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Enhancement of the second harmonic signal from Hg1xCdxTe
(MCT) in the presence of an anodic oxide film.
A.W. Wark, K. McErlean, F.R. Cruickshank and L.E.A. Berlouis
WestCHEM, Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow G1 1XL,
UK.
P.F. Brevet
Laboratoire de Spectrometrie Ionique et Moleculaire, UMR CNRS 5579, Université Claude Bernard
Lyon 1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne cedex, FRANCE.
Abstract
Second harmonic generation (SHG) is now widely regarded as a valuable tool for
investigating electrode surfaces. Typically, most studies have been limited to substrates
which lack bulk symmetry and monitoring events such as sub-monolayer formation and
surface reconstruction. Here, the development of a model that can be used to
quantitatively describe the enhanced SH signal observed in the presence of an anodic
oxide film on a non-centrosymmetric substrate, Hg1xCdxTe (MCT), is described. The
aim is to further expand the utility of SHG for probing different electrode systems. The
growth of the high quality oxide films was first followed by in-situ ellipsometry. For thin
films (<100 nm) grown at a constant current density of 150 A cm2, an effectively
uniform oxide layer is found with a refractive index n of ~2.15  0.05 and exhibiting no
absorption of the incident radiation at 632.8 nm (1.96 eV). In the presence of such an
oxide film of 58 nm thickness, the second harmonic (SH) signal intensity measured in
reflection is found to be significantly enhanced in both the PIN-POUT and PIN-SOUT
polarization configurations. To quantify the changes observed, each layer in the model is
assigned its own symmetry and optical constants (at the fundamental,  and harmonic 
(= 2) frequencies and a defined thickness. Modeling of the SH rotational anisotropy
experiments carried out at different angles of incidence indicated that most of this
increase could be accounted for by multiple reflections of the fundamental wave  =
1064 nm (1.17 eV) in the composite ambient/oxide/MCT layer, with little contribution
from charge accumulation at the buried MCT/oxide interface for this oxide thickness.
Keywords:
HgCdTe, anodic oxide, ellipsometry, SHG, modeling.
1
Introduction
The alloy semiconductor Hg1-xCdxTe (MCT) is one of the most important materials used
in the fabrication of infra-red devices1. By varying the composition x of this ternary
compound semiconductor, the band-gap can be altered and thus allow the device to
access different wavelengths in the infra-red region. One particular region of interest is
the atmospheric transmission window between 8 - 12 m wavelength and to access this,
an alloy composition of x = 0.22 is employed.
As with all devices based on the
separation and flow of charge due to photon absorption, the electrical properties and
efficiency of such devices have to be well characterised and controlled. However, the
surface states present in such narrow gap semiconductors (for x ~ 0.2, Eg = 0.1 eV at 77
K) can dominate the desired properties of the material. Passivation layers2 are employed
to not only confer the correct degree of accumulation or flat band conditions to the
MCT/passivant interface but also to provide chemical and physical protection during
further processing and incorporation into the device. Typical surface passivation
methodologies employed include the use of SiO2 by photo-chemical vapour deposition3,
ZnS4 as well as the native anodic oxides5 and sulphides6,7,8. Anodic oxide layers are used
in the passivation of photoconductors, leading to accumulation of the majority carrier at
the surfaces of the n-type material. During the electrochemical formation of the anodic
oxide layer, the MCT substrate material is consumed and sharp interfaces have thus been
reported to form2. Oxide growth is usually carried out using the well established constant
current anodisation method5,9,10 in 0.1 M KOH in 90% ethylene glycol /10% H2O.
Optical second harmonic generation (SHG) is a nonlinear process by which two photons
at a fundamental frequency  are converted into one photon at the harmonic frequency,
 = 2. SHG by reflection has proven to be particularly useful as a surface or interface
probe when the media are centrosymmetric and do not allow, in the dipole
approximation, SHG from the bulk11. At any interface though, the inversion symmetry is
broken, thus allowing SHG by reflection from such structures to be highly surface
specific. For non-centrosymmetric materials, where bulk SHG is allowed, it would be
expected that the bulk response would overwhelm this surface contribution. However,
2
studies of non-centrosymmetric zinc blende-type materials by a number of workers12-22
have also demonstrated a surface-sensitive SHG response in reflection. Both Stehlin et
al12 and Buhenko et al13 observed large variations in the reflected SH intensity during the
vacuum deposition of tin and the adsorption of trimethylgallium on GaAs(001) surfaces
respectively. Work by Armstrong et al23-26 showed that changes in both the rotational
anisotropy pattern and a significant drop in the SH intensity could result on removal of a
thin oxide overlayer. Rotational anisotropy studies by Yamada and Kimura14,15,16 were
able to demonstrate surface effects through surface reconstruction and, in their discussion
of the relative bulk and surface contributions, included the possible mixing of the SHG
response from two different faces through either miscuts or vicinal faces. Berlouis et al
17=22
have shown that the use of SHG in-situ was extremely useful in examining and
characterising the growth of thin non-centrosymmetric anodic sulfide films on MCT.
The above studies have a direct relevance to the work presented here on the effect of the
anodic oxide film on MCT. Whereas the MCT has a zinc-blende structure similar to that
of GaAs, the anodic oxide consists of a mixture of CdTeO3, HgTeO3 and TeO2 and is
thus essentially centrosymmetic. Previous measurements on an oxide-covered MCT
sample revealed that in the presence of the oxide film, the SH intensity was substantially
increased over that of the bare MCT surface27. This observation suggests that SH
generation within the MCT, at the MCT/oxide film and at film/air interfaces have all got
to be carefully accounted for in order to quantify the various contributions to the
observed SH signal from the oxide-covered MCT surface. The flexible multilayer model
developed here expands on the work of Yamada and Kimura16, where each layer is
assigned its own symmetry and optical constants as well as a defined thickness. We note
that for MCT, the reflected SHG signal is generated over a thin layer of material ca. 4060 nm thick, known as the coupling depth, immediately at the interface17.
3
Model geometry
The geometry described in Figure 1 is general and can be extended to any number of
layers where each layer is a semi-infinite parallel slab of a defined thickness, di. As
described in the above figure the laboratory frame (0, x, y, z) is defined with the sample
surface normal oriented along the z axis pointed upwards28. The y and x axes are oriented
in the surface plane with the laboratory origin defined at the interface between medium 1
(representing air or electrolyte) and medium 2, with the top surface of the reflecting
substrate at z = 0. The relationship between the laboratory and crystallographic axes will
be defined later. Each slab is defined with its own complex refractive index, ni and ni
at the fundamental  and harmonic   2 frequencies respectively.
The fundamental wave is incident at the medium 1/medium 2 interface at an angle of 1 .
Owing to the laws of refraction, the fundamental beam propagates within medium 2 at an
angle  2 and  3 in medium 3 and so on. Similarly, the harmonic beam propagates at
angles  1 ,  2 and  3 all of which can be related using nonlinear Snell’s law for SHG29
where 1 is the incidence angle at the air/nonlinear material interface i.e.
n1 sin  1  n2 sin  2  n2 sin  2
Eq. 1
Additionally, reflection and transmission at each interface is characterised using the
Fresnel coefficients.
The complex expression for the incoming wave in medium 1 is
E1 (r , t ) 

