Electronic surface properties of SrTiO3 derived from a surface photovoltage study

Surface Science 612 (2013) 1–9

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Electronic surface properties of SrTiO3 derived from a surface photovoltage study E. Beyreuther ⁎, J. Becherer, A. Thiessen, S. Grafström, L.M. Eng Institut für Angewandte Photophysik, Technische Universität Dresden, D-01062 Dresden, Germany

a r t i c l e

i n f o

Article history: Received 30 November 2012 Accepted 31 January 2013 Available online 15 February 2013 Keywords: Strontium titanate SrTiO3 Surface photovoltage SPV Surface state SPV transient Kelvin probe

a b s t r a c t In the past, surface photovoltage (SPV) analysis has been successfully applied to derive the electronic defect status of a number of wide-bandgap semiconductor surfaces. Here, the method is applied to the model perovskite strontium titanate, whose SPV phenomena are comprehensively studied over seven decades of excitation-light intensity. The SPV was recorded by a Kelvin probe setup as a function of wavelength in order to extract the energetic positions of electronic surface states within the bandgap. At selected wavelengths addressing distinct surface states, SPV transients were measured as a function of light intensity and temperature. Several models known from the literature were used to estimate and cross check surface state parameters such as surface state densities, capture cross sections for photons and electrons, and the surface band bending in the dark and under illumination. In contrast to other wide-bandgap materials, SPV transients of SrTiO3 exhibit highly complex shapes, i.e. they (i) show signatures of multiple carrier transitions, (ii) mixtures of surface and bulk contributions, as well as (iii) both ex- and intrinsic SPV processes. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Among complex oxides, currently the perovskite structure marks one focus of scientific interest, mainly because it is able to adopt a wide variety of chemical compositions. This property provides the opportunity to manufacture all-oxide heterostructures in the form of thin films, epitaxially grown on each other [1]. Additionally, several perovskite compounds show (i) promising functional properties such as ferroic order, (ii) an extreme sensitivity to external stimuli – e.g. electric, magnetic, strain, and photonic fields, or doping – making basic characteristics such as carrier density or ferroic order tunable, and (iii) switchable interface functionalities [2,3]. Within this context, strontium titanate (SrTiO3) plays the role of a model perovskite due to its undistorted cubic structure as well as its paraelectricity and paramagnetism. SrTiO3 is one of the most frequently used substrates for the epitaxial growth of other perovskite films, such as ferroelectrics (e.g. PZT), magnetic oxides (e.g. manganites, cobaltites, ferrites), or superconductors (e.g. YBCO). On the other hand, SrTiO3 has attracted interest by its own (i) as a possible gate oxide in field effect transistors [4], (ii) because it shows locally confined memory-resistive switching [5], and (iii) in more chemistry-related applications as a photocatalyst, an oxygen sensor, and as an anode in solid oxide fuel cells ([6] and Refs. therein). Like in elemental- and III–V-semiconductor-based technology, the performance and reliability of oxide electronic devices are supposed to be crucially influenced by the distribution and properties of electronic surface and interface states. Though studying the electronic properties ⁎ Corresponding author. Tel.: +49 351 4633 4903; fax: +49 351 4633 7065. E-mail address: [email protected] (E. Beyreuther). 0039-6028/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.susc.2013.01.022

of the basic perovskite SrTiO3 should provide an excellent ground for understanding heterostructure transport, surprisingly little is known about electronic defects in the bulk 1 as well as at interfaces of SrTiO3. The main reason for this lack of systematic data is the low intrinsic carrier density and the high work function of undoped SrTiO3, which make most standard electrical characterization methods (e.g. capacitance–voltage, current–voltage, or deep-level transient spectroscopies) fail, since they need a certain level of electric conductivity and good ohmic contacts. In the current work we follow a different approach, namely contactless detection of the surface photovoltage (SPV), i.e., of surface potential changes occurring under optical excitation. This method has been shown to be a successful alternative for investigating wideband-gap materials [13], especially their surfaces and interfaces. The present work is a comprehensive SPV analysis of SrTiO3. Up to now, similar studies have been made almost exclusively on elemental, III–V, and II–VI semiconductors. The work of Mavroides and Kolesar [14] on SrTiO3 dating back to 1978 seems to be the only SPV study of a perovskite surface so far. As the measurements were performed in a liquid, this work appears to be of limited relevance, though. The current knowledge on the electronic configuration of SrTiO3 surfaces 2 is puzzling and partly contradictory. Concerning the surface crystal structure in the sense of possible surface reconstructions, much 1 Within the framework of the investigation of SrTiO3 as a possible alternative gate dielectric, some theoretical work covering the calculation of the energy levels of several bulk point defects has been accomplished (e.g. [7,8] and Refs. therein), but rarely directly proven experimentally within electrical measurements [9,10]. Alternatively, some bulk defects were investigated within photoluminescence experiments [11,12]. 2 We limit the following literature survey to investigations on either undoped or oxygen-vacancy-doped SrTiO3, since doping by cation substitution with Nb or La changes the band structure in a subtle way [6] and is beyond the scope of the present work.

