Study on Quantum Dot Lasers and their advantages

Study on Quantum Dot Lasers and their advantages Tae Woo Kim Electrical and Computer Engineering University of Illinois, Urbana Champaign Abstract Basic ideas for understanding a Quantum Dot Laser were introduced in this paper. The discussions on laser operation, p-n junction, and quantum confinement effect will be helping understanding the Quantum Dot Laser. Also, the history and fabrication methods of Quantum Dot were introduced. Finally, the advantages of Quantum Dot Laser were predicted based on the discussions made throughout the whole paper. Keywords: Quantum Dot Laser, p-n junction, quantum confinement effect, fabrication. 1. Introduction As the portion of semiconductor laser in laser technology grows, the desire of achieving better semiconductor gain medium becomes one of the most important tasks to develop a semiconductor laser. The quantum confinement effect made a huge step forward in developing a semiconductor gain medium. Quantum Well Lasers were introduced first as an application of the quantum confinement effect. After the development of Quantum Well Lasers, the concept of the quantum confinement effect developed more and achieved 3- Dimensional quantum confinement effect which is directly related to the Quantum Dots. The development of Quantum Dots was a terrific development because of its atom-like characteristic. Because of its atom-like characteristic, many factors that make a Quantum Dot laser s characteristic became able to be controlled artificially and precisely. Other than the tunability of factors, Quantum Dot laser has many more advantages compared to other lasers and became one of the greatest laser techniques. In this paper, we will be introducing the basic idea of Quantum Dot Lasers and the related basis to understand a Quantum Dot Laser. Also, based on the discussion of basic laser operation, semiconductor operation, discussion on quantum confinement effect and the nano-structures, we will be discussing the advantages of Quantum Dot Laser that make the Quantum Dot Laser extraordinary. 2. Laser Before we start our discussion on Quantum Dot lasers, it is necessary to have an idea of how a laser operates. Also, we need to see how a semiconductor laser is different from other solid state lasers. A. p-n junction As we can see from its name, p-n junction is formed by making a contact between a p-type doped semiconductor layer and an n-type doped semiconductor layer. Since the p-type side and the n-type side of the junction are doped differently, they have different energy characteristic from each other and this

difference makes the energy characteristic of the p-n junction interesting. Figure 1. Schematic of a p-n junction with highly doped p-type semiconductor[1] and an Energy Diagram of a stable p-n junction with highly doped p-typed semiconductor Since the Fermi level, E, must be same for both p- and n- type semiconductor in a non-biased p-n junction the energy diagram of a p-n junction will have a barrier between p-type side and n-type side. This barrier makes it possible for a p-n junction to act as a current rectifier. In the discussion of semiconductor lasers, p- and n-type semiconductors act as charge carrier supplier to the active layer, which is Quantum Dot layer in the case of this study. Since we can control the amount of charge carrier by controlling the doping level for both sides, it is possible to control the power of the semiconductor laser by changing the doping level. B. Spontaneous and Stimulated Emission Spontaneous Emission and Stimulated Emission are the two major factors that operate a laser. These two emission process are the processes which provides an enormous number of photons into a laser system. Spontaneous Emission is also called as natural emission because it is a process that happens naturally without any outside factor. In a system of two or more energy level, electron can stay in the upper level for a certain amount of time called lifetime. After the lifetime, electrons emit energy in the form of either phonons or photons and moves to the lower state. Spontaneous emission radiation is caused when the released energy is in the form of photons. In the language of semiconductors, this process can be explained as an electron recombining with a hole after the lifetime. In other words, an electron reoccupies the position of the hole and emits a photon with same energy as the energy difference between the electron and the hole. Figure 2. Spontaneous Emission[2] and Stimulated Emission[3] Stimulated Emission happens when a photon with energy same as the energy difference between the two levels or the energy difference between the electron and the hole injects into the system. This photon stimulates an electron to release energy and go to lower state or recombine with a hole and release energy. Therefore stimulated emission requires one photon to be happened, and emits two photons, one of them is the injected photon and the other one is the photon emitted by the electron.

