{"id":101,"date":"2018-12-06T06:40:35","date_gmt":"2018-12-06T06:40:35","guid":{"rendered":"http:\/\/msp08.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=101"},"modified":"2018-12-06T07:01:42","modified_gmt":"2018-12-06T07:01:42","slug":"density-of-states-dos-and-potential-applications-of-the-semiconductor-nanostructures","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/chapter\/density-of-states-dos-and-potential-applications-of-the-semiconductor-nanostructures\/","title":{"rendered":"Density of States (Dos) and potential applications of the semiconductor nanostructures"},"content":{"raw":"
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\"epgp<\/a>\r\n<\/span><\/div>\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

Quantum confinement effects are discussed by bottom-up approach. The variation of density of states in various semiconductor nanostructures is also discussed along with their applications.<\/p>\r\n \r\n\r\n(b) Bottom-Up Approach: Nanoscrystal as a Large Molecule<\/em><\/strong>\r\n\r\n \r\n

In the bottom-up approach a QD is considered as a big molecule or a cluster. Analogous to the quantum chemical approaches to obtain molecular orbitals (which can be described as linear combination of atomic orbitals or LCAO), total wave function in a quantum dot may be built of single atomic orbitals.<\/p>\r\n \r\n

A fundamental instance of a molecule with multiple electrons is that of the diatomic hydrogen ( 2) molecule where, two atomic orbitals (or AOs) merge to generate two molecular orbitals (or MOs) which spread over both the H atoms \u2013 i.e. one bonding and one anti-bonding MO. Out of these, bonding MO has lower energy than individual AOs, while anti-bonding MO has higher energy than that of individual AOs. These MOs are filled with electrons in a way that the molecular potential energy in minimized. In 2 molecule, both the electrons initially in 1s AOs of separate hydrogen atoms are held within the bonding MO, so as to leave anti-bonding MO empty. The highest filled MO is termed as HOMO while the lowest vacant MO is called LUMO.<\/p>\r\n\r\n<\/div>\r\n\"\"\r\n

\r\n\r\n \r\n

Figure 1 Development of energy band structure from an imaginary diatomic molecule (at far left) to the bulk semiconductor (at far right).\u00a0\u00a0\u00a0\u00a0 and\u00a0\u00a0\u00a0 represent the energy-gap between HOMO and LUMO respectively for the nanocrystal and bulk.<\/strong><\/p>\r\n \r\n

Similar method can be applied to the large molecules, clusters and also the bulk material. As a molecule acquire bigger size, number of AOs combining to create MOs rises, resulting in progressive increase in the number of energy levels and gradual decrease in HOMO-LUMO energygap (Figure 1<\/strong>). Every MO group possesses a definite energy, however MOs having intermediate energies are more than those having energy values near the maximum and minimum values (that is, completely bonding or completely anti-bonding). It implies that MO states have maximum density at the intermediate energy values, and reducing to minimum density at both the energy extremes. If very large number of atoms combines (in case of bulk materials) the energy-levels are so numerous and so closely distributed that they form a quasi-continuum (an energy band), equivalent to CB and VB explained earlier. The HOMO level is top of VB, while LUMO represents bottom of CB (Figure 1<\/strong>).<\/p>\r\n \r\n

The semiconductor nanocrystal may be considered as a big molecule or a cluster consisting of a few tens to a few thousand atomic valence orbitals, producing equal number of MOs. Thus, its electronic structure can be described by \u2018energy bands\u2019 having high density of energy-levels at intermediate energy values and \u2018discrete energy-levels\u2019 close to the band-edges, wherein MO states have low density. In addition, HOMO-LUMO energy gap is greater than that for bulk and also size-dependent, increases with decrease\u00a0in nanocrystal size (<\/span>Figure 1<\/strong>). This describes both the quantum confinement effects referred in <\/span>earlier section from the molecular viewpoint.<\/span><\/p>\r\n \r\n

