D.W. Brenner et al- Simulated Engineering of Nanostructures

8/3/2019 D.W. Brenner et al- Simulated Engineering of Nanostructures

1/16

Proceedin gs of the 4th Foresight Conference, su bm itted to N an otechn ology

SIMULATED ENGINEERING OF NANOSTRUCTURES

D.W. Br enn er a , S.B. Sinnott b , J.A. Harrison c , an d O.A. Shend erova a

a

Department of Materials Science and Engineering, North CarolinaState University, Raleigh, NC 27695-7907

b Department of Chemical and Materials En gineering, University ofKentucky, Lexington, KY 40506-0046

c Chemistry Depart ment, United States Naval Academy, Annapolis,MD 21402

ABSTRACT

Results are reported from two molecular-dynamics simulations de-

signed to yield insight into the engineering of nanometer-scale struc-

tur es. The first is the initial sta ges of the indenta tion of a silicon sub-

str at e by an at omically-sha rp diamond tip. U p to an indenta tion depth of

approximately 0.6nm the substrate responds elastically and the profile

of the disturbed region of the substrate normal to the surface reflects

the shape of the t ip apex. The disturbed region in the plane of the sur-

face, however, reflects the symmetry of the substrate rather than that

of the tip. As indentation progresses the da mage to the substrat e be-comes irr eversible, and t he pr ofile of the dam age norm al to th e substr at e

surface approximat ely ma tches th at of the t ip, while the in-plane profile

appears roughly circular rather than displaying the symmetry of either

the t ip or substrate. The tip maintains its integrity throughout the sim-

ulat ion, which h ad a ma ximum indenta tion dept h of 1.2nm. The second

study demonstra tes pa tterning of a diamond substrat e using a group of

ethynyl r adicals att ached to a diamond tip. The tip is designed so that

the terrace containing the radicals has an atomically-sharp protrusion

that can protect the radicals during a tip crash. At contact between thetip and substrate the protrusion is elastically deformed, and five of six

chemisorbed ra dicals a bstra ct hydrogen at oms dur ing th e 1.25 picosec-

onds t he t ip is in conta ct with the surface. Displacement of the tip an

ad ditional 2.5A, however, resu lts in perm an ent d am age to th e protru sion

with little deform at ion of the substra te.


2/16


I . Int r odu c t i on

Ne w te c h n iq u e s fo r p a tte rn in g a n d e n g in e e rin g ma te ria ls a t th e

na nometer-scale u sing scann ing-pr obe microscopes (SPM) are beginn ing

to ma ke possible t he long-sta nding goal of na nometer-scale mecha nicalan d electr onic devices. Examp les like the direct writing of na nometer-

scale met allic lines by field-evapora tion from a SPM t ip, lithograph ic pro-

cesses th at ta ke ad van ta ge of th e nan ometer-scale resolution of electr ons

emitted from SPM tips, and nanomachining of surfaces via mechanical

forces have all been demonstrated.1 Despite these advances, however,

formida ble challenges rema in t o the development an d especially ma nu-

facturing of nanometer-scale structures. Among these is overcoming theinher ent ly slow th rough-put for sin gle tips, routin e r eproducible produc-

tion of high-quality nanometer-scale structures, and the positioning of

nanometer-to-macroscopic-scale interfaces.

To meet t hese challenges in n an ometer-scale device development a nd

ma nufacturing n ot only new innovat ions in engineering are needed, but

also a thorough understanding of the atomic-scale processes responsi-

ble for the production of nanometer-scale str uctures. One powerful ap-

proach that is bringing new an d un ique insights into ma terials proper-

ties a t na nometer scales is a tomistic molecular-dyna mics simulat ion. In

th is t echn ique, tr ajectories of a collection of at oms subject to given int er-

at omic forces are obta ined by nu mer ically int egrat ing classical equa tions

of motion. Fr om car eful an alysis of the tr ajectories and their relation to

properties such a s str ess and potent ial energy distr ibutions, one can un -

ders ta nd comp licat ed atomic-scale dyna mics in t erm s of na nometer-scale

bonding and mat erials properties. A number of researchers have used

at omistic simulat ions to m odel t ip-surface intera ctions.2 These have in-

cluded the indentation of various metals,3 ionic solids4, and covalent ma-

ter ials su ch as s ilicon5 and diamond.6 Simulations have also been used to

2


3/16


explore t he possible pat ter ning of a diam ond s ur face via chemical forces

using m odified SPM tips.7

Results are reported from two representative molecular-dynamics

simulations designed to yield insight into the engineering of nanometer-scale str uctures. The first is a simula tion of th e initial sta ges of indenta -

