotidiana, como puede ser
comprobado con la aparición de displays, semáforos y
lámparas de iluminación casera hechas con LED's basados
en nitruros, así como con la creación de LD de longitud de
onda de 405 nm usados en los nuevos discos ópticos, los
llamados blue-ray disc, que tienen una capacidad de
almacenamiento de entre 25 y 50 GB.

Tabla 1. Parámetros de amarre fuerte de los compuestos GaN e InN (en eV).

E(s,a)    E(p,a)    E(s,c)  E(p,c) E(s*,a) E(s*,c) V(s,s) V(x,x)

GaN   -12.9156  3.2697 -1.5844 9.1303 14.0000 14.0000 -8.8996 5.4638

InN   -12.8605 2.7081 -0.3994 8.7518 15.0000 15.0000 -4.2285 4.8684

V(x,y)  V(sa,pc) V(sc,pa) V(s*a,pc) V(pa,s*c) λa λc Δ0

GaN 8.7208 6.7152 7.3524 7.8440 2.3827 0.003 0.015 0.018

InN 6.7505 3.3231 5.6091 8.9764 3.0144 0.003 0.002 0.010

Superficies y Vacío 19(3), 12-15, septiembre de 2006 ©Sociedad Mexicana de Ciencia y Tecnología de Superficies y Materiales


Figura 1. Brecha energética prohibida de la aleación InxGa1-xN en la

estructura de zincblenda como función de la concentración de In. Los
diamantes representan resultados experimentales.

Figura 2. Energía de transición como función del ancho del pozo en la

ley de escalamiento de Harrison para diferentes valores de BO y

concentración x = 0.2.

Figura 3. Energía de transición como función del ancho del pozo en la

ley de escalamiento de Arriaga diferentes valores de BO y

concentración x = 0.2.

La parte esencial de un LED o un LD es un pozo
cuántico. Los pozos cuánticos de GaN/InGaN/GaN han
sido estudiados anteriormente debido a su uso como
regiones activas en láseres; por ejemplo, estos pozos con
relación de espesor de pozo/barrera de 2/12 nm han
mostrado alta eficiencia en diodos láser [3]. Además,
heteroestructuras hechas con éstos, muestran intensa
luminiscencia y fotoluminiscencia [4] y presentan baja
sensibilidad a los cambios de temperatura [5].
Adicionalmente, Haberer y colaboradores [6], han
fabricado microdiscos tomando como región activa pozos
cuánticos múltiples de InGaN utilizando el método
denominado grabado foto-electroquímico.
Hasta ahora, la mayoría de los trabajos dedicados a
pozos cuánticos basados en nitruros se ha concentrado en la
parte experimental, dejando el lado teórico con poca
atención. Con el objeto de entender mejor los procesos
involucrados en estos sistemas, en el presente trabajo
estudiamos teóricamente la energía de transición 1h-1e de

pozos cuánticos (001) de GaN/InxGa1-xN/GaN como

función del ancho del pozo para valores de la

concentración x = 0.1 y 0.2. Usamos el método de amarre

fuerte empírico (ETB) junto con el método Surface Green
Function Matching (SGFM), tomando en cuenta la tensión
en el pozo. Por otra parte, el band offset (BO) en
heteroestructuras cuánticas es una información
fundamental para el diseño de dispositivos, sin embargo,
para los nitruros hay pocos datos y varían mucho los
valores reportados [7-9], por esa razón los cálculos los
hemos realizado también variando el valor del BO para
analizar su efecto en las energías de transición.

2. Modelo teórico

El estudio lo realizamos en cuatro etapas. En la primera
se calcula la estructura electrónica de los compuestos
binarios volúmicos puros GaN e InN. En la referencia [10]
está descrita la obtención de la estructura electrónica de
ellos, usando ETB con una base de orbitales atómicos

sp3s*, interacción a primeros y segundos vecinos y

tomando en cuenta el acoplamiento espín-órbita. En este
trabajo hacemos un estudio de las propiedades electrónicas

de pozos cuánticos en el centro (punto Γ) de la zona de

Brillouin (ZB) bidimensional, incorporando sólo primeros
vecinos. Consideramos que no es importante tomar en
cuenta interacciones hasta segundos vecinos, ya que incluir
éstos sólo modifica un poco la estructura de bandas de los
materiales puros en el punto L de la ZB, y las propiedades
optoelectrónicas más importantes provienen del centro de
la ZB. Los parámetros ETB (ETBP) se obtienen ajustando
a datos experimentales de estructura de bandas o cálculos
de primeros principios. Posteriormente, en la segunda
etapa, usamos la aproximación de cristal virtual (VCA)

