Lallart M. Ferroelectrics: Characterization and Modeling

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Characterization of Ferroelectric Materials by Photopyroelectric Method

299

As presented in the theoretical section, the normalized phase of the FPPE signal, for a

detection cell composed by three layers - air, pyroelectric sensor and substrate - is given

by:

(1 )exp( )sin( )

arctan

1(1 )exp( )cos( )

sp pp pp

ppppp

RaLaL

+−

Θ=

−+ −

(4.10)

Eq. (4.10) is valid for opaque pyroelectric sensor and for thermally thick substrate. The

normalization signal was obtained with empty, directly irradiated sensor. When performing

measurements at two different chopping frequencies we obtain:

)]

tan()

sin()

)[cos(

exp(

)]

tan()

sin()

)[cos(

exp(

)

tan(

)

tan(

Θ+−

(4.11)

with a

p1,2

= (π f

1,2

/α

)

1/2

. Eq. (4.11) indicates that one can obtain the thermal diffusivity of the

pyroelectric material, used as sensor in the detection cell, by performing two measurements

at two different chopping frequencies, providing the geometrical thickness of the sensor is

known.

Typical results, obtained for the phase of the PPE signal for a 500 µm thick TGS single

crystal, with silicon oil as substrate (together with the normalization signal - directly

irradiated empty sensor) are displayed in Fig. (4.11). An external electric field of 6 kV/m

was additionally applied.

42 44 46 48 50 52

-3.2

-3.0

-2.8

-2.6

-2.4

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

with substrate

with substrate : full symbol

normalization signal : empty symbol

normalization

signal

f=12Hz

f=3Hz

PPE phase (rad)

Temperature (

Fig. 4.11 Temperature scans of the phase of the PPE signal, for a 500µm thick TGS single

crystal, around the ferroelectric Curie temperature, for 3Hz and 12Hz chopping frequencies,

and an external electric field of 6kV/m.

Ferroelectrics - Characterization and Modeling

300

42 44 46 48 50 52

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

f=12Hz

f=3Hz

Normalized PPE phase (rad)

Temperature (°C)

Fig.4.12 Same as Fig.4.11, but for the normalized phase.

Fig. 4.12 presents the normalized phases of the PPE signal for the two frequencies. The

critical behaviour of the thermal diffusivity for three values of the external electric field, as

obtained from Eq.(4.11), is displayed in Fig. 4.13.

46 47 48 49 50 51

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

0 kV/m

1 kV/m

10 kV/m

Temperature (°C)

thermal diffusivity x10

/s)

Fig. 4.13 Critical behaviour of the thermal diffusivity of TGS for 0 kV/m (squares); 1 kV/m

(circles) and 10 kV/m (triangles).

Fig. 4.13 displays a typical behavior (critical slowing down) of thermal diffusivity for a

second order phase transition. The external electric field has the well known influence on

the phase transition: it increases the Curie temperature and enlarges the critical region. The

Characterization of Ferroelectric Materials by Photopyroelectric Method

301

values of the Curie points are in good agreement with those obtained from the direct

measurement of the PPE amplitude (Fig. 4.14).

42 44 46 48 50 52

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0 kV/m

1kV/m

10kV/m

0246810

48.0

48.2

48.4

48.6

48.8

49.0

49.2

49.4

49.6

49.8

50.0

PPE amplitude

th. d iffu s ivity

Curie temperature (

electric field (kV/m)

TG S single crystal

PPE amplitude (V)

Temperature (°C)

Fig. 4.14 Typical behaviour of the amplitude of the PPE signal for empty TGS sensor and for

three values of the external electric field. Insertion: The Curie temperature vs. electric field,

as obtained from thermal diffusivity and PPE amplitude (inflection point).

In conclusion to this sub-section, the PPE calorimetry, in the “front” detection configuration,

was used to measure the critical behaviour of the thermal diffusivity of TGS single crystal.

