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Semiconductor nanodevices Semiconductor nanodevices Document Transcript

  • SEMICONDUCTOR NANOSTRUCTURESBY: ATIF SYED
  • Atif SyedSemiconductor Nanostructures11. Introduction and Short History about Semiconductors:Semiconductors are one of the widely used and building blocks of the modern dayelectronics. Its ability to change its properties by adding impurities (known asdoping) has led to toggle its properties from being a conductor or insulator since theconductivity ranges in between103− 10−8𝑠𝑖𝑒𝑚𝑒𝑛𝑠/𝑐𝑚.The introduction of Semiconductors in Nanotechnology leads to a new division ofSemiconductors known as Semiconductors Nanostructures. Ever since the firsttransistor was invented in Bell Labs by Shockley, Bardeen, and Brattain, theminiaturization process of the transistors was already started and it was in 1949when the first pnp transistor was invented by Shockley which is similar to thepresent day bipolar transistors. By 1970, the transistors were scaled down to as lowas 10 µm. This introduces the concept of Moore’s law where he predicted that thesize of transistors will decrease exponentially. If we assume that is true, then within5-10 years the structure sizes will reach of the order of the electron’s wavelength(lhn, 2010, p. 4). Figure 1 shows a general form of the applications of SemiconductorNanostructures. When we look into nanostructures, quantum effects take place.This will discussed further in the report.SemiconductorNanodevicesQuantumComputingOpticalSciencesMaterialSciencesQuantumMechanicsLowTemperaturePhysicsElectronics Medicine Nano-RobotsFigure 1: A general overview of Semiconductor Nanostructures applications
  • Atif SyedSemiconductor Nanostructures22. Basic Physics in Semiconductor Nanostructures:Before the physical properties of the semiconductor nanostructures are discussed, theinitial background behind this lies in the De-Broglie’s Wavelength equation given by𝝀 =𝒉𝒑2. 1This leads to the introduction of the state function which is simply a form of a wavewhich is in absence of any electromagnetic potential. Thus an electron in a vacuum at aposition s can be described as:𝝍 = 𝒆𝒊( 𝒌.𝒔−𝝎𝒕)2. 2Where 𝜔 is the angular frequency and 𝑡 is the time and 𝒌 is given by:𝒌 = | 𝒌| =𝟐𝝅𝝀2. 3The momentum described here is a quantum mechanical momentum which is given by:−𝒊ħ𝛁𝝍 = 𝒑𝝍 2. 4Where ∇ is given by:𝝏𝒊̂𝝏𝒙+𝝏𝒋̂𝝏𝒚+𝝏𝒌�𝝏𝒛2. 5This leads to the time dependant 𝑆𝑐ℎ𝑟𝑜̈ 𝑑 𝑖𝑛𝑔𝑒𝑟′𝑠 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 which is also associated with theDe-Broglie’s Wave-particle duality and is given by:𝒊ħ𝝏𝝍𝝏𝒕= 𝑬𝝍 2. 6Where E is the total energy which is equal to the Kinetic Energy (K.E) of an electron in avacuum which is given by:𝑬 =ħ 𝟐 𝒌 𝟐𝟐𝒎2. 7Where m is the mass of electronFigure 2 gives an approximate by using the equations of energy and the wave vector.
  • Atif SyedSemiconductor Nanostructures32.1 Quantum Wells:The idea behind quantum wells is that it is a potential/quantum confinement wellwith finite/discrete energy values which is comparable to the electrons and holeswhich in turn exhibit the so called 2-Dimensional Properties in quasi nature. Thefabrication of quantum wells are done by using GaAs sandwiched with AlAs. Thefabrication of quantum wells is discussed in the later sections of the report. Toexplain the working of quantum well, the concept of Heterostructures andHeterojunctions is important.2.1.1 Concept of Heterostructures, Heterojunctions andEffective Mass Approximation:If we consider that the crystal potential of any nanostructure can be derived through aconstant value, then the 𝑆𝑐ℎ𝑟𝑜̈ 𝑑 𝑖𝑛𝑔𝑒𝑟′𝑠 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 will be valid and the equation 2.6becomes, where 𝑚∗is the effective mass approximation:ħ 𝟐𝟐𝒎∗ 𝛁 𝟐𝝍 = 𝑬𝝍 2. 8Using the idea behind equation 2.8, Heterojunctions are nothing but 2 differentsemiconductors placed adjacent to each other and Heterostructures are formed by 2 ormore HeterojunctionsEkFigure 2: Energy of an electron in vacuum versus wave vector curve