 


1  
E1 eˆ1 exp  i t  k1  r  c.c.
2
Eq. 2
with the sign +/- in the subscripts used to denote the direction of propagation: the
negative sign for the wave propagating downwards, towards negative z values, and the
4
positive sign for the wave propagating upwards, towards positive values of z in Figure 1.
ê1 thus represents a unit vector for the fundamental wave travelling in medium 1
towards the interface with medium 2. The different electric field vectors can be
decomposed within medium i as
Ei/   Eis sˆ  Eip pˆ i/ 
Eq. 3
where the two unit vectors ŝ and p̂ i- /  span the plane perpendicular to the direction of
propagation and are defined according to
sˆ  -yˆ
pˆ i  cos i xˆ  sin  i zˆ
pˆ i   cos i xˆ  sin  i zˆ
Eq. 4
Eq. 5
The polarisation of the incident fundamental electric field is defined through the
relations:
sˆ  eˆ1  sin 
Eq. 6
pˆ 1  eˆ1  cos  e i
Eq. 7
where  is angle of polarisation of the fundamental wave and  is the dephasing angle
between E p and E s . Corresponding values evaluated at the harmonic frequency is
denoted with capital letters. These include Fresnel coefficients, polarisation angles and
the P̂i and Ŝ unit vectors. For example the polarisation state of the outgoing SH wave
is defined with angles of polarisation  and dephasing angle  as:
Sˆ  eˆ1  sin 
Eq. 8
Pˆ1  eˆ1  cos ei
Eq. 9
5
For convenience, the propagating fundamental wave is described as the m wave in the
downwards direction and the p wave in the upward direction. Similarly the downwards
and upwards propagating harmonic waves are referred to as M or P respectively. The
electric field vectors for these waves within medium 2 can be expressed as:


m
e2  sˆt12s sˆ  pˆ 2t12p pˆ 1w-  eˆ1
p
e2  sˆt12s r23s sˆ  pˆ 2 t12p r23p pˆ 1w  eˆ1
M

