Surface Scattering and Quantized Conduction in Semi Conducting

Surface Scattering and Quantized conduction in semi conducting nano materials B.Jyothi(Research Scholar) and Asst.prof of physics ,Aditya Engineering College , Surampalem. Dr.K.L.Narasimham ,Professor (A.U.Retired)

Abstract Electronic configurations of nano materials make changes in the density of electronic energy levels which will cause strong variations in the optical and electrical properties with size. The effects of size on electrical conductivity of nanostructures play a major role in several new technologies. The electronic properties of ultrafine wire structures are studied theoretically. If the scattering probability of such size-quantized electrons is calculated for Coulomb potential then it is suppressed drastically because of the one-dimensional nature of the electronic motion in the wire. For this material In this paper I want to study few mechanisms responsible for enhanced electrical conductivity in semi conducting nano materials.

1.Introduction Semiconductor nano crystals are tiny crystalline particles that exhibit size-dependent optical and electronic properties. With typical dimensions in the range of 1-100 nm, these nano crystals bridge the gap between small molecules and large crystals, displaying discrete electronic transitions reminiscent of isolated atoms and molecules, as well as enabling the exploitation of the useful properties of crystalline materials. Bulk semiconductors are characterized by a composition-dependent band gap energy (Eg), which is the minimum energy required to excite an electron from the ground state valence energy band into the vacant conduction energy band . With the absorption of a photon of energy greater than Eg, the excitation of an electron leaves an orbital hole in the valence band. The negatively charged electron and positively charged hole may be mobilized in the presence of an electric field to yield a current, but their lowest energy state is an electro statically bound electron-hole pair, known as the exciton. Relaxation of the excited electron back to the valence band annihilates the exciton and may be accompanied by the emission of a photon, a process known as radiative recombination.

1.1 Significance of the study

Nanotechnology is a field of science and technology of controlling matter on a nano scale. It is a highly multidisciplinary field, including electrical and mechanical engineering, physics, chemistry, and biosciences. Nanotechnology will radically affect all these disciplines and their application areas . It is commonly attributed for the technologies leading to produce nano-scaled materials (10-9 m) at nanometer dimension. This feather of nano-particles provides a larger surface space per unit mass than those which are not in nano size . To create nano-structured materials there are two commonly routine techniques can be used, top-down technique and bottom-up technique, which their main difference is based on the size of primary entities applied to build nano components with or without atomic level control . One of the main applications of nanotechnology and therefore a driving force for nano science

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is the electronics industry. Over the past few decades, the transistor has been continually miniaturized. Modern integrated circuits incorporate transistors with feature as small as 32nm . Nanotechnology broadly includes all technologies that handle nano - scale materials, and in a narrow sense, technologies that handle unique phenomena that arise in the 10 -to-100 -nm size range..

1.2. How properties varies from bulk materials?

Nano materials are significantly different from that of their bulk counterpart .Thus, electronic configuration of these materials changes. These changes arise through systematic transformations in the density of electronic energy levels as a function of the size. It causes strong variations in the optical and electrical properties with size.

In the case of metals the energy level spacing is very small, the electronic and optical properties more closely resemble those of continuum. The density of energy levels is so high that a noticeable separation in energy levels within the conduction band (intra band transition) is only observed when the nano particle is made up of ~100atoms. The spacing, between energy levels depends on the Fermi energy of the metal, EF, and on the

number of electrons in the metal, N, as given by:

Fermi energy Ef is typically of the order of 5 eV in most metals. The discrete electronic energy level in metal nano particles has been observed in far-infrared absorption measurements of gold nano particle. In semiconductors, the Fermi level lies between two bands, so that the edges of the bands are dominating the low- energy optical and electrical behavior. It is possible even for crystallites as large as 10,000 atoms. For insulators, the band gap between two bands is too big.

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2. Material Design and selection The ability to produce new high-performance semi conductor device is the matter on which the future growth of solid-state electronics depends. The preparation of semi conductor is proceeding above several distinctly different , but equally important directions. For Si, it requires highly advanced state of crystal perfection , so economically it is high. So ,there is a need for design of new materials.

Fig :Spacing, effective masses in eV , meV and mo(rest mass of electron) respectively

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3. Methods of Approach Materials of these sizes have been prepared using two techniques, the top-down and the bottom-up methods Top-Down Approach : This approach, which leads physicists and engineers to manipulate progressively smaller pieces of matter by photolithography, Electron-beam lithography, X-ray lithography and related techniques, has operated in an outstanding way up until now. Bottom-Up Approach An alternative and most promising strategy to exploit science and technology at the nanometer scale is offered by the bottom-up approach, which starts from nano- or subnano-scale objects (namely, atoms or molecules) to build up nanostructures. The bottom-up approach is largely the realm of nanoscience and nanotechnology.

4.Electrical Conductivity The effects of size on electrical conductivity of nanostructures and nano materials are complex, since they are based on distinct mechanisms. These mechanisms can be generally grouped into categories i) surface scattering including grain boundary scattering ii) quantized conduction including ballistic conduction iii) coulomb charging and tunneling iv) widening and discrete of band gap v) change of microstructures. In addition, increased perfection, such as reduced impurity, structural defects and dislocations, would affect the electrical conductivity of nanostructures and nano materials.