Density of States (DoS) in 2D, 1D, and 0D Systems<\/em><\/strong><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n

The density of states (DoS) function defines the number of states available in a system and is important for deciding carrier concentration as well as the energy distribution of the charge carriers in a semiconductor.<\/p>\r\n \r\n

In semiconductor nanostructures, free movement of carriers can be restricted to \u2013 two, one, or zero spatial dimensions. After applying semiconductor statistics on the systems of these spatial dimensions, DoS in quantum wells (2D), quantum wires (1D), and quantum dots (0D) differ from the bulk as shown in Figure<\/strong> 2<\/strong>.<\/p>\r\n \r\n\r\n\"\"\r\n\r\n \r\n

Figure 2 Density of electronic states in a semiconductor as a function of dimension.<\/strong><\/p>\r\n \r\n\r\nDoS in 2D Systems<\/em><\/strong>\r\n\r\n \r\n

One can imagine a semiconductor as an infinite 2D quantum <\/span>well having sides of length \u2018L\u2019 (<\/span>Figure 11<\/strong>).\u00a0<\/span>Electron of mass\u00a0\u00a0\u00a0?\u2217 is confined in the well.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n

Figure 3 Schematic representation of a semiconductor as an infinite quantum well (2D) of sides L.<\/strong><\/p>\r\n \r\n\r\nIf the potential energy within the well is set to zero, solution of Schr\u00f6dinger equation gives\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nThis allows the equation to hold for all possible ? and ? terms only if terms involving ??(?) and ??(?) are separately equal to a constant.\r\n\r\n<\/div>\r\n\"\"\r\n

\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nFrom DoS of a bulk (3D) Semiconductor, we obtain:<\/em><\/strong>\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n\"\"\r\n\r\n \r\n\r\n<\/div>\r\n \r\n
\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

To calculate DoS for the 2D structure (that is, a quantum well), similar approach can be employed, but the earlier equations undergo following change:<\/p>\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nThe density per unit energy can be calculated from the chain rule as:\r\n\r\n<\/div>\r\n\"\"\r\n

\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n

One\u00a0 important\u00a0consequence\u00a0of\u00a0the\u00a0above\u00a0relation\u00a0is\u00a0that\u00a0the\u00a02D\u00a0DoS\u00a0 is\u00a0independent of\u00a0energy. Immediately upon reaching the top of energy gap, significant number of states becomes available.<\/p>\r\n \r\n\r\nb)<\/em><\/strong>\u00a0\u00a0 DoS of a One Dimensional (1D) System<\/em><\/strong>\r\n\r\n \r\n\r\nTo calculate DoS for a 1D structure (a quantum wire), previous equations with the following modifications can be employed:\r\n\r\n\"\"\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n\"\"\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nc)\u00a0<\/em><\/strong>DoS of a Zero Dimensional (0D) System<\/em><\/strong>\r\n\r\n \r\n\r\nWhile considering the DoS for the 0D structure (a quantum dot, QD), free movement is restricted. As no -space is available which can be occupied by the electrons and all the available states occur only at discrete energy values, DoS for 0D can be expressed by using a delta function:\r\n\r\n \r\n\r\n?(?)0?<\/sub> = 2?(? \u2212 ??<\/sub> )\r\n\r\n \r\n\r\nFigure 4 <\/strong>shows the functional dependence of the density of states on the energy of a semiconductor.\r\n\r\n<\/div>\r\n\"\"\r\n
\r\n

Figure 4 Electron DoS for semiconductors having 3, 2, 1, and 0 degrees of freedom for electronic movement. Systems with 2, 1, and 0 degrees of freedom are termed as quantum wells, quantum wires, and quantum dots, respectively.<\/strong><\/p>\r\n \r\n\r\nPotential applications of the semiconductor nanostructures:<\/em><\/strong>\r\n\r\n \r\n