C. Laser Diode Simply, Laser diodes or Semiconductor lasers are p-n junctions that emit light. In semiconductor lasers, the conduction band and valance band work as two different energy levels. Therefore, spontaneous emission occurs when the electrons in the conduction band and the holes in the valance band annihilate together. The photons generated by this spontaneous emission process act as the injected photons for the stimulated emission process, again, for the conduction band and the valance band. These emitted photons now go into the gain medium embedded in the waveguide layers. This waveguide layers are basically the route that the generated light follows. At the two ends of this waveguide, two reflectors are placed to form a Fabry-Perot resonator which makes the photons go through the gain medium again and again. As the photons go through the gain medium, the light is amplified by the stimulated emission process[4]. Electrons can lose their energy in two different ways, photon (light) and phonon (vibration). So, to make our laser more efficient, we have to minimize the energy that emitted in the form of phonon. This is why compound semiconductors, such as Gallium Arsenide, indium Phosphide, or Gallium Nitride, are commonly used to make a laser diode because they can achieve direct bandgaps unlike single-element semiconductors such as Silicon or Germanium. Figure 3. Energy Diagram of an Indirect Bandgap[5] and and Direct Bandgap[6] In the indirect bandgap, electrons have to spend more energy to go from the conduction band to the valance band because they have to spend their energy in the form of momentum since the energy bandgap is dislocated. Therefore it is much better to use compound semiconductors for laser diodes for the sake of efficiency. 3. Quantum Confinement and Quantum Dots Quantum Dots are significant features that utilize the advantages of Quantum Confinement. As its name is saying, quantum confinement effect is caused by confinement of electron and hole in a small physical dimension which is comparable to the de Broglie Wavelength of particles. A. Quantum Confinement Consider a 1-Dimensional infinite potential well with width L, the energy that a particle with mass inside the infinite potential well will be determined by its state, n, and the well width L [7]. E 2 L 8 L Since the energy has an inverse-square dependence on the well width L, the energy will increase as the well width decreases. In other words, particles have higher energy when they are confined in a small dimension. Of course in real life, the potential well are not infinite, but the fact that the energy and the dimension are inversely dependent does not really change. So the quantum confinement will still be

effective. When the well width is much larger than the wavelength of the particle, the particle will just act like a particle in a free space, so there will be no dependence on the shape or dimension of the confining area. But once the dimension gets smaller and becomes comparable to the wavelength of the particle, the effect of this confining area on the particle takes part. This is why quantum confinement has to be considered in a small dimension. B. 1-Dimensional and 2-Dimensional Confinement Assuming that we are using a 1-dimension confined infinite well, as examined earlier, the energy of a particle inside this well will be dependent on the well width inversely. Physically, this potential well can be achieved from a thin layer surrounded by other layers with higher potential. This thin layer can be implemented between n-side and p-side of a p-n junction as quantum well. Once the particle is confined in two, small enough dimensions, in other words, if it has only one degree of freedom in motion, its energy gets higher. Basically, the energy of the particle is sum of its energy as if it is confined in one dimension. The physical realization of 2-Dimensional confinement is called Quantum Wires because it has only one dimension of freedom which looks like E, 2 L L where, are states in x dimension and y dimension The significance of 2-Dimensional confinement compared to 1-Dimensional confinement comes from the degenerated states. Since the energy function is in the form of combination of energy functions in two different axes, it is possible for a particle to have a same energy but different states. For example, if the well widths, L and L, are the same, then there are some set of numbers (states) with same energy such as m=2, n=1 state and m=1, n=2 state. The existence of degenerated states allows more particles to stay in an energy level. In other words, the density of state is higher with degenerated states than without degenerated states. State E/E0 Quantum Well Quantum Wire Quantum Dot Number of Degenerated states E/E0 Number of Degenerated states E/E0 Number of Degenerated states 1 1 1 2 1 3 1 2 4 1 5 2 6 3 3 9 1 8 1 9 3 4 16 1 10 2 11 3 5 25 1 13 2 12 1 6 36 1 17 2 14 6 7 49 1 18 1 17 3 8 64 1 20 2 18 3 9 81 1 25 2 21 6 10 100 1 26 2 27 1 Table 1. The energy and the number of degenerated states for Quantum Well, Quantum Wire, and Quantum Dot from the ground state to 9th excited states. E0 refers to the energy of a ground state particle confined in a Quantum Well. Since we want as many electrons with lower energy as possible in the conduction band to achieve higher efficiency in lasers, it is legitimate to tell that Quantum confinement effect is a useful concept for semiconductor lasers to improve its efficiency.

C. Quantum Dots Quantum Dots, or Quantum Boxes, are physical features that have no degree of freedom in momentum. In other words, it is confined in all 3-Dimensions. Similar to the case of 2-Dimensional confinement, the energy of a particle in a Quantum Dot is represented by a sum of three energies in 1- Dimensional confinement. E,, 2 L L L As showed in the Table 1, Quantum Dots are able to hold more electrons in the states with lower energy other features such as Quantum Wells or Quantum Wires. This significance gets stronger when the dimension of the dot gets smaller because of the inverse dependence of the Energy and well widths. Figure 4. Graphs of Density of State for Bulk, Quantum Well, Quantum Wire and Quantum Dot [8]. As we can see in the Figure 4., the Density of State is more quantized as the system is more confined. Furthermore, this quantization of Density of State gives higher density for lower states when the particle is more confined. Which means the Conduction band can provide more electrons and the Valance band can provide more holes to recombine. Also, the energy of the lowest states in Conduction and Valance band is higher for the features confined in more dimensions. The combination of higher energy and more electrons and holes to recombine makes Quantum Dots exceptionally efficient than other features. The Quantization of Density of State also gives a fact of Atom-like nature of Quantum Dots. This atomic nature is the key to make it possible to control the energy of emitted photons from Quantum Dots. Controllable energy means precise control of the photon wavelength which is one of the greatest advantages of a Quantum Dot Laser that makes Quantum Dot Lasers favorable among many of the laser techniques. 4. Quantum Dot Lasers With the fact that Quantum Dot provides more charge carriers, electrons and holes, it is not hard to tell that Quantum Dot makes a good gain medium for a laser, because more number of charge carriers means higher chance of carrier recombination that emits a photon with same energy as the energy difference of the electron and the hole.