  • Atif SyedSemiconductor Nanostructures42.2 Quantum Wires and Quantum Dots:A quantum wire is just like any other electrically conducting wire which exhibits 1-Dimensional properties in quasi nature and the quantum effects are affecting thetransport of current. The difference is that the resistivity is not calculated using theclassical formula but instead it is calculated through the transverse energies of theconfinement of electrons. A point to note is that the dimensions are simply an indicationto the degree of freedom of electron momentum therefore in quantum wires theelectron is confined in 2 directions as compared to only 1 in quantum wells. A quantumdot on the other hand is a semiconductor whose degree of freedom is confined in 3directions hence leaving 0 Dimensions. Therefore the degrees of freedom can beexpressed by the equation given below:𝑭 𝒇 + 𝑭 𝒄 = 𝟑 2. 9Where 𝐹𝑓 and 𝐹𝑐 stand for degrees of freedom and direction of confinementrespectively.The following table describes equation 2.9 for different dimensional systems:System 𝑭 𝒇 𝑭 𝒄Bulk Material 0 3Quantum Well 1 2Quantum Wire 2 1Quantum Dot 3 0Table 1: Equation 2.9 compared by different systemsFigure 3: Quantum Wire showing the single degree offreedom (Harrison, 2005, p. 245)
  • Atif SyedSemiconductor Nanostructures52.3 Comparing the Density of States of Nanostructures:The density of states is nothing but the ratio of the number of states per energy ofreal space. It is given by the equation below:𝑺( 𝑬) =𝒅𝑵𝒅𝑬2. 10Where 𝑁 is defined as:𝑵 = 𝟐𝟒𝝅𝒌 𝟑𝟑( 𝟐𝝅) 𝟑 2. 11If we combine equations 2.10, 2.11 and 2.8 we will get:𝑺( 𝑬) =𝟏𝟐𝝅 𝟐 �𝟐𝒎∗ħ 𝟐 �𝟑𝟐√ 𝑬 2. 12Similarly the density of states equation for 2D, 1D and 0D can be obtained:𝑺 𝟐𝑫( 𝑬) =∑𝒎∗𝝅ħ 𝟐 𝑯(𝑬 − 𝑬 𝒏) 2. 13𝑺 𝟏𝑫( 𝑬) =∑𝒎∗𝝅ħ�𝒎∗𝟐( 𝑬−𝑬 𝒏)2. 14𝑺 𝟎𝑫( 𝑬) = 𝟐(𝑬 − 𝑬 𝒏) 2. 15Where 𝐸 𝑛 is the nth energy level and 𝐻 is the Heaviside function.Figure 4: Quantum Dot showing the zero degree offreedom (Harrison, 2005, p. 246)
  • Atif SyedSemiconductor Nanostructures6The density of states can be drawn as follows:yxzFigure 5: 3D Density StatexyFigure 6: 2D Density State
  • Atif SyedSemiconductor Nanostructures7The major differences between the nanostructures and the 3D structures (bulk) can beexplained through the table and the graph below:𝑭 𝒇Density of States Formula3 (3D)𝑆( 𝐸) =12𝜋2�2𝑚∗ħ2�32√𝐸2 (2D)𝑆2𝐷( 𝐸) =∑𝑚∗𝜋ħ2𝐻(𝐸 − 𝐸 𝑛)1 (1D)𝑆1𝐷( 𝐸) =∑𝑚∗𝜋ħ�𝑚∗2( 𝐸 − 𝐸 𝑛)0 (0D)𝑆0𝐷( 𝐸) = 2(𝐸 − 𝐸 𝑛)xFigure 7: 1D Density StateTable 2: Comparison of Density of States of 3D, 2D, 1D and 0DFigure 11: 3D Figure 8: 0DFigure 9: 1DFigure 10: 2DS(E) S(E) S(E) S(E)E E E E
  • Atif SyedSemiconductor Nanostructures82.4 Fermi-Dirac Distribution Function and the Concept ofFermi Energy/Level:The Fermi-Dirac probability function describes the electron occupation states. This indetail can be explained occupation of electron states at some finite temperature andis given by:𝒇( 𝑬) =𝟏𝟏+𝒆𝑬−𝑬 𝒇𝒌𝑻2. 16Where 𝑘 is the Boltzmann’s constant and 𝑇 is the temperature in Kelvin.𝐸𝑓 is the Fermi Energy or Fermi Level. It is determined when the temperature is 0 andequation 2.16 yields ½. The electron probability for 150K, 300K, 600K and 0K is givenbelow assuming that the energy is 8eV and we are supposed to find the electronprobability at 8.1eV.𝒇( 𝟖. 𝟏𝒆𝑽, 𝟏𝟓𝟎𝑲) =𝟏𝒆�(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟏𝟓𝟎�+𝟏≈ 𝟎. 𝟏 2. 17𝒇( 𝟖. 𝟏𝒆𝑽, 𝟑𝟎𝟎𝑲) =𝟏𝒆�(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟑𝟎𝟎�+𝟏≈ 𝟎. 𝟐 2. 18𝒇( 𝟖. 𝟏𝒆𝑽, 𝟔𝟎𝟎𝑲) =𝟏𝒆�(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟔𝟎𝟎�+𝟏≈ 𝟎. 𝟏𝟒 2. 19𝒇( 𝟖. 𝟏𝒆𝑽, 𝟎𝑲) =𝟏𝒆�(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟎�+𝟏= 𝟎. 𝟓 2. 20
  • Atif SyedSemiconductor Nanostructures93. Fabrication of Quantum Wells, Wires and Dots:Before the concept of fabrication is discussed, it is important to know how Silicon (Si) isextracted.3.1 Silicon Extraction:The earth’s crust contains around 28% of Silicon on its crust and in production; Silicon ismade from Silica by burning it around 2000 𝑜𝐶 and reducing it from Carbon whichfollows the following chemical reaction:𝑺𝒊𝑶 𝟐 + 𝟐𝑪 → 𝑺𝒊 + 𝟐𝑪𝑶 Chemical Reaction 3. 1The above equation is the most common form of extracting Silicon. There are manyother methods of extracting Silicon. This brings us to the concept of Layer by Layergrowth and one of these methods is known as Molecular Beam Epitaxy (MBE) Growth.3.2 Molecular Beam Epitaxy (MBE):If we have a Silicon Wafer present, one could grow crystals with the MBE growthmethod. So as to explain the method in detail and to give a broader point of view,one would say that it is a refined evaporation technique which requires a pressureof 10−10− 10−11𝑚𝑏𝑎𝑟. The solid particle is placed in the evaporation chamber insuch a way that the distribution of atoms can take place. The particle is constantlyrotated so that the distribution of atoms can be even which in turn improves thegrowth pattern. An Ultra High Vacuum (UHV) chamber is used in MBE. The furtherpart of the process deals with the concept of the Crystal Lattices. The atomic beamhits the heated substrate and the atoms stick to the substrate. They will diffuse onthe surface only after gaining an acceptable place in the Crystal Lattice1. Normallythe growth procedure takes place at 500 𝑜𝐶 − 600 𝑜𝐶 and the growth rate