2

E. Beyreuther et al. / Surface Science 612 (2013) 1–9

work has been done on the SrTiO3 (100) surface, which has been shown to be more stable and easier to prepare than the (110) and (111) surfaces [15]. A variety of surface reconstructions occurring after certain surface treatments have been shown impressively by STM and LEED [16,17], or have been predicted theoretically [18,19]. The latter two papers stress that the surface structure is a sensitive function of oxygen partial pressure and temperature and that the TiO2-terminated surface behaves very differently from the SrOterminated one. One of the few surface investigations on as-grown stoichiometric SrTiO3 was performed by atomic force microscopy [20]. The electronic surface properties are, of course, inherently interlinked with the lattice structure. Also here, no clear picture can be derived from the literature. There are indications that shallow as well as midgap surface states exist [19,21–23], depending on the history of sample treatment in experimental studies or on the model assumed in theoretical works. While an early theoretical (LCAO) calculation predicted midgap surface states for the (001) surface [21], a subsequent photoemission study could not detect any such states [22]. However, later a combined UPS/EELS/Auger investigation found evidence for residual surface states even for vacuum-cleaved crystals. They could not be removed by annealing but their density decreased under oxygen flow [23]. Further results were given in two more recent XPS works [24,25], where no intrinsic states were found (or the intrinsic states were completely empty) and the residual states were classified to be purely extrinsic. Furthermore, all cited photoemission studies agree that Ar + bombardment is a method to intentionally induce a high concentration of surface defect states. Finally, it must be mentioned that quite recent results revealed the existence of a two-dimensional electron gas (2DEG) at pure SrTiO3 surfaces [26,27]. This phenomenon, whose discovery came as a surprise after decades of SrTiO3 research, is currently a highly topical field besides a similar 2DEG at certain LaAlO3/SrTiO3 interfaces. In summary, the surface defect state configuration of SrTiO3 – and this applies to other perovskites, too – appears to be hardly predictable for a given specimen, since it dramatically depends on the details of the real structure. This motivated us to search for a nondestructive easy-to-use characterization method, which is usable within a wide range of sample conductivity in any ambient. This is exactly the point where the SPV approach comes into play. The paper is structured as follows: In Section 2 the setup for sample illumination and SPV detection – a Kelvin probe in our case – as well as some details of the sample investigated are described. Section 3 is dedicated to a brief explanation of surface photovoltage phenomena and their information content with respect to the surface electronic structure. Four different approaches from the literature to quantitatively extract surface state parameters from SPV transients are introduced. In Section 4 we present and discuss the results of the wavelength-dependent SPV recording (SPV spectroscopy) first. Afterwards, SPV transients taken under various experimental conditions and evaluated according to the four different methods are presented. In Section 5 we discuss the reliability of the data and make several suggestions for further comparative measurements, which shall improve the correct interpretation of the complex SPV transients of SrTiO3.

allow for high-intensity illumination (photon fluxes: 1015…1017 s −1), while the lamp covers several decades of lower intensity (photon fluxes: 10 11…1014 s−1). The Kelvin probe measures the contact potential difference (CPD) between the sample surface and a reference gold electrode, which oscillates perpendicularly to the sample surface. The SPV is the difference of the CPD under illumination and in the dark: SPV :¼ CPDillum: −CPDdark

:

ð1Þ

It is thus a differential quantity independent of the absolute work function of the electrode material. For a more detailed description of the Kelvin probe and the illumination setup, refer to [28]. During wavelength-dependent SPV recording, the photon flux was kept constant by adjusting the light intensity by means of a motorized neutral density filter. For the measurements of SPV transients the light beam was blocked or released via a PC-controlled shutter. Measurements at elevated temperatures were realized by resistive heating of the copper sample holder, with the temperature being kept constant via a software PID loop. All measurements were carried out under ambient conditions, but with stabilized temperature. 2.2. Samples A nominally undoped3 one-side-polished SrTiO3 (100) single crystal (Crystec GmbH, Berlin), 10 × 5 × 1 mm3 in size, was slightly reduced by heating in an ultrahigh vacuum (2 h, 670 °C) to achieve a moderate n-type conductivity. After the annealing procedure the sample was fixed by conductive silver paste with its unpolished rear side on the sample holder of the Kelvin probe. 3. Theoretical background In brief, the change of the band bending at a semiconductor surface or interface under illumination, which is induced by a redistribution of photoexcited charge carriers, is denoted as surface photovoltage. Depending on whether the SPV is generated by excitation with photon energies below or above the bandgap, the terms sub- and super-bandgap SPV are used. Sub-bandgap SPV provides access to defect states within the bandgap. Sub-bandgap SPV has been used to gain a deeper insight into the distribution and properties of surface and interface states of a number of semiconductor materials as well as semiconductor heterostructures. The topic has been extensively reviewed [37,38]. In Ref. [38] a mathematical description of the charge dynamics associated with the SPV process is given. However, mathematical SPV models are typically coupled to rigid assumptions which narrow their validity seriously, because the SPV is extremely sensitive not only to surface/interface-state-related processes but also to bulk processes, and all these processes might dramatically change with wavelength, intensity, and temperature. In this paper, we use four different approaches described in the literature to extract quantitative data on surface states of SrTiO3 and to cross-check the validity of the respective underlying models for our material. In the following, the four approaches, denoted “Method (1)–Method (4)”, are described in short. To avoid confusion, all symbols used are listed and explained in Table 1.

2. Experimental 3.1. Method (1) 2.1. Setup In order to measure the SPV as a function of the illumination wavelength and intensity as well as to record SPV transients after switching light on and off, we combined a home-built variable-temperature Kelvin probe with an illumination setup. Depending on the experiment, the latter uses either an Ar+ (esp. the 458- and 514-nm lines) or HeNe (633 nm) laser or a monochromatized Xe arc lamp (providing a wavelength range between 370 and 800 nm) as the light source. The lasers

According to the algorithm described in Ref. [34] a whole set of parameters characterizing one distinct surface state level, i.e. φs0, φs1, Kph, 3 In general, SrTiO3 exhibits a band gap of 3.2 eV (387 nm) [29,30]. The Fermi level position of undoped crystals was estimated [10] from conductivity measurements and the mobility data of Ref. [31] to be located at 0.71 eV above the valence band edge, while the electron affinity and work function are χ=3.2 eV and ϕ=5.7 eV, respectively [10], which means p-type behavior. Undoped high-quality SrTiO3 single crystals exhibit high specific resistances between 107 Ωm [32] and 1011 Ωm [33].