tion of a silicon substrate by an atomically-sharp diamond tip, where the

dam age profile in th e substr at e as well as dam age to the t ip is char acter-

ized. The second st udy demonstr at es pat tern ing of a diam ond substr at e

using a group of ethynyl radicals att ached t o a diamond t ip. The tip is

designed so that the terra ce containing the radicals ha s an atomically-

sharp protrusion that protects the chemisorbed radicals during a tipcrash.

I I . Nanome t e r - Sc al e I nde nt at i on of Si l i c on

The focus of the simu lation is the initial stages of indenta tion where

th e s u bs tra te re sp on s e ch a n g es from a n e la s t ic d e forma tion to irre-

v ers ib le p la s t ic d a ma g e. Of pa rt icu la r in te res t is wh eth e r th e n e t-

work structure of an atomically-sharp diamond tip is sufficiently well-

developed to cleanly indent a silicon substrate, and whether the shape

of an atomically-shallow indent is governed by the tip shape or is deter-

mined by th e substrat e. Both of these are importan t issues in nanometer-

scale materials engineering because they test the limitations of feature

size an d shap e tha t can be produced on a silicon subst ra te via nan omet er-

scale machining.

For t he initia l silicon subst ra te, at oms ar e placed in a diam ond lat tice

at t he experim ent al latt ice const an t with th e (111) sur face exposed. A to-

ta l of 18 layer s ar e used, ea ch wit h 256 s ilicon at oms, for a tota l of 4608

at oms. A semi-infinite slab is modeled by applying periodic bounda ry

3


4/16


conditions in the two directions in t he su rface plane. No initial recon-

str uction of the surface or term inat ion of surface ra dicals is a tt empted.

The int erat omic forces used to deter mine t he at omic tra jectories a re ob-

ta ined from th e th ird ver sion of Ters offs bond -ord er potent ial for silicon.8

This analytic function is composed of a sum of two exponential pair-

additive terms, one representing core-core repulsion and a second rep-

resenting bonding from valence electrons. The many-body aspect of the

potential energy function enters through empirical bond-order functions

th at modulate t he bonding pair term s a ccording t o local a tomic bonding

environments. The pair terms and bond-order functions a re fit t o an

extensive data base that includes bulk elastic properties, energies and

bond lengths for a variety of low and high-coordination solid structures,

an d t he ener gy of vacancies a nd var ious interst itial point defects.

The end of the tip is illustra ted at the t op of Figure 1a. It is pyram i-

dal in shap e with exposed (111) facets. Surface r adicals on ea ch of the

facets are eliminated by chemisorbed hydrogen. The tip symmetry in the

surface plan e of the su bstra te is an equilatera l triangle, an d the a pex is a

hydrogen-terminated six-membered carbon ring. The interatomic forcesfor the tip a toms a re derived from a bond-order function similar to tha t

used for the silicon substrate.9 It has also been fit to solid-state elastic

properties as well as energy and bond lengths of various low and high-

coordina tion str uctures. In addition, t he bond-order function describes

bond lengths, energies, and vibrational frequencies for a wide range of

hydrocar bon molecules. Becau se both solid-sta te and molecular str uc-

tures are described, the interatomic forces are appropriate for the tip

where t he bonding network is intermediate between these two regimes.

The interactions between the tip and substrate atoms are modeled

by pair-additive Lennard-Jones 12-6 potentials with parameters taken

4


5/16


from r eference 10. Although convenient, this choice eliminates chem-

ical interactions between the tip and substrate because the formation

of chem ical bonds is not possible. Noneth eless, th is choice is su fficient

for m odeling physical intera ctions an d r esulting dynamics in the tip a nd

substrate.