In a standard PPE experiment (section 4.3.1) the information on the sample’s properties is

collected and processed. In this approach, we collect the information on the thermal

properties of the pyroelectric sensor itself.

We selected the phase of the PPE signal (and not the amplitude) as source of information

due to the well known advantages: the phase is independent on the fluctuations of the

incident radiation and the signal to noise ratio is higher than in the case of using the

amplitude of the signal. Measurements at two different chopping frequencies and

calibration procedures were necessary in order to eliminate the instrumental factors and to

obtain a mathematical equation depending on solely one thermal parameter, which is the

thermal diffusivity.

The applied external electric field has a typical influence on the critical region of the para-

ferroelectric phase transition of TGS: both the Curie temperature and the thickness of the

critical region slightly increase with increasing value of the electric field.

The results obtained for the value of the thermal diffusivity of TGS and for the value of the

Curie temperatures are in good agreement with data reported in the literature and obtained

by other techniques (del Cerro et al., 1987).

Finally, we must emphasize that this configuration speculates the fact that the investigated

ferroelectric material is pyroelectric as well. The method was used on a classical TGS crystal,

but it appears to be a suitable alternative in studying the thermal properties of the

ferroelectric liquid crystals, when the ferroelectric state is imposed by a given layered

geometry.

Ferroelectrics - Characterization and Modeling

302

5. Discussions and conclusions

5.1 Comparison with other techniques

It is not possible to perform an exhaustive analysis and comparison of the PPE

calorimetry with other types of calorimetry, but some particular advantages of this

technique can be mentioned. First of all, due to the fact that the pyroelectric sensor “feels”

the temperature variation (and not the temperature), no special thermostatic precautions

are requested. This is an advantage compared with adiabatic types of calorimetry, for

example. If we compare PPE with differential scanning calorimetry (DSC), PPE is more

accurate in detecting the critical temperature (Curie point for ferroelectrics), due to the

possibility of scanning very slow (few mK/min – see for example Marinelli et al., 1992)

the temperature of the detection cell. In the case of DSC, it is known that the sensitivity

increases with increasing temperature variation rate (decreasing the accuracy in

measuring the critical temperature).

We cannot overtake two general features that make the PPE calorimetry “unique”: (i) it is

the only calorimetric technique able to give in one measurement the value of two (in fact all

four) thermal parameters; (ii) it is the only technique which, in the critical region of a phase

transition, for a given anomaly in the thermal parameters, produces an enhanced signal

anomaly.

Finally, some comparison with other PT techniques is welcome. Marinelli et al., 1992 tried

to compare the performances of the PPE technique in detecting phase transitions, with

another photothermal technique largely used for phase transitions investigations: the

photoacoustic (PA) method.

If we follow only the phase channels, they are given in the standard configuration, with

optically opaque and thermally thick sample by the equations (Zammit et al., 1988; Marinelli

et al., 1992):

()

/21tan

−−=Θ

−

;

()

1/2

βαω

= (5.1)

for PA phase, and

()

ePPE

/1tan

−−=Θ

−

ωτ

;

()( )

2/1

/2/1

ωα

Lq = (5.2)

for PPE phase.

The sensitivity of the two techniques to changes in p and q, respectively, are:

()

−



=++





(5.3.a)

2−













PPE

(5.3.b)

An analysis of Eqs. (5.3.a,b) leads to the conclusion that the maximum sensitivity of the PA

technique is reached when p=0 and has the value ½. In the mean time the sensitivity of the

PPE technique can go (at least theoretically) to infinity, denoting once again the suitability of

this technique for phase transitions detection.

Characterization of Ferroelectric Materials by Photopyroelectric Method

303

5.2 General features of the PPE calorimetry

PPE technique is a sensitive and accurate calorimetry for thermal inspection of solid state

matter. Concerning ferroelectric materials, the main feature of the method is that two

detection configurations can be separately or together used for thermal characterization; the

ferroelectric material under investigation can be sample or sensor in the PPE detection cell.