isabout 1𝜇𝑚/ℎ𝑟. At UHV, the In-situ analysis of crystal growth takes place. This callsthe method known as RHEED (Reflected High Energy Electron Diffraction). Thismethod is carried out by scattering the electron beam and observing the pattern ona fluorescent screen2. In MBE growth, the intensity of RHEED is rotated periodically.1Lattices are infinite set of points which are given by the Bravais Lattice Equation𝑹 = 𝑛1 𝑎1 + 𝑛2 𝑎2 +𝑛3 𝑎3. In Crystal Structure, the atoms are arranged in a particular way which shows some kind ofsymmetry and the patterns are then seen and explained through the lattices. This is collectively known asCrystal Lattices.2A fluorescent screen is a sheet coated with a fluorescent material which emits visible light when it is hitby radiating beams such as X-ray or E-Beam.
  • Atif SyedSemiconductor Nanostructures103.2.1 Advantages and Disadvantages of MBE:MBE’s main advantage is the ability to control the layer thickness on a very minutescale. The growth is homogeneous in nature and the homogeneity is maintained bythe process of rotation of the substrate. An interesting point to note is that since thesubstrate are grown, for example, a quantum dot grown in MBE is known as SelfAssembled Quantum Dots (SAQD) and they have their own interesting propertiesdiscussed later in the report.MBE’s main disadvantage is the cost and maintenance of the machine. MBE’s can bevery complex at times and due to its strict vacuum procedures and requirements, itcan be a bit expensive and time consuming.3.3 Optical and Electron Beam Lithography and their limits:Ever since the miniaturization trend started three decades ago, semiconductorstoday are produced with 60-65 nm dense features. Optical Lithography has enabledthis process to be seen more clearly at the sub-atomic level. Today most IntegratedAsCracker CellShutterMBE ChamberSampleTo PumpsRHEEDEffusion CellFigure 12: Schematic diagram of MBE and important labeling.Ga
  • Atif SyedSemiconductor Nanostructures11Circuits (IC) have been patterned using this technique. The pattern is transferred towhat is known as “mask” which is then placed on a thin layer of Photoresist3.Optical Integrator4Photomask5Projection Lens∅Wafer3A Photoresist (DiazoNaphtoQuinon-(DNQ) Sulfonate) is a photosensitive material which reacts to lightand Inden Carboxylic Acid.4An Optical Integrator is used to evenly distribute a light source un-diverted and un-disrupted.5A Photomask is an opaque plate with holes or transparencies that allow light to shine through in adefined pattern. They are commonly used in photolithography (Photomask: Wikipedia, 2011)LaserCondenser LensFigure 13: Schematic Diagram of OpticalLithography. The Optical Integrator andCondenser Lens are collectively known as theIlluminator
  • Atif SyedSemiconductor Nanostructures12In Figure 13, the laser light is directed towards the optical integrator which then divertsthe light into the condenser lens. The Optical Integrator and the Condenser arecollectively known as the Illuminator. This process expands the beam which is passedthrough the Photomask. The Photomask patterns the image to be imaged onto thewafer substrate. The Photoresist is present on the wafer. The Projection Lens is presentthere to reduce the projection pattern by 2-5 factor which finally is directed to thewafer. The following diagram summarizes the optical lithography process.On the other hand, Electron Beam Lithography is done through the scattering ofelectrons through a beam on the resist (similar to the optical beam lithography). E-BeamLithography is also used to create nanostructures which are then transferred into thewafer (substrate) by the etching method.Due to the fact that the e-beam lithography’s beam can be controlled and directed inonly one direction, it is preferred usually in many research facilities all over the globe. Itcan be written down up to 30-40 nm structures. Similar to the Optical Lithography,resists are used. In EBL, one of the most common resist which is used is PMMA(Polymethyl Methacrylate) and the common name for this is acrylic. This brings to theconcept of different types of resists:- Positive Resists are dissolved in the open areas during the development.- Negative Resists are dissolved in the closed areas during the development.Cleaning of theWaferSpinning ofPhotoresistExposure toUVResistDevelopmentEtching of theSemiconductorFigure 14: Process of Optical Lithography