The motion of the atoms are determined by numerically integrat-

ing classical equa tions of motion using a Nordsieck integrat or 11 with a

constan t timestep of 0.5 femtoseconds. The tip a nd substrate are first

relaxed to their m inimum energy configurat ions. The relat ive positions

of the a toms in th e bottom two layers of the substra te a nd the top t wo

layers of th e tip ar e then held rigid by not integra ting equat ions of motionfor these atoms. To simulate indentation, tip atoms are given an initial

velocity of 100 m/sec towar d th e su bstra te. This ra te of indenta tion is

then maintained by moving the atoms in the top two layers of the tip

5x10 5nm at ea ch timestep up t o a total indenta tion depth of 1.2nm. No

ther mostats or other t empera tur e regulation of the system is perform ed

during th e simulated indentat ion.

Figure 1b illustrates the system after the tip has penetrated the sur-

face 1.2nm. None of the silicon a toms a ppear above the surface of the

substrate, but instead form a highly-localized, dense region surrounding

th e t ip. T h is is in con tra s t to me ta ls , wh ere in de n ta tion re s u lts in a

build-up of materia l above the substr at e sur face.12 To more clear ly illus-

trate the indentation profile in the substrate, Figure 2 shows side and

top views of only th ose subst ra te at oms whose binding energies ar e dis-

turbed by more than 0.1eV ( 2% of the bulk atomic binding energy of

silicon). Figures 2a a nd d are for an indenta tion depth of 0.2nm. The

dama ge profile of the disturbed region norma l t o the surface (the side

view) approximately mat ches that of the tip apex. The profile in t he

plane of the surface, however, has three-fold symmetry indicative of the

5


6/16


top layer of th e substra te. After t he tip is removed the substr at e regains

its initial str ucture indicat ing an elastic deform at ion.

Figures 2b a nd e a re for an indentat ion depth of 0.5nm, or approx-

imat ely two at omic layers int o the silicon su bstra te. The pr ofile of thedisturbed region normal to the surface again approximates the shape of

the tip apex. The profile in t he sur face plane, however, appears as a

slightly distorted hexagon. This is indicative of the hexagonal symmetry

of the su bstra te (if more tha n one layer is ta ken int o account ) rath er t ha n

the triangular symmetry of the indentor. After t he t ip is removed th e

substrate regains its initial structure with no permanent deformation of

the lattice.

Illustrated in Figures 2c and f are profiles for an indent depth of

1.2nm. The bonding topology in th e distur bed region h as been altered

from that of the initial substrate and forms a highly-localized disordered

region surrounding the tip. The in-plane profile of the disordered region

of the substrate no longer m atches that of the tip or substrat e. Instead,

it appears approximately circular, with a few pertur bed a toms visible

several lattice spacings away from the disordered region.

Figure 3 illustra tes the tip atoms at the ma ximum indent at ion depth.

The r elative displacements of the a toms a re sm all compa red to th ose of

the silicon substrate, and the tip maintains its bonding connectivity

throughout the simulation. This is despite the bonding network of a

diamond lattice not being fully developed in the tip apex.

Several conclusions can be drawn from this simulation. First, th e

da ma ge to the su bstr at e is highly-localized an d consist s of a high-densit y

region surrounding th e t ip. No atoms appear above the surface plane,

an d n o additional long-ra nge atomic displacements ar e observed. Sec-

ond, the profile of the perturbed surface atoms normal to the surface is

6


7/16


dicta ted by tip sh ape for both elastic an d plast ic deform at ions. Third, as

long as the damage is reversible when the tip is removed, the in-plane

profile of the indent is governed by the substrate symmetry rather than

that of the tip. However, as the dama ge becomes perma nent due t o the

rebonding of substrat e a toms, the in-plane profile of the indent ha s nei-

th er th e tip nor subst ra te symmetr y, but ra ther appea rs circular. We ar e

currently studying stress distributions in the substrate during inden-

tat ion t o try to better understa nd th e origin of this result. It a ppears,

however, tha t the in-plane sha pe of the indent at these scales is not con-

tr olled by the symm etry of the t ip. Finally, we find th at the tip ma inta ins

its integrity du ring th e indent . As discussed below, this is n ot tru e for a

diamond substrate. We are currently using simulations to characterize

tip sta bility during scra ping as a function of tip sha pe and indent d epth.