E. Beyreuther et al. / Surface Science 612 (2013) 1–9 Table 1 Description of the symbols used in the paper. The equations given in this table for Nt,nt0, nt1,φs0,φs1,Kph,Kn,C, and ΔV are valid within the framework of Method (1), as described in detail in Ref. [34], while equations used by the other models (Method (2), Method (3), and Method (4)) are given in the text. Fundamental semiconductor physics relations, i.e., the equations for Nc and vn, are taken from Ref. [35]. Symbol Description  nb q Nc m∗ vn Et − Ec I C ΔV φs0 φs1 Kph σn Kn

Nt nt0 nt1

Dielectric constant (= 310 for SrTiO3 [32]) multiplied by the vacuum permittivity 0 Electron concentration in the bulk Elementary charge Effective density of states in the conduction band: Nc =(2π2)−1(2m*kT/h2)3/2 Effective mass of electrons in the conduction band, Literature values for SrTiO3 vary in a range of 3–13 me (e.g. Refs. [31,36]) Thermal velocity; vn = [kT/(2πm*)]1/2 Energetic position of the surface state under investigation, as derived from SPV spectra (Fig. 1) Photon flux density: I=Pλ/(hcA) with P being the light intensity and A the illuminated area Negative ratio of the initial slopes of the light-off (dφ=dt t¼t þ1 ) and light-on (dφ=dt t¼tþ ) transients (Fig. 3) 0 Difference of the band bending in the dark and under illumination Steady-state surface band bending in the dark; φs0 = ΔV/(1 − C) Steady-state surface band bending under illumination; φs1 =CΔV/(1−C)= Cφs0 Surface state capture cross section for photons (optical cross section); Kph = dφs0/dt|t= t+0 /(2|φs0|)I Surface state capture cross section for electrons Surface state capture cross section for electrons multiplied with the thermal velocity; Kn = Kphnt1I/{(Nt − nt1)nb exp[qφs1/(kT)] − nt1Nc exp[(Et − Ec)/(kT)]} Concentration of the surface state per unit area; Nt = nt0 + nt0nb−1Nc exp [(Et − Ec − qφs0)/(kT)] Steady-state carrier concentration in the surface state in the dark; nt0 = (2nb|φs0|/q)1/2 Steady-state carrier concentration in the surface state under illumination; nt1 = (2nb|φs1|/q)1/2

Kn, Nt, nt0, nt1, can be derived by extracting the steady-state SPV as well as the initial slopes of both the light-on and the light-off SPV transients. The calculation is based on a rate equation, Shockley– Read–Hall expressions, and the Poisson equation (Eqs. (1)–(6) of Ref. [34]) under the following simplifying assumptions, whose validity will be discussed in Section 4: (i) The observed photoeffects stem exclusively from a surface state and not from the underlying bulk; (ii) surface states and bulk are in thermal equilibrium and a steady state is reached during illumination; (iii) the illumination intensity is low enough not to change the free-carrier concentration in the bulk; (iv) the addressed surface state interacts with one band only; and finally (v) the surface is depleted. After some formula manipulations the authors present a set of algebraic equations (Eqs. (14)–(19) of Ref. [34]) which give access to the seven unknown parameters of the surface state under consideration. Note that for this method only one light-on and one light-off transient at a given wavelength are needed.

3

3.3. Method (3) A completely diverse approach is related to the well established semiconductor characterization method of deep-level transient spectroscopy (DLTS) [40] and is indeed referred to as SPV-DLTS [38,41,42]. Here, in contrast to Method (1) and Method (2), only the light-off transients at varied temperatures are analyzed. The so-called “DLTS signal”, which is the difference of the SPV values at two different times t1 and t2 whose ratio Q = t2/t1 is kept constant, is plotted versus the time difference t2 − t1, also referred to as “rate window”. Assuming (at least the tail of) the light-off transient to be exponential, one can show mathematically that the DLTS-signal-versusrate-window curve has a local extremum, from which a characteristic time constant t0 can be calculated. The time constant is connected to the temperature via the relation 1 E −Et ¼ γ n σ n exp c kT t0 T 2

;

ð2Þ

with γn ¼

vn Nc T2

and K n ¼ vn σ n

;

ð3Þ

which can be depicted in an Arrhenius plot according to ln

1 E −Et ¼ lnγ n σ n þ c kT t0 T 2

:

ð4Þ

From the ordinate intersection of the corresponding linear fit curve the value of Kn can be derived and cross-checked with the Kn value from Method (1). The slope of the Arrhenius plot gives an activation energy – however, in SPV-DLTS this energy cannot always be correlated with a trap state energy [38]. 3.4. Method (4) In their quite recent and comprehensive work [43] on SPV phenomena in the wide-bandgap semiconductor GaN, Reshchikov et al. presented a phenomenological model for compounds in which the diffusion length is smaller than the width of the depletion region. 4 Reshchikov et al. evaluated the initial slope of the light-on transient over several decades of photon flux density in a – compared to the high intensities commonly used in Method (1), Method (2) and Method (3) – low-intensity regime. For sub-bandgap excitation, the photon capture cross section Kph can be derived from the slope of this linear dependence. Unlike in Method (2) it is not a precondition that optical processes are dominant. Moreover, the steady-state SPV and the logarithmic decay of the SPV after switching the light off were evaluated, but they appear not to be accessible in the case of SrTiO3, as will be demonstrated later in Section 4.2.2. 4. Results and discussion

