Electronic structure of amorphous carbon

Journal of Non.Crystalline Solids 77 & 78 (1985) 83-86 North-Holland, Amsterdam

83

ELECTRONIC STRUCTURE OF AMORPHOUS CARBON

E.P. O'REILLY [, J. ROBERTSON 2 AND D. BEEtIAN 3 I. 2. 3.

Dept. of Physics, University of Surrey, Guildford, GU2 5XH, UK Central Electricity Research Labs., Leatherhead, KT22 7SE, UK Dept. of Physics, Harvey tludd College, Claremont, Ca 91711, USA

The electronic structure of amorphous carbon and its dependence on the ratio of 3-fold to 4-fold coordinated sites and hydrogen content is studied. The J~ electron system is shown to be stabilised by the presence of the band gap and requires greater positional correlations of the 3-fold sites than found in current structural models.

Amorphous carbon (a-C) has attracted attention because of its hardness. properties

depend

Techniques that

such

a-C

is

strongly

as

Raman,

on

nuclear magnetic

predc~ninantly

hydrogenation

introduces

deposition

3-fold

4-fold

the gap of a-C

calculating

Here,

the

we

clearly

study

electronic

bonded, and

As graphite

is interesting;

it out.

of

hydrogen

and

as

Its

content.

photoemission

in graphite,

increases

the band

show

and

That

gap

from

itself is metallic the origin of

disorder

The origin

structure

and

resonance

(sp 3) sites

about 0.7 eV towards 4 eV [I-4].

washes

(sp 2)

method

of

creates

the gap

various

a gap rather than

in a-C and

random

networks

a-C:H and

by

model

structures. Figs.

la,b show

graphite recursion valence

for reference

calculated

using

the

electrons

delocalizes

are

recursion

in ~ bonds

EF, set at E = O.

random networks of a-C containing first [7].

and the gap

(DOS)

consisting We

of warped

see that all

of diamond

method

is 5.5 eV.

~ bonds in the hexagonal

[5]

with

and 20

In diamond, all the In graphite

three

layers and the fourth electron

in the p~ states (shown dashed) which

have energies around

rings

of states

levels and with the parameters of the Table [6].

electrons per site f o m

the

the density tight-binding

lie normal to the layers and

Figs.

Ic,d,e show the DOS of possible

respectively

100%, 86% and 51% of sp 2 sites,

graphitic

three

layers but with many

networks

are metallic

high density of ~ states, contrary to experiment.

5- and 7-fold

with E F

Thus, merely

lying

in a

introducing sp3

sites does not automatically create a gap; the sp 2 sites must also be spatially correlated The

in some way.

origin

of

the

unsaturated bonding. so that

creating

gap

depends

entirely

on

the

~

states,

as

usual

for

The key feature of ~ states is that they are half-filled,

a gap

in their

spectrum

0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

at EF tends

to

lower the occupied

E.P. O'Reilly et al. / Electronic structure o f amorphous carbon

84

state energy and stabilise the resulting structure. simple structures.

Let us now consider some

The ~ orbitals of two adjacent but isolated sp 2 sites will

create an occupied ~ state and an empty ~* state.

The ~ orbitals will tend to

align parallel, as in ethylene, to ma×imise the binding energy of the filled state.

This

rings,

if

also

the

~

maximises orbitals

the

~-~*

have

a

nearest

splitting.

n

=

Turning

neighbour

to

planar N-fold

interaction

V,

the

eigenstates are En Thus

in

=

2V cos (2~n/N)

benzene,

with

N

=

6,

En

I,...N

avoid

E

= 0

(Fig.

2a),

structure, more stable than three separate double bonds.

giving

a

stable

In contrast, cyclo-

octatetraene with N = 8 has two states at E = 0 and distorts instead into a tub structure to give four independent double bonds [81 . to

propose

stability graphite

that

rings

[8].

with

Turning

to

4N+2

~

infinite

This behaviour led Huckel

electrons

possessed

structures,

a single

extra

"aromatic"

infinite

layer of

is a zero band gap semiconductor, due to symmetry but with a wide dip

in the ~ DOS at EF (Fig. 2b).