Quantum dot (0D) \u2013 <\/strong>A quantum dot represents a semiconductor crystal which can confine electrons, holes, or excitons to zero dimensions. Quantum dots or QDs because of their high extinction coefficient are principally promising candidates for optical applications. They work much similar to single electron based transistors and demonstrate Coulombic blockade effects (increased resistance at small bias voltages). These structures are also being proposed in realization of qubits (quantum bits) for applications in quantum information processing.<\/p>\r\n \r\n

Controlling the size of QD leads to several promising applications. For example, larger QDs exhibit greater red shift in comparison to the smaller ones. Besides, quantum behavior is less pronounced in the\u00a0larger QDs. On the contrary, smaller QDs provide the advantages of more subtle quantum effects. As QDs are zero-dimensional (0D), they exhibit a sharp density of states (DoS) than the structures having larger dimensions. Accordingly, they exhibit better transport as well as optical behaviors. The most promising applications of quantum dots are in diode lasers, amplifiers, and biosensors.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n \r\n

Quantum wires (1D) \u2013 <\/strong>A Quantum wire is an electrically conducting wire, wherein quantum transport effects are prominent. These are generally referred as nanowires. Quantum wires can be used in transistors and thus find wide-ranging applications in today\u2019s electronic circuits. The crucial challenge of ensuring proper gate control over the channel can be readily resolved using nanowires owing to their large aspect ratios. By wrapping gate dielectric around the nanowire channel, good electrostatic control over channel potential can be achieved.<\/p>\r\n \r\n

Similar to FET devices where the variation in conductance is controlled by change in electrostatic potential (gate-electrode) of conduction channel charge density, a biological- or chemical-FET works by detecting the variation in charge density (also termed as the \u201cfield effect\u201d), which characterizes the recognition event between a target molecule and the surface receptor. The variations in the surface potential affect the chemical FETs similar to the \u2018gate\u2019 voltage effects, resulting in a detectable and measurable change in the device conduction.<\/p>\r\n \r\n

Quantum wells (2D) \u2013 <\/strong>Quantum wells are potential wells which confine particles to one dimension, constraining them within a planar region. As the thickness of the well is reduced down to match the de Broglie wavelength of carriers (electrons or holes), quantum confinement effects become more apparent.<\/p>\r\n \r\n

Because of their quasi-two dimensional (2D) character, electrons in quantum wells have a density of states (DoS) as a function of energy having distinct steps, versus a smooth square root dependence similar to the bulk materials. Moreover, the effective mass of holes in the valence band becomes comparable to that of electrons in the conduction band. Both these factors, along with reduced amount of active material in quantum wells, result in the enhanced performance of quantum well based optical devices such as laser diodes. Consequently, quantum wells are extensively used in diode lasers, including red lasers for DVDs and laser pointers, infra-red lasers in fiber optic transmitters, or in blue lasers. They are also employed to fabricate HEMTs (High Electron Mobility Transistors), which are used in low-noise electronics. Quantum well infrared photodetectors are also based on quantum wells, and are used for infrared imaging.<\/p>\r\n \r\n