  • Atif SyedSemiconductor Nanostructures13One interesting thing to note is that e-beam lithography is done by using ScanningElectron Microscope (SEM) and Scanning Tunneling Electron Microscope (STEM).Since SEM had a resolution of about 10nm, the need for more powerful resolutionled to the introduction of Scanning Tunneling Electron Microscope (STEM) which hasa resolution of about 100nm with very less scattering of high energy electrons andsmaller electron probe diameter. The reduction of exposure has lead to higherresolution images.Just like in Photolithography6, positive and negative resists are used in e-beamlithography. In e-beam lithography, electrons are used instead of photos on theresist. EBL has more resolution because the wavelength of electrons is smaller thanphotons. Another difference from optical lithography is that electrons can be morefocused on the substrate (e.g. Si wafer) and only the areas which we are interestedin can be exposed. This in turn eliminates the need of mask in EBL. The electronscattering on the other hand is done in two ways described below:- Forward Scattering: In this, the electron path is deflected by the Coulomb’sPotential7which forces the trajectory to be in a cone like shape.- Backward Scattering: In this, the electron path is deflected at an angle greaterthan 90 𝑜which forces the electrons to go back and focus a much wider area.The SEM has relatively low beam energy roughly about 10keV but can go up to30keV. This creates a new problem called back scattering in EBL’s. For example, thebackscatter will expose the entire area between them hence the accuracy is lost inthe process. Hence the need of STEM is more preferable despite the fact that manyEBL’s do not currently have STEM technology.6Optical Lithography is also known as Photolithography7Coulomb’s Potential is a scalar point which is equal to work per unit charge and is represented by theequation14𝜋𝜀 𝑜𝑞1 𝑞2𝑟where 𝑞1 𝑎𝑛𝑑 𝑞2 the electric charge are by 2 ions and r is the distance between them.Resist ElectronsLensFigure 16: Backscattering of ElectronsFigure 15: Front Scattering of Electrons
  • Atif SyedSemiconductor Nanostructures14The following table shows the basic limits and differences of Optical and E-BeamLithography.Electron Beam Lithography Optical LithographyBest used for hard and complex shapesand patternsBest used for huge and large shapes andpatternsThe ability to expose it to the point wherewe are interested and to be able to gethigh resolutionThe ability to expose parallel and to beable to get high resolutionSlow Speed Fast SpeedResolution 10nm by SEM or 100nm bySTEMResolution 50nm-100nmNot limited to Diffraction Limited to DiffractionElectron GunLensSubstrateAperture (typically includes 3apertures and 1 deflector)Figure 17: Basic Schematic Diagram of Electron Beam LithographyTable 3: Limits and differences of Optical and Electron Beam Lithography
  • Atif SyedSemiconductor Nanostructures154. Characterization of Semiconductor Nanostructures:Semiconductor Nanostructures have unique and very useful characteristics. One of themain characterizations and important Physical property is the Electron Transport. Theelectron transport is better achieved by using III-V elements in the periodic table andmore preferably Si. Of all the things discussed in the report, the spin of electron hasbeen neglected. With the introduction of band structures playing a major role in thecharacterizations, the Bloch Theorem and the Band Structure equation will be discussed.4.1 Bloch Theorem and the Band Structure Equation:The band structure has the property of the 𝑆𝑐𝑟𝑜̈ 𝑑 𝑖𝑛𝑔𝑒𝑟′𝑠 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 which is given by:�−ħ 𝟐𝟐𝒎∆ + 𝑽( 𝒈)� 𝝍( 𝒈) = 𝑬𝝍( 𝒈) 4. 1Where 𝑉( 𝑔) is given by:𝑽( 𝒈) = 𝑽(𝒈 + 𝑮) 4. 2And G is an arbitrary vector that moves the lattice by itself. If we apply Fouriertransform to equation 4.2, the final band structure equation is given by:�−ħ 𝟐𝟐𝒎∆ + ∑𝑽 𝒓 𝒆𝒊𝑮𝒓� 𝝍( 𝒈) = 𝑬𝝍( 𝒈) 4. 3One important approximation in the band structures is the Tight-Binding Approximation.4.2 Tight-Binding Approximation:It regards the atoms in the lattice as weakly interacting, such that the atomic orbitalremain (almost) intact. The wave function for electrons in a particular band is alinear combination of degenerate wave functions that are not too different fromatomic wave functions. The linear combination is chosen such that the wavefunction fulfills Bloch’s theorem (lhn, 2010) (Ashcroft, Neil W, Mermin, David N,1976). One of the most important and useful approximation led to the calculation ofGraphene structures. Graphene is a 2-D plane of carbon atoms that are arranged inthe shape of a honeycomb. Graphene shows an excellent quantum Hall Effect(Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva,I.V., Dubonos, S.V., and Firsov, A.A., 2005) which will be discussed later in thissection.