Eq. 10


Eq. 11

s ˆ
e2  SˆT21s R23
S  Pˆ2T21p R23p Pˆ1  eˆ1
P


e2  SˆT21s Sˆ  Pˆ2T21p Pˆ1  eˆ1
Eq. 12
Eq. 13
where the electric field vectors within medium 2 are now no longer unit vectors. For
multiple layers additional Fresnel reflection (r and R) and transmission (t and T)
coefficients are added to Eq’s 10-13 accordingly to describe the electric field vector for
that layer. Thus through Eq’s 2 – 13, the directional and polarisation properties of the
fundamental and harmonic waves can be fully expressed within the laboratory reference
frame in Figure 1 and the electric field vectors projected onto the laboratory cartesian
axes.
Phase dependence
For layers with a finite thickness it is necessary to take into account the effect of phase
shifts on the value of the measured SH intensity. With reference to the geometry in
Figure 1 it can readily be shown that the path difference between the m and p waves is
given by
 path  2d2 cos 2
Eq. 14
for the fundamental wave and similarly

 path
 2d 2 cos 2
Eq. 15
6
for the harmonic wave. For waves traversing across the slab layer only once the phase
(  k2 path ) is shifted by half the values in Eq’s 14 and 15.
The phase shift of the wave is normally presented in complex form. For reference
purposes the phase of the fundamental wave is defined as zero at the medium 1/medium 2
interface i.e. at z = 0. It is clear from Figure 1 that both the m and p waves accumulate
phase as they move downwards away from the interface. However, the increase in phase
for the p wave will be greater than that of the m wave by an amount equivalent to the path
length AB + BC. By considering the phase difference between the m and p components,
the phase shift of each wave transmitting through medium 2 can be represented as a
function of z using the following equations with a similar argument applying to the M
and P waves:

m
exp i  2 z
p
exp i 2 z
M
P



 
exp i  z 
exp i 2 z

2
Eq. 16
Eq. 17
Eq. 18
Eq. 19
where 0  z  d 2 and
2 
 2 
2
o
4
o
n2 cos  2
Eq. 20
n2 cos  2
Eq. 21
where in both cases o is the wavelength of the fundamental wave in vacuum and
which is usually regarded as equal to air . Similarly, in the description of the phase shift
7
in medium 3, passage of the incident and reflected waves through medium 2 have to be
taken into account:

 
m
exp i  3 z  z23  2 d 2
p
exp i 3 z  z23  2 d 2


 


 


 

M
exp i 3 z  z23  2 d 2
P
exp i  3 z  z23  2 d 2
Eq. 22
Eq. 23
Eq. 24
Eq. 25
where z23 refers to the interface between media 2 and 3. Furthermore 0  z  z23  d3 ,
and
3 
 3 
2
o
4
o
n3 cos  3
Eq. 26
n3 cos  3
Eq. 27
For the fundamental wave in medium 2, the electric vector, expressed as the sum of the m
and p components is given by




Eq. 28

Eq. 29
e2  e2 exp i  2 z  e2 exp i 2 z  m  p
and for the harmonic wave



e2  e2 exp i 2 z  e2 exp i  2 z  M  P
8
Multiple reflections
It has been previously shown30 that SH waves reflected from a thin film may be
significantly enhanced by multiple reflections of the SH and fundamental waves within
the film. Although the effects of multiple reflections were discussed in the early stages of
SHG theory by Bloembergen and Pershan31, they were not properly taken into account
until the work by Schoji et al32 who reviewed the absolute values of the nonlinear
coefficients for a large range of materials. The reason for this neglect is that for films or
crystal slabs, whose thicknesses are much less than that of the propagating wavelength, or
have a refractive index of around 2 or lower, then the effects of multiple reflections could
be regarded as small and well within the generally large experimental error associated
with the measurement of nonlinear coefficients. In the case of CMT itself, multiple
reflection effects can be ignored as it is a highly absorbing material at room temperature.
However, this does not apply to the anodic oxide layer as this has a refractive index of
2.22 at the harmonic frequency.
Considering the propagation of a wave within medium 2 in Figure 1, the multiple
reflection effect can be accounted for by multiplication of the amplitude of the
propagating wave by a factor
1
1  r21r23 exp i 2 2 d 2 
Eq. 30
which is the convergent term for a sum to infinity of a geometric series with phase
r21r23 exp i 2 2  . Thus for the s and p-polarised components of the m, p, M and P waves
the relevant factors are:
 2s   2s 
1
1  r r exp i 2 2 d 2
 2p   2p 