3.2. Method (2)

4.1. Surface photovoltage spectroscopy

Another approach (by the same authors) [39] assumes the initial part of the light-on transients to be dominated by solely optical processes (and no thermal ones) at sufficiently high illumination intensities and fits them with a simple exponential model. It is shown that the time constant t0 of this initial part must be inversely proportional to the photon flux density I — this means, that in contrast to Method (1) several SPV transients have to be recorded at varied (highenough) light intensities. The slope of the I −1-vs.-t0 plot is equal to the photon capture cross section Kph. Thus the Kph value from Method (1) can be cross-checked.

To first get an insight into the distribution of electronic defect states within the bandgap of the reduced SrTiO3 crystal, the surface photovoltage was recorded as a function of excitation wavelength in the range between 780 nm and 395 nm under a constant photon flux of 3.62 × 10 14 s −1. The resulting SPV spectra are shown in Fig. 1. For technical reasons (change of edge filter and the diffraction grating of the monochromator) the measurement was performed in 4 To what extend this condition applies for SrTiO3 is not unambiguously to estimate, since there is no data available on the materials' typical diffusion lengths.

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E. Beyreuther et al. / Surface Science 612 (2013) 1–9

a

b

4.2. SPV transients — Calculation of surface state parameters 4.2.1. SPV under high-intensity illumination

Fig. 1. SPV spectra of the moderately oxygen-deficient SrTiO3 sample. Regions of constant slope are fit by straight lines. The intersections of those lines, i.e., the positions of slope change in the SPV spectrum, are associated with the energetic positions of trap states. The trap states are summarized in Table 2.

two overlapping spectral ranges [parts (a) and (b)]. The data were recorded in wavelength steps of 1 nm with a waiting time of 90 s between switching to a new wavelength and the subsequent CPD measurement. The SPV spectra were recorded three times in order to distinguish artefacts from true spectral features. Points of slope change in the spectra correspond to trap state energies and are extracted from the intersections of straight lines fitting the regions of constant slope. The six energy levels that were found are summarized in Table 3. Level E0 corresponds to carrier excitation across the fundamental bandgap, which in SPV spectra typically appears at lower photon energies than in optical absorption spectra due to shallow states and the Franz–Keldysh effect [38]. Levels E2 and E6 are related to bulk states, levels E1 and E4 could stem from either bulk or surface states, and level E3 can be classified as a surface state, while the nature of level E5 remains unclear. The classification into surface and bulk states was made on the basis of a broad set of SPV data of both bare and thin-film-covered SrTiO3 crystals as well as additional spectral photoconductivity measurements, similarly as in Ref. [28]. Measurements of the optical absorption, which at a first glance should be the best way to distinguish between surface and bulk contributions, showed a flat curve below the bandgap, with the exception of one spectral feature approximately at level E6.

Table 2 Summary of the electronic defect states as derived from the SPV spectra for the oxygen-reduced SrTiO3 sample. The numbering in the first column corresponds to the numbering in Fig. 1, while the second column contains the corresponding photon energy. We are reluctant to reference the energetic positions to either the conduction or the valence band edge for the following reason: While in a simple model (e.g. [44]) the type of the carrier transition (i.e. either between in-gap state and conduction band or between valence band and in-gap state) can be derived from the sign of the slope change in the SPV spectrum, the situation under multiple carrier transitions, which are likely for SrTiO3, is ambiguous. In the third column possible origins of the respective trap state are given. Level

Energy

Description

E0 E1

3.09 eV 2.90 eV

E2 E3 E4 E5 E6

2.35 2.20 1.94 1.74 1.65

Indirect band gap Bulk or surface state, specific to reduced SrTiO3 Bulk state Surface state Bulk or surface state Uncertain Bulk state