I I I . Sur f ac e Pat t e r ni ng vi a Che mi c al For c e s

Exploring a suggestion first made by Drexler,13 Sinnott et al. used

MD simulations to model the abstraction of a single chemisorbed hydro-

gen atom from a diamond surface via an ethynyl radical chemisorbed

to an atomically-sharp diamond tip.7 This pr oposed process is an other

way in which the SPM can be used to nanoengineer surfaces by spatially

directing chem ical forces. Rat es an d mecha nism s of ener gy flow after a b-

straction were monitored and it was concluded that energy dissipation

is sufficiently fast to ma ke th is reaction inst an ta neous an d irr eversible.

However, it was also found that events such as tip crashes and the rad-

ical defects can destroy the tip. To eliminate these possibilities, a novel

tip design was pr oposed where a sperities ar e placed ar ound the reactive

site. These asperities keep the reactive site from coming too close to the

sur face an d th e tip from being destroyed during a crash. Fur ther more, it

was found tha t t he load on the t ip due to the intera ction of the a sperities

with th e sur face can be used as a signal tha t a bstra ction h as occurr ed.

7


8/16


Building on t his concept of protecting th e r eactive region with a sper i-

ties, we ha ve simu lat ed hydrogen abst ra ction from a hydrogen-ter mina ted

diamond (111) surface using the t ip design illustr at ed in F igure 4a . The

end of the tip has a terrace on which six ethynyl radicals have been

chemisorbed that surround an atomically-sharp protrusion. One of the

ra dicals is visible in t he cent er-foreground of the ima ge, while two oth er

pairs of radicals are visible on either side of the protrusion about half-

way back and in the far background, respectively. The sixth r adical is

behind the protru sion. With t his arr an gement the protrusion acts as the

load sen sor while six abstr actions can in prin ciple be car ried out simu lta -

neously. The diamond substrate used has a hydrogen-terminated (111)

sur face exposed. The subst ra te a nd tip ar e first allowed to rela x to a min-

imum energy configura tion using t he h ydrocar bon/diam ond int erat omic

forces described above. The r elat ive positions of th e t op t wo layer s of th e

tip and t he bott om t wo layers of the su bstra te ar e then m aint ained while

the t ip and su bstra te a toms ar e equilibrated to 300K. The tip is lowered

toward the substrate following the procedure outlined above.

Figure 4b illustr at es the simula tion a fter th e protrusion conta cts t hesubstrate but before any of the abstraction reactions have taken place.

The protrusion has deformed slightly, with no visible deformation of the

lattice. Figure 4c illustra tes t he system approximately 0.5ps after the

protrusion first conta cts th e sur face. The ra dicals chemisorbed to the tip

in th e foreground an d far ba ckground on the left have both abstr acted a

hydr ogen at om from the diam ond substr at e. The tip is left in cont act with

the substrate for 1.25ps before being retracted with the same approach

used t o lower th e tip. As illustr at ed in F igure 4d, five of the six ra dicals

abstract hydrogen, with the remaining ethynyl radical visible to the

right of the pr otrusion halfway back. Note t hat the initial form of the

protrusion is reta ined after the tip is removed.

8


9/16


The five abstra ction sites on the substrate m atch th e patt ern of the

ra dicals on t he t ip. Becau se th ese ar e highly-reactive sites, this patt ern

can be used as a templat e in a subsequent nan ometer-scale engineering

step su ch as th e chemisorpt ion of molecular species to the surface. By

continu ing this process of r adical form at ion/chemisorpt ion, it could in

pr inciple be possible to system at ically engineer complex na nostr uctur es.

Figure 5 illustra tes the system a fter t he tip is displaced an additional

2.5 A towar d the substra te a fter t he protru sion first conta cts t he sur face.

The protrusion has been crushed and the ethynyl radicals effectively de-

str oyed. It is appar ent from t his figur e tha t t he m ajority of deform at ion

occurs in t he protrusion with little deforma tion of the substrate. Thisis different from the silicon substrate simulated above, and is a result

of the higher h ar dness of the diamond substra te relative to silicon. Be-

cau se th e pr otr usion, which is identical t o the first few layers of the t ip

used above, is destroyed before the substrate is deformed, mechanical

indenta tion cannot be used to modify the diamond latt ice. While an

at omically-shar p diamond can indent a silicon su bstra te, appa rent ly the

net work st ru ctu re of diam ond is not su fficiently well developed in the t ipto give it a mechanical str ength compa ra ble to a bulk diam ond su rface.

