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Influence of Nanostructure Geometry on Electronic Properties A. Tavkhelidze Ilia State University, Cholokashvili Ave. 3-5, Tbilisi 0162, Georgia

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Outline Introduction Density of quantum states in nanograting geometry Growth and characterization of nanograting amorphous metal films Geometry induced doping or G-doping Electronic properties of multiple homojunction nanograting layers Electronic properties of multiple heterojunction nanograting layers G-doping for high electron mobility applications Thermoelectric properties of semiconductor nanograting layers Conclusions

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Geometry dependent quantum effects Periodic curved surfaces Ono S, Shima H 2010 Physica E, 42 1224-1227 Kartashov Y V, Szameit A, Keil R, Vysloukh V A, and Torner L 2011 Optics Letters 36 3470 Nanotubes Gupta S and Saxena A 2011 J. Appl. Phys. 109 074316 Cylindrical surfaces with non-constant diameter Fujita N 2004 J. Phys. Soc. Jpn. 73 3115-3120 Strain-driven nanostructures Ortix C, S. Kiravittaya S, Schmidt O G, and van den Brink J 2011 Phys. Rev. B. 84 045438 Quantum billiards E. N. Bulgakov, D. N. Maksimov, and A. F. Sadreev, Phys. Rev. E 71, 046205 (2005) O. Bengtsson, J. Larsson, and K.-F. Berggren, Phys. Rew. 71, 056206 (2005) Introduction

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Density of state (DOS) of nanograting layer DOS in plain layerDOS in nanograting layer where, G >1 is a geometry factor. According to Fermi's golden rule, the electron scattering rate is proportional to Consequently,

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Geometry factor calculation The approximate analytical expression known as Weyl’s formula allows the calculation of TM modes by using a ratio of layer surface area and volume. H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Wissenschaftsverlag, Mannheim 1976). B. Eckhardt, Phys. Rep. 163, 205-297 (1988). is number of TM modes from 0 to k. for w=a and Hk >2.5. Mathematically, there is no difference between DOS reduction and electromagnetic (TM) mode depression. The Helmholtz equation and Dirichlet boundary conditions are used in both cases. J. H. Kim, M. Barth, U. Kuhl, H.-J. Stockmann and J. P. Bird, Phys. Rev. B 68, 045315 (2003). K.-F. Berggren, I. I. Yakimenko and J. Hakanen, New J. Phys. 12, 073005 (2010).

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Software for mode calculation in ridged waveguides : FIMMMWAVE, photon design software (A fully vectorial 2D Mode Solver), ttp://www.photond.com/products/fimmwave.htm.ttp://www.photond.com/products/fimmwave.htm CONCERTO, software for electromagnetic design, Vector Fields, http://www.vectorfields.com.http://www.vectorfields.com Perturbation method was used to obtain approximate formula G=(2H-a)/2a within the range of 3 >a. A.Tavkhelidze, V. Svanidze and I. Noselidze, J. Vac. Sci. Technol. B, v. 25(4), p.1270, (2007). Geometry factor calculation Literature related to Casimir effect, review: T. Emig, Casimir Forces and Geometry in Nanosystems, Nonlinear Dynamics of Nanosystems, ed. by G. Radons, B. Rumpf, H. G. Schuste (Wiley-VCH Verlag GmbH & Co. KGaA, 2010)

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Nanograting layer cross section Energy diagrams metal Energy diagrams semiconductor Electronic properties of metal and semiconductor Nanograting layer

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Sample preparation and characterization Au, Nb, Cr films were quench deposited At T=300 K and T=80 K. Kelvin probe was used to measure difference in work function between nanograting and plain areas.