eV eV eV eV eV

4.2.1.1. General features. After having identified the energetic distribution of in-gap states by analyzing the SPV spectrum, we recorded SPV transients under various experimental conditions. In a first step, the temporal development of the SPV under excitation with different laser lines as well as the SPV decay after switching off the illumination was measured. Fig. 2 shows the light-on and light-off transients for both super-bandgap (Ar+ laser, UV multi-line mode, λ = 351–364 nm) and sub-bandgap excitation (Ar+ laser, VIS single-line mode, λ =458, 514 nm; HeNe laser, λ =633 nm) at a comparatively high photon flux of 4.9 × 1016 s−1. In the super-bandgap case (Fig. 2(a)) the light-on as well as the light-off transient obviously contain two components — a fast initial rise and a slow component with opposite sign. When the light is switched on, the SPV rapidly increases to around 300 mV, and then slowly relaxes reaching a steady state only after hours of illumination. Concerning the SPV response after switching the illumination off, there is initially no relaxation towards zero SPV, which one may expect intuitively: the first part of the light-off transient is a rapid decay to large negative values, followed by a slow relaxation towards zero. In other words, the light-off transient seems to be an inverted version of the light-on transient, suggesting a recovery of both SPV processes, however exhibiting larger time constants. After 20 h the SPV is still clearly above the noise level, so one could speak of a persistent change of the electronic configuration, which possibly originates from photoadsorption or desorption processes [45]. The transients in the sub-bandgap range (Fig. 2(b)) turn out to be even more complex, in some cases exhibiting signatures of more than two charge transfer processes with different characteristic time constants, weights, and signs. Also, on the qualitative level, the shape of the transients does not change in a monotonic way with the wavelength, i.e., the transients at the three different excitation wavelengths show very individual features, probably reflecting the fact that different surface (or, more general, in-gap) states are addressed. The strongest photoresponse occurs under 458-nm excitation. The fast initial part of the light-on transient peaks at about −400 mV, which – in terms of absolute values – is more than under superbandgap excitation at the same photon flux. While at a first glance one may think that the light-on part of the 458-nm transient looks like an inverted version of the super-band gap light-on transient, a closer look makes clear that we are faced with a curve consisting of (at least) three different contributions: a fast initial one, a slower second one with opposite sign and a still slower third one with the same direction as the first one. On the other hand, the light-off transient is a monotonic – however, nonexponential – rise to zero, which then crosses zero, ending up at positive SPV values. At a wavelength of 514 nm, the light-on transient is qualitatively similar to the 458-nm case but with smaller SPV and smaller time constants, while the light-off transient exhibits a quite different shape: An initial drop to even more negative SPV values is followed by a rise, then followed by a drop, and finally followed by a rise towards zero (all four components having successively larger time constants). The light-on transient under 633-nm excitation differs decisively from the two previous cases. Here, a monotonic build-up of a negative SPV is observed. However, the transient cannot be fitted by a simple exponential function, and at least two different charge transfer processes with different time constants are present. This is also reflected in the light-off transient, but there the two processes appear with opposite signs. As in all other cases, within the observed time span, full relaxation to zero is not reached. How, on a qualitative level, can these transient shapes be understood? Nonexponential SPV transients have been described in the literature many times before and commonly are ascribed to the nature

E. Beyreuther et al. / Surface Science 612 (2013) 1–9

5

Table 3 Summary of input and output quantities of the complete quantitative analysis according to Ref. [34] (“Method (1)”). Note that, considering the SPV spectrum, only for the 514-nm case a distinct surface state is addressed. The values for nt0 and nt1 were calculated assuming an effective mass of m∗ = 3me, while the values in brackets are valid for m∗ = 10me. The photon and electron capture cross sections (Kph, Kn, σn), which were also derived by Method (2), Method (3) and Method (4), are listed separately in Table 4.

λ

Input quantities as extracted from SPV transients dφ dφ þ þ I dt t¼t 0 dt t¼t 1 −1

m

−2

)

(mV s

−1

)

(mV s

Calculated quantities according to Method (1) ΔV

C

−1

)

φs0

φs1

nt0(≈Nt) 13

(nm)

(s

(mV)

(mV)

(mV)

(10

514

7.9 × 1021

−97

15

0.16

308

364

56

458

3.0 × 1021

−213

22

0.10

445

496

51

5.2 (16) 6.1 (18)

of the rate equation, e.g. [38]. SPV transients exhibiting fast and slow components have been observed, too. Here, several explanations have been put forward: In principle an SPV can arise (i) from charge exchange with extrinsic (induced by adsorbed species) or intrinsic (induced by symmetry breaking) surface states, (ii) from (deep) defect levels within the depletion region (here, first of all oxygen defect levels are expected to play a role), or (iii) from specific bulk effects such as the Dember effect. In the case of SrTiO3 all scenarios are reasonable and probably interfere with each other, so only further comparative investigations could reveal a detailed picture on how these contributions determine the exact shape of the transients. Third, persistent changes of the dark CPD value after an illumination cycle have occurred for other materials, too [45]. Now, let us continue with the quantitative evaluation of the laser transients according to the Method (1), Method (2), and Method (3). 4.2.1.2. Method (1): Initial slopes of the light-on and light-off laser transients. First, we apply the method of Kronik et al. [34], which is based on the rate equation as described in Section 3, to extract the band bendings in the dark and under illumination, the capture cross sections for photons and electrons, as well as the concentration of the surface state and its occupation under illumination and in the dark (all relevant quantities are summarized in Table 1). In order to record a surface photovoltage transient whose shape is determined by the interaction of surface state level E3 with the conduction band, we choose an excitation energy hν that satisfies the relation EC − Et b hν b EG [34]: the 514-nm line of an Ar+ laser.

a

m

−2

nt1 )

(10

nt0/nt1 13

2.1 (6.2) 2.0 (6.0)

m

−2

) 2.5 3.1

Both the light-on and the light-off transients of the reduced SrTiO3 crystal are shown in Fig. 3(a) and (b). Part (a) contains the full data set, while part (b) depicts only the initial sections right after the illumination was switched on and off, respectively. From this data we are able to calculate the unknown surface state parameters of level E3 step by step as follows: First, three quantities have to be extracted from the SPV transient: the initial slopes of the light-on transient, dφ=dt t¼t þ , and the light-off 0 þ transient, dφ=dt t¼t , as well as their negative ratio, C, and the differ1