  • Atif SyedSemiconductor Nanostructures164.3 Characterization Techniques:There are many techniques and the most frequently used are discussed below:4.3.1 Optical Spectroscopy:As discussed in section 3 where we discussed about the Optical Lithography and itslimits and advantages, we can see that optical techniques are very useful in solid dueto their speed and that it can be easily manipulated hence the examination of thetopography, different parts of a structure can be easily determined. This methodcreates 2-D map properties which in turn mean that the layer thickness or theimpurity distribution can be seen with finest details. 3-D mapping is also possible inthis technique if the light propagates perpendicular to its surface and thepenetration depends solely on the wavelength of the light.4.3.2 Raman Spectroscopy:Raman Signals are usually weak as compared to the excitation intensity. In Figure 18,the laser light enters the system and the light is passed through the lens A whichconverges the beam into about 10𝜇𝑚 pinhole. The lens C present in the figure makesthe laser light so as to spot the laser width and that the laser light since the lens C isLaserPinholeCCDdectectorBeam SplitterDBGACFEFigure 18: Schematic of Raman Spectroscopy Microscope
  • Atif SyedSemiconductor Nanostructures17movable. The mirrors reflect the beam into the optical path of the microscope. Thesample can then be observed through the eyepieces which has a focus on the sample.After the light has been passed through the CCD, the Rayleigh light is completelyremoved due to the total backscattering of the light (laser) which makes the Raman lightthe only visible light through the eyepiece. The CCD (Charged Coupled Device) cameraconverts each pixel falling inside the camera into a charge. After the exposure of CCD tothe beam, it emits Photoelectrons. All of the data results can be seen on the computerwhere the measurements and the data can be stored for further use. The conversion ofpixels into charge is done due to the fact that the CCD has rectangular 2-D Arrays.4.3.3 Photoluminescence:PL is one of the most useful optical methods for analyzing the intrinsic and extrinsicproperties of the semiconductors. This process absorbs photon which results in highelectronic energy states. While returning back to the low energy state it again emitsa photon. This process helps in identifying the impurities in the semiconductorswhich affects the material’s properties and performance.4.3.4 Tunneling Electron Microscopy (TEM):By the use of TEM’s one could get the information about the topography such assize, shape, composition, crystal structures etc. The working of TEM is fairly simple;the laser beam in the TEM is emitted through the electron gun and is manipulatedusing a magnetic lens. After this the images of the sample can be formed by theexcitation of electrons which follows a similar concept of E-Beam Lithography butcontrary to optical methods, this method uses a magnetic lens.4.3.5 Electron Transport in Quantum Dots:Electrons act like a wave in Quantum Dot which in turn plays the role of partialwaves of light. The electron transport in quantum dots is seen in the following twoways/scenarios:- Two Quantum Dots connected in Parallel- Two Quantum Dots connected in Series4.3.5.1 Two Quantum Dots connected in Parallel:The main idea behind this is that the quantum dots are connected in parallel so thatthey eventually allow current to flow either or both QD’s with resonance which inturn creates electrochemical potential. Another experiment with this includes two
  • Atif SyedSemiconductor Nanostructures18quantum dots were connected in parallel with finite tunneling coupling betweenthem were performed (Hofmann, F., Heinzel, T., Wharam, D.A., Kotthaus, J.P., Bohm,G.,Klein, W., Trankle, G., and Weimann, G., 1995). Quantum dots connected inparallel with mutual tunneling coupling can also be realized by vertical stacking (lhn,2010).4.3.5.2 Two Quantum Dots connected in Series:Quantum Dots are connected in series is entirely different from the parallelconnection. Series connections are more often found in today’s electronic devices. Ifwe are to achieve the electron flow at low source-drain bias, it is only possible byusing triple points of charge stability.In Figure 19, the Coupled Quantum Dots are arranged in such a way that the 2 dotsare perfectly aligned with each other with the electrochemical potential in betweenthe leads. The transfer of electrons in this configuration is done elastically. InFigures 20 and 21, the alignment is done only in one Quantum Dots. In this typearrangement, the electron transfer from source to the drain is done due to the weaktunneling coupling between the leads and the dots. The coupling between thequantum dots and the leads can lead to different characteristics. Stronger couplingcan be achieved by increasing the gate voltage8. For weaker coupling, the transporthappens only at the triple points. If we try to increase the coupling even further, thephenomenon known as quantum dot regime is observed.8Gate Voltage is the voltage applied to the gate of the electrode in a Field Effect Transistors (FET’s). GateSource voltage on the other hand is the direct current voltage between the gate and the sourceelectrodes.Dot 1 Dot 2Dot 1 Dot 2 Dot 1 Dot 2Figure 20: Last QD’s alignedFigure 21: 2 QD’s aligned Figure 19: First QD aligned
  • Atif SyedSemiconductor Nanostructures195. Applications of Semiconductor Nanostructures:Semiconductor Nanostructures are used in many applications. Since the field is quitevast, this report will be brief and will cover some interesting applications.5.1 Quantum Information Processing:Information processing in general is based on physical systems and processes. Ever sincethe exchange of information has started, this field has seen enormous amount ofachievement and merits. But as time passes by and with the introduction ofnanotechnology, the shrinking and miniaturization process of everything has started,the biggest question arises, does the laws of Quantum Physics change the way we seethe information processing now? If yes, then how is it possible? More questions like, canwe transmit radio signals, electron by electron and photon by photon? Can we use theelectron spin and do much more complicated calculations much better than what weare able to today? Many more questions like this can be answered and we will try tounderstand the concept behind all this and how this can be achieved.5.1.1 The Classical Bit:The information processing is an entirely probabilistic entity. Keeping this in mind andgetting inspired from (lhn, 2010) and (Timpson, 2004) the following example can begiven to better explain this concept. If we assume that there are X number of possibleoutcomes that can occur with a probability of 𝑝 =1𝑥and we give the outcomes beforeand after the uncertainty has occurred as 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 𝑎𝑛𝑑 𝑄 𝑎𝑓𝑡𝑒𝑟 respectively then thefollowing equation is valid:∆𝑮 = 𝑸 𝒃𝒆𝒇𝒐𝒓𝒆 − 𝑸 𝒂𝒇𝒕𝒆𝒓 5. 1With this concept in mind9, the Shannon Entropy is given by the equation:𝑯({ 𝒑𝒊}) ≡𝑸𝑵= −∑𝒑𝒊 𝒍𝒐𝒈 𝟐 𝒑𝒊 𝒃𝒊𝒕 5. 29For simplicity and compactness sake, the derivation is not given in this report but can be found in manyQuantum Computers/Information Processing textbooks.