[10-15] para obtener los ETBP de la aleación InxGa1-xN. En

el marco de la VCA, los ETBP de la aleación se calculan
promediando con la siguiente fórmula

EInGaN (x) = (1x)EGaN + xEInN (1)

Superficies y Vacío 19(3), 12-15, septiembre de 2006 ©Sociedad Mexicana de Ciencia y Tecnología de Superficies y Materiales


Figura 4. Energía de transición como función del ancho del pozo en

la ley de escalamiento de Harrison y de Arriaga; el valor del BO es de

20% y la concentración es x = 0.2.

Figura 5. Energía de transición como función del ancho del pozo

para x = 0.1 y x = 0.2 en la ley de escalamiento de Harrison; los

resultados son mostrados para x = 0.1 y 0.2 y un BO de 20%.

donde Ej (j = GaN, InN) son los ETBP de los compuestos

binarios dados en la Tabla 1. Cabe mencionar que la VCA
trata una aleación como un cristal perfectamente periódico,
suponiendo que su estructura es idéntica a la de los
constituyentes; por lo tanto, no describe los distintos
entornos atómicos locales en materiales inhomogéneos y
falla en casos especiales [11]. Sin embargo, la VCA tiene
la ventaja de su simplicidad y de que es
computacionalmente eficiente. Ya ha mostrado ser útil en
cálculos de TB reportados anteriormente [10,12]. Además,
esta aproximación se ha usado exitosamente para obtener
las propiedades estructurales y termodinámicas de muchos
materiales [13], así como las propiedades dieléctricas y
piezoeléctricas de otros más [14]. También explica el
ferromagnetismo como función de la concentración en
algunos casos [15]. En la tercera etapa del cálculo,
tomamos en cuenta la tensión en el pozo. La constante de
red de la aleación InGaN es apreciablemente mayor que la
del GaN a las concentraciones de In que usamos.
Asumimos que en la heteroestructura, el GaN, que es el
material de la barrera, permanece relajado con su constante
de red original y que la constante de red del material del
pozo, el InGaN, se acopla a la del GaN. Por lo tanto, el
InGaN está sujeto a tensión biaxial compresiva. Este efecto
se incorpora escalando los ETBP del InGaN obtenidos

mediante la Ec. 1, usando la siguiente expresión

E j E j r (2)

siendo α y β los tipos de orbitales de los ETBP de la Tabla

1. El cociente r/r0 es la distancia de los átomos de la red

deformada entre la distancia de los átomos de la red sin

deformar. Si hacemos el exponente ηαβ = 2 para todos los

tipos de orbitales, se tiene la parametrización de Harrison
[16]. Uno de los coautores de este trabajo (J. Arriaga),
realizó anteriormente [17] un estudio teórico de la
dependencia de la brecha energética prohibida (gap) de los
materiales GaAs y GaP bajo presión hidrostática, usando
diferentes exponentes. Encontró que usando la

parametrización ηss = 3.7 y para los demás tipos de

orbitales ηαβ = 2, se reproducían mejor los datos

experimentales. Estos valores de exponentes son similares
a los obtenidos por Priester y colaboradores [18]. Los datos
experimentales para la variación del gap de los nitruros
cúbicos con la presión hidrostática o tensión biaxial o
uniaxial, son escasos y es difícil realizar un ajuste. Por lo
anterior, en nuestros cálculos utilizamos ambos conjuntos
de exponentes (Harrison y Arriaga) para el escalamiento y
comparamos los resultados.
En la etapa final del cálculo, el tratamiento teórico de la
heteroestructura lo hacemos con el llamado método de
SGFM, el cual incorpora los efectos de las dos interfaces
de manera adecuada. Mediante este método calculamos las
energías de los estados ligados de huecos y electrones

como función del número de monocapas n de InxGa1-xN.

Este método está descrito en detalle en la referencia [19].

