Proof of asymmetry in the Cd-arachidate bilayers of ultrathin Langmuir-Blodgett multilayer films via X-ray interferometry

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Proof of asymmetry in the Cd-arachidate bilayers of ultrathin Langmuir-Blodgett multilayer films via X-ray

interferometry

S. Xu, M. Murphy, S. Amador, J. Blasie

To cite this version:

S. Xu, M. Murphy, S. Amador, J. Blasie. Proof of asymmetry in the Cd-arachidate bilayers of ultrathin

Langmuir-Blodgett multilayer films via X-ray interferometry. Journal de Physique I, EDP Sciences,

1991, 1 (8), pp.1131-1144. �10.1051/jp1:1991195�. �jpa-00246398�

J.

Phys.

I France 1

(1991)

l131-l144 Ao0T1991, PAGE l131

Classification Physics Abstracts

61.10F

Proof of asymmetry ^{in the} Cd-arachidate bilayers of ultrathin

Langmuir-Blodgett n~ultilayer ^{rams da} X-ray interferometry

S.

Xu,

M. A.

Murphy,

S. M. Amador

(*)

^and J. K. Blasie

Department

of

Chemistry,

and the

Laboratory

for Research _on the structure of Matter,

University

of

Pennsylvania, Philadelplfia,

PA I9I04, U-S-A-

(Received10 April1991, accepted

30

April 1991)

Amtract. X-ray

interferometry

was used to

study

the

profile

structures of ultrathin

Langmuir- Blodgett

films of Cd-arachidate

deposited

on

alkylated gerrnanium/silicon multilayer

substrates.

The relative electron

density

profiles of the _one, two and three

bilayer

films _on the

Ge/Si multilayer

substrates, derived via

X-ray interferometry employing

a

highly

constrained, real _space

refinement

algorithm,

have shown the _same kind of asymmetry ^{in the}

bilayers

of such ultrathin films

deposited

_on

alkylated

silicon _or

alkylated glass,

_as derived less

directly

and described

previously [lJ.

THs _paper demonstrates

experimentally

the power of the X-ray

interferometry

method [2J for

solving

_an unknown structure

by placing

_a known structure beside it, and furthermore _proves the correctness of the

upstroke-downstroke

asyInrnetry ^{in the} Cd-arachidate

bilayers

due to the

Langmuir-Blodgett deposition technique.

Inwoducfion.

X-ray

diffraction [3J can in

principle

be used to

investigate

the structure of very thin

multilayer

films

containing

from _one to many molecular

monolayers deposited

_on solid substrates

by

the

Langmuir-Blodgett (LB) technique.

One would like _to ascertain whether the structures of the individual

monolayers

differ from _one another and

particularly

whether the substrate

perturbs specific

individual

monolayers

in the film. Previous

analyses

of the meridional

X-ray

diffraction from such

multilayer

films have

employed

either _a

nonunique modeling

of the

multilayer

electron

density profile

to fit the observed diffraction data

[4J,

_or direct methods

(multilayer profile

Patterson-function deconvolution

[5-8J,

and counterion

isomorphous replacement _[9J)

to

uniquely

^derive the electron

density profile

of the

presumed symmetric biJayer (or bilayer pair) repeated

N times in the

multilayer.

A

non-unique

box- refinement

technique [1, 7, 8,

_10J has been _more

recently

^utilized to

provide

the relative electron

density profile

for the entire

multilayer

such that each individual

monolayer

in the

multilayer

_can be

distinguished. Although application

of the box-refinement

technique

to _a

homologous

series of

multilayer

structures

[7,

_8J

provides

further

support

^{for the} correctness

(*)

Present address:

Physics

Deparhnent, Haverford College, Haverford, PA 19041, U-S-A-

1132 JOURNAL DE PHYSIQUE I hf ₈

of the derived

multilayer profile

structures where _no assumptions ^of

bilayer

_{symmetry or}

repetition

_were made, these

profile

structures must still be

regarded

as non-unique.

In this paper, we

employ,

a

powerful

method for

uniquely determining

the

profile

structure of _an unknown

multilayer

structure

placed

next to a known

multilayer profile

_structure,

namely X-ray interferometry

as first

proposed

in 1971

[2].

Modern nanofabrication

techniques

make it

possible

to achieve this situation

by depositing

the organic

multilayers

of

interest via

Langmuir-Blodgett

or

self-assembly

methods upon

known,

stable _inorganic

multilayer

structures made

by sputtering [[[j

_or Molecular Beam

Epitaxy (MBE).

^Phase information for the unknown structure in such _a

composite

system can be

obtained,

if the

inorganic multilayer

structure is known

precisely,

from the interference of

X-ray photons

diffracted

by

the known and unknown _structures [2~

1?].

^A

precise knowledge

of the electron

density profile

of the known (or

reference)

_structure is

essential,

and the reference _structure

must be stable _to the

deposition

of the unknown

organic multilayer

structure onto its surface.

Synthetic inorganic Ge/Si multilayer

structures made

by

magnetron

sputtering

_or MBE _can therefore

provide

_a suitable reference structure that _can be

independently

determined

by

X- ray diffraction in the absence of the

organic multilayer.

We have collected accurate meridional

X-ray

diffraction data from

multilayers composed

of one, two and three

bilayers

of Cd-arachidate

deposited

via the

Langmuir-Blodgett technique

simultaneously

_on both

alkylated

two or three

bilayer

Ge/Si

multilayer

substrates and

alkylated

silicon substrates. Profile structures for the Cd-arachidate

multilayers

on the

alkylated Ge/Si multilayer

substrates derived via

X-ray interferometry agreed

with those _on

alkylated

silicon derived via box-refinement _as well _as with those _on

alkylated glass

described

previously [I].