However, strips of graphite of infinite length

but finite width have a gap at E = 0 whose size the strip width

(Fig. 2c).

partly

graphitic

bounded

is inversely proportional

Thus a gap can exist regions.

If

to

in structures consisting of

however,

5-

and

7-fold

rings

are

introduced, this tends to fill

in the dip around E = 0 (Fig. 2d,e) and makes

gap formation more difficult.

As opening a gap lowers the total energy, this

suggests that odd-membered

rings are destabilising.

s-band

band,

in a-Si,

mechanism

of

a

gap

filled formation

in which

is bond

odd

(This contrasts with the

rings

alternation.

are

allowed.)

If N(E F)

A

final

is finite

it is

often energetically favourable for alternate bonds to lengthen and shorten as this creates a gap, as regions

where

calculated

~

DOS

bonded

in Fig.

in polyacetylene. atoms 2 show

form

a

This may occur in a-C especially quasi

that these

one-dimensional

various mechanisms

network.

in The

are capable of

creating a 0.7 eV gap even if the proportion of sp a sites is small. Hydrogen generally saturates sp 2 sites converting them to sp a sites. removes ~ states from around E = 0 and converts them to ~ states deep bands Fig.

If.

At any stage of hydrogenation the remaining sp 2 sites will be

such as to maximise the ~-~* gap, as discussed above. of hydrogenation

This in the

is to remove aromaticity and

Thus, the initial effect

leave pairs of sp2 sites.

The

gap therefore will

increase towards the ~-~* gap of ethylene, 5.8 eV without

parameters.

hydrogenation opens

Thus,

than in a-Si:H.

up the gap

in a-C:H more dramatically

85

E.P. O'Reilly et al. / Electronic structure o f amorphous carbon

2 3 s p sp (o)

Iol 0

C TOTAL Crr

0:100

I. E l . c

(b) 100:0

~2

[

I

I

(.n w k-

A

ct~

LL O >I--

J5

b

I

I

I

I

(c) 100:0

U3 LU t--

Z U. I O

>I--

i

(e)

L/3 Lt_ 0

(d) 5 - 7

r

I

R

I

N

i

~

~'l ~'

(d) 86:1/-, C340 -15

Z UJ tm

C

I

I

I

I

-lo

-5

o

5

lo

E N E R G Y (eV) i

f

(el 50:50

I

i

/

l

I

k

.....

-20

-10 0 ENERGY (eV)

10

FIGURE I Density of states for (a) diamond, (b) graphite layer, (c,d,e) random networks L7], (f) a puckered ~CH site in a graphite layer.

FIGURE 2 band DOS for (a) benzene, (b) graphite, (c) a thin graphitic strip, (d) graphite with two 5and 7-fold rings and (e) the C280 sp 2 network with warping effects removed.

E.P. O'Reilly et al. / Electronic structure o f amorphous carbon

86

The densities

of states

The main valence

of Fig.

I help explain

various

experimental

p band peaks at -8 eV, as seen by photoemission

data.

[3,9 I.

The

occupied ~ states form a peak or step at -3 eV which declines as sp 2 sites are removed.

Hydrogen

separated

CH

related

bonds

photoemission.

states

lie around

Transitions

edge structure

[21.

-20

lie

deep

eV,

but

in the have

valence

not

yet

band; been

to the empty ~* states are seen

those

of

observed

by

in the X-ray near

~ states which do not bond remain as radicals and are seen

by electron spin resonance [I0-121. We

conclude

facilitated stability

a-C

is enhanced

bound graphitic

TABLE

that

is stabilised

if sp 2 sites

up

by the

and

by maximising

regions

Interaction

pair

align

presence their

C

-6.

H

-3.

a gap.

This

is

if aromatic

the number of 6-fold rings and if sp 3 sites

in a correlated manner.

parameters

in eV

found

by

fitting

structures of graphite and diamond and the molecular

E(s)

of

~ orbitals,

E(p)

E(s*)

V(ss)

0

14

on

average

the

band

levels of methane.

V(sp)

V(po)

V(p~)

V(pz~)

V(ps*)

-4.5

5.2

5.5

-I .6

-2.9

3.6

-7.8

8.9

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15

Films

120