  • Atif SyedSemiconductor Nanostructures20Where N is the total number of outcomes and 𝑝𝑖 is the different possible probabilities.With this, the unit of measurement for Shannon Entropy is the bit as mentioned inequation 5.2.The classical bit can now be defined in terms of quantum physics and by using the DiracNotation10. If we want to use the Dirac Notation on the binary bit 00102 it will bewritten as|0010 >. Classical bits can be represented, copied and transferred n numberof times. But with the introduction of Qbits, the evolution process has already started.Quantum Computer promises much advancement like better memory management,more information stored on minute sizes and this information can be stored without theneed of actually destroying them ever.5.1.2 Quantum Bits (Qbits):The smallest Hilbert space suitable for information storage is spanned by twoorthogonal quantum states (lhn, 2010). A qbit is represented by the superposition oftwo bits. In other words, the classical bit 0 and 1 can be used twice or together by thesuperposition and this is achieved by the theory of Spin Theory and Azimuthal QuantumNumbers. The Qbits can be represented by using the Dirac Notations, one general formof this given below:| 𝝍 > = 𝜶 𝟎| 𝟎 > +𝜶 𝟏|𝟏 > 5. 3With reference to equation 5.3, a feature called normalization feature occurs which isnothing but the sum of the squares of the 2 state bits is always equal to 1:𝜶 𝟎𝟐+ 𝜶 𝟏𝟐= 𝟏 5. 4If the wave functions of the two bits cannot be written as the product of two single bits,then it is called as entanglement or entangled bits which are given by the followingexample:|𝝍 > =𝟏√ 𝟐(|𝟎𝟎 > ±|11 >) 5. 5A qbit can be represented by using a spherical diagram known as the Bloch sphererepresentation. To explain that in a better way, density matrix of a single quantum bitcan be written as:10A Dirac Notation is a representation of two quantum states where one is represented by bra <|x andthe ket y|>.
  • Atif SyedSemiconductor Nanostructures21𝝆� =𝟏𝟐�𝟏 + 𝑷 𝒛 𝑷 𝒙 − 𝒊𝑷 𝒚𝑷 𝒙 + 𝒊𝑷 𝒚 𝟏 − 𝑷 𝒛� 5. 6Where,𝑃𝑥 = sin 𝜃 cos 𝛿𝑃𝑦 = sin 𝜃 sin 𝛿𝑃𝑧 = cos 𝜃|𝜓 >𝜃𝛿|0>|0>-|1>|0> - i|1>|1>|0>|0> + |1>Figure 22: Quantum Bit represented as a sphere following the Bloch Spherical Representation
  • Atif SyedSemiconductor Nanostructures22Figure 23: Prototype of a Quantum Computer (lhn, 2010) (Bucktard, G., Engel, H.-A., and Loss, D., 2000)As far as the uses of quantum computers are concerned, it is pretty much told by theamount of possibilities quantum computers can bring about in the computer industry.With Quantum Computers, every computer can be a super computer because trillions ofcalculations can be done with very few quantum bits, for example 9 qbits represent 512values and 10 represents 1024 and so on, doubling the number of values in eachincrease of quantum bit. With this in mind, calculating a trillion worth of values will onlytake probably around 40 qbits which is 100,000 times less bits used as compared totoday’s classical bits. "A supercomputers going to take trillions of steps, and thisalgorithm will take a few hundred," says mechanical engineering professor Seth Lloyd,who along with Avinatan Hassidim, a postdoc in the Research Lab of Electronics, and theUniversity of Bristols Aram Harrow 01, PhD 05, came up with the new algorithm(Quantum computing may actually be useful, 2009). With qubits, however, "you canmake any measurement you like," Lloyd says, "You can figure out, for instance, theiraverage value. You can say, okay, what fraction of them is bigger than 433?" Suchmeasurements take little time but may still provide useful information. They could,Lloyd says, answer questions like, "In this very complicated ecosystem with, like, 10 tothe 12th different species, one of which is humans, in the steady state for this particularmodel, do humans exist? Thats the kind of question where a classical algorithm canteven provide anything." (Quantum computing may actually be useful, 2009). To yieldaccurate results, a weather prediction model might require data from millions ofsensors transmitted continuously over high-speed optical fibers for hours. Suchquantities of data would have to be loaded into quantum memory, since they wouldoverwhelm all the conventional storage in the world. Once all the data are in, however,the resulting forecast needs to be calculated immediately to be of any use. (Quantumcomputing may actually be useful, 2009).