All four static (specific heat) and dynamic (thermal conductivity, diffusivity and effusivity)

thermal parameters can be measured by this technique, and phenomena associated with

changes in time, composition or temperature (phase transitions-for example) can be studied.

The sensitivity of the method and the accuracy of the results, when investigating

ferroelectric materials, depend on various experimental parameters. The possibility of

selecting and adjusting these experimental parameters can lead to an optimization of the

performances of the method.

The performances of the method depend practically on: the sensor's detectivity, the

precision in monitoring the main experimental parameters (chopping frequency, sample's

thickness control, temperature, etc), the quality of the sensor-sample thermal contact, the

way of performing the acquisition and processing of experimental data. Some typical

experimental data are: the detectivity of the pyroelectric LiTaO

sensors is higher than 10

cm Hz

1/2

-1

; minimum detectable temperature variation: 1 μK; minimum controllable

temperature variation rate: 10 mK; frequency stability:

-4

Hz.

The main limitations of the technique concerning ferroelectric materials are imposed by the

Curie temperature of the pyroelectric sensor, by the properties of the coupling fluid (always

necessary when inserting the ferroelectric material as a sample) and by the geometry of the

investigated sample (it must be a disk of tens-hundreds of micrometers thick, with polished

surfaces).

6. References

Bentefour E.H., Glorieux C., Chirtoc M. &Thoen J. (2003). Characterization of pyroelectric

detectors between 170 and 300 K using the photopyroelectric technique,

Review of

Scientific Instruments

, Vol. 74, No. 1,(January 2003), pp. 811-813, ISSN 0034-6748

Bhalla A. S. , Liu S. T. (1993). 4.2.3 Pyroelectric coefficients of ferroelectric pyroelectrics, In

Electrical Properties - Low Frequency Properties of Dielectric Crystals - Piezoelectric,

Pyroelectric, and Related Constants , The Landolt-Börnstein Database

, D.F. Nelson (Ed.),

Vol. 29b, Springer Verlag, ISBN 978-3-540-55065-5.

Chirtoc, M., Glorieux, C. & Thoen, J.(2009). Thermophysical Properties and Critical

Phenomena Studied by Photopyroelectric (PPE) Method, In:

Thermal Wave Physics

and Related Photothermal Techniques: Basic Principles and Recent Developments,

E. M.

Moraes, (Ed), 125-159, Transworld Research Network, ISBN 978-81-7895-401-1,

Kerala, India

Chirtoc, M. & Mihailescu, G.(1989). Theory of Photopyroelectric Method for Investigation of

Optical and Thermal Materials Properties.

Physical Review, Vol. B40, No. 14,

(November 1989), pp. 9606-9617, ISSN 1098-0121

Clark N. and Lagerwall S. T.(1980). Submicrosecond Bistable Electro-Optic Switching in

Liquid Crystals.

Applied Physic. Letters. 36 (1980) pp899-901, ISSN 0003-6951

Coufal, H. (1984). Photothermal Spectroscopy Using a Pyroelectric Thin-Film Detector.

Applied Physics. Letters, Vol. 44, No. 1, (January 1984), pp.59- 61, ISSN 0003-6951

Ferroelectrics - Characterization and Modeling

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del Cerro, J., Ramos, S. & Sanchez-Laulhe, J. M. (1987). Flux Calorimeter for Measuring

Thermo-physical Properties of Solids: Study of TGS.

Journal of Physics E: Scientific

Instruments,

Vol. 20, No. 6, (June 1987), pp. 612-615, ISSN 0957-0233

Delenclos, S., Chirtoc, M., Hadj Sahraoui, A., Kolinsky, C. & Buisine, J. M. (2002).

Assessement of Calibration Procedures for Accurate Determination of Thermal

Parameters of Liquids and their Temperature Dependence Using the

Photopyroelectric Method.