3. Resultados y Discusión

Los valores de los parámetros de red y las constantes
elásticas de los compuestos GaN e InN con estructura de
zincblenda los tomamos de las referencias [20,21]. Los
ETBP correspondientes están dados en la Tabla 1 [10].
Ambos semiconductores son de gap directo con valores de
3.3 eV y 0.8 eV, respectivamente. Asimismo, sus
constantes de red son 4.52 y 4.98 Å, respectivamente. En la
figura 1 presentamos la evolución del gap como función de
la concentración de In para la aleación ternaria en los

puntos de alta simetría Γ, X y L. Los diamantes representan

resultados experimentales de fotoluminiscencia en
películas de InGaN [22].
Calculamos los estados electrónicos de pozos cuánticos

de GaN/InxGa1-xN/GaN crecidos en la dirección (001) en el

centro de la ZB. Presentamos los resultados de los niveles

de energía como función del número de monocapas n de

Superficies y Vacío 19(3), 12-15, septiembre de 2006 ©Sociedad Mexicana de Ciencia y Tecnología de Superficies y Materiales


InxGa1-xN con 2 n 20. Una monocapa contiene dos

capas atómicas, una de aniones y otra de cationes. Nuestro
análisis incluye valores del BO de 20, 40 y 60 % para las
bandas de valencia, y calculamos la energía de transición

1h-1e para x = 0.1 y x = 0.2. En la figura 2 mostramos la

energía como función del ancho del pozo para x = 0.2

utilizando la ley de escalamiento de Harrison para los tres
valores de BO. Los resultados obtenidos en el caso de la
ley de escalamiento de Arriaga se muestran en la figura 3
para el mismo valor de la concentración de In y los mismos
valores de BO. Podemos observar que en ambos casos, la
energía de transición decrece cuando el ancho del pozo se
incrementa, esto debido a que los niveles energéticos del
hueco y del electrón se aproximan al fondo de sus pozos
respectivos. En el límite, cuando el ancho del pozo tiende a
infinito, el electrón y el hueco se comportarían como
partículas libres y su energía del estado base sería la del
fondo del pozo, es decir, la transición 1h-1e tendería al
valor del gap del material tensionado del pozo, al del

InxGa1-xN. Para x = 0.1 y 0.2, los valores del gap son 2.98 y

2.65 eV, respectivamente, para el material tensionado.
Podemos observar que la energía de la transición
disminuye al aumentar el valor del BO en la banda de
valencia, principalmente para pozos estrechos. Esto es así
porque en pozos estrechos solamente hay un nivel de
energía, el cual es muy sensible a la variación de la
profundidad del pozo al variar el BO. Con el objetivo de
comparar las dos leyes de escalamiento que estamos
utilizando, en la figura 4 presentamos los resultados

obtenidos para x = 0.2 y BO = 20 %. Podemos observar

que la energía de transición muestra una dependencia
apreciable con la ley de escalamiento, lo cual es más
notable al aumentar el ancho del pozo. Con los exponentes
de Arriaga, las energías de transición son más elevadas y
tienden con más lentitud al gap del InGaN tensionado, al
aumentar el ancho del pozo. Un comportamiento similar es
observado para BO = 40 % y 60 %. También hemos

obtenido la energía de la transición para x = 0.1. En la

figura 5 comparamos estos resultados con los obtenidos

para x = 0.2 y BO = 20 % en la ley de escalamiento de

Harrison. Se ve claramente que la energía de transición
disminuye conforme la concentración de In aumenta. Esto

es debido a que el gap de la aleación disminuye conforme x


4. Conclusiones

Hemos calculado la energía de la transición fundamental
1h-1e en el centro de la ZB, de pozos cuánticos

GaN/InxGa1-xN/GaN cúbicos crecidos en la dirección

(001). Se utilizó la aproximación de amarre fuerte con una

base de orbitales atómicos sp3s* en conjunto con el método

SGFM. El cálculo se realizó para concentraciones x = 0.1 y

0.2, variando el ancho de los pozos de 2 a 20 monocapas,
para varios valores del BO y usando escalamientos
diferentes para la variación de los ETBP al tomar en cuenta
la deformación del pozo. Al aumentar el ancho de los
pozos, la energía de transición tiende a la del gap de la
aleación InGaN del pozo tensionado. La energía de
transición disminuye cuando la concentración de In
aumenta. El aumento en el valor del BO de la banda de
valencia ocasiona que las energías de transición
disminuyan, efecto que es más notable en los pozos
estrechos. Por el contrario, al aumentar el valor del

exponente ηss de escalamiento de los ETBP por la tensión,

de 2.0 a 3.7, las energías de transición aumentan, siendo
más notorio el efecto para pozos anchos.

Jorge L. Polentino U.