^These

unique

structural results achieved via

X-ray interferometry

therefore prove that the

non-unique

results obtained

previously using

^the box-refinement

technique

_are

correct, and

firmly

establish the

upstroke-downstroke

asymmetry in these

bilayers deposited by

the

Langmuir-Blodgett technique.

Methods.

Two types ^{of substrates} were used for this initial

study

with

Ge/Si multilayer

substrates. These

substrates _were manufactured

by

Ovonic

Synthetic

Materials

(Troy, Michiganj using

magnetron

sputtering.

One type of substrate

(Si)

_{was a}

polished

Si wafer 30 mil thick _upon

which _was

deposited

_a

501layer

_{of Si to}

_improve

_{the smoothness of the substrate. The}

second type ^{of substrate}

(Ge/Si)

_was based _on the first type _upon ^{which alternate}

layers

of

germanium

and silicon _were

deposited

_to result in _a

201

_{thickness for each Ge}

or Si

layer

and _a

bilayer

unit cell _» with _a

profile

thickness of

401.

_This

_profile

_thickness

was chosen to

roughly

coincide with the

profile

thickness of the

lipid bilayer

in the

organic multilayer

film to be

subsequently deposited,

thus

generating

_strong

X-ray

diffraction from the reference

Ge/Si multilayer

structure over

regions

of

reciprocal

_space

perpendicular

to the substrate

plane,

I-e-

along

the q=

axis,

in which diffraction from the

organic multilayer

is also strong.

Furthermore

by using

_very few

bilayers

in the reference

multilayer,

_e-g- two or

three,

_{one can} generate ^continuous

X-ray

diffraction _{over a} broad _range of _q~ thus

ensuring

the _maximum

degree

of interference with the diffraction from the unknown

organic multilayer

adsorbate

system. ^{Because of the} fundamental limitations in the

sputtering technique,

each

monolayer

so

produced

cannot be much thinner and _can

easily

have _an

uncertainty

of _±

21

_{the former}

severely

limits the maximum value _{of q= to} which diffraction from the reference

multilayer,

and hence the essential interference

phenomena,

_can be detected.

The

preparation

of the

organic multilayers

via the LB

technique

_was

previously

described [7] and will

only

be summarized. Substrates of each type ^diced to an area I cm

by

2 _cm were

thoroughly

cleaned and rendered

hydrophobic by covalently attaching

_a

monolayer

of

bt 8 X-RAY INTERFEROMETRY AND BILAYER ASYMMETRY IN LB FILMS I133

octadecyltrichlorosilane (OTS)

to the surface

[13J.

^A monomolecular

layer

of arachidic acid

was

spread

onto _a clean air-water interface. The

subphase

_{was a} 0.25mM solution of

Cdcl~

ⁱⁿ

Milli-Q

filtered _water with 0.I mM

NaHCO~

_or TItIS buffer of

pH

-~ 7 at the

temperature

^of17.5 °C. The

spread

films _were

compressed

to a constant surface pressure of

30dyne/cm,

which _was maintained

during deposition.

One of each of the two types ^of

substrates,

I-e-

alkylated

Si and

alkylated Ge/Si,

_were

passed simultaneously through

the

monomolecular

layer-water

interface

cyclically

at a rate of

3mm/min

to

produce

_a two

monolayer (one bilayer)

film _on each substrate _per

cycle.

The

resulting bilayer

is _« head-to- head _», where the

carboxyl

end _{groups are}

juxtaposed

at the center of the

bilayer.

This

cycle

was

repeated

N times to

produce

_an

N-bilayer

film. We

thereby

made _one, two and three

bilayer

films of Cd-arachidate

simultaneously

_on both

types

^of substrates. The LB

trough system, monolayer

film

properties,

and details of the

deposition

_are further described

elsewhere

[14J.

Meridional

X-ray

diffraction _was obtained from these various

multilayer specimens

_{as a}

function of

(qz

= 2 sin

IA ) corresponding

to elastic

photon

momentum transfer

parallel

to the z-axis

perpendicular

to the substrate

plane.

This meridional

X-ray

diffraction arises from the

projection

of the three dimensional

multilayer

electron

density

distribution

along

radial vectors

lying

in the

layer planes perpendicular

to the z-axis onto the z-axis _; this

projection

is defined _as the electron

density profile

for the

multilayer.

The incident

X-ray

beam defines _an

angle

_w with the substrate

(xy) plane.

Meridional

X-ray

diffraction is observed for

w

equal

to @, where 2@ is the

angle

between the incident and scattered beams. The

multilayers

_were therefore

positioned

_on the _w axis of _a 4-circle diffractometer which _was oscillated _{over an}

appropriate

_range of D-values

permitting

the collection of the meridional diffraction data with _a low

impedance position-sensitive

detector

(PSD) aligned along

the

q~ direction and mounted _on the 2 axis

[7J.

An Elliott

(GX-13) rotating

anode

X-ray

generator operating

at _a

target loading

of 27

kW/mm~

_was used _to

produce

the incident Cu

emission

spectrum.

The

CuKaj

line

(A

=

1.5411)

was selected

using

_a

cylindrically

bent

Ge(I

II

)

monochromator

crystal

which

produced

a line-focused

X-ray

beam. The

specimen

to detector distance _was 350 _mm.

X-ray

beam width and the PSD system resolution resulted in _a

Aq~

^{resolution of}

~0.001l~'

_{The full}

height

of the diffracted line-focused beam _was

intercepted by

the

3-mm-high

entrance

aperture

of the PSD for all diffraction maxima. The full 100-mm active

length

of the PSD _was

digitized

into 1024 channels

by

a multichannel

analyzer.

A PDP 11

/24 computer (Digital Equipment Corp., Marlboro, MA)

_was used to

control the diffractometer and the electronics associated with the PSD. Further details

regarding multilayer sample

conditions

during

diffraction data collection and _{w scan}

parameters

have been described in _a

previous

_paper

[8J.