By doping either the well itself, or preferably, the barrier of a quantum well with donor impurities, the two-dimensional electron gas (2DEG) can be produced. This type of structure forms the conducting channel of a HEMT, and demonstrates fascinating properties at lower temperatures. One such property is\u00a0the quantum Hall effect, observed at elevated magnetic fields. A two-dimensional hole gas (2DHG) is also possible where acceptor dopants are used.<\/span><\/p>\r\n\r\n<\/div>\r\n\r\n\r\n\r\n
you can view video on Density of States (Dos) and potential applications of the semiconductor nanostructures<\/strong><\/td>\r\n\"\"<\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u00a0 \u00a0 References & Suggested Reading:<\/strong>\r\n
    \r\n \t
  1. T. Pradeep, A Textbook of \u201cNanoscience and Nanotechnology\u201d, McGraw Hill Education, 2012.<\/li>\r\n \t
  2. https:\/\/www.azonano.com\/article.aspx?ArticleID=1079<\/li>\r\n \t
  3. https:\/\/www.ttu.ee\/public\/m\/Mehaanikateaduskond\/...\/Lecture11_Synthesis.pdf<\/em><\/li>\r\n \t
  4. www.dummies.com\/...\/nanotechnology\/nanotechnology-top-down-or-bottom-up\/<\/li>\r\n \t
  5. http:\/\/alan.ece.gatech.edu\/ECE6451\/Lectures\/StudentLectures\/King_Notes_Density_of_S tates_2D1D0D.pdf<\/li>\r\n \t
  6. https:\/\/courses.cit.cornell.edu\/mse5470\/handout27.pdf<\/li>\r\n \t
  7. https:\/\/en.wikipedia.org\/wiki\/Density_of_states<\/li>\r\n \t
  8. Walter Ashley Harrison (1989). Electronic Structure and the Properties of Solids. Dover Publications.<\/li>\r\n \t
  9. Charles Kittel (1996). Introduction to Solid State Physics (7th ed.). Wiley. Equation (37), p. 216.<\/li>\r\n \t
  10. Wang, Fugao; Landau, D. P. (Mar 2001). \"Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States\". Phys. Rev. Lett. American Physical Society. 86 (10): 2050\u20132053.<\/li>\r\n \t
  11. Ojeda, P.; Garcia, M. (2010). \"Electric Field-Driven Disruption of a Native beta-Sheet Protein Conformation and Generation of a Helix-Structure\". Biophysical Journal. 99 (2): 595\u2013599.<\/li>\r\n \t
  12. Adachi T. and Sunada. T (1993). \"Density of states in spectral geometry of states in spectral geometry\". Comment. Math. Helvetici. 68: 480\u2013493.<\/li>\r\n \t
  13. Chen, Gang. Nanoscale Energy Transport and Conversion. New York: Oxford, 2005<\/li>\r\n \t
  14. Streetman, Ben G. and Sanjay Banerjee. Solid State Electronic Devices. Upper Saddle River, NJ: Prentice Hall, 2000.<\/li>\r\n<\/ol>","rendered":"
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    \n<\/span><\/div>\n

     <\/p>\n

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     <\/p>\n

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    Quantum confinement effects are discussed by bottom-up approach. The variation of density of states in various semiconductor nanostructures is also discussed along with their applications.<\/p>\n

     <\/p>\n

    (b) Bottom-Up Approach: Nanoscrystal as a Large Molecule<\/em><\/strong><\/p>\n

     <\/p>\n

    In the bottom-up approach a QD is considered as a big molecule or a cluster. Analogous to the quantum chemical approaches to obtain molecular orbitals (which can be described as linear combination of atomic orbitals or LCAO), total wave function in a quantum dot may be built of single atomic orbitals.<\/p>\n

     <\/p>\n

    A fundamental instance of a molecule with multiple electrons is that of the diatomic hydrogen ( 2) molecule where, two atomic orbitals (or AOs) merge to generate two molecular orbitals (or MOs) which spread over both the H atoms \u2013 i.e. one bonding and one anti-bonding MO. Out of these, bonding MO has lower energy than individual AOs, while anti-bonding MO has higher energy than that of individual AOs. These MOs are filled with electrons in a way that the molecular potential energy in minimized. In 2 molecule, both the electrons initially in 1s AOs of separate hydrogen atoms are held within the bonding MO, so as to leave anti-bonding MO empty. The highest filled MO is termed as HOMO while the lowest vacant MO is called LUMO.<\/p>\n<\/div>\n

    \"\"<\/p>\n

    \n

     <\/p>\n

    Figure 1 Development of energy band structure from an imaginary diatomic molecule (at far left) to the bulk semiconductor (at far right).\u00a0\u00a0\u00a0\u00a0 and\u00a0\u00a0\u00a0 represent the energy-gap between HOMO and LUMO respectively for the nanocrystal and bulk.<\/strong><\/p>\n