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AFM image of Au Nanogratilg layer

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A.Tavkhelidze et al., J. Vac. Sci. Technol. B 24(3), p. 1413 (2006). Sample preparation and characterization Films deposited at T=300 K had polycrystalline internal structure. Films deposited at T=80 K had amorphous internal structure. Maximum work function reductions of 0.5 eV in Au, 0.4 eV in Cr, 0.35 eV in Nb and 0.2 eV in SiO 2 films were observed. Electrons with energies E<

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PEEM images of Nanograting Au film surface Rempfer G F, Skoczylas W P, and Hayes Griffith O 1991 Ultramicroscopy 36 196

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Geometry induced doping or G-doping Electron concentration n in the CB increases, which can be termed as geometry-induced electron doping or G-doping. There are no ionized impurities. Charge carrier scattering is preserved to intrinsic semiconductor level. G-doping is T-independent Modulation doping Recently introduced polarization doping J. Simon, V. Protasenko, C. Lian, H. Xing and D. Jena,, Science 327, 60-64 (2010). B. Yu, M. Zebarjadi, H. Wang, K. Lukas, H. Wang, D. Wang, C. Opeil, M. Dresselhaus, G. Chen, and Z. Ren,, Nano Lett. 12, 2077 (2012).

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Geometry factor G, density of states Number of rejected electrons Density of forbidden quantum states Where, Integration takes place over the energy regions depicted with red hatch. Electron confinement energy regions

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Electron confinement to the NG layer is needed to obtain G-doping We investigate G-doping in multiple nanograting layers, including main and barrier layers, forming a series of hetero- or homojunctions Electronic properties of multiple homojunction nanograting layers is donor concentration in barrier layer main and barrier layers are relatively thick such that the electron wave functions do not overlap and we can ignore the mini-band formation.

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Material [cm -3 ][meV][cm -3 ][meV] Si 3 x 10 18 456 x 10 17 10358 1 x 10 19 641 x 10 18 8925 3 x 10 19 871 x 10 18 77-10 1 x 10 20 1262.8 x 10 18 62-64 GaAs 1 x 10 18 473.2 x 10 17 3.4-44 3 x 10 18 868 x 10 17 -29-115 5 x 10 18 1191.3 x 10 18 -52-172 1 x 10 19 1972.8 x 10 18 -110-297 A Electron concentration and Fermi levels in the main and barrier layers for Si and GaAs materials. Energy was measured from the corresponding CB edge layer. Electron concentration and Fermi level in homojunction nanograting layers T=300 K

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Electron concentration and Fermi level in heterojunction nanograting layers A condition of continuity of electric displacement at the interface gives: A condition of equality of Fermi levels (zero external bias) gives:

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Materials [main/barrier][meV] [cm -3 ] [meV Ga 0.52 In 0.48 P/ /Al 0.45 Ga 0.55 As 257141.021.281581.3 x 10 18 1.1 x 10 19 118 InP/ /In 0.52 Al 0.48 As 34251.21.81311111.3 x 10 18 4.8 x 10 19 98 Si/ /Si 0.5 Ge 0.5 56241.11.00628151.4 x 10 18 2.1 x 10 18 13 Electron concentration and other parameters of nanograting type-II heterojunctions. Electron concentration and Fermi level in heterojunction nanograting layers The values of and were varied to obtain G-doping levels of 10 18 -10 19 cm -3 S. Adachi, Properties of Semiconductor Alloys: Group-IV, III–V and II–VI Semiconductors (John Wiley & Sons 2009) M. S. Hybertsen, Appl. Phys. Lett. 58, 1759 (1991). P. Roblin and H. Rohdin, High-speed heterostructure devices (Cambridge University Press 2002)

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G-doping for high electron mobility applications In a multi-junction solar cell the window, emitter, and tunnel junction layer doping level is roughly 10 18 cm -3. At this doping level, ionized impurities reduce electron mobility by a factor: 4 in GaAs, and 10 in Si. Solar cells use transparent conductive oxides with doping levels of 10 20 -10 21 cm -3. At this doping level, ionized impurities reduce electron mobility by a factor of 30-50 in GaAs. Cross-sectional, transmission electron microscopy micrograph of the sample grown using an interfacial superlattice with a growth rate of 1.0 ML/ sec. The diffraction grating can be seen at the bottom of the figure and the planarized DBR layers can be seen near the top of the micrograph. G. W. Pickrell et al., JOURNAL OF APPLIED PHYSICS V 96, 4050, 2004