The meridional

X-ray

diffraction data _were also collected from these _same

specimens utilizing

the Biostructures

Participating

Research Team beamline X-9A at the National

Synchrotron Light

Source

~NSLS),

Brookhaven National

Laboratory (Upton, NY), using

much _more intense

X-ray

beams to

get

^better

counting

statistics at

higher

values of

q~,

especially

for the _one

bilayer

films of Cd-arachidate _on both

alkylated

Si and

alkylated Ge/Si

substrates.

During

data collection the

synchrotron operated

at an electron energy of 2.5

GeV,

and the current in the

ring decayed during

_a fill from 200 _to 90 mA. A constant-exit-

height,

double

Si(ill) crystal

monochromator _was used to select the energy of the

X-ray

radiation incident _on the

samples.

Radiation from the monochromator

(FWHM

2.5

elf~

_was collected and

linearly

focused

using

_a

cylindrically-bent

horizontal mirror

~Ni-coated _A1)

with

its center at 1340 _cm from the

bending-magnet

_source. The

scattering geometry

^and

instrumental setup were otherwise the _{same as} those described above

using

the

rotating-

anode

X-ray

_source. To protect the total-count-rate limited

PSD,

_we utilized _an automated

1134 JOURNAL DE PHYSIQUE t4~ 8

Al foil

changer»

to attenuate the incident beam

intensity appropriately

which _was monitored

by

a

N~-filled

ionization chamber

positioned

between the beam

defining

slits and the

guard

slits

immediately

_upstream from the

specimen

chamber.

Omega

scans were

recorded

by

both

oscillating

the

multilayer

_over the

angular

_range 0.3°

~ w ~ 6.5° for data

collection _over the full range of q= and over the _more limited

angular

_range 1.8°

~ w ~ 6.5°

for better

counting-statistics

data collection at

higher

values of q=. Further details of the diffraction instrumentation _are

given

in references

[15,16].

Results.

Figure

shows the three meridional diffracted

intensity

functions

I~(q=),

corrected for

specular scattering

and _a Lorentz factor of q= ^as

previously

described

[7J,

^{relevant for the} one

bilayer

Cd-arachidate

film, namely (a)

the

alkylated

three

bilayer Ge/Si

^substrate

16)

_one

bilayer

Cd-arachidate _on the

alkylated

Si substrate

(c)

one

bilayer

Cd-arachidate _on the

alkylated

^three

bilayer Ge/'Si

substrate. The _structure factor modulus

squared

for the Cd- arachidate

bilayer

on the

Ge/Si multilayer

will be denoted here _as

)Fjc~s~~~~~~j~(q=))~.

Following

reference

[5],

^the

intensity

function

Ic(q=)

for

figure

lc _is

given by equation II):

~ ~ ~

l~lGe,S~)jAA

)~

(~z

_~

l~jGe

_S~h

(~=)

₊

FjAA

_)1(~=

~ ~ )l~(Ge S~)~(~z) )l~(AA_Ii

(~r)

_C°S

II

~

Ice S>j~(~=)

l)

~IAA)jlq=11

+ 2 _"qz A(GeS~)~IAA) )

where

)Fjc~s,~~(q=))~

^{is the structure factor modulus}

squared

for the Ge/Si

multilayer

provided by I~(q~)

^from

figure

la,

Fj~~ _~~(q.)

^{~is the} structure factor modulus _square for the Cd-arachidate

bilayer provided by I~(q~)

^from

figure 16,

_{#r~~~s~~~(q~)} and

#r~~~~~(q=)

^{are the}

phases

^{of their}

respective

structure factors

(each

referenced _to the center of _mass of their

respective profile

structure), ^and A~c~,s~~~j~~j~ ^{is the distance}

along

_z between the center of

mass of the

Ge/Si multilayer

and the Cd-arachidate

bilayer.

Given the kinematical diffraction

expression

of

equation II),

^the

I~(q~)

^{functions of}

figure

have all been truncated for the

same q~ ~ (q=)~~~ ^0.02

l~

' since the

specular scattering

from the bulk silicon substrate surface tends _to dominate the total

scattering plus

diffraction

along

_q~ from the

specimens

for lower

q=-values.

The effect of the third _term in

equation (I),

^the critical interference between the

Ge/Si multilayer

and the Cd-arachidate

bilayer,

is most

readily

_apparent in the

I~(q~)

function of

figure

lc

by

the presence of zero-level minima _at

q~-values

for which the

I~(q~

) functions of

figures

la and 16 are not

simultaneously

_zero and

by

the

higher-frequency

modulations _not present ^{in the}

I~(q~)

functions of

figures

la _or 16. We note here that the

large profile

width of the Ge and Si

layers

in the

Ge/Si multilayer ii-e-

²⁰

hi _severely

limits the

detectability

^of

I~(q~)

from the

Ge/Si multilayer

_{for q~}

~

lqz)~~,

=

0.09

l~

' and likewise the

detectability

^{of the critical} interference term in

figure

lc

The Fourier transform of the corrected meridional

intensity

function

I~(q~) yields

the autocorrelation function P z) of the

corresponding multilayer

relative electron

density profile

&p

(z) [7, 8].

That P

(=)

is the autocorrelation of the relative and not the absolute

multilayer

electron

density profile ii-e-

&p

(=)

vs. p

(z) itself~

is _a

simple

consequence of the truncation of

I~(q=j

for _q~

~

(q=)~,~

mentioned above. Such autocorrelation functions for the

alkylated

three

bilayer Ge/Si

substrate, the _one Cd-arachidate

bilayer

_on the

alkylated

Si substrate and

one Cd-arachidate

bilayer

_on the three

bilayer Ge/Si

substrate _are shown in

figure

2. These

typical multilayer profile

autocorrelation functions each

decay monotonically

to

essentially

bt 8 X-RAY INTERFEROMETRY AND BILAYER ASYMMETRY IN LB FILMS lI35

(a)

iox

~s

N (~)

$

w H

(c)

O.OO O.03 O.08 o-lo O.13 O.16

q~(I-i)

Fig.