Review of Scientific Instruments, Vol. 73, No.7, (July 2002),

pp.2773-2780, ISSN 0034- 6748

Fullem, T. Z., and Y. Danon, Electrostatics of pyroelectric accelerators.

Journal of Applied

Physics

Vol. 106, No 7, (October 2009), ISSN 0021-8979

Jalink, H., Frandas, A., van der Schoor, R. & Bicanic, D. (1996). New Photothermal Cell

Equiped with Peltier Elements for Phase Transition Studies.

Review of Scientific

Instruments

, Vol. 67, No. 11, (November 1996), pp.3990-3993, ISSN 0034- 6748

Lagerwall S. T.,

Ferroelectric and Antiferroelectric Liquid Crystals. (1999). Wiley-VCH, ISBN

978-3527298310, New York

Mandelis, A. (1984). Frequency Domain Photopyroelectric Spectroscopy of Condensed

Phases: A New, Simple and Powerful Spectroscopic Technique.

Chemical Physics

Letters

, Vol. 108, No. 4, (July 1984), pp. 388-392, ISSN 0009-2614

Mandelis, A. & Zver, M. M. (1985) J. Theory of Photopyroelectric Effect in Solids.

Journal of

Applied Physics, Vol. 57, No. 9, (May 1985), pp. 4421-4430, ISSN 0021-8979

Mandelis, A., Care, F., Chan, K. K. & Miranda, L. C. M. (1985). Photopyroelectric Detection

of Phase Transitions in Solids.

Applied Physics A, Vol. 38, No. 2, (October 1985), pp.

117-122, ISSN 0947-8396

Marinelli, M., Zammit, U., Mercuri, F. & Pizzoferrato, R.(1992). High Resolution

Simultaneous Photothermal Measurements of Thermal Parameters at a Phase

Transition with the Photopyroelectric Technique.

Journal of Applied Physics, Vol. 72,

No. 3, (August 1992), pp.1096-1100, ISSN 0021-8979

Nakamura M., Takekawa S & Kitamura K, Anisotropy of thermal conductivities in non- and

Mg-doped near-stoichiometric LiTaO3 crystals,

Optical Materials, Vol. 32, No 11,

(September 2010), pp. 1410-1412, ISSN 0925-3467

Tam, A. C. (1986). Applications of Photoacoustic Sensing Techniques.

Review of Modern

Physics

, Vol. 58, No. 2, (February 1986), pp. 381-431, ISSN 0034-6861

Zammit, U., Marinelli, M., Mercuri, F.,Pizzoferrato, R., Scudieri, F. & Martelucci, S.

Photoacoustics as a Technique for Simultaneous measurement of Thermal

Conductivity and Heat Capacity.

Journal of Physics E-Scientific Instruments, Vol. 21,

No. 10, (October 1988), pp.935-941, ISSN 0957-0233

Whatmore R.W., Pyroelectric Devices and Materials,

Reports on Progress in Physics, Vol. 49

(December 1986), pp1335-1386, ISSN 0034-4885

For many years, heterojunctions have been one of the fundamental research areas of

solid state science. The interest in this topic is stimulated by the wide applications

of heterojunction in microelectronics. Devices such as heterojunction bipolar transistors,

quantum well lasers and heterojunction ﬁeld effect transistors (FET), already have a signiﬁcant

technological impact. The semiconductor-ferroelectric heterostructures have attracted much

attention due to their large potential for electronic and optoelectronic device applications

(Lorentz et al., 2007; Losego et al., 2009; Mbenkum et al., 2005; Voora et al., 2009; 2010). The

ferroelectric constituent possesses switchable dielectric polarization, which can be exploited

for modiﬁcating the electronic and optical properties of a semiconductor heterostructure.