  • Atif SyedSemiconductor Nanostructures235.2 Nanorobotics:Nanorobots are another important and very interesting application in the field ofnanotechnology. There are many applications of Nanorobots and this report willfocus on some of them. Just like its counterpart, macro robots, Nanorobots alsofollow some of the same concepts.5.2.1 Working of Nanorobots and its applications:The main idea behind Nanorobots is the construction and fabrication of robots atnano scale. The challenges hidden behind this are:- Construction of robots at nano scale- Programming the robots- Manipulation and Self-Assembly of NanorobotsThe dimensions of Nanorobots are comparable to that of cells and organelles andhence the biggest useful application of Nanorobots is in the field on medicine knownas bio Nanorobots. Just imagine that (Nanorobots) patrol the blood circulatorysystem and destroy any harmful pathogens without them causing any harm to thehuman body or may be able to repair the damaged cells.5.2.2 Design, Control and Programming of Nanorobots:In this section we will focus briefly on the working on Nanorobots step by step.Sensors:Just like a normal robots, Nanorobots will also use sensors. A true nanoscale sensordoesn’t exist but according to Kong who says, “A device that exploits the change inconductivity of a carbon nanotube when it is exposed to a specific gas is perhaps theclosest to a true nanosensor” Many things like bacteria or chemical sensors can beused for the Nanorobots sensors but it is still under research.Actuators:- Artificial Molecular Machines:There is a good progress in this part of the research. These machines are eithersingle molecules or supramolecular systems of interlocked molecules. In either case,they are atomically precise, that is, each atom is in a known and preciselyestablished location with respect to the others (Nanorobots, NEMS and
  • Atif SyedSemiconductor Nanostructures24Nanoassembly, 2002). The two molecular machines synthesized are: a linear shuttle(A. M. Brower, C. Frochot, F. C. Gatti, D. A. Leigh, L. Mottier, F. Paolucci, S. Roffia andG. W. H. Wurpel, 2001, pp. 2124-2128) and a rotary motor (Feringa, 2001, pp. 504-513)- Biomotors:Biomotors tend to be on the range of 10s of nm, and are typically larger than thesynthetic molecular machines discussed above, which have overall sizes of only afew nm. Noji and his team were the first to directly image the motion of a Biomotors( H. Noji, R. Yasuda, M. Yoshida and K. Kinosita, Jr., 1997, pp. 299-302)Communication:Communication among Nanorobots by means of waves is they are acoustic,electrical or optical, is likely to be difficult because of the small antenna sizes. Thecommunication in Nanorobots can be better understood if we look at nature. Beescommunicate by dancing, ants communicate by chemical signals which vary withrespect to the environment and bacteria releases chemicals as well and one of thechemical signals released by bacteria is more commonly known as quorum sensingwhich assess similar bacteria near them. (Nanorobots, NEMS and Nanoassembly,2002)Programming:One of the main things that are needed in Nanorobots programming is the fact thatbetter co-ordination is needed. Yet again, bacteria or organelles play an importantrole in it. Bacteria show very limited coordination behavior; ants use elaboratealgorithms (E. Bonabeau, M. Dorigo and G. Theraulaz, 1999); and the humanimmune system has an extremely complex coordination and (chemical) signalingscheme, which is still far from being completely understood (L. A. Segel and I. R.Cohen, 2001).