Eq. 31
1
1  r r exp i 2 2 d 2
Eq. 32
s s
23 21
p p
23 21



9
 2S   2S 
1
1  R R exp i 2 2 d 2

Eq. 33
 2P   2P 
1
1  R R exp i 2 2 d 2

Eq. 34
S
23
P
23
S
21
P
21


Substituting Eq’s 31-34 into Eq’s 10-13, respectively gives:


e2  sˆt12s  2s- sˆ  pˆ 2t12p  2p- pˆ 1w-  eˆ1

Eq. 35

e2  sˆt12s r23s  2s sˆ  pˆ 2 t12p r23p  2p pˆ 1w  eˆ1

 Sˆ T 

s
e2  SˆT21s R23
 2S Sˆ  Pˆ2T21p R23p  2P Pˆ1  eˆ1
e2
s
21
S
2

Sˆ  Pˆ2T21p  2P Pˆ1  eˆ1
Eq. 36
Eq. 37
Eq. 38
As can be deduced from the above equations, the effect of multiple reflections is the
generation of an interference pattern, dependent on both incident angle and layer
thickness. This pattern is superimposed on the Maker Fringe pattern33 but has a much
smaller oscillation period compared to the Maker fringe transmission coherence length.
MCT belongs to the crystallographic group 43m and for such a surface covered by a thin
oxide film, the overall harmonic electric field amplitude for the reflected Pmm wave can
be written as