I.-Meridional

intensity

^functions

I~(qz)

for

(a)

an

alkylated

three

bilayer Ge/si multilayer

substrate; 16) _one bilayer of Cd-arachidate _{on an}

alkylated

si substrate; (c) _one

bilayer

of Cd-

arachidate _{on an}

alkylated

three

bilayer Ge/si multilayer

substrate.

(a)

i

(b)

M

~

~

~

(c)

i

O. 67. 133. 200. 267. 333. 400.

z (i)

Fig.

2.

Multilayer profile

autocorrelation function or Patterson function

P(z)

for

(a)

an

alkylated

three bilayer

Ge/si multilayer

substrate _; (b) one

bilayer

of Cd-arachidate _{on an}

alkylated

Si substrate

(c)

_one

bilayer

of Cd-arachidate _{on an}

alkylated

three

bilayer Ge/si multilayer

substrate. The various

P(z)

have

nonsignificant

fluctuations for _z

~ z~~~ indicated

by

the arrows in

(a)-(c).

l136 JOURNAL DE PHYSIQUE ~ 8

zero for _=~z~~~ which defines the extent of the

corresponding multilayer profile

z~~~ was

thereby

found to be

~1501, ~1001

_and

~2501

_{for the three}

bilayer

Ge,/Si

multilayer

substrate, one Cd-arachidate

bilayer

and _one Cd-arachidate

bilayer

_on Ge,>'Si

respectively.

The

multilayer profile

autocorrelation functions all contain small

amplitude.

low~frequency

oscillations around the zero-baseline for ₌

~ =~~~ due _to the truncation of the corrected

intensity

functions

I~(q~)

for _q~

~

(q=)~,~

m

0.0?

l~

'

Again following

reference

[2],

the autocorrelation function for the

multilayer

relative electron

density profile

for the Cd-

arachidate

bilayer

on the

alkylated

three

bilayer

Ge/Si

multilayer

substrate denoted

by

~lGe>S~)~j~~

)~

(Z)

"

hP

jGe<S~);IAA

l~

IT)

_*

hP

jGe S~)/AA _Ii (~ Z "

l'(Ge

S>h(AA )j ^{Z IS} g'V~Tl

b)

equation (2).

~lGe Si)~i~A)i(Z

^~

0)

~

l'(Ge

_{S>)~(Z ~}

0)

+

I'jAA

Ii

IT ~ 0)

+ hP _jGe

S>)~~

~)

_* hP

(AA )j

(+ Z)

_* ~ (Z ~

jGe 91;1,iA11 (2) where

~iGe

_S~)~(Z)

"

Ap

jGe'S>)~(Z) *

Ap

(Ge S>)~(~ Z)

,

l'(AA) (Z)

"

Ap

~A )~(Z) ^* hP

j~~ )1~ ^°

and _* denotes the convolution

operation.

Hence, for _z less than the

larger

of

(z~~, )j~~

_s~j~ or

(=~~~

jj~~~~, Pjc~,s,~~j~~

_j,

(=)

is dominated

by

the

superposition

of the first _two autocorrelation function _terms of

equation (2). Only

the third _term of equation

(2),

the cross-correlation of

&p jc~js~j~(z)