ence of the band bendings in the dark and the illuminated states, ΔV, which equals the steady-state SPV under illumination. 5 According to the relations given in Ref. [34] (see also Table 1) the surface band bending in the dark then follows as φs0 = 364 mV and the surface band bending under the given illumination is φs1 = 56 mV, which means that sub-bandgap illumination flattens the bands. At a laser intensity of P = 60 mW and a wavelength of λ = 514 nm with an illuminated area (which here equals the area of the Kelvin probe) of A = 2 × 10−5 m−2, we get a photon flux density I = 7.8 × 1021 s-1 m-2 and, again according to the model of Ref. [34] (Table 1), a photon capture cross section Kph =1.7 × 10−23 m 2. For the extraction of the remaining surface state parameters (concentration of surface states Nt, electron capture cross section Kn, steady-state carrier concentration in the surface state in the dark nt0, steady-state carrier concentration under illumination nt1) the values of the bulk carrier concentration nb and the effective density of states of the conduction band NC are needed. Values for nb given in the literature depend strongly on the doping and the crystal quality. They vary between 1016 and 1019 cm−3 for reduced crystals [46–48] and between 108 and 1012 cm−3 for undoped ones [10,31]. Therefore an individual determination of nb is indispensable. In anticipation of the results of Method (3), we continue our calculations with nb = 2 × 1012 cm−3 (for m∗ = 10me). For the calculation of the effective density of states in the conduction band,6 NC, the effective electron mass m∗ is needed as well, for which the literature values vary between 3me [31] and 13me [36]. We calculate nt0, nt1, Nt exemplarily for two different effective masses (3me, 10me), the results are given in Table 3. For m∗ =3me we get nt0 ≈ 5.2× 1013 m −2 and nt1 ≈2.1 × 1013 m −2, which corresponds to a ratio nt0/nt1 = 2.5, meaning that under illumination carriers are released from the surface state.   In the expression N t ¼ n0t þ nn N C exp E −EkT−qφ , the second summand turns out to be much smaller than nt0 for deep states such as the state at E3 (Et − EC = 2.2 eV). In other words, we get Nt ≈ nt0, which means full occupation of the surface state in the dark. Finally, we are able to estimate Kn as 4.9× 10 −21 m 3 s −1 for m ∗ = 10me or 4.4 × 10 −20 m 3 s −1 for m ∗ = 3me, respectively. At room 0 t

t

C

0 s

b

b Fig. 2. SPV transients recorded under illumination with several lines of an Ar+ ion laser at a constant photon flux of 4.9 × 1016 s-1: (a) super-bandgap illumination, (b) subbandgap illumination; the insets zoom in on the initial parts of the light-on and light-off transients to resolve the different components of the transients more clearly. Note that for better visibility the time axis is divided into two parts with the scale of the second part being logarithmic. Altogether, an illumination period of 4 h was applied, while the subsequent relaxation of the SPV signal was monitored for 20 h.

5 As a closer look on the light-on transients in Fig. 3(a) and (c) reveals, the steady state is not reached completely. Thus the ΔV values are only estimates. Finding the true steady-state SPV via curve fitting is problematic, as described in the supplement (Fig. S3). 6 The values for NC read 1.47 × 1026 m−3 and 8.95 × 1026 m−3, assuming m∗ = 3me and m∗ = 10me, respectively.

6

E. Beyreuther et al. / Surface Science 612 (2013) 1–9

a

b

c

d

Δ

Δ

Fig. 4. Initial parts of the 514-nm light-on SPV transients at five different intensities in   the high-intensity regime with exponential fit curves (SPV ¼ SPVsat þ A exp −tt ) for the first 10 s — the corresponding time constants t0 are listed in the legend. 0

Fig. 3. (a) SPV transient of reduced SrTiO3 at 514-nm laser illumination (photon flux: 1.55× 1017 s−1). Some of the quantities needed for the quantitative SPV analysis are indicated: t0, t1, and ΔV. (b) Enlarged view of the curves around the points where the light was switched on and off. The initial parts of the light-on and light-off transients are fit by straight lines to determine the slopes dφ=dt t¼tþ and dφ=dt t¼tþ . (c) and (d) Similar 0 1 plots of the SPV transient at 458-nm laser illumination (photon flux: 6.05× 1016 s−1).

temperature, the corresponding electron capture cross sections σn are 5.9 × 10 −25 m 2 or 2.8 × 10 −24 m 2, respectively. All parameters are summarized in Tables 3 and 4. For comparison, the whole procedure was repeated for the 458-nm transient (Fig. 3(c) and (d)), even though from the SPV spectroscopy results we do not expect a resonant surface state excitation there. Thus the values might be interpreted as effective values at the given wavelength. In order to cross check and verify at least part of the surface state parameters derived from Method (1), two alternative approaches were additionally used, namely the extraction of Kph from intensitydependent light-on transients (Method (2)) and the extraction of Kn from the temperature-dependent recording of the light-off transients (Method (3)). 4.2.1.3. Method (2): Intensity-dependent SPV transients. At sufficiently high illumination intensities the initial part of the light-on SPV transient is dominated by (fast) optically stimulated carrier migration. For this regime, the method described by Kronik et al. [39], which considers only optical and no thermal processes in the SRH statistics, can be applied. The basic relation under these conditions reads t0 ∼ (IKph) −1, where t0 stands for the time constant of the initial part of the light-on SPV transient, which is commonly extracted by assuming a simple exponential behavior. Plotting the inverse photon flux density I −1 versus the time constant t0 should then give a linear relationship, whose slope is the photon capture cross section Kph. Fig. 4 depicts the initial parts of SPV light-on transients at five different intensities of 514-nm laser illumination. The first ten data

Table 4 Summary of the values calculated for Kn and Kph by the different methods at several wavelengths. Note that for Method (4) the wavelengths are 450 nm, 500 nm, 600 nm, respectively. The Kn values were calculated assuming an effective mass of m∗ = 10me. For a smaller effective mass of m∗ = 3me Kn would be around one order of magnitude higher, while Kph is unaffected by m∗. Note also that the real capture cross sections for electrons must be derived from Kn according to σn = Kn/vn. For m∗ = 10me we get σn =(1.2×10−4 ⋅Kn)m2, thus σn is quite small (in the range of 10−24–10−25 m2). λ (nm)