Hysteresis properties of the ferroelectric polarization allows for bistable interface polarization

conﬁguration and potentially for bistable heterostructure operation modes. Therefore, the

The heterostructures of wurtzite semiconductors and perovskite ferroelectric oxide integrate

the rich properties of perovskites together with the superior optical and electronic properties

of wurtzites, thus providing a powerful method of new multifunctional devices. The electrical

and optical properties of the heterostructures are strongly inﬂuenced by the interface band

offset, which dictates the degree of charge carrier separation and localization. It is very

important to determine the valence band offset (VBO) of semiconductor/ferroelectric oxides

in order to understand the electrical and optical properties of the heterostructures and to

design novel devices. In this chapter, by using X-ray photoelectron spectroscopy (XPS),

we determine the VBO as well as the conduction band offset (CBO) values of the typical

semiconductor/ferroelectric oxide heterojunctions, such as ZnO/SrT iO

,ZnO/BaTiO

InN/SrTiO

and InN/BaTiO

, that are grown by metal-organic chemical vapor deposition.

Based on the values of VBO and CBO, it has been found that type-II band alignments

form at the ZnO/SrTiO

and ZnO/BaTiO

interfaces, while type-I band alignments form at

InN/SrTiO

and InN/BaTiO

interfaces.

1. Introduction

Valence Band Offsets of ZnO/SrTiO

, ZnO/BaTiO

InN/SrTiO

, and InN/BaTiO

Heterojunctions

Measured by X-ray Photoelectron Spectroscopy

Caihong Jia

1,2

, Yonghai Chen

, Xianglin Liu

, Shaoyan Yang

and ZhanguoWang

Key Laboratory of Semiconductor Material Science, Institute of Semiconductors,

Chinese Academy of Science, Beijing

Key Laboratory of PhotovoltaicMaterials of Henan Province and School of Physics

Electronics, Henan University, Kaifeng

China

Measured by X-Ray Photoelectron Spectroscopy

2 Will-be-set-by-IN-TECH

heterostructures of wurtzite semiconductors and perovskite ferroelectric oxides integrate the

rich properties of perovskites together with the superior optical and electronic properties of

wurtzites, providing a powerful method of new multifunctional devices (Peruzzi et al., 2004;

Wei et al., 2007; Wu et al., 2008). It is well known that the electrical and optical properties of

the heterostructures are strongly inﬂuenced by the interface band offset, which determines

the barrier for hole or electron transport across the interface, and acts as a boundary condition

in calculating the band bending and interface electrostatics. Therefore, it is very important

to determine the valence band offset (VBO) of semiconductor/ferroelectric oxides in order to

understand the electrical and optical properties of the heterostructures and to design novel

devices.

Zinc oxide (ZnO) is a direct wide bandgap semiconductor with large exciton binding energy

(60 meV) at room temperature, which makes it promising in the ﬁeld of low threshold

current, short-wavelength light-emitting diodes (LED) and laser diodes (Ozgur et al., 2005).

It also has a growing application in microelectronics such as thin ﬁlm transistors (TFT) and

transparent conductive electrodes because of high transparency and large mobility. Indium

nitride (InN), with a narrow direct band gap and a high mobility, is attractive for the near

infrared light emission and high-speed/high-frequency electronic devices (Losurdo et al.,

2007; Takahashi et al., 2004). Generally, ZnO and InN ﬁlms are grown on foreign substrates

such as c-plane and r-plane sapphire, SiC (Losurdo et al., 2007; Song et al., 2008), (111)

Si and GaAs (Kryliouk et al., 2007; Murakami et al., 2008). SrT iO

(STO) single crystal is

widely used as a substrate for growing ferroelectric, magnetic and superconductor thin

ﬁlms. Meanwhile, STO is one of the important oxide materials from both fundamental

physics viewpoint and potential device applications (Yasuda et al., 2008). The electron density

and hence conductivity of STO can be controlled by chemical substitution or annealing in

a reducing atmosphere. Furthermore, a high-density, two-dimensional electron (hole) gas

will lead to tailorable current-voltage characteristics at interfaces between ZnO or InN and

STO (Singh et al., 2003). In addition, the lattice polarity of ZnO and InN (anion-polarity or

cation-polarity) is expected to be controlled by the substrate polarity considering the atomic

conﬁguration of STO surface, which is also important to obtain a high-quality ZnO or InN

epitaxial layer (Murakami et al., 2008). Thus, it is interesting to grow high quality wurtzite

ZnO and InN ﬁlms on perovskite STO substrates, and it is useful to determine the valence

band offset (VBO) of these heterojunctions.