 
E2,Pmm  C e2  Rφ Rvic  423m : e2e2 E1
2
Eq. 39
where C is a numerical constant,  4( 23)m is the susceptibility tensor for the material. R and
Rvic deal with tensor transformation due to sample rotation around the surface normal (the
z direction) and the transformation from the pure {100} surface to the vicinal surface,
respectively16,21 (see Figure 2).
10
Experimental
The epitaxial MCT samples were obtained from the QinetiQ Malvern Technology Centre
(formerly the Defence and Evaluation Research Agency, Malvern, UK). These were
grown using the inter-diffused multi-layer process by metal-organic vapour-phase epitaxy
(IMP-MOVPE) on a vicinal GaAs {100} substrate34, with an off-angle of 4o towards the
110 direction in order to improve the lattice match between the II-VI epilayer and the
III-V substrate. The MCT layers were of the order of 15 m thick and were capped by a
ca. 2000 Å layer of CdTe in order to prevent the out-diffusion of Hg during the final
anneal stages of the IMP-MOVPE process. Prior to sample use, the capping layer was
removed by an electrochemical etching process35 and the underlying MCT layer was
examined by the technique of electrolyte electroreflectance (EER)36,37 in order to
determine the alloy composition x. Growth of the anodic oxide was carried out in a
solution of 0.1 M KOH in 90 vol% ethylene glycol in water. A platinum gauze served as
the counter electrode and a saturated (KCl) calomel electrode (SCE) was used as a
reference electrode. This has a potential of 0.242 V at 25oC versus the standard hydrogen
electrode (SHE). Removal of the anodic oxide, where necessary, was carried out by
dissolving in 10% volume of lactic acid in water. All solutions were prepared using
Analar grade reagents in singly distilled water.
The experimental set-up for the in-situ ellipsometry experiments has been described
elsewhere38. Briefly, a computer-controlled Gaertner L116B rotating analyser
ellipsometer employing a HeNe laser of wavelength  = 632.8 nm (1.96 eV) was incident
onto the sample surface at an angle of 70o. The samples were mounted in a special
electrochemical cell constructed of Perspex and fitted with quartz windows for the
incident and reflected beams. The ellipsometry angles of  and  were automatically
recorded at specified time intervals, 5 s. The details of the apparatus used for the
reflection SHG measurements have been reported previously17. Essentially, infra-red
laser pulses (20 ns) with a fundamental wavelength of 1064 nm are incident on the MCT
surface. The incident radiation is S- or P-polarised and the reflected beam, containing
both fundamental and harmonic responses is passed through a polariser (P or S) into a
Thorn-EMI 9813B photomultiplier (PMT) tubes masked by a 532 nm narrow band-pass
11
filter. The signal from the PMT is digitised (Tektronix 7D20) and sent, via the General
Purpose Interface Bus (GPIB), to a personal computer (PC) fitted with a National
Instruments MC-GPIB card, running custom written software. The MCT sample was
mounted on an optical rotation stage controlled by an Ealing Electro-Optics 4-axis DPS
controller which was in turn controlled by the PC over the GPIB. The sample stage was
typically rotated at 5o degrees intervals with the rotation angle and the measured SH
signal stored onto disk allowing complete characterisation of the rotational anisotropy
pattern.
Each anisotropy pattern reported here is the average of three repeat 360º
rotations. Measurements of SH intensity at a fixed sample position over a period of time
indicated a signal variation of ~8%. Calculation of the SH intensities and modeling of the
SHG rotational anisotropy data were carried using custom written software in Igor Pro
3.13 (WaveMetrics Inc.)
Results and Discussion
Anodic oxide growth
The cyclic voltammogram obtained for the MCT sample (x = 0.277) in a solution
containing 0.1 M KOH in 90 % ethylene glycol and 10 % water (pH = 12.2) is given in
Figure 3. Here, the potential was swept at a scan rate of 10 mV s-1 from an open circuit
value of –0.110 V to a final value of 1 V before reversing back to –0.1 V. For the second
cycle the potential was swept to a value of 1.5 V before returning to –0.1 V. The initial
anodic oxidation curve exhibited two distinct current maxima,  and , at 0 V and 0.46 V
with corresponding peak values of 5 and 230 A cm2 respectively. These were followed
by a passivation region where the growth current remained at a constant value of ca. 63
A cm2.
The data here can be directly compared to the work performed by Seelmann-Eggebert39
which involved XPS analysis of the HgTe (and MCT) surfaces during anodic oxide
growth. It is very likely that the anodic peak I is associated with the oxidation of
elemental Hg according to the reaction
Hg  2OH   Hg OH 2  2e 
12
which occurs at a potential of ~ 0.070 V vs. SCE. The Hg atom is the most weakly bound
element in the MCT lattice and there have been a number of reports examining Hgevaporation from the MCT surface and Hg-accumulation/depletion effects at various
MCT/film interfaces40-42. It is feasible therefore that the residue film promotes an
accumulation of Hg at the MCT surface.
The initial stages of the oxide film growth have long been considered to occur by a
dissolution-precipitation mechanism9. On scanning the potential positive, dissolution of
the semiconductor surface continues at an increasing rate until the concentration of the
dissolved species approaches its solubility limit. At this point, a precipitate forms on the
anode surface and is associated with the formation of the passivation peak II. Beyond
this, growth of the oxide layer is supported by a high-field growth mechanism43,44
(electric field ~ 106 to 107 V cm1) whereby the field is able to drive ions through the film
at a rate such that growth can be sustained. Thus, on the second scan, no further film
growth is observed until the applied potential is positive enough to provide the electric
field necessary for that process to occur.
The ellipsometry plot for growth of the anodic oxide at a constant current density of 150
A cm2 is shown in Figure 4. A three-phase model (ambient-film-substrate)45 was