A. History Quantum Dot Laser was suggested for the first time by Y. Arakawa and H. Sasaki in 1982. In their paper Multidimensional Quantum Well Laser and temperature dependence of its threshold current, Quantum Dot Laser was proposed as 3-D Quantum Well Laser that is a device with no dependence on the temperature of the device [9]. Study on a Quantum Dot Laser s characteristic was continuously done by many groups, such as gain and threshold values was done by M. Asada, Y. Miyamoto, and Y. Suematsu in 1986. Also, many theoretical developments of Quantum Dot Laser were proposed until 1990s and fabrication of actual Quantum Dot had been attempted by many groups in 1990s. Researches to advance the techniques for Quantum Dot were also started and done by many of research groups and companies like Fujitsu, which is one of the leading companies in Quantum Dot Researches. B. Fabrication Since the de Broglie wavelength of an electron is in nanometer scale, the size of a Quantum Dot must be in the nanometer scale too. Usually the size of a nanostructure that gives a quantum confinement effect is fabricated with size around 2 to 10 nm. There are three main techniques for Quantum Dot fabrication [10]. Figure 5. Quantum Dot Fabrication methods i. The first method is achieved by mixing nano-scale crystallites with smaller bandgap energy into a tub of molten semiconductor with higher bandgap energy. This method is suggested by Rocksby in 1932 and its quantum confinement effect is confirmed by Ekimov and Onushenko in 1984. ii. As an alternative to the mixing method, fabrication of Quantum Dots using Lithography has been developed. Lithographic method is the most direct method to build a Quantum Dot because of its direct patterning nature. The advantages of this techniques are (1) the size of Quantum Dot can be chosen arbitrarily depending on the lithographic technique used, (2) the continuous improvement of lithographic techniques, and (3) general compatibility with modern VLSI semiconductor technology. iii. The other method for Quantum Dot fabrication is growing. This method is also called as Stranski- Krastanov growth which is done by the self-assembling of Quantum Dot of atoms on the semiconductor substrate. This growing of Quantum Dots is achieved only when the lattice constant of

the doping medium and the substrate medium is different by a lot (higher than 8% difference). In this case, the doping medium will make a cover layer, called wetting layer, on the substrate surface and will grow in 3-Dimensional pyramid-shaped structure because of the difference of the tension between the doped layer and the substrate layer (Figure 6). When the lattice constant difference of the doping medium and the substrate medium is small, the doping medium atoms compress themselves to match the substrate lattice and form Quantum Dots. Once the Quantum Dot growing is done, the Dots will be covered by lattice-matched materials to make the Dot s energy band be embedded in the energy band of the substrate materials. Figure 6. Stranski-Krastanov growth and Strain-induced Lateral confinement [8] C. Structure and Requirements Quantum Dot Lasers need to fulfill following requirements in room temperature. i. Small Quantum Dot Size for confinement effect Quantum Dot size must exceed 2 to have at least one energy level that has an electron or a hole [10]. ii. Uniform Quantum Dot shape and size

Figure 7. Broadening effect caused by non-homogeneous Quantum Dots Since the energies of the particles confined in a Quantum Dot are dependent on the shape and size of the Quantum Dot, non-uniform Quantum Dots gives different energy for the electrons. This fact results to different energy and wavelength of the emitted photons and finally results to the broadening of the wave. Therefore the laser will lose its preciseness in controlling the wavelength which is one of semiconductor laser s advantages. iii. No defects in between materials Since the device is in nanometer scale, defects in the device can cause a big degradation of the device. The structure of a Quantum Dot Laser is not really different from other lasers. Figure 8. Schematic of a laser cavity In the schematic, the couplers are basically mirrors that make the light travel more than one round trip inside the cavity. Since the Output coupler s reflection constant is 80%, 20% of the light that arrives at the output coupler will be emitted when the cavity lases. The Active Medium, in other words gain medium, is where the stimulated emission happens to generate more photons. Also, pumping process gives enough population inversion between energy bands so that the population distribution of charge carriers will