This work is supported by the Office of Naval Research. DWB is

also support ed by the Nat ional Science Founda tion thr ough a CAREER

development grant. R.J. Colton and C.T. White ar e t hanked for many

insightful discussions.

9


10/16


R e f e r e n c e s

1 For a collection of pa pers on th is su bject, see J. Vac. Sci. Technol. B ,

13 , (1995).

2 J.A. Ha rr ison a nd D.W. Brenn er, in CR C Han dbook of Micro/ N an otribology

Busha n. Ed. (CRC Publishers, 1995), cha pter 10.

3 U. Lan dma n, W.D. Luedtk e, N.A. Burn ha m, a nd R.J. Colton, S cience,

248, 454 (1990); H. Raffi-Tabor, J.B. Pethica, and A.P. Sutton, M at .

Res. S oc. S ymp. Proc., 239, 313 (1992); O. Tomagnini, F. Ercolessi,

an d E. Tosat ti, Surf. Sci, 287/288 , 1041 (1993).

4 U. Lan dma n, W.D. Luedtk e, an d E .M. Ringer, Wear, 153, 3 (1992).

5 J.S. Ka llma n, W.G. Hoover, C.G. Hoover, A.J. D eGr oot, S.M. Lee, a nd

F. Wooten , Phys. Rev. B , 47, 3318 (1993).

6 J.A. Harrison, C.T. White, R.J. Colton, and D.W. Brenner S u r f . S c i,

271, 57 (1992)

7 S.B. Sinnott, R.J. Colton, C.T. White, and D.W. Brenner, S urf. S ci .,

316, L1055 (1994).

8 J. Tersoff, Phys. Rev. B , 39, 5566 (1989).

9 D.W. Br enn er, Phys. Rev. B , 42 9458 (1990). The version used here

includes a slight ly different form t ha t im proves th e elast ic propert ies

for diamond (D.W. Brenner, S.B. Sinn ott and J.A. H ar rison, unpu b-

lished).

10 M.P. Allen a nd D.J. Tildesley, Com puter Sim ulation of Liquid s (Claren-

don Press, Oxford, 1987), pg. 21; parameters for carbon are used for

silicon.

11 C.W. Gear, N um erical In itial Value Problem s in Ordinary Differential

Equations (Prentice-Hall, Englewood Cliffs, NJ, 1971), pg. 148.

12 J. Belak and I.F. Stowers in Fundamentals of Friction: Macroscopic

an d Mi croscopic-S cale Processes, (Kluwer, Dordrecht, 1995), pp.511-

520.

13 K.E. Drexler, N anosystem s: Molecular Machinery, Manu facturing

and Com putation , (Wiley, N ew York , 19 92).

10


11/16


(a ) (b )

Figure 1: Snapshots illustrating the surface region during indentation. The

s ma ll s ph e res on th e d ia mon d t ip a re h y d roge n a toms . a ) In it ia l

configuration. (b) Indentation of 1.2 nm.

11


12/16


Top

Top

Top

Side

Side

Side

(a)

(b)

(c)

(d)

(e)

(f)

12


13/16


Figure 2: Illustration of silicon atoms whose binding energies are disturbed

by more t han 0.1eV. (a), (d) Indentation depth of 0.2nm. (b), (e)

Indentation depth of 0.5nm. (c), (f) Indentation depth of 1.2nm.

13


14/16


Figure 3: Illustra tion of the t ip atoms at the m aximum simulated indentation

depth of 1.2nm.

14


15/16


(a ) (b )

(c ) (d )

Figure 4: Sna pshots illustrating the tip used to m odel chemical abstraction.

The top of the figure shows the tip and chemisorbed ethynyl radicals,

while th e bottom is a hydrogen-term ina ted diam ond (111) sur face. (a)

Initial configurat ion. (b) J ust after t he pr otru sion on th e tip conta cts

th e sur face. (c) System 0.5ps after protrusion conta cts surface. (d)

After the tip is lifted from t he su bstra te.

15


16/16


Figure 5: Illustrat ion of th e system after t he t ip is lowered an a dditional 2.5A.

The protru sion is irreversibly dama ged.

16

D.W. Brenner et al- Simulated Engineering of Nanostructures

Documents

Transcript of D.W. Brenner et al- Simulated Engineering of Nanostructures