Influence of Nanostructure Geometry on Electronic Properties

A. Tavkhelidze

Ilia State University, Cholokashvili Ave. 3-5, Tbilisi 0162, Georgia

Outline

IntroductionDensity of quantum states in nanograting geometryGrowth and characterization of nanograting amorphous metal filmsGeometry induced doping or G-dopingElectronic properties of multiple homojunction nanograting layersElectronic properties of multiple heterojunction nanograting layersG-doping for high electron mobility applicationsThermoelectric properties of semiconductor nanograting layersConclusions

Geometry dependent quantum effects

Periodic curved surfacesOno S, Shima H 2010 Physica E, 42 1224-1227Kartashov Y V, Szameit A, Keil R, Vysloukh V A, and Torner L 2011 Optics Letters 36 3470

NanotubesGupta S and Saxena A 2011 J. Appl. Phys. 109 074316

Cylindrical surfaces with non-constant diameterFujita 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 billiardsE. 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

Introduction

Density of state (DOS) of nanograting layer

)(ρ0 EDOS in plain layer DOS in nanograting layer )ρ(E

where, G >1 is a geometry factor.

According to Fermi's golden rule, the electron scattering rate is proportional to Consequently,

)(E

0 G

GEE /)(ρ)ρ( 0

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).

Software for mode calculation in ridged waveguides: FIMMMWAVE, photon design software (A fully vectorial 2D Mode Solver), ttp://www.photond.com/products/fimmwave.htm.CONCERTO, software for electromagnetic design, Vector Fields, http://www.vectorfields.com.

Perturbation method was used to obtain approximate formula G=(2H-a)/2a within the range of 3<.G<10 and for the case H, w>>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)

Nanograting layer crosssection

Energy diagrams metal

Energy diagrams semiconductor

Electronic properties of metal and semiconductor Nanograting layer

Sample preparation and characterization

Au, Nb, Cr films were quench depositedAt T=300 K and T=80 K.

Kelvin probe was used to measure difference in work function between nanograting and plain areas.

AFM image of Au Nanogratilg layer

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 hadamorphous 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 SiO2 films were observed.

Electrons with energies E<<EF do not participate in charge and heat transport but still diffract on Nanograting

PEEM images of Nanograting Au film surface

Rempfer G F, Skoczylas W P, and Hayes Griffith O 1991 Ultramicroscopy 36 196

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).

Geometry factor G, density of states GEE /)(ρ)ρ( 0

Number of rejected electrons

)1()(ρ/)(ρ)(ρ)(ρ 1000FOR

GEGEEEDensity of forbidden quantum states

CON1

CON0

CON

1FORREJ )1()(ρ)1()(ρ nGEdEGEdEn

CON

0CON )(ρ EdEnWhere,

Integration takes place over the energy regions depicted with red hatch.

Electron confinement energy regions

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

02)1(4

3ln

13

42ln23

2/3

2/32/3

C

db

mV

dbm

m

m

C

V

NnG

GNnGG

GG

NN

TkE Bcon

dn 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.

Material[cm-3] [meV] [cm-3] [meV] [meV]

Si3 x 1018 45 6 x 1017 103 58

1 x 1019 64 1 x 1018 89 25

3 x 1019 87 1 x 1018 77 -10

1 x 1020 126 2.8 x 1018 62 -64

GaAs1 x 1018 47 3.2 x 1017 3.4 -44

3 x 1018 86 8 x 1017 -29 -115

5 x 1018 119 1.3 x 1018 -52 -172

1 x 1019 197 2.8 x 1018 -110 -297

dn conE rn )(mFE )(b

FE

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

02.1mG 1.1bG T=300 K

Materials

[main/barrier] [meV] [meV] [meV] [meV] [cm-3] [cm-3] [meV

Ga0.52In0.48P/

/Al0.45Ga0.55As

257 14 1.02 1.2 81 58 1.3 x 1018 1.1 x 1019 118

InP/

/In0.52Al0.48As

34 25 1.2 1.8 131 111 1.3 x 1018 4.8 x 1019 98

Si/

/Si0.5Ge0.5

56 24 1.1 1.006 28 15 1.4 x 1018 2.1 x 1018 13

CE VE mG bG )(mbiE )(b

biE )(mrn )(b

rn tbE

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 1018 -1019 cm-3mG bG

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)

G-doping for high electron mobility applications

In a multi-junction solar cell the window, emitter, and tunnel junction layer doping level is roughly 1018 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 1020-1021 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

Thermoelectric properties of nanograting layers

)/( le2 SZ Materials having high S have low

Increasing leads to an increase in e (Wiedemann–Franz law)

We present large enhancement in S without changing e

)d()(eff TaTa

)G(G T

Calculate Z and compare with Zo where, Zo corresponds to )G(G T

J0

in Boltzmann transport equations and calculate S asWe insert

J0 SSS

A. Tavkhelidze, Nanotechnology 20, 405401 (2009).

Charge and heat transport

GDepletion 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

TG

TeJ 1211 / LL TeJ Q 2221 / LL and

jiLWithin the parabolic bands approximation are integrals

)(y)τ()ρ()(Ω 20

)( v EEEEfdEE

The NG does not change dispersion relation and consequently yv

Chemical potential of nanograting layer

GEE /)(ρ)ρ( 0 )(τ)τ( 0 EGE For NG layer 2

yv)τ()ρ( EE

and and consequently

product is G independent.