^with

&p

~~~_j~

(=

centered about ₌

= + A

~c~ s,~~j~~

~~

can exist for _z greater ^{than the}

larger

of (=~~,)~~~,,s,~~ ^or

(=~~~)j~~~~

^this cross-correlation _term arises

explicitly

from the interference _term of

equation (I).

Hence, the

significant

features in

Pj~~,s,~~j~~ j,(=

^{shown in}

figure

2c for

=~1501

are a direct manifestation of the critical interference effects of

figure

lc.

la)

lox

r~

#

(b)

~/

u e

(c)

O.00 O.03 O.05 O.08 o-lo 0.13 O.16

qz('-~)

~ig. 3.- Meridional intensity ^functions

I~(q=)

for (a) _an

alkylated

three

bilayer

Ge,Si muliilajer substrate _: dotted line _is the calculated intensity function for the best electron

density profile

model of the

alkylated

three

bilayer

Ge,'Si

multilayer

substrate 16 two

bilayers

of cd-arachidate _{on an}

alkylated

Si substrate, (c) two bilayers of cd-arachidate _{on an} alkylated three bilayer Gel'si multilayer substrate.

bt 8 X-RAY INTERFEROMETRY AND BILAYER ASYMMETRY IN LB FILMS l13?

Figure

3 contains the

Ic(q=)

functions for

(a)

the

alkylated

three

bilayer Ge/Si multilayer substrate, (b)

two

bilayers

of Cd-arachidate _{on an}

alkylated

Si substrate and

(c)

two

bilayers

of Cd-arachidate _on the

alkylated

three

bilayer Ge/Si multilayer

substrate. The critical interference

effects,

_as identified above for the _one Cd-arachidate

bilayer

_on the

alkylated

three

bilayer Ge/Si multilayer substrate,

_are

readily apparent

ⁱⁿ

figure

3c for _{q= w}

(q~)~~~

₌

0.091~ '.

_For

q~ ~

0.101~ ',

_the

_Ic(q~)

_for

_figure

_{3c is}

essentially

that of

figure

3b for the two

bilayer

Cd-arachidate

multilayer only, again

due to the _presence of

only

broad

201wide

features in the

Ge/Si multilayer profile.

The

corresponding

autocorrelation functions _are

shown in

figure4.

Both

P~c~js;~~(z)

^and

P~AA~~(z)

^{have no}

significant

features for

z ~z~~~

=1501

_while

P~~jsi~~~A~~~(z)

^has

significant

features

extending

to z~~~ m

3001 thereby again directly verifying

the _presence of the critical interference effects in the

Ic(q=)

function of the

corresponding figure

3c.

(a)

i

(b)

I

~

2

(c)

i

O. 67. 133. 200. 267. 333. 400.

z(1)

Fig. 4.-Multilayer profile

autocorrelation function _or Patterson function

P(z)

for

(a)

_an

alkylated

three

bilayer

Ge/si

multilayer

substrate _; dotted line is the calculated Patterson function for the best electron

density profile

model of the alkylated three

bilayer Ge/si multilayer

substrate _; 16) two bilayers of Cd-arachidate _{on an}

alkylated

si substrate _;

(c)

two

bilayers

of Cd-arachidate _{on an}

alkylated

three

bilayer Ge/si multilayer

substrate. The various

P(z)

have

nonsignificant

fluctuations for _z>z~~~

indicated

by

the _arrows in

(a)-(c).

Figure

5 contain the

Ic(q~)

functions for

(a)

the

alkylated

two

bilayer Ge/Si multilayer substrate, ~b)

the three

bilayers

Cd-arachidate

multilayer

_on an

alkylated

Si substrate and

(c)

three

bilayers

of Cd-arachidate _on the

alkylated

two

bilayer Ge/Si multilayer

substrate. The critical interference

effects,

as identified above for _{one or} two

bilayers

of Cd-arachidate _on the three

bilayer Ge/Si multilayer substrate,

_are not _so

readily _apparent

in the

Ic(qz)

of

figure

5c for tills _case.

Nevertheless, inspection

of the

corresponding

autocorrelation

functions of

figure

6 shows that

P~~~js~~~(z)

^{has no}

significant

features for _{z ~ z~~} 100

1

_and

l138 JOURNAL DE PHYSIQUE t4~ 8

(a)

lox

rN

#

(b)

$

H

(c)

O.00 O.03 O.05 O.08 o-lo O.13 O.16

qz(I-1)

Fig.5.-Meridional

intensity functions

I~(q=)

for (al an alkylated two bilayer Ge/Si multilayer substrate (bj three

bilayers

of cd-arachidate _{on an} alkylated Si substrate. (c) three bilayers of cd-

arachidate

on an alkylated t~40 bilayer Ge/Si multilayer substrate

(a)

(b)

N ~

~

~

(c) 1

0. 67. 133. 200. 267. 333. 400

z (i)

Fig. 6. Multilayer

profile

autocorrelation function _or Patterson function Pin) for (a) _an alkylated t~,o

bilayer Ge,'Si

multilayer

substrate (b) three bilayers of cd-arachidate _{on an} alkylated Si substrate, (c) three bilayers of cd-arachidate _{on an} alkylated two bilayer Ge,'Si multilayer substrate The _various P(=) ha~e nonsignificant fluctuations for _± ~=~~, indicated by the _{arrows in} (a)-(c)

bt 8 X-RAY INTERFEROMETRY AND BILAYER ASYMMETRY IN LB FILMS 1139

that

P~~~~~

^{has no}

signifibant

features for _z

~z~~~-~2001

while

P~~~js~~~~~~~~ does have

significant

features

extending

out to z w z~~~

3301. _Hence,

_{the critical} interference effects do indeed exist in the

Ic(qz)

function of

figure

5c for qz w

(qz)~~~

= 0.09

l~ '.

Hence,

_a

simple inspection

of these three different sets of the corrected meridional

intensity

functions and their

corresponding

Fourier transforms _as described above for

figures

1-6

firmly

establishes the existence of the effects of interference between the

X-ray

diffraction from the two different

Ge/Si multilayer

substrates and the diffraction from

thi

_{three different Cd-}

arachidate

multilayers

_on the

alkylated

surfaces of these substrates for 0.02

l~~

=

(qz)m~n « qz ^«

(qz)max

^0.09

A~

Analysis.

The

multilayer

electron

density profile

can be determined

by computing

the inverse Fourier transform of the structure factor

[8J

^{for the}

profile. However,

since the corrected meridional diffracted

intensity

function is

proportional

to the modulus

squared

of the structure factor for the

multilayer profile,

it therefore _{appears not to} contain the

phase angle

information

required

to compute the inverse Fourier transform. The

phase angle

information is

generally

not

explicitly

measured

experimentally,

and _one must _use either direct _or indirect methods to determine the lost

phase

information. As described in the

Introduction,

the direct methods

are based _on