Kn (10−21 m3 s1)

458 514 633

7.4 4.9 –

points (10 s) were used for the exponential fit. Fig. 5(a) shows the t0-versus-I −1 plot as well as the calculated Kph value. Two aspects must be discussed. First, it is already clear from the transients' shapes that the transient measured at the lowest of the five intensities does not satisfy the condition of an optically dominated initial part. Therefore, it is not included in the linear fit. For the other four intensities the linear relationship is well fulfilled. Second, the Kph value of 1.4 × 10 −22 m 2 is around one order of magnitude higher than the value provided by Method (1). One may speculate that the discrepancy is mainly due to the incomplete fulfillment of the restrictions of the model underlying Method (1). Especially, bulk contributions cannot be excluded due to the large width of the space charge region. Furthermore a steady state is not completely reached during the illumination period. For further comparison, we repeated this kind of analysis for 633-nm and 458-nm transients, see Fig. 5(b) and (c). While for the 458-nm case only the data sets with the three highest intensities provide a straight line, all tested 633-nm data sets give a linear relation. The calculated photon capture cross section at 633 nm turns out to be higher than the values at 458 nm and 514 nm, which is clearly in conflict with the results of Method (4), which will be shown later in the

a

b

c

Kph (10−23 m2) from Method (1)

Method (2)

Method (4)

7.2 1.7 –

440 14 (560)

49 43 11

Fig. 5. Time constants t0 from exponential fits of the initial parts of the light-on transients plotted against the corresponding inverse photon flux densities for three different laser wavelengths. The slopes of the fitted lines can be associated with the photon capture cross sections Kph.

E. Beyreuther et al. / Surface Science 612 (2013) 1–9

a

(a)

7

b

d

(b)

c Fig. 6. SPV transients at two different temperatures, recorded at 458-nm illumination. Regarding the light-off transients, a faster relaxation at the higher temperature is well visible. Inset (a) shows the corresponding “DLTS peaks”, which are used to extract characteristic time constants for each temperature. Those time constants as a function of temperature yield an Arrhenius plot, see inset (b), whose linear fit bears information on the activation energy and the electron capture cross section.

paper, and leaves doubts whether the initial parts of the 633-nm transients are really optically dominated. These doubts are emphasized by the obviously different shape of the 633-nm transients, which we already mentioned when discussing Fig. 2.

4.2.1.4. Method (3): Temperature-dependent SPV transients. Under 458-nm laser illumination a set of SPV transients was recorded at temperatures between7 room temperature and 80 °C. Two of the curves are depicted in Fig. 6. For the DLTS algorithm only the light-off transients are evaluated. The difference of the SPV values at two different times t2 and t1, also referred to as DLTS signal, is then plotted as a function of t2 − t1. This time difference is called rate window. Note that the ratio t2/t1 must be fixed, in our case t2/t1 = 4. The characteristic time constants t0 as derived from the local extrema of the DLTS curves give an Arrhenius plot with a slope of (−7460 ± 520) K and an intercept of (4.3 ±1.6). From the slope, an activation energy of (0.64±0.04) eV can be derived. From the intercept we derive – using an effective mass of m∗ =10me – the electron capture cross section: Kn =7.4×10−21 m3 s-1. Inserting this Kn value in the equation for Kn from Method (1) (cf. Table 1) allows us to extract an estimate for the bulk carrier concentration nb, which we already discussed and used within the calculations of Method (1). The dependence of Kn and – in turn – nb on the exact value of m∗ is visualized in Fig. S1. In the relevant m∗ range both quantities vary over more than one order of magnitude. The values found for nb are approximately between 1011 and 2 × 1012 cm−3, which indicate a comparably weak n doping.

4.2.2. SPV at low illumination intensities In contrast to the laser experiments, illumination with a monochromatized white-light source offers the possibility to observe gradual changes of the SPV transients with wavelength. Thus, in the following we discuss a broad set of SPV transients, taken at 11 different wavelengths, ranging from 750 nm (corresponding to around half the bandgap of SrTiO3) over 387 nm (corresponds to the bandgap energy) to a super-bandgap wavelength of 370 nm, over 4 decades of photon flux, well below the photon fluxes used in the laser experiments. 7 In order to check whether the heating changes the defect state distribution (e.g. by inducing Ag-related defects from the back contact) we compared SPV spectra before and after the heating experiments, but found no differences concerning the spectral features.

Fig. 7. SPV transients at a constant photon flux of 9.4× 1013 s−1 for 11 different wavelengths. A version of this diagram zooming into the initial part of the light-on transients is shown in Fig. 8.

4.2.2.1. General features. Due to the large amount of data, we show only the SPV transients for the second-highest photon flux in Figs. 7 and 8, with Fig. 8 simply depicting the initial parts of the curves of Fig. 7, and export some further diagrams into the supplement (Figs. S2–S4). In Fig. 7, diagram (a) shows the light-on and light-off transients for the infrared and red wavelengths. We observe (similarly as for the 514-nm laser transient) a threefold structure in the light-on part and a twofold structure in the light-off part (in the range shown here), while time constants and weights of the three parts seem to change gradually with wavelength. The magnitude of the SPV is comparatively low. At 550 nm (Fig. 7(b)) the changes become much more pronounced with respect to both the shape of the curve and the magnitude of the SPV. The SPV is particularly strong at 500 nm (Fig. 7(c)) and again at 420 nm, but weaker at 450 nm. Astonishingly, at resonant bandgap illumination (387 nm), the maximum SPV value is not that large. Fig. 7(d) shows the super-bandgap transient for 370-nm illumination. As for the UV-laser transient the SPV transients have changed their sign here, compared to the sub-bandgap case. The fact, that the sign of the SPV changes – possibly due to a pronounced Dember effect under superbandgap excitation – also explains why the total SPV values at 387 nm are much smaller than those at some of the sub-bandgap wavelengths (e.g. 420 nm): an annihilation of the typical sub- and superbandgap transient shapes with their opposite signs seems to take place. 8 Concerning the Dember effect, we note that in a pronouncedly photoconducting material exhibiting strongly different mobilities for electrons and holes [49] the Dember potential VD can reach values as large as several hundred millivolts according to [50]:  VD ¼