employed to fit the experimental data, with a value of 1.43 employed for the refractive
index of the oxide growth solution. As can be seen from the figure, the model used
provides an excellent fit to the experimental data. The initial oxide layer grown in this
medium had a refractive index of 2.1 and this is consistent with data from the literature.
27,46
. The layer here consisted of essentially CdTeO3 and HgTeO3 39. Beyond a thickness
of 30 nm, a small change in the refractive index of the growing film was found and this is
associated with a small variation in the composition/morphology of the layer.
Significantly though, the extinction coefficient for the layer up to at least 100 nm
thickness remained at zero indicating that the oxide layer did not absorb any of the
incident radiation of 632.8 nm (1.96 eV).
13
SHG analysis
The SH rotation anisotropy pattern obtained in air for the MCT (100) vicinal surface
before and after the removal of an anodic oxide is displayed in Figure 5. The angle of the
incident beam was 56º with respect to the sample normal. Both the PIN-POUT and PIN-SOUT
patterns in the figure were obtained as a result of averaging over 3 repeat runs. The
anodic oxide was grown at a constant current density of 70 A cm2 to a cell voltage of
13 V, consuming a total charge density of 73.67 mC cm2. On comparing the anodic
charge density passed and the final anode voltage with the ellipsometry measurements
discussed earlier, the film thickness was calculated to be 58  3 nm. Removal of the
oxide, using a 10 vol% lactic acid solution in water, was performed within the
electrochemical cell with no alteration in either the sample position or optical set-up.
The data in Figure 5 reveals that the presence of the oxide results in a substantial increase
in the reflected SH intensity with respect to the bare surface. Indeed, if the measured SH
intensity for the oxide present is plotted against the SH intensity when the oxide is
removed for each corresponding angle in the anisotropy pattern, then the linear
relationships shown in Figure 6 are obtained. The plots of the measured intensities in the
PIN-POUT and PIN-SOUT configurations indicate that the presence of the oxide increases the
intensity of the rotational anisotropy pattern by a constant multiple but has no significant
effect on the symmetry of the anisotropy pattern itself. As described by SeelmannEggebert39 and Stahle et al47, the composition of the bulk anodic oxide consists of a
mixture of HgTeO3, CdTeO3 and TeO2.
These components are not symmetrically
distributed within the oxide layer and it is unlikely therefore that any long range order
exists within the bulk oxide. It is thus centrosymmetric and no SH generation within the
bulk oxide is allowed under the electric dipole approximation. Also these measurements
were performed in air and so no electric field polarisation effects across the film need be
considered which could affect the centrosymmetry of the oxide film.
From the above discussion, it is clear from the anisotropy results in Figure 5 that the
increased SH signal must originate from the MCT bulk signal. Two possible explanations
for the source of the SH signal increase can be considered, viz.,( i) charge accumulation at
14
the MCT/oxide interface and (ii) multiple reflections of the fundamental and harmonic
beams within the oxide layer. From capacitance-voltage (C-V) measurements it is known
that the growth of the anodic oxide on n-type MCT leads to an accumulation of positive
fixed charge (due to oxygen vacancies) of the order of 5.0 – 9.0  1011 cm2 on the oxide
surface48,49,50. This leaves the MCT surface slightly accumulated with the formation of a
small space charge region, and it is this increase in electron density that could be
associated with the rise in SH intensity through an increase in the (2) susceptibility
tensor. It has been shown in previous work51 that the intensity of SH waves reflected
from a thin film may be strongly enhanced through multiple reflections of the
fundamental and harmonic beams within the film. In this case and as in subsequent work
on SH waves in thin films52, the films themselves were non-centrosymmetric and
therefore generated SH. However, the anodic oxide film here is centrosymmetric and any
increase in the SH intensity due to multiple reflections within the oxide film would be as
a result of an increased interaction of the fundamental beam with the CMT substrate.
In order to investigate more deeply the effects due to multiple reflections, a study was
carried in which the SH intensity was measured over the whole anisotropy pattern as a
function of the angle of incidence of the fundamental beam. A total of three angles of
incidence, viz. 32º, 45º and 56º with respect to the sample surface normal were employed.
At all angles care was taken in the arrangement of the experimental optics to ensure that
the path length travelled by the laser beam, before and after reflection, remained constant.
Anisotropy patterns were obtained in both the PIN-POUT and PIN-SOUT configurations at
each incidence angle before and after removal of an oxide film, the latter grown under
exactly the same conditions as described for Figure 5. Comparison of the results in
Figures 7 and 8 clearly demonstrate that changes in the angle of incidence has a marked
influence on the intensity of the SH rotational anisotropy pattern. Table I summarises the
results obtained at each incident angle from a linear plot of the SH intensity when the
oxide is present against the measured SH intensity on oxide removal at each
corresponding rotational angle over the whole anisotropy pattern. From Table I it is clear
that, in the PIN-POUT configuration, as the angle of incidence is increased, the constant
factor by which the oxide induces an increase the SH intensity of the anisotropy pattern is
15
reduced. However, for the PIN–SOUT configuration the opposite trend is observed. The
intercept of the calculated slope is included in the table to provide an indication of the
noise level.
Modeling of the effect of multiple reflections within the oxide film on the amplitude of