The heterojunction of semiconductor-ZnO or InN/ferroelectric-BaTiO

(BTO) provides an

interesting optoelectronic application due to the anticipated strong polarization coupling

between the ﬁxed semiconductor dipole and the switchable ferroelectric dipole (Lorentz et al.,

2007; Losego et al., 2009; Mbenkum et al., 2005; Voora et al., 2009; 2010). ZnO TFT, highly

attractive for display applications due to transparency in the visible and low growth

temperatures, are limited by large threshold and operating voltages (Kim et al., 2005). BTO,

as a remarkable ferroelectric material with a high relative permittivity, can be used as the

gate dielectric to reduce the operating voltages of TFT for portable applications (Kang et al.,

2007; Siddiqui et al., 2006), and as an attractive candidate as an epitaxial gate oxide for

ﬁeld effect transistor. In addition, the free carrier concentration in the ZnO channel can be

controlled by the ferroelectric polarization of BTO dielectric in the ZnO/BTO heterostructure

ﬁeld-effect-transistors, thus demonstrating nonvolatile memory elements (Brandt et al., 2009).

In order to fully exploit the advantages of semiconductor-ferroelectric heterostructures, other

combinations such as InN/BTO should be explored. As a remarkable ferroelectric material

with a high relative permittivity, BTO can be used as a gate dielectric for InN based ﬁeld

306

Ferroelectrics - Characterization and Modeling

Valence Band Offsets of ZnO/SrTiO

, ZnO/BaTiO

,InN/SrTiO

, and InN/BaTiO

Heterojunctions Measured by X-ray Photoelectron Spectroscopy 3

effect transistor. More importantly, InN/BTO heterojunction is promising for fabricating

optical and electrical devices since oxidation treatment is found to reduce the surface electron

accumulation of InN ﬁlm (Cimalla et al., 2007). Therefore, it is important to determine

the VBO of these semiconductor/ferroelectric heterojunctions to design and analyze the

performance of devices.

In this chapter, we will ﬁrst present several methods to determine the energy discontinuities.

Then, by using x-ray photoelectron spectroscopy (XPS), we determine the VBO as well as

the conduction band offset (CBO) values of the typical semiconductor/ferroelectric oxide

heterojunctions, such as ZnO/STO, ZnO/BTO, InN/STO, and InN/BTO, that are grown by

metal-organic chemical vapor deposition. Based on the values of VBO and CBO, it has been

found that type-II band alignments form at the ZnO/STO and ZnO/BTO interfaces, while

type-I band alignments form at the InN/STO and InN/BTO interfaces.

2. Measurement methods

The energy band edge discontinuities at heterostructures can be determined by applying a

large variety of experimental techniques, such as electrical transport measurements including

capacitance-voltage (C-V) and current-voltage (I-V), optical measurement, photoemission

measurement (Capasso et al., 1987). For many years, analysis of the capacitance-voltage

and current-voltage of heterojunctions have proven to be important probes for determining

the energy barriers of pn junction, Schottky barriers and heterojunctions. The energy

discontinuities can be determined by C-V measurement, since the C(V) function has the form

of:

2(

+ 

)

q



−V)