     <\/p>\n

    Similar method can be applied to the large molecules, clusters and also the bulk material. As a molecule acquire bigger size, number of AOs combining to create MOs rises, resulting in progressive increase in the number of energy levels and gradual decrease in HOMO-LUMO energygap (Figure 1<\/strong>). Every MO group possesses a definite energy, however MOs having intermediate energies are more than those having energy values near the maximum and minimum values (that is, completely bonding or completely anti-bonding). It implies that MO states have maximum density at the intermediate energy values, and reducing to minimum density at both the energy extremes. If very large number of atoms combines (in case of bulk materials) the energy-levels are so numerous and so closely distributed that they form a quasi-continuum (an energy band), equivalent to CB and VB explained earlier. The HOMO level is top of VB, while LUMO represents bottom of CB (Figure 1<\/strong>).<\/p>\n

     <\/p>\n

    The semiconductor nanocrystal may be considered as a big molecule or a cluster consisting of a few tens to a few thousand atomic valence orbitals, producing equal number of MOs. Thus, its electronic structure can be described by \u2018energy bands\u2019 having high density of energy-levels at intermediate energy values and \u2018discrete energy-levels\u2019 close to the band-edges, wherein MO states have low density. In addition, HOMO-LUMO energy gap is greater than that for bulk and also size-dependent, increases with decrease\u00a0in nanocrystal size (<\/span>Figure 1<\/strong>). This describes both the quantum confinement effects referred in <\/span>earlier section from the molecular viewpoint.<\/span><\/p>\n

     <\/p>\n

    Density of States (DoS) in 2D, 1D, and 0D Systems<\/em><\/strong><\/p>\n<\/div>\n

    \n

     <\/p>\n

    The density of states (DoS) function defines the number of states available in a system and is important for deciding carrier concentration as well as the energy distribution of the charge carriers in a semiconductor.<\/p>\n

     <\/p>\n

    In semiconductor nanostructures, free movement of carriers can be restricted to \u2013 two, one, or zero spatial dimensions. After applying semiconductor statistics on the systems of these spatial dimensions, DoS in quantum wells (2D), quantum wires (1D), and quantum dots (0D) differ from the bulk as shown in Figure<\/strong> 2<\/strong>.<\/p>\n

     <\/p>\n

    \"\"<\/p>\n

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    Figure 2 Density of electronic states in a semiconductor as a function of dimension.<\/strong><\/p>\n

     <\/p>\n

    DoS in 2D Systems<\/em><\/strong><\/p>\n

     <\/p>\n

    One can imagine a semiconductor as an infinite 2D quantum <\/span>well having sides of length \u2018L\u2019 (<\/span>Figure 11<\/strong>).\u00a0<\/span>Electron of mass\u00a0\u00a0\u00a0?\u2217 is confined in the well.<\/span><\/p>\n<\/div>\n

    \n

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    Figure 3 Schematic representation of a semiconductor as an infinite quantum well (2D) of sides L.<\/strong><\/p>\n

     <\/p>\n

    If the potential energy within the well is set to zero, solution of Schr\u00f6dinger equation gives<\/p>\n

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    This allows the equation to hold for all possible ? and ? terms only if terms involving ??(?) and ??(?) are separately equal to a constant.<\/p>\n<\/div>\n

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    From DoS of a bulk (3D) Semiconductor, we obtain:<\/em><\/strong><\/p>\n

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    To calculate DoS for the 2D structure (that is, a quantum well), similar approach can be employed, but the earlier equations undergo following change:<\/p>\n

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    The density per unit energy can be calculated from the chain rule as:<\/p>\n<\/div>\n

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    One\u00a0 important\u00a0consequence\u00a0of\u00a0the\u00a0above\u00a0relation\u00a0is\u00a0that\u00a0the\u00a02D\u00a0DoS\u00a0 is\u00a0independent of\u00a0energy. Immediately upon reaching the top of energy gap, significant number of states becomes available.<\/p>\n