    b−1 kT R ln dark : bþ1 e Rillum

ð5Þ

Here, b is the ratio of the electron and the hole mobilities: b ¼ μμ . For intrinsic and slightly doped semiconductors we can assume b ≫ 1 [51]. Furthermore, RR represents the ratio of the sample resistances in darkness and under illumination. If f denotes the order of magnitude of the photoconductivity according to Rdark = 10f ⋅ Rillum, we get a linear dependence of VD on f, namely VD[mV] ≈60⋅ f. From test measurements we know that our STO sample shows a photoconductivity of at least 3 e

h

dark

illum

8 Note in this context that the excitation light from the monochromatized white-light source has – compared to the laser sources – a broadband output of around±10 nm.

8

E. Beyreuther et al. / Surface Science 612 (2013) 1–9

a

b

c

d

Fig. 8. SPV transients at constant photon flux for 11 different wavelengths — same conditions as in Fig. 7, but zoomed into the initial parts of the light-on transients.

order of magnitude, well matches the 514-nm result of Method (2), see also Table 4. For 450 nm, the agreement between Method (2) and Method (4) is less satisfying (Table 4), which suggests that we are not faced with a single isolated surface state at this wavelength. Furthermore, the increase of Kph with decreasing wavelength as depicted in the inset of Fig. 9 is reasonable, while a closer look at the linear fits shows that for some wavelengths the matching to the experimental data is quite low, especially for the red wavelengths. While the linear fits above might still be acceptable, the evaluation of the steady-state SPV under illumination and of the slope of the logarithmic decay of the light-off transients to extract Kph and the flow rate of free electrons from the surface to the bulk in the dark, respectively, fail for SrTiO3. In the first case, the saturation SPV under illumination would have to be taken from the asymptote of the light-on transient, since the saturation value is not reached within a reasonable time span. As shown in Fig. S3, exponential fitting fails and a more refined model can, at the current state of knowledge, not easily be developed. In the second case, the logarithmic plots of the light-off transients (Fig. S4) reveal the coexistence of a number of different decay processes.

5. Summary and outlook orders of magnitude. This would correspond to a Dember potential of around 180 mV, which interferes with the SPV contribution. Having a closer look at the initial parts of the light-on transients (Fig. 8) we see that the threefold structure is confirmed, except for the 370-nm case, for which we identify even 5 processes. In general, a detailed explanation for the distinct features, e.g. the non-trivial shape changes upon intensity variation (see Fig. S2), cannot be given without further comparative experiments. Some suggestions will be given in Section 5. Nevertheless, here we continue with a quantitative analysis. 4.2.2.2. Quantitative analysis according to Method (4). We apply the model of Reshchikov et al. [43], which we have already described as Method (4). First of all, from the initial slopes of the light-on transients as a function of light intensity, the photon capture cross section Kph can be calculated according to the following equation: d ðSPVÞ ≈2φ0s K ph I. From linear fits through the origin, as depicted in dt Fig. 9, we derive the Kph values shown in the inset of the same figure. For 500 nm we obtain Kph = 4.3 × 10 −22 m 2, which, regarding the

Surface photovoltage (SPV) phenomena in a slightly reduced n-type SrTiO3 (100) single crystal were comprehensively investigated by means of a Kelvin probe setup, both qualitatively and – utilizing four different theoretical approaches from the literature – quantitatively. A map of defect states across the bandgap was extracted from the wavelength-dependent recording of the SPV at constant photon flux (“SPV spectroscopy”). Furthermore, the temporal development of the SPV after switching optical excitation on and off (“light-on and light-off transients”) was recorded over 7 decades of photon flux. Several features of the transients were analyzed in order to determine various surface state parameters such as densities, the band bending, and capture cross sections for photons and electrons. In all intensity regimes, the SPV transients show a complex shape indicating that several processes contribute. Therefore the different models, which are only valid under rigid assumptions can be applied only with reservation. Nevertheless, cross checking the surface state parameters derived from the different models allowed us to deduce at least an order-of-magnitude estimate of the parameters. An exact assignment of each part of the transients to one certain type of charge carrier transition would need further comparative SPV measurements under vacuum conditions to exclude extrinsic SPV mechanisms, with gradually changed doping to derive the manifestation of oxygen vacancy defects within the SPV behavior more precisely, and in a modified illumination geometry to evaluate bulk contributions. Thus, a statement on the general applicability of the SPV method for the characterization of the electronic defect configuration of arbitrary perovskite interfaces must be postponed at present. Acknowledgments This work was financially supported by the German Research Foundation (FOR 520, BE 3804/2-1). Appendix A. Supplementary data Supplementary data to this article can be found online at http:// dx.doi.org/10.1016/j.susc.2013.01.022.

Fig. 9. Low-intensity regime (excitation with monochromatized white-light source): Absolute values of the initial slopes of the light-on transients as a function of photon flux. Straight lines are the corresponding linear fits through zero. From the slopes the photon capture cross sections Kph depicted in the inset were derived.

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