assumptions,

_e-g-

repetition

of _a

symmetric

unit cell

profile

to

provide

_a

periodic multilayer profile,

which _{are not}

necessarily

true in the real systems

[7J.

^{An indirect}

method,

box-refinement,

which makes _use

only

of the fact that the relative electron

density profile

for

a

multilayer

with _a finite number of

layers

_must be _nonzero

only

_{over a} finite range of the

profile

coordinate _{z, can}

provide

_a valid solution to the

phase problem,

but the solution

cannot be _proven

unique [17,18J.

In the

following analysis,

the

phase problem

_was solved

unambiguously utilizing X-ray interferometry employing

_a known

profile

structure to

phase

the

adjacent

unknown

profile

structure. These

unique

results _were then

compared

to those obtained

previously [7, 10,

_19J via box-refinement.

In this paper, we choose _{to use a}

highly constrained,

real space refinement

algorithm

to

implement

the interferometric

phasing

rather than the

point by point phasing

in qz-space as

described in reference

[2J.

The

advantage

of this

algorithm

is that _{we can} avoid several

sources of _error to which the qz-space

point by point phasing

is

highly sensitive, especially

cofinting

statistics _{errors over}

regions

_{of qz for} which the structure factor for either the known

or unknown

profile

structure is small and _errors in the relative

scaling

of the three different meridional

intensity

functions

employed [2J.

^{For either of the above}

approaches

to

implement

interferometric

phasing,

_we first need _to establish the relative electron

density profile

for the

« known _»

Ge/Si multilayer

substrate. The initial models for the two and three

bilayer Ge/Si multilayer

substrates _were established _{on an} absolute electron

density

scale

guided by

_our

specifications

for their fabrication. Electron

density

levels for

amorphous

Ge and Si _were calculated based _on relevant data in the reference

[20].

The initial calculated values for

amorphous

Ge and Si in absolute electron

density

scale _were

1.40e~/l~

_and

0.70e~/l~

respectively

in this _case. The initial models _were then relaxed via _a model refinement

procedure utilizing comparisons

of the calculated meridional

intensity

and Patterson functions for the models with their

respective experimental intensity

and

corresponding

Patterson functions. The _same values of

(qz)~d~

^and

(qz)~~~

truncation described for the

experimental intensity

functions

(see Results)

_were

applied

to the model

intensity

functions in order to

properly

match the

experimental intensity

and

corresponding

Patterson function data and thus

produce (see below)

a relative electron

density profile

for the two and three

bilayer Ge/Si multilayer

substrates

fully

consistent with such truncation.

By successively adjusting

these

JOURNAL DE PHYSIQUE I T I, M 8,AOOT [WI 45

1140 JOURNAL DE PHYSIQUE I M 8

absolute electron

density

models within their fabrication _{errors, we were} able to finalize the

models

yielding

the best agreement with the

experimental intensity

and

corresponding

Patterson functions. The best three

bilayer Ge/Si multilayer

absolute electron

density

model is shown for

example

in

figure

7a and its calculated

intensity

and

corresponding

Patterson

functions _are shown _as the dotted lines in

figures 3a,

4a. The calculated

intensity

function for the best model of the three

bilayer Ge/Si multilayer

substrates _was then either

doubly

Fourier

transformed,

_or

subjected

to box-refinement

[17,18] utilizing

an

arbitrary

trial function

(phase-shifted cosine), using

the _same

(q~)~,~

and

(qz)~~~

^truncation to

provide

the relati~e electron

density profiles

for the best model.

Figure

7b, _c shows for

example

these relative electron

density profiles

_so calculated for the

thereby

known three

bilayer Ge/Si multilayer substrate,

_as

subject

to the

(q~)~,~

and

(q~)~~~

^truncation

operative

in these

interferometry experiments (see Results).

Two

points

^should be noted

a)

^the

identity

of the small features denoted

by

_« Si _» and CDS _{» at} the

alkylated

surface of the two

slightly

different relative electron

density profiles

so-calculated for the three

bilayer Ge/Si

substrate have been

firmly

established

by

their

unique correspondence

with variation of the

sharpness

of these known features in the absolute electron

density

model and

b)

the best absolute electron

density

model is

actually

_an excellent fit to the

experimental intensity

and

corresponding

Patterson

functions

[this

_can be _more

directly

evaluated

by utilizing

for

example

the relative electron

density profile

of

figure

7c

(which

has the dotted line

intensity

and Patterson functions of

Ge Ge Go

I I I

(b)

Go Go G.

i I ^~~~

(a)

~

Ii

_(c)

~ N

m _~

i

_c~

~

~

'Nj ^I

~

CDS

~~ ~~~

Si Si

© (d)

(

-200. -67. 200.

z >)

I I

S oos

-200. -67. 67. 200

z(i)

Fig.

7. (a) ^Electron

density profile

_p (=j for the best alkylated three

bilayer

Gel'si multilayer model

on an absolute scale

(b) corresponding

relative electron

density profile

&p (z) ^{for the best three} bilayer Ge/Si multilayer model via box-refinement; (cj corresponding relative electron density profile Ap

(±)

for the best three

bilayer

Ge/Si

multilayer

model via double Fourier transformation. (d)

fully-

relaxed relative electron

density profile &p(z)

for the best three

bilayer Ge/'Si

multilayer model _i,ia

highly-constrained,

real space refinement. «CDS» in (a)-(d) indicates the alkylated octadecylsilane chain feature.

bt 8 X-RAY INTERFEROMETRY AND BILAYER ASYMMETRY IN LB FILMS 1141

Figs. 3a, 4a)

_as the trial function in _a

highly-constrained,

real space refinement described below to

produce

the

thereby fully

relaxed relative electron

density profile

^of

figure

7d

(which

has the