     <\/p>\n

    b)<\/em><\/strong>\u00a0\u00a0 DoS of a One Dimensional (1D) System<\/em><\/strong><\/p>\n

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    To calculate DoS for a 1D structure (a quantum wire), previous equations with the following modifications can be employed:<\/p>\n

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    c)\u00a0<\/em><\/strong>DoS of a Zero Dimensional (0D) System<\/em><\/strong><\/p>\n

     <\/p>\n

    While considering the DoS for the 0D structure (a quantum dot, QD), free movement is restricted. As no -space is available which can be occupied by the electrons and all the available states occur only at discrete energy values, DoS for 0D can be expressed by using a delta function:<\/p>\n

     <\/p>\n

    ?(?)0?<\/sub> = 2?(? \u2212 ??<\/sub> )<\/p>\n

     <\/p>\n

    Figure 4 <\/strong>shows the functional dependence of the density of states on the energy of a semiconductor.<\/p>\n<\/div>\n

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    Figure 4 Electron DoS for semiconductors having 3, 2, 1, and 0 degrees of freedom for electronic movement. Systems with 2, 1, and 0 degrees of freedom are termed as quantum wells, quantum wires, and quantum dots, respectively.<\/strong><\/p>\n

     <\/p>\n

    Potential applications of the semiconductor nanostructures:<\/em><\/strong><\/p>\n

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    Quantum dot (0D) \u2013 <\/strong>A quantum dot represents a semiconductor crystal which can confine electrons, holes, or excitons to zero dimensions. Quantum dots or QDs because of their high extinction coefficient are principally promising candidates for optical applications. They work much similar to single electron based transistors and demonstrate Coulombic blockade effects (increased resistance at small bias voltages). These structures are also being proposed in realization of qubits (quantum bits) for applications in quantum information processing.<\/p>\n

     <\/p>\n

    Controlling the size of QD leads to several promising applications. For example, larger QDs exhibit greater red shift in comparison to the smaller ones. Besides, quantum behavior is less pronounced in the\u00a0larger QDs. On the contrary, smaller QDs provide the advantages of more subtle quantum effects. As QDs are zero-dimensional (0D), they exhibit a sharp density of states (DoS) than the structures having larger dimensions. Accordingly, they exhibit better transport as well as optical behaviors. The most promising applications of quantum dots are in diode lasers, amplifiers, and biosensors.<\/span><\/p>\n<\/div>\n

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    Quantum wires (1D) \u2013 <\/strong>A Quantum wire is an electrically conducting wire, wherein quantum transport effects are prominent. These are generally referred as nanowires. Quantum wires can be used in transistors and thus find wide-ranging applications in today\u2019s electronic circuits. The crucial challenge of ensuring proper gate control over the channel can be readily resolved using nanowires owing to their large aspect ratios. By wrapping gate dielectric around the nanowire channel, good electrostatic control over channel potential can be achieved.<\/p>\n

     <\/p>\n

    Similar to FET devices where the variation in conductance is controlled by change in electrostatic potential (gate-electrode) of conduction channel charge density, a biological- or chemical-FET works by detecting the variation in charge density (also termed as the \u201cfield effect\u201d), which characterizes the recognition event between a target molecule and the surface receptor. The variations in the surface potential affect the chemical FETs similar to the \u2018gate\u2019 voltage effects, resulting in a detectable and measurable change in the device conduction.<\/p>\n

     <\/p>\n

    Quantum wells (2D) \u2013 <\/strong>Quantum wells are potential wells which confine particles to one dimension, constraining them within a planar region. As the thickness of the well is reduced down to match the de Broglie wavelength of carriers (electrons or holes), quantum confinement effects become more apparent.<\/p>\n