the incident fundamental wave and the SH wave generated on reflection at the MCT
surface was carried out using the expressions described above. Using values of n  2.15
and n   2.22 for the refractive indices of the oxide film at the fundamental and
harmonic waves, respectively, and n   3.54 , k = 0.4 and n   3.485 , k = 1.405 for the
MCT layer53, Figure 9 compares modeled anisotropy curves for both the PIN-SOUT and
PIN-SOUT polarisation configurations with experimental data acquired in the presence of a
58 nm thick anodic oxide film and after its removal. The angle of incidence employed in
these calculations was 45º and the vicinal angles were  = 2.3º and  = 55º. With all
model parameters unchanged except for the oxide layer thickness, an increase in the SH
intensity by factors of 1.59 and 2.27 for the PIN-POUT and PIN-SOUT polarisation
configurations, respectively, were calculated giving excellent agreement with the
experimental data. Table II lists the calculated increase in the SH response for both these
polarisation configurations at all the incidence angles employed. On comparing the
results in Tables I and II, it can be seen there is excellent correspondence between the
values obtained at the three different angles of incidence. This indicates that multiple
reflections can thus account for most of the experimentally observed SH increase and that
charge accumulation at the MCT/oxide interface for the oxide thickness employed in this
study does not play a significant role in the SH increase. It may well be that for a
different oxide thickness, the charge accumulation at the buried MCT/oxide interface
could vary and so affect the SH intensity to a much greater extent than in the present
case. This will be explored in future work. However, it is also interesting to note that a
closer match between the experimental and calculated values is obtained for the PIN-POUT
configuration compared to the PIN-SOUT configuration. A possible explanation for this
could be that the s-polarised beam along the MCT/oxide interface is more affected by
scattering at the MCT/oxide interface due to small scale roughening54 in this region.
16
Conclusions
The growth of the anodic oxide film on MCT has been followed using in-situ
ellipsometry and the information obtained used to help support the development of a
quantitative model that describes the enhancement in the second harmonic signal in the
presence of the oxide film. Analysis of the ellipsometry data shows that for thin films
(<100 nm) grown galvanostatically at 150 A cm2, the layer is essentially uniform with
a refractive index of ~2.15 and exhibits no absorption of the 1.96 eV incident radiation.
SHG rotational anisotropy carried out on the bare MCT surface and in the presence of a
58 nm thick anodic oxide film shows a clear increase in SH intensity when the oxide film
is present but no change in the anisotropy pattern occurs. This confirms that the oxide
film is centrosymmetric and that the increase in the observed SH intensity must arise
from the underlying MCT. Careful modeling of the data, at different angles of incidence
and polarization configurations of PIN-POUT and PIN-SOUT indicate that this increase can be
largely attributed to multiple reflections of the fundamental beam of frequency  within
the composite layer (ambient/oxide/MCT). The model could successfully reproduce the
experimentally observed variations in the magnitude of the incremental factor with
increasing angle of incidence for both the PIN-POUT and PIN-SOUT polarization
configurations.
Acknowledgements:
The authors are particularly grateful to Dr M G Astles of the QinetiQ Malvern
Technology Centre (formerly the Defence and Evaluation Research Agency, Malvern,
UK) for making the MCT samples available to us.
17
Tables
Angle of
incidence
32o
45o
56o
Table I
PIN-POUT
Increment
Intercept
factor
-0.032
1.77  4 %
-0.007
1.56  4 %
-0.006
1.26  4 %
Measured increase in SH intensity due to presence of a 58 nm thick anodic
oxide film, as per analysis method of Figure 6.
Angle of
incidence
32o
45o
56o
Table II
PIN-SOUT
Increment
Intercept
factor
-0.029
2.02  4 %
-0.039
2.34  4 %
-0.009
2.48  4 %
PIN-POUT
Increment factor
1.87
1.59
1.29
PIN-SOUT
Increment factor
2.21
2.27
2.34
Calculated increase in SH intensity of an oxide covered MCT surface due
to multiple reflections within the 58 nm anodic oxide layer.
18
Figure Captions
Figure 1
Schematic of the different waves present within the multilayer model. For
the layer of thickness d2, the difference in geometrical path for reaching C
directly or by reflection at the interface at B is path = AB + BC.
Figure 2
Definition of vicinal surface and showing sample rotation about the
surface normal.
Figure 3
Cyclic voltammograms of an MCT sample (x = 0.277) in a 0.1 M KOH
solution in 90 vol% ethylene glycol/10 vol% water.
Figure 4
In-situ ellipsometry    plot for the growth of an anodic oxide film on
MCT at a constant current density of 150 μA cm2 in a 0.1 M KOH
solution in 90 /10 vol% ethylene glycol/water.
Figure 5
Rotational anisotropy SH intensity patterns obtained in air in the (a) PINPOUT and (b) PIN-SOUT polarisation configurations, before and after the
removal of the anodic oxide film (~58 nm thick). The angle of incidence
was 56º.
Figure 6
Plots of the measured SH intensity for the oxide present against the SH
intensity measured when the oxide is removed, for each corresponding
rotation angle in the (a) PIN-POUT and (b) PIN – SOUT anisotropy patterns of
Figures 5 (a) and (b) respectively.
Figure 7
Rotational anisotropy patterns for the PIN-POUT polarisation configuration
measured at incidence angles of 32º, 45º and 56º before (a) and after (b)
removal of a 58 nm oxide film.
Figure 8
Rotational anisotropy patterns for the PIN-SOUT polarisation configuration
measured at incidence angles of 32o, 45o and 56o before (a) and after (b)
removal of a 58 nm oxide film.
Figure 9
Experimental data and modelled rotational anisotropy patterns for the (a)
PIN-POUT and (b) PIN-SOUT polarisation configurations at an incidence
angle of 45º, comparing the effects of multiple reflections within the
ambient/oxide/MCT layer.
19