The NG influences integrals )(Ω )( E by changing alone.

jiji0LL

C2/3

CB /2/ln NnNnTk

CBcon2/3

CBconB )1(2)1(ln NGnNGnTk

CBcon02/3

0B0 2)1/(1ln NnGGGGTk

)( 00 G

)1(COND GnNIntroduction of defines reference material as n+-type semiconductor with electron concentration of or NG having constant geometry

factor 0GG 0)/( TG

T θ0

TG

GTGG

GG

kB 1

121

11

lnθ 00

CBcon2/3 /2 Nn

Charge and heat transport

TeeJ // 110

1200

110 LLL

TeeJ Q // 210

2200

210 LLL

eSeS // 0110

110

120

LLL

0110

210

110

120

210

220 /)/( eeee

LLLLLL

0110 L

Geometry factor temperature dependence

)d()(eff TaTa

dTTdaGdTdGTG /)d(/)/(/ eff

2/1

Bbi

DAD

AS 2)(

2)d(

eTk

NNNN

eT

eE gbipbinbi

2/1

11Bg

co2

S

)]1(1[)1(

)2(2)d(

GG

TkE

neT

n

Acon / Nn

BBB1

np 23)1(2/35//)( kGkkTTETG )/(2 VA

2/3 NN

1)1()1(2

)2( B1

11

Bgnp GG

TkGG

GGG

GTkEE da /eff

CBcon2/3 /2 Nn

Seebeck coefficient of nanograting layer with p+–n+ junctions

TG

GeTk

SS 1

1B0

**)(F*)(F

2/32/5

1/2r

3/2rB0

rr

ek

S

r is a scattering parameter

TkB/*

200/ SSZZ

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 efficiency2 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 2572Tavkhelidze A, Svanidze V. and Tsakadze L 2008 J. Vac. Sci.Technol. A 26 5Tavkhelidze A, 2010 J. Appl. Phys. 108 044313

eV4e eV4.02.0 e

eV32 e eV1eLaB6 has and Mo-Cs and Ag-O-Cs

Metal nanograting film on semiconductor substrate

3/22/3gm

2/30mm /1

eχeeEGGeee

Condition electron number conservation in CB. Number of electrons rejected from the below of is equal to the number of electrons accommodated above .(0)

FE

(0)FE

0(0)Fm eEe where, is substrate electron affinity and

3/22/3g

2/3m

12/30mm /1 eEGeee m

ee

We use electron number conservation in Nanograting layer conduction band again.

Metal nanograting film on metal substrate

2/3m

11 SSG 2/30m

2/3m

.

Substrate material (eV) (eV) (cm-3)

r

( Ohm cm)

Pd (mW) at

10 Acm-2

(Wcm-1K-1)

(K) at

10 Wcm-2

Si 1.12 4.05 8 1020 2 10-4 2 1.6 0.6

GaAs 1.42 4.07 8 1019 1 10-4 1 0.5 2.0

GaN 3.20 4.10 1 1019 7 10-3 70 5.0 0.2

Mo 5.3 10-6 5.3 10-2 1.4 0.7

Ni 6.2 10-6 6.2 10-2 0.9 1.1

Parameters of electrode base materials. The and are given for 1 mm thick substrate. dP T

gE e DN T

Material pairs for nanostructured layer coated electrode

Characteristic energies for some metals and values of , calculated for G=10e

NG layer

Material (eV) (eV) (eV)

(eV) on

Si GaAs GaN

Ag 4.26 5.48 7.5a 3.32 3.10 2.02

Nb 4.30 5.32 5.5b 3.36 3.14 2.06

W 4.55 6.7c 3.58 3.34 2.14

Cu 4.65 7.0 9.1a 3.65 3.43 2.20

Mo 4.60 5.0d 3.63 3.41 2.32

Au 5.10 5.53 9.4a 4.09 3.85 2.64

Ni 5.15 5.0e 4.14 3.90 2.81

Pt 5.65 10f 2.95

(0)FEe Band

FE e

(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

Plain LaB6 which shows =2–3.2 eV , =10 eV.

Nanograting LaB6 layer on semiconductor substrates

e BandFE

Inserting these values in above equations we get: =0–0.85 eV for Nanograting LaB6 layer on GaN substrate =0.94–2.05 eV Nanograting LaB6 on GaAs substrate =1.15–2.28 eV Nanograting LaB6 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).

eee

These values were low enough for thermotunnel and thermionic devices operating at temperatures 400-1000 K

Metal nanograting layers on metal substrates

Electron confinement energy region emerges only if of a substrate materialis less than Fermi energy of nanograting layer material.

BandFE

Ni and Mo are good choices for substrates as they have low BandFE

Au, Pt, Cu are suitable for nanograting layers as they have high and at the same time can be grown epitaxially on Ni substrate.

BandFE

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: e

Cu/Ni G=8.2; Au/Ni G=7.2; Pt/Ni G=6.5

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

PSI, Laboratory for Micro- and Nanotechnology

Fabrication – X-ray Interference lithography

Conclusions1. 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 1017 -1018 cm-3 was obtained at a barrier layer donor doping of 1018 -1020 cm-3 at and .

5. For type-II heterojunctions Ga0.52In0.48P/Al0.43Ga0.57As, InP/In0.52Al0.48As, and Si/Si0.9Ge0.1, a main layer G-doping level of 1018 cm-3 was obtained at a barrier layer G-doping level of 1018 -1020 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.

T

1.1bG1.1mG