experimental

solid line

intensity

and Patterson functions of

Figs. 3a,

4a

Figs.

7d and 7c _are

nearly

identical _over the

profile

_extent of the three

bilayer Ge/Si multilayer

for

1241«

z w

41).

A

highly-constrained,

real space refinement

algorithm utilizing

the normal box constraint and the

especially

restrictive known relative electron

density profile

of the

appropriate Ge/Si multilayer

substrate as the trial _{structure was} then

applied

to the meridional

intensity

functions from _one, two and three

bilayers

of Cd-arachidate

deposited

_{on an}

alkylated Ge/Si multilayer

substrate. The box-refinement

algorithm

is well known _{to converge} to the local structure solution closest to the trial structure

[17, 18J.

The «

especially

restrictive _nature of the known relative electron

density profiles

for these

particular Ge/Si multilayer substrates, namely

for

so-determining

the relative electron

density profiles

of these

particular

^ultrathin

Cd-arachidate

multilayers,

is

easily

understood

by

consideration of the

expression:

F(Ge/s>)~(AA

)~(qz)

=

F(Ge/si)~ (qz)

_{+ F(AA)~}

(qz) (3)

in the

complex plane

^where #i~~~js~~~(qz) is known _;

#i~~~~~(qz)

^and ji~~~js~~~~AA~~(qz) ^are both unknown. The _pressure for iteration of the

phase #i~c~js;~~~~~~~(q~)

^{function away from the} initial trial

phase

function

#i~~~js;~~(qz)

^is

generated by

the difference between the moduli

)F~o~js;~~~~~~~(qz))

^vs.

)F~~js~~~(qz)). ^Thus,

as

F~c~js~~~(qz) progressively

becomes _more dominate _over

F~AA~~(qz), #i~~js;~~~~~~~(qz) necessarily approaches #i~c~jsi~~(qz).

^{Given that} the contrast in

&p ~~js;~~(z)

^is

^greater

^{than that within}

Ap ~~A~~(z),

^{this situation is therefore} best satisfied

by

the _p

~~js;~~~~~~~

(z) profile

structure and least satisfied

by

the _p ~c~js;~~~~~~~(z)

profile

structure in this work.

Therefore,

the

highly constrained,

real space refinement

algorithm

utilized in this work for

implementation

of the interferometric

phasing

of F~~~jsi~~~AA~~(qz)

simply

_uses this dominance of the known reference _structure factor

F~~~js~~~(qz)

^{to force the} box-refinement

algorithm

to converge to the correct solution for

Ap

_{~~~js;~ ~AA)}

(z)

_among the several

possible

solutions

[18] by initiating

the refinement in the

~' ~

(qz)max

correct solution's local minimum in the function

[)F~c~js~~~~AA~(qz)(~-

qz)n~n

~

(qz)mm

Ic(qz)Jdqz/ I~(q~) dqz. Finally,

normal box-refinement

using only

the box-constraint

qz)min

and _an

arbitrary

cosine trial function _were also

applied

to the meridional

intensity

functions from _one, two and three

bilayers

of Cd-arachidate _{on an}

alkylated

Si substrate for

comparison

with the

unique

results obtained with the interferometric method. The box constraint for each

multilayer sample

was determined from the extent of its Patterson function for the

multilayer profile _[7J

and the same values of

(qz)~~

and

(qz)~~~

were utilized in all _cases. The derived relative electron

density profiles

for _{one, two} and three

bilayers

of Cd-arachidate _as

deposited simultaneously

_on

alkylated Ge/Si multilayer

substrates and _on

alkylated

Si substrates _are shown in

figure

8.

Discussion.

Figures

7b and _c show the two

slightly

different versions

(see Analysis section)

of the known relative electron

density profiles

for the

alkylated

three

bilayer Ge/Si multilayer

substrates _as

subject

to the

(qz)~~~

and

(qz)~~~

^truncation described. In the three

bilayer Ge/Si multilayer

1142 JOURNAL DE PHYSIQUE I hf 8

Ge Ge Ge

I I I

ii,,,

i, (_a) (b)

i

, 'i _i (CGG>~cd

'( '( ^' 1~ j

J'~

i '(

/-,---,

I I I I

Si Sl Sl CH~ CH~

~s (C) I _(d)

N ~/

~i ~

~3

(e) (f)

-200 -67. 67. 200. -200. -67. 67. 200,

z(i) z(1)

Fig. 8. Relative electron density

profiles

&p (z) for (a) one bilayer of

Cd~arach14ate

_{on an} alkylated three

bilayer

Gel'si multilayer substrate _using either the highly-constraining trial function of

figure

7b (solid line) _or of

figure

7c (dotted line) _; (b) _one

bilayer

of cd~arachidate _{on an}

alkylated

Si substrate, (c) two

bilayers

of cd-arachidate _{on an}

alkylated

three bilayer Ge/Si

multilayer

substrate, (d) _two

bilayers

of cd-arachidate _{on an} alkylated Si substrate; (e) three

bilayers

of cd-arachidaie _{on an}

alkylated

_two

bilayer

Ge/Si

multilayer

substrate (f~ three

bilayers

of cd-arachidate _{on an} alk~lated St substrate. The boxes outline the cd-arachidate bilayer(s) _m each _case,

case, there _are three electron dense

germanium peaks

and two electron deficient silicon

troughs,

and _two less

prominent

features _at the

right edge uniquely

due to the surface silicon

layer

and the

alkylated

chain

layer respectively.

The two

bilayer Ge/Si multilayer

_{case i~}

similar to the three

bilayer

_case except that it contains _one less

bilayer (not sho~&,nj.

^The results obtained via

X-ray interferometry

_as described

using

these

profiles

_as the kno~&n

profile

structure are shown in

figures

8a, c and _e. The left side of each _contains the

appropriate

two or three

bilayer Ge/Si multilayer profile

while the

right

side of each contains the

profile

of _one, two or three

bilayers

of Cd-arachidate. Each Cd-arachidate

bilay.er.

_at this

spatial

resolution determined

by (q~)~~, truncation,

contains _two

predominant troughs

and

one

predominant

central

peak representing

the two electron deficient terminal

methyl

end group and the electron dense

carboxyl

head _group features of the head-to-head

bilayer.

Additional Cd-arachidate

bilayers

_are thus

recognized

_upon

comparison

of the _one, two and three Cd-arachidate

bilaj,er multilayers

_on the

alkylated

Ge/Si

multilayer

substrates.

Figures

8b,

d,

f contain the

corresponding multilayer profile

for _one, t~&>o and three

bilayers

of Cd-arachidate _as