z
p

m
P
1
 1
1

y
2
d2
M
2
C
2
x
A
B
 3
3
Figure 1
20
z
y
y'
z'



x
x'
Figure 2
21
250
i D (A cm-2 )
II
200
150
100
1st cycle
2nd cycle
50
0
-0.1
I
0.3
0.7
1.1
1.5
Potential /V
Figure 3
22
400
350
300
250
Film 1: n = 2.1, k = 0.0,  = 30 nm
Film 2: n = 2.2, k = 0.0,  = 70 nm
200
 /º
Data
Film 1
Film 2
150
Start: Bare MCT
100
50
0
0
10
20
30
40
50
60
-50
 /º
Figure 4
23
0.6
(a)
P IN - P OUT
SH intensity /a.u.
0.5
oxide film
0.4
bare MCT
0.3
0.2
0.1
0
0
60
120
180
240
300
360
Rotation angle /º
1.2
(b)
P IN - S OUT
1
SH intensity /a.u.
oxide film
bare MCT
0.8
0.6
0.4
0.2
0
0
60
120
180
240
300
360
Rotation angle /º
Figure 5
24
0.6
(a)
PIN - POUT SHG (oxide)
0.5
0.4
0.3
0.2
0.1
0
0.05
0
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.3
0.35
0.4
P IN - P OUT SHG (MCT)
1.2
(b)
PIN - SOUT SHG (oxide)
1
0.8
0.6
0.4
0.2
0
0
0.05
0.1
0.15
0.2
0.25
P IN - S OUT SHG (MCT)
Figure 6
25
SH intensity /a.u.
0.6
(a)
0.5
56º (oxide)
45º (oxide)
0.4
32º (oxide)
0.3
0.2
0.1
0
SH intensity /a.u.
0
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
60
120
180
240
Rotation angle /º
300
360
300
360
(b)
56º (bare MCT)
45º (bare MCT)
32º (bare MCT)
0
60
120
180
240
Rotation angle /º
Figure 7
26
(a)
SH intensity /a.u.
1
56º (oxide)
45º (oxide)
0.8
32º (oxide)
0.6
0.4
0.2
0
0
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
60
120
180
240
Rotation angle /º
(b)
300
360
56º (bare MCT)
SH intensity /a.u.
45º (bare MCT)
32º (bare MCT)
0
60
120
180
240
Rotation angle /º
300
360
Figure 8
27
SH intensity/a.u.
0.4
bare MCT
oxide film
model fit bare MCT
model fit with oxide film
(a) PIN - POUT
0.3
0.2
0.1
0.0
0
50
100
150
0.6
SH intensity/a.u.
200
Rotation angle/º
250
(b) P IN - SOUT
0.5
300
350
bare MCT
oxide film
model fit bare MCT
model fit with oxide
0.4
0.3
0.2
0.1
0.0
0
50
100
150
200
Rotation angle/º
250
300
350
Figure 9
28
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