−1/2

,(1)

where 

and 

are the dielectric constants of materials 1 and 2, N

and N

are the dopant

concentrations of materials 1 and 2, V

is the diffusion potential, while q is the electronic

charge. Therefore, the plot of C

−2

versus V gives a straight line, intercepting the V-axis

exactly at V=V

. Based on this quantity, the conduction band discontinuity energy, ΔE

,can

be obtained to be

ΔE

= qV

+ δ

−(E

−δ

),(2)

for anisotype pN heterojunctions; and

ΔE

= qV

+ δ

−δ

,(3)

for isotype nN heterojunctions. Where δ

and δ

refer to the position of the Fermi energies

relative to the conduction band minimum (or valence band maximum) in n (or p)-type

materials 1 and 2, respectively. That is,

= kT ln(

), i = 1, 2. (4)

Here, kT is the Boltzmann energy at the temperature T, N

is the effective conduction band

density of states,

2(2πm

∗

kT)

,(5)

307

Valence Band Offsets of ZnO/SrTiO

, ZnO/BaTiO

InN/SrTiO

, and InN/BaTiO

Heterojunctions Measured by X-Ray Photoelectron Spectroscopy

4 Will-be-set-by-IN-TECH

which is a function of the reduced effective mass of the electron (m

∗

) and of temperature (T).

Therefore, the difference in the Fermi energies between materials 1 and 2 can be simpliﬁed to

give

−δ

= kT ln(

kTl n

(

∗

),(6)

for an nN heterojunction. Thus once the diffusion potential V

is determined, it is relatively

straightforward to obtain the conduction band discontinuity. Indeed, as can be seen from the

equation above, it is not necessary to have a highly precise measurement of any of the material

parameters such as the bulk free carrier concentration or the effective density of states, since

ΔE

depends only logarithmically on these parameters. On the other hand, the dependence

of ΔE

on V

is linear, and, therefore, it is important that the measurement of the diffusion

potential be as accurate as possible.

The current density is given simply by

= A

∗

ex p(−

qφ

),(7)

where φ

is the barrier height, from which the energy band offset can be determined. The

transport measurements have the advantage of being a relatively understanding means of

acquiring data using simple structures, but the accuracy of these techniques has never been

considered to be particularly high, basically due to the existence of parasitic phenomena

giving rise to excess stray capacitances or dark currents, which introduces variables cannot

be easily treated in the overall analysis and confuse the measurements.

The optical measurement techniques are based on the study of the optical properties of

alternating thin layers of two semiconductors. The quantized energy levels associated with

each well depend on the corresponding discontinuity, on the width of the well and on the

effective mass. The processes involving the localized quantum well states will introduce series

of peaks both in the absorption and photoluminescence spectra. From the position in energy

of the peaks in each series, it is possible to retrieve the parameters of the well and in particular

the value of ΔE

and ΔE

. However, this approach requires the fabrication of high-quality

multilayer structures with molecular beam epitaxy, and can only be applied to nearly ideal

interface with excellent crystal quality.

For x-ray photoelectron spectroscopy (XPS), it is well established that the kinetic energy,

, of electrons emitted from a semiconductor depends on the position of the Fermi level,

, within the semiconductor band gap. This aspect of XPS makes it possible to determine

relative to the valence band maximum, E

, in the region of the semiconductor from

which the photoelectron originate. Therefore, besides analyzing the interface elemental and

chemical composition, XPS can also be used as a contactless nondestructive and direct access

to measure interface potential related quantities such as heterojunction band discontinuites.

This technique was pioneered by Grant ea al (Grant et al., 1978). Since the escape depths of

the respective photoelectrons are in the order of 2 nm only, one of the two semiconductors has

to be sufﬁciently thin. This condition may be easily met when heterostructures are grown by

molecular beam epitaxy (MBE) or metal-organic chemical vapor deposition (MOCVD). The

XPS method for determining VBO is explained by the schematic band diagram displayed in

Fig. 1, in which an idealized ﬂat band was assumed. Based on the measured values of ΔE

the core level to E

binding energy difference in bulk semiconductors A and B, (E

-E

)and

308

Ferroelectrics - Characterization and Modeling