     <\/p>\n

    Because of their quasi-two dimensional (2D) character, electrons in quantum wells have a density of states (DoS) as a function of energy having distinct steps, versus a smooth square root dependence similar to the bulk materials. Moreover, the effective mass of holes in the valence band becomes comparable to that of electrons in the conduction band. Both these factors, along with reduced amount of active material in quantum wells, result in the enhanced performance of quantum well based optical devices such as laser diodes. Consequently, quantum wells are extensively used in diode lasers, including red lasers for DVDs and laser pointers, infra-red lasers in fiber optic transmitters, or in blue lasers. They are also employed to fabricate HEMTs (High Electron Mobility Transistors), which are used in low-noise electronics. Quantum well infrared photodetectors are also based on quantum wells, and are used for infrared imaging.<\/p>\n

     <\/p>\n

    By doping either the well itself, or preferably, the barrier of a quantum well with donor impurities, the two-dimensional electron gas (2DEG) can be produced. This type of structure forms the conducting channel of a HEMT, and demonstrates fascinating properties at lower temperatures. One such property is\u00a0the quantum Hall effect, observed at elevated magnetic fields. A two-dimensional hole gas (2DHG) is also possible where acceptor dopants are used.<\/span><\/p>\n<\/div>\n\n\n\n
    you can view video on Density of States (Dos) and potential applications of the semiconductor nanostructures<\/strong><\/td>\n\"\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u00a0 \u00a0 References & Suggested Reading:<\/strong><\/p>\n

      \n
    1. T. Pradeep, A Textbook of \u201cNanoscience and Nanotechnology\u201d, McGraw Hill Education, 2012.<\/li>\n
    2. https:\/\/www.azonano.com\/article.aspx?ArticleID=1079<\/li>\n
    3. https:\/\/www.ttu.ee\/public\/m\/Mehaanikateaduskond\/…\/Lecture11_Synthesis.pdf<\/em><\/li>\n
    4. www.dummies.com\/…\/nanotechnology\/nanotechnology-top-down-or-bottom-up\/<\/li>\n
    5. http:\/\/alan.ece.gatech.edu\/ECE6451\/Lectures\/StudentLectures\/King_Notes_Density_of_S tates_2D1D0D.pdf<\/li>\n
    6. https:\/\/courses.cit.cornell.edu\/mse5470\/handout27.pdf<\/li>\n
    7. https:\/\/en.wikipedia.org\/wiki\/Density_of_states<\/li>\n
    8. Walter Ashley Harrison (1989). Electronic Structure and the Properties of Solids. Dover Publications.<\/li>\n
    9. Charles Kittel (1996). Introduction to Solid State Physics (7th ed.). Wiley. Equation (37), p. 216.<\/li>\n
    10. Wang, Fugao; Landau, D. P. (Mar 2001). “Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States”. Phys. Rev. Lett. American Physical Society. 86 (10): 2050\u20132053.<\/li>\n
    11. Ojeda, P.; Garcia, M. (2010). “Electric Field-Driven Disruption of a Native beta-Sheet Protein Conformation and Generation of a Helix-Structure”. Biophysical Journal. 99 (2): 595\u2013599.<\/li>\n
    12. Adachi T. and Sunada. T (1993). “Density of states in spectral geometry of states in spectral geometry”. Comment. Math. Helvetici. 68: 480\u2013493.<\/li>\n
    13. Chen, Gang. Nanoscale Energy Transport and Conversion. New York: Oxford, 2005<\/li>\n
    14. Streetman, Ben G. and Sanjay Banerjee. Solid State Electronic Devices. Upper Saddle River, NJ: Prentice Hall, 2000.<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["dr-s-s-islam"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-101","chapter","type-chapter","status-publish","hentry","contributor-dr-s-s-islam"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/pressbooks\/v2\/chapters\/101","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/pressbooks\/v2\/chapters\/101\/revisions"}],"predecessor-version":[{"id":119,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/pressbooks\/v2\/chapters\/101\/revisions\/119"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/pressbooks\/v2\/chapters\/101\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/wp\/v2\/media?parent=101"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/pressbooks\/v2\/chapter-type?post=101"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/wp\/v2\/contributor?post=101"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp08\/wp-json\/wp\/v2\/license?post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}