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4.1 Surface scattering Electrical conduction in metals or Ohmic conduction can be described by the various electron scattering, and the total resistivity, of a metal is a combination of the contribution of individual and independent scattering, known as Matthiessen’s rule

is the thermal resistivity and the defect resistivity Impurity atoms, defects such as vacancies, and grain boundaries locally disrupt the periodic electric potential of the lattice and effectively cause electron scattering . In nano wires and thin films, the surface scattering of electrons results in reduction of electrical conductivity. When the critical dimension of thin films and nano wires is smaller than the Joint Initiative of IITs and IISc – Funded by MHRD Page 7 of 12 electron mean-free path, the motion of electrons will be interrupted through collision with the surface. The electrons undergo either elastic or inelastic scattering. In elastic, also known as specular, scattering, the electron reflects in the same way as a photon reflects from a mirror. In this case, the electron does not lose its energy and its momentum or velocity along the direction parallel to the surface is preserved. As a result, the electrical conductivity remains the same as in the bulk and there is no size effect on the conductivity. When scattering is totally inelastic or non specular or diffuse, the electron mean-free path is terminated by impinging on the surface. After the collision, the electron trajectory is independent of the impingement direction and the subsequent scattering angle is random. Consequently, the scattered electron loses its velocity along the direction parallel to the surface or the conduction direction, and the electrical conductivity decreases. There will be a size effect on electrical conduction. 4.2 STRUCTURE OF THE GRAINS AND THE GRAIN BOUNDARIES OF NANOMATERIALS The structure of the grains (crystallites) in nano crystalline materials has been normally accepted to be the same as in a coarse-grained material. High-resolution transmission electron microscope (HRTEM) experiments have indicated that nano crystalline materials consist of small crystallites of different crystallographic orientations separated by grain boundaries. Even though not frequently reported, the grains contain a variety of crystalline defects such as dislocations, twin boundaries, multiple twins and stacking faults. The grain boundary structure determines the diffusivity and consequently the rate of deformation by grain boundary diffusion (Coble creep) and the rates of interesting and grain growth. The present status of the structure of grain boundaries in nano crystalline materials can be found in some recent publications (Baier et al 2011; Nowak and Carter 2009). Figure 1.1 shows a schematic representation of hard-sphere model of an equinaxed nano crystalline metal.The magnitude of the electrical resistivity (and hence conductivity) in nano composites can be changed by altering the grain size. For example, by changing the volume fraction of iron particles in a nano crystalline iron–silica system, the electrical conductivity could be changed by 14 orders of magnitude.

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Fig 1.1 Schematic depiction of nano structured materials showing atoms in grain interiors (gray) and atoms in grain boundaries (white)

5. Qantized Conduction including ballistic conduction First, consider transport in large, macroscopic systems. In bulk materials and devices, transport has been well described via the Boltzmann transport equation or similar kinetic equation approaches. The validity of this approach is based on the following set of assumptions: (i) scattering processes are local and occur at a single point in space; (ii) the scattering is instantaneous (local) in time; (iii) the scattering is very weak and the fields are low, such that these two quantities form separate perturbations on the equilibrium system; (iv) the time scale is such that only events that are slow compared to the mean free time between collisions are of interest. In short, one is dealing with structures in which the potentials vary slowly on both the spatial scale of the electron thermal wavelength and the temporal scale of the scattering processes.

Ballistic conduction occurs when the length of conductor is smaller than the electron mean-free path. In this case, the conductance jumps insteps of(see the adjacent figure for the case of FET conductance). Another important aspect of ballistic transport is thatno energy is dissipated in the conduction, and there exist no elastic scattering. The latter requires the absence of impurity and defects. When elastic scattering occurs, the transmission coefficients, and thus the electrical conductance will be reduced, which is then no longer precisely quantized. Ballistic conduction of carbon nanotubes was first demonstrated by Frank and his co-workers. Extremely high stable current densities have been attained. 1209.122−Ω==kheG2710cmAJ>

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Coulomb blockade or Coulomb charging occurs when the contact resistance is larger than the resistance of nanostructures and when the total capacitance of the object is so small that adding a single electron requires significant charging energy. Metal or semiconductor nano crystals of a few nanometers in diameter exhibit quantum effects that give rise to discrete charging of the metal particles. Such a discrete electronic configuration permits one to pick up the electric charge one electron at a time, at specific voltage values. This Coulomb blockade behavior, also known as "Columbic staircase" and has originated the proposal that nano particles with diameters below 2-3 nm may become basic components of single electron transistors (SETs).

5.1 Ballistic transport If the system size L < lm , then the charge carriers can moves without scattering except with the surface. The carrier momentum grows due to the accelerating force of the electric field.

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Conclusion

For Semi conducting nano materials Quantum size effect and energy level spacing in materials was studied. Different techniques for preparing nano materials was discussed. Electrical conductivity of semi conductor nano materials can be studied by two distinct mechanisms namely (i) Surface scattering and (ii)Quantized Conduction including ballistic conduction .In this juncture we studied how surface scattering is influenced by structural grain boundaries. Enhanced electrical conductivity was observed in semi conductor nano materials , which are very useful in future technologies.

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