simultaneously deposited

_on

alkylated

Si substrates and obtained via box- refinement.

Note,

_as will be discussed

below,

these

profiles

had to be somewhat smoothed iia convolution with _a Gaussian function of width

(FWHM)

=

201

m order to facilitate the

comparison

with their counterparts ⁱⁿ

figure 8a,

_{c, e.} Otherwise, the

predominant fatty-acid

chain

endgroup

^features and the less

predominant

(at this

spatial resolution) intervening

chain

bt 8 X-RAY INTERFEROMETRY AND BILAYER ASYMMETRY IN LB FILMS 1143

methylene

_group features of the various Cd-arachidate

bilayers

_on

alkylated

Si substrates _are

virtually

identical to those of the

corresponding

Cd-arachidate

bilayers

_on

alkylated Ge/Si multilayer

substrates.

Hence,

the

non-unique

Cd-arachidate

bilayer profiles similarly

derived

previously

via box-refinement for ultrathin

multilayers containing

_one, two, three and five

bilayers deposited

on

alkylated glass [1, 7, 8, 10,

19J ca1K now be considered _{as proven} via X- ray

interferometry.

In

particular,

_a number of

phenomena previously

described at substan-

tially higher spatial

resolution for these

particular Langmuir-Blodgett deposition

conditions have

thereby

been _{even more}

firmly established; namely a)

disorder of the arachidate

monolayer

_at the

multilayerlair

interface

[7, 10J, b) upstroke-downstroke _asymmetry

in the

arachidate

bilayers

caused

by

_average

area/chain

differences and

incomplete overlayer-

induced

ordering

of the disordered surface

monolayer [1, 19J,

and

c)

the

dependence

of the low

temperature

^thermal

melting

of the less dense

upstroke

arachidate

monolayers

_on the

number of arachidate

bilayers

in the

multilayer [19J.

There _are several other

aspects

^{of this work of}

worthy

discussion.

Firstly,

these Cd- arachidate

multilayers

contain

asymmetric (upstroke/downstroke) bilayers

and exhibit the effects of lattice disorder of the second kind

[3J propagating

outward from the

alkylated

substrate

surface,

_as

previously

described

[8J. Thus,

the macromolecular features

distinguish-

able in _a

bilayer profile

at a

particular spatial

resolution _are most

apparent

^{for the}

bilayer

_on

the

alkylated

substrate surface and these features become

progressively

broadened

(smeared)

for

bilayers increasingly

further from the substrate surface. This disorder is _a

property

of the

particular fatty-acid coupled

with the

deposition

conditions

employed

and not a result of substrate surface

roughness

it is manifested in the meridional

intensity

function

I~(qz)

via

interference of the _structure factor for the Cd-arachidate

multilayer profile _F~AA~~(qz)

with itself to

provide _F~~~~~ (qz)

~.

Secondly,

_we noted above that the various features of Cd-arachidate

bilayer profiles

in the ultrathin

multilayers deposited

_on

alkylated Ge/Si multilayer

substrates _{were more} broad

(at

constant

spatial

resolution via the _same

(qz)~~J

with

respect

to those for the otherwise

identical

multilayers deposited simultaneously

_on

alkylated

Si substrates. Since the Cd- arachidate

multilayer profile

_{appears on} the surface of the

alkylated Ge/Si multilayer profile

via the critical interference of the

Ge/Si multilayer profile

structure factor

F~~js~~~(qz)

^with

the Cd-arachidate

multilayer profile

structure factor

F~~~~~(qz), roughness

of the

Ge/Si

interfaces in the

Ge/Si multilayer

substrate is _most

likely responsible

for this

Debye-Waller [3J type

^effect on the interference term of

equation (I).

Finally,

_we

again

note that

(qz)~~~

and hence the

spatial

resolution of the

multilayer

electron

density profiles

determined

unambiguously

via

X-ray interferometry,

_was

severely

limited in this

study by

the minimum thickness

(m 201)

_{of the electron}

_density

_contrast

producing

Ge and Si

layers

in the

Ge/Si multilayer

substrates achievable

by

magnetron

sputtering. Ge/Si multilayers produced by

MBE should not

only

_remove this limitation since the Ge

layer

thickness _can be reduced to _a

single

atomic

monolayer,

but it should also

provide

for

improvement

in the smoothness of the

Ge/Si

interfaces in the

multilayer.

Conclusions.

We have utilized

X-ray interferometry employing

_a

highly constrained,

real space refinement

algorithm,

_to derive

unambiguously

the relative electron

density profiles

of ultrathin

multilayers composed

of from _one to three

bilayers

of Cd-arachidate

deposited

via the

Langmuir-Blodgett technique

_on the

alkylated

surface of

synthetic Ge/Si multilayer

subs- trates. These results confirm several earlier results for such ultrathin arachidate

multilayers

_on

alkylated glass

_or Si substrates

utilizing

the

non-unique

box-refinement method for

phasing

l144 JOURNAL DE PHYSIQUE I hf 8

the meridional

X-ray

diffraction

data, including

_asymmetry within each

bilayer

of the

multilayer

associated with the

upstroke/downstroke

of the

Langmuir-Blodgett deposition.

Realization of the

X-ray

interferometric method _as described

provides

_a

powerful

method for

unambiguously deriving

the

profile

structure of both

periodic

and

nonperiodic organic/bio- organic monolayer

or

multilayer

_systems

placed

_{on or}

immediately adjacent

to the surface of

an

appropriate

known

multilayer profile

structure.

Acknowledgments.

This work _was

supported by

^{the National Science Foundation}

(NSF)

Materials Research

Laboratofles

(MRL) Project

under Grant No. DMR-85-19059 and the National Institute of

Health

(NIH) grants

GM-33525 and RR01633.

References

[1] ^{FiscHETTi R.} F., SKITA V., GARITO A. F. and BLASIE J. K., Phj>s. Rev. B 37 (1988) 4788 [2] LESSLAUER W, and BLASIE J. K., Acia

Crysiallogr.

A 27 (1971) 456.

[3] HOSEMAN R. and BAGCHI S. N., Direct

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