  • Atif SyedSemiconductor Nanostructures25Figure 24: Bio Nanorobots: An Overview (Ummat A., Dubey A., Sharma G., Mavroidis C)Figure 25: The working of Nanorobots in the field of medicine. (Adriano Cavalcanti, Robert A. Freitas Jr., 2005)Figure 26: Nanorobot Molecule Delivery (Adriano Cavalcanti, Robert A. Freitas Jr., 2005)
  • Atif SyedSemiconductor Nanostructures26Figure 27: Nanorobots with sensors and obstacle detectors. (Adriano Cavalcanti, Robert A. Freitas Jr., 2005)Figure 28: Nanorobots using chemical sensors to avoid and detects objects. (Adriano Cavalcanti, Lior Rosen, Luiz C.Kretly, Moshe Rosenfeld, Shmuel Einav, 2004)Figure 29: Vein inside view without the red blood cells. The target plaque is represented by the pinkspheres surrounding the vessel wall. The Nanorobots swim in a near-wall region searching for theatherosclerotic lesion. (Adriano Cavalcanti, Lior Rosen, Luiz C. Kretly, Moshe Rosenfeld, Shmuel Einav,2004)
  • Atif SyedSemiconductor Nanostructures275.3 Will Nanotechnology solve the Solar Cells problem?Figure 30: Working of a Solar Cell. (How Solar Cells Work, 2005)The solar power/cells we have currently have little effect on the large power gridsystems in place and it’s impossible to replace everything with solar power with thecurrent technology in solar cells. Scott Aldous, an engineer for the North Carolina SolarCenter explains that, “These two effects alone account for the loss of around 70 percentof the radiation energy incident on the cell” (How Solar Cells Work, 2005). The biggestquestion now arises is that, does the current system in place is efficient enough? Themaximum efficiency achieved today is only around 25 percent (An unexpected discoverycould yield a full spectrum solar cell., 2002). Some chemists at UC, Berkeley hasmanaged to produce cheap plastic solar cells which can adapt any surface whatsoever.The plastic solar cells utilize small nanorods which are then dispersed in a polymer.Nanorods behave similar to Quantum Wires because they can absorb light and emitelectrons. These electrons keep on flowing until they reach Aluminum electrode andconduct electricity. (Sanders, 2002)Figure 31: Working of a Nano-Solar Cell (Sanders, 2002)Konarka, a company specializing in making solar nano cells says they have “built fullyfunctional solar cells that have achieved efficiencies of around 8%” Currently, the
  • Atif SyedSemiconductor Nanostructures28researchers have been successful in tuning the nanorods such that they absorb certainwavelengths of light so as to exploit a wider range of color spectrum. If solar cells havebeen integrated into large scale, the environment will be protected and the utilization ofrenewable energy will be at its epitome. Nano Solar Cells will also eradicate the problemof electricity in rural and poorer countries where generating a large amount ofelectricity could be a costly affair. Although it might be a bit skeptical to use nano solarcells on a large scale but the opportunities on a medium or small scale is enormous. Thequestion is still open for discussion and debate while a lot of researchers and companiesare getting involved in making this a reality.ReferencesH. Noji, R. Yasuda, M. Yoshida and K. Kinosita, Jr. (1997). Direct observation of the rotation ofF1-ATPase. Nature .A. M. Brower, C. Frochot, F. C. Gatti, D. A. Leigh, L. Mottier, F. Paolucci, S. Roffia and G. W. H.Wurpel. (2001). Photoinduction of fast, reversible translational motion in a hydrogen-bondedmolecular. 2124-2128.Adriano Cavalcanti, Lior Rosen, Luiz C. Kretly, Moshe Rosenfeld, Shmuel Einav. (2004).NANOROBOTIC CHALLENGES IN BIOMEDICAL APPLICATIONS, DESIGN AND CONTROL. IEEE ICECSInt’l Conf. on Electronics, Circuits and Systems .Adriano Cavalcanti, Robert A. Freitas Jr. (2005). Nanorobotics Control Design: A CollectiveBehavior Approach for Medicine . IEEE TRANSACTIONS ON NANOBIOSCIENCE , 133-140.An unexpected discovery could yield a full spectrum solar cell. (2002, 11 18). Retrieved 04 01,2011, from Berkeley Lab: http://www.lbl.gov/Science-Articles/Archive/MSD-full-spectrum-solar-cell.htmlAshcroft, Neil W, Mermin, David N. (1976). Solid State Physics.Bucktard, G., Engel, H.-A., and Loss, D. (2000). Fortschr. Phys.E. Bonabeau, M. Dorigo and G. Theraulaz. (1999). Swarm Intelligence: From Natural to ArtificialSystems. Oxford: Oxford University Press.Feringa, B. L. (2001). In control of motion: from molecular switches to molecular motors.Accounts of Chemical Research , 504-513.Harrison, P. (2005). Quantum Wells, Wires and Dots. Leeds: Wiley.
  • Atif SyedSemiconductor Nanostructures29Hofmann, F., Heinzel, T., Wharam, D.A., Kotthaus, J.P., Bohm, G.,Klein, W., Trankle, G., andWeimann, G. (1995). Phys. Rev.How Solar Cells Work. (2005, 05 22). Retrieved 01 04, 2011, from How Stuff Works:http://science.howstuffworks.com/environmental/energy/solar-cell1.htmL. A. Segel and I. R. Cohen. (2001). Design Principle for the Immune System and Other DistributedAutonomous Systems. Oxford: Oxford University Press.lhn, T. (2010). Semiconductor Nanostructors. Oxford Publishing.Nanorobots, NEMS and Nanoassembly. (2002). Retrieved 04 01, 2011, from USC:http://ilab.usc.edu/classes/2002cs597f/RequichaProc9-5.pdfNovoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos,S.V., and Firsov, A.A. (2005). Nature.Photomask: Wikipedia. (2011, 03 30). Retrieved 03 30, 2011, from Wikipedia:http://en.wikipedia.org/wiki/PhotomaskQuantum computing may actually be useful. (2009, 10 09). Retrieved 04 01, 2011, from MIT:http://web.mit.edu/newsoffice/2009/quantum-algorithm.htmlSanders, B. (2002, 03 28). Cheap, Plastic Solar Cells May Be On The Horizon. Retrieved 04 01,2011, from UC Berkeley Campus News:http://www.berkeley.edu/news/media/releases/2002/03/28_solar.htmlTimpson, C. G. (2004). Quantum Information Theory.Ummat A., Dubey A., Sharma G., Mavroidis C. Nanorobotics.