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Thermoelectric properties of nanograting layers Materials having high Shave low Increasingleads to an increase in(Wiedemann–Franz law) We present large enhancement in S without changing Calculate Z and compare with Zo where, Zo corresponds to in Boltzmann transport equations and calculate S asWe insert A. Tavkhelidze, Nanotechnology 20, 405401 (2009).

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Charge and heat transport Depletion depth depends on Y, and geometry factor gradient appears in the Y-direction. and modify the electron distribution function and cause electron motion from the hot side to the cold side and Within the parabolic bands approximation are integrals The NG does not change dispersion relation and consequently

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Chemical potential of nanograting layer For NG layerand and consequently product is G independent. The NG influences integralsby changing alone. Introduction ofdefines reference material as n + -type semiconductor with electron concentration ofor NG having constant geometry factor

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Charge and heat transport

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Geometry factor temperature dependence

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Seebeck coefficient of nanograting layer with p+–n+ junctions r is a scattering parameter

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Electron emission properties of metal nanograting films Why increasing the electron emission is that important for applications? 1 Thermionic energy converters working at low temperatures with high conversion efficiency 2 Thermotunnel energy converters 3 Cold emission for electron microscopy and other electron sources Waste heat from combustion sources is avialale at 400- 1000 K Yamamoto S 2006 Rep. Prog. Phys. 69 pp 181–232 Koh W S and Ang L K 2008 Nanotechnology 19 235402 Hishinuma Y, Geballe T H, Moyzhes B Y and Kenny T W 2001 Appl. Phys. Lett. 78 2572 Tavkhelidze A, Svanidze V. and Tsakadze L 2008 J. Vac. Sci.Technol. A 26 5 Tavkhelidze A, 2010 J. Appl. Phys. 108 044313 LaB6 has and Mo-Cs and Ag-O-Cs

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Metal nanograting film on semiconductor substrate Condition electron number conservation in CB. Number of electrons rejected from the below of is equal to the number of electrons accommodated above. where, is substrate electron affinity and

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We use electron number conservation in Nanograting layer conduction band again. Metal nanograting film on metal substrate.

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Substrate material (eV) (cm -3 ) r ( Ohm cm) P d (mW) at 10 Acm -2 (Wcm -1 K -1 ) (K) at 10 Wcm -2 Si1.124.058 10 20 2 10 -4 21.60.6 GaAs1.424.078 10 19 1 10 -4 10.52.0 GaN3.204.101 10 19 7 10 -3 705.00.2 Mo5.3 10 -6 5.3 10 -2 1.40.7 Ni6.2 10 -6 6.2 10 -2 0.91.1 Parameters of electrode base materials. The and are given for 1 mm thick substrate. Material pairs for nanostructured layer coated electrode

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Characteristic energies for some metals and values of, calculated for G=10 NG layer Material(eV) (eV) on Si GaAs GaN Ag4.265.487.5 a 3.323.102.02 Nb4.305.325.5 b 3.363.142.06 W4.556.7 c 3.583.342.14 Cu4.657.09.1 a 3.653.432.20 Mo4.605.0 d 3.633.412.32 Au5.105.539.4 a 4.093.852.64 Ni5.155.0 e 4.143.902.81 Pt5.6510 f 2.95 (a) E. Lassner and W.-D. Schubert, Tungsten: properties, chemistry, technology of the element, alloys, and chemical compounds (Kluwer academic/plenum publishers (New York) NY 1999). (b) U. Mizurani, Electron theory of metals, (Cambridge University Press 2001) p. 27. (c) T. McAvoy, J. ZhangJ, C. Waldfried, D. N. McIlroy, P. A. Dowben, O. Zeybek, T. Bertrams, and B. S. Barrett, The European Physics Journal B 14, 747–755 (2000). (d) N. E. Ashkroft and N. D. Martin, Solid State Physics (NY: Saunders 1976). (e) Ch. E. Lekka, M. J. Mehl, N. Bernstein and D. A. Papaconstantopoulos, Phys. Rev. B 68, 035422 (2003). (f) A. Yamasaki and T. Fujiwara, J. Phys. Soc. Jpn. 72, 607-610 (2003). Material pairs for nanostructured layer coated electrode