fulfill the lasing condition. As a result of the round trip of the light, pumping process, and light amplification, the loss of light at the output coupler is recovered with the gain and the cavity becomes able to emit continuously and constantly. Figure 9. Energy diagram of a Quantum Dot Laser [12] As we can see in the energy diagram, the energy band of the Quantum Dot layers is much lower than the semiconductor cladding layers. This structure is achieved so that the semiconductor cladding layers can supply charge carriers to the Quantum Dot layer for the annihilation. As a summary, a Quantum Dot Laser has three main components. The Couplers, Pumping source, and the Quantum Dot gain medium. The way how a Quantum Dot laser operates is almost same as any other lasers because the process is basically emitting light that has been amplified by the round trips made by couplers, pumping source and the gain medium. Therefore a Quantum Dot laser is basically a laser with Quantum Dot as its gain medium. 5. Advantages of Quantum Dot Lasers Based on the discussions that we had so far, we were able to predict or deduce five advantages that a Quantum Dot Laser has. A. Tunable wavelength Unlike other lasers, the energy of photon from a semiconductor laser, including Quantum Well, Quantum Wire, and Quantum Dot laser, is determined by the bandgap while the energy of photons from different kind of lasers is determined by the energy level. With the fact that a bandgap of a Quantum Dot can be tuned by changing the material, we can predict that the energy of a photon from a semiconductor laser can be tuned by changing the Quantum Dot materials used in the laser. B. Higher gain As a result of its quantized density of state and higher density of the charge carriers compared to those of Quantum Well or Quantum Wire lasers, a Quantum Dot laser allows higher chance of stimulated emission than any other semiconductor lasers. In other words, there is higher probability for an injected photon to stimulate an electron to emit a photon. Therefore it gives higher gain than other semiconductor lasers. C. Small volume Because of its 3-Dimensionally confined nature, a Quantum Dot laser can be built in a smaller volume than a Quantum Wire or a Quantum Well laser. This fact results into a smaller laser cavity size and it gives following advantages. i. Low power and low threshold current are needed to operate the laser cavity ii. Higher frequency can be achieved from the laser iii. Sharper emission peak can be achieved D. Temperature independence As discussed earlier, Quantum Dot has almost no temperature dependence. Therefore the laser that

uses Quantum Dot as its gain medium also has almost no temperature dependence. This fact can be characterized by temperature stability of the threshold current to operate the laser cavity. I T I T e T T T where T is the temperature, T is the reference temperature, and T is the characteristic temperature that is experimentally determined Since T is really high in Quantum Dot lasers, the Temperature in the exponential part of the equation will have only a little effect on the threshold current. E. Reduced leakage Since Quantum Dots are confining the charge carriers in themselves, they prevent the charge carriers from diffusion effect. Therefore there will be less charge carriers that are not used due to the diffusion and it results into the reduced leakage of the carriers. 6. Conclusion Based on the discussions that have taken placed in this paper, Quantum Dot Laser is a laser that takes a lot of advantages from Quantum Confinement Effect. Using Quantum Dot as its gain medium, a laser can become tunable, efficient, smaller, and temperature independent. These advantages are the main advantages of a Quantum Dot laser and they make a Quantum Dot laser extraordinarily better than other semiconductor lasers. Since many of fabrication methods to make Quantum Dots are being developed and improved, there is high possibility of improving the advantages Quantum Dots to make them superior gain media for a laser. Therefore, Quantum Dot laser can still be considered as a developing field of engineering.

Reference [1] Wikipedia, available online at http://en.wikipedia.org/wiki/p-n_junction [2] Wikipedia, available online at http://en.wikipedia.org/wiki/spontaneous_emission [3] Wikipedia, available online at http://en.wikipedia.org/wiki/stimulated_emission [4] J. Verdeyen, Laser Electronics, Prentice Hall, 1994 [5] Wikipedia, available online at http://en.wikipedia.org/wiki/indirect_bandgap [6] Wikipedia, available online at http://en.wikipedia.org/wiki/direct_bandgap [7] D. Griffith, Introduction to Quantum Mechanics, Benjamin Cummings, 2004 [8] M. Datta, Z. Dilli, and L. Wasiczko, Quantum Dot Lasers [9] Y. Arakawa and H. Sasaki, Multidimensional Quantum Well Laser and temperature dependence of its threshold current, 1982 [10] D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures, Wiley, 1999 [11] H. Diwu and B. Arda, Quantum Dot Lasers [12] B. Agnarsson, Quantum Dot Lasers lecture in modern optics by Bjorn Agnarsson [13] V. Ustinov et al., Quantum Dot Lasers, Oxford University Press, 2003 [14] L. Banyai and S. Koch, Semiconductor Quantum Dots, World Scientific Publishing, 1993 [15] B. Webb, Quantum Dots, Utah State University [16] B. Streetman and S. B. Banerjee, Solid State Electronic Devices, Prentice Hall, 2006