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Plain LaB 6 which shows =2–3.2 eV, =10 eV. Nanograting LaB 6 layer on semiconductor substrates Inserting these values in above equations we get: =0–0.85 eV for Nanograting LaB 6 layer on GaN substrate =0.94–2.05 eV Nanograting LaB 6 on GaAs substrate =1.15–2.28 eV Nanograting LaB 6 on Si substrate G=10 was used in all cases M. A. Uijttewaal, G. A. de Wijs, and R. A. de Groot J. Phys. Chem. B 110, 18459-18465 (2006). These values were low enough for thermotunnel and thermionic devices operating at temperatures 400-1000 K

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Metal nanograting layers on metal substrates Electron confinement energy region emerges only if of a substrate material is less than Fermi energy of nanograting layer material. Ni and Mo are good choices for substrates as they have low Au, Pt, Cu are suitable for nanograting layers as they have high and at the same time can be grown epitaxially on Ni substrate. M. A. Uijttewaal, G. A. de Wijs, and R. A. de Groot J. Phys. Chem. B 110, 18459-18465 (2006). W. D. Luedtke and U. Landman, Phys. Rev. B 44, 5970 (1991). A. Tesauro, A. Aurigemma, C. Cirillo, S. L. Prischepa1, M. Salvatoand C. Attanasio, Super cond. Sci. Technol. 18, 1-8 (2005). G value needed to obtain =0.5 eV was determined for following material pairs: Cu/Ni G=8.2; Au/Ni G=7.2; Pt/Ni G=6.5

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Fabrication – UV Interference lithography H. S. Jang et al. Current Applied Physics, 10, 2010, pp. 1436–1441 C. P. Funcetola, H. Korre, and K. K.Berggren. Low –cost interference lithography. J.Vac. Sci. Technol. B 27, (2009) Low cost <1000 $ interference lithography from MIT

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PSI, Laboratory for Micro- and Nanotechnology Fabrication – X-ray Interference lithography

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Conclusions 1.Nanograting on the surface of thin layer reduces density of quantum states and increase chemical potential (Fermi level). 2.Work function reduction has been observed in nanograting films made from Au, Cr, Nb. 3.In semiconductors, nanograting induces impurity free doping or G-doping. 4.For Si and GaAs homojunctions, main layer G-doping level of 10 17 -10 18 cm -3 was obtained at a barrier layer donor doping of 10 18 -10 20 cm -3 at and. 5.For type-II heterojunctions Ga 0.52 In 0.48 P/Al 0.43 Ga 0.57 As, InP/In 0.52 Al 0.48 As, and Si/Si 0.9 Ge 0.1, a main layer G-doping level of 10 18 cm -3 was obtained at a barrier layer G-doping level of 10 18 -10 20 cm -3 and geometry factor values of 1.02-1.2 and 1.006-1.8. It was found that a high G- doping level could be attained only when the bandgap difference was low. 6.When p-n junctions are grown on the top of NG additional builds up under influence of. This leads to dramatic increase in ZT. 7. Large areas of nanograting having pitch of 10 nm can be fabricated using interference lithography without masks. 8. Multiple NG layers can be fabricated using interference lithography and epitaxial grown on nanograting base substrate.

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