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We report the excitation of the non-steady-state photoelectro-motive force in a monoclinic gallium oxide crystal. The crystal grown in an oxygen atmosphere is insulating and highly transparent for a visible light, nevertheless, the formation of dynamic space-charge gratings and observation of the photo-EMF signal is achieved under the laser illumination with wavelength λ = 532 nm. The induced ac current is studied for the cases of zero and non-zero external electric fields, which imply the non-resonant and resonant mechanisms of space-charge recording. The dependencies of the signal amplitude versus the frequency of phase modulation, light intensity, spatial frequency, light polarization and value of the external dc electric field are measured. The material demonstrates the anisotropy along the [100] and [010] directions, namely, there is a weak difference of the transport parameters and a pronounced polarization dependence of the signal. The photoconductivity and diffusion length of electrons are estimated for the chosen light wavelength.
© 2015 Optical Society of America
1. Introduction
The investigation of transport properties in high-resistive semiconductors is often complicated not only by the small values of electric current, diffusion and drift lengths but also by the formation of the space charge near blocking contact. An elegant solution of this problem was proposed, when the non-steady-state photo-EMF effect, or nonstationary holographic current in other terminology, was discovered [1–3]. The effect reveals itself as an alternating electric current arising in a semiconductor illuminated by an oscillating interference pattern. The related techniques realized with an interference pattern running with constant velocity are called as holographic current [4] or moving photocarrier grating technique [5]. The space charge formation produces no harmful action on these effects; on the contrary, it takes part in the excitation of the signal, because the resulting electric current appears due to spatial shifts of the space-charge and photoconductivity distributions in the crystal volume.
The excitation of the non-steady-state photo-EMF signal involves processes of carrier generation, diffusion, drift in an electric field and recombination to local centers. This complex nature of the effect makes it a powerful tool for determination of photoelectric parameters such as type and value of photoconductivity, carrier lifetime, mobility and diffusion length, density of recombination centers, etc. [3, 5–10]. Besides the tasks of material characterization the non-steady-state photo-EMF is also used for the detection of phase- and frequency-modulated optical signals [11–15]. Being defined by the drift component of the current averaged over interelectrode spacing the non-steady-state photo-EMF is an integral effect. This feature as well as the fact, that arising current is alternating, allow observation of the effect not only in single crystals but also in polycrystalline, amorphous, composite and polymer media. Moreover, these also allow the detection of optical signals with complex wavefronts, even speckle light patterns.
In this work we apply the non-steady-state photo-EMF technique for the investigations of a β-Ga2O3 crystal. The interesting optical and electrical properties of this material attracts the attention of researchers during last years. The band gap of β-Ga2O3 is of 4.8 eV, so the crystal is highly transparent for the visible light and partially for UV. This advances the development of solar-blind detectors of deep ultraviolet radiation based on nanowires [16], nanobelts [17], thin films [18,19], and bulk crystals [20]. Oxygen vacancies endow a β-Ga2O3 crystal with the electronic conductivity, and this can be utilized for the fabrication of transparent electrodes [21]. The refractive index n ≃ 1.9 can make such electrodes deposited on A3B5 semiconductors to be antireflective for the certain wavelength, e.g. 885 nm for Ga2O3/GaAs structure [22]. Thin films of Ga2O3 grown with oxygen deficiency exhibit the switching memristor behavior promising for nonvolatile memory applications [23]. The crystal possesses the photocatalytic properties and can be used as an photoelectrode for the water splitting under UV radiation [24]. The application of the material for the development of field-effect transistors and gas sensors was also proposed [25–27]. In spite of the great interest to β-Ga2O3 for ultraviolet applications, the perspective of the crystal utilization in the visible and even infrared range should not be ignored. Here we report on the photoelectric properties at λ = 532 nm (hν = 2.33 eV) and reveal the material’s anisotropy measuring the signal along the [100] and [010] axes. Both the nonresonant and resonant techniques of the photo-EMF excitation are implemented in the experiments.
2. Experimental arrangements
The experiments with the excitation of the non-steady-state photo-EMF in β-Ga2O3 are carried out with the arrangement (Fig. 1) used earlier for investigations of other wide-bandgap semiconductors and nanostructured materials [9,10]. The second harmonic of Nd:YAG dc laser with the wavelength of λ = 532 nm is split into two beams, which then create the interference pattern with spatial frequency K, contrast m = 0.98 and average intensity I0 on the crystal surface. The electro-optic modulator introduces phase modulation with amplitude δ = 0.61 and frequency ω into the signal beam. The photocurrent arising in the sample produces a voltage across the load resistor, which is amplified and then measured by the lock-in voltmeter. The experiments with an applied external voltage are performed at higher light intensities and lower contrast m = 0.11. This is achieved by additional illumination using the powerful laser pointer operating at the same wavelength. The polarization plane containing electric field vector is perpendicular to the incidence plane (TE-polarization) in the most of the experiments. The placement of the half-wave plate in front of the sample allows the rotation of the polarization plane, when it is necessary.
Fig. 1 Experimental setup for the investigation of the non-steady-state photo-EMF. EOM is the electrooptic modulator, BS is the beam splitter, M is the mirror, A is the amplifier.
β-Ga2O3 is a monoclinic crystal with the cell dimensions a = 12.23 Å, b = 3.04 Å, c = 5.80 Å and β = 103.7° [28]. The band gap is indirect with Eg = 4.84 eV [29]. The static dielectric constant of the material is a tensor with eigenvalues ε11 = 10.84, ε22 = 11.49 and ε33 = 13.89 [30].
The crystal of gallium oxide was grown by the floating zone method at URN-2-ZM machine produced in MPEI [31]. The single crystal was grown from the ceramic bar obtained by the conventional technology. The seed was oriented so that the crystal grew along the [010] direction. The growth rate of 10 mm/h was chosen to ensure the stability of the crystallization processes. The quality of the obtained single crystals depends on the type of the atmosphere and its pressure. The studied crystal was grown in the 60 bar oxygen atmosphere, which provided the highest sample’s quality.
The investigation of the crystal using conventional X-ray diffraction and light transmission spectroscopy was performed in the previous work [32]. The X-ray Laue method allowed us to orient the crystal, confirmed the lattice constants known from literature [28], and showed the absence of the crystal twinning. The light transmission spectrum practically coincides with the previously reported spectra [33–35], i.e. the crystal demonstrates the transmittance about 80% in the visible and near infrared ranges 400 – 1100 nm and the absorption edge below 270 nm corresponding to interband transitions. There is also a shoulder at 270 – 275 nm, which can be due to both the crystal structure and the presence of Ga3+ vacancies [35].
The sample used in our studies has the dimensions of 2.00 × 2.15 × 1.35 mm along the crystallographic directions [100], [010] and direction perpendicular to the plane (001), respectively. The front and back surfaces (2.00 × 2.15 mm) are the (001) crystal’s cleaved facets, no additional treatment was applied to them. The silver paste electrodes are deposited on the opposite pairs of lateral surfaces in the experiments with the light pattern grating vector K‖[100] and K‖[010].
3. Experimental results
3.1. Diffusion regime of signal excitation
The typical signal amplitude is of 10−12 – 10−9 A, which is two orders of magnitude lower than the values observed in model sillenite crystals Bi12Si(Ti,Ge)O20 [2, 36]. Nevertheless such an amplitude is sufficient for the detection with the signal-to-noise ratio of 0 – 60 dB. The phase of the signal clearly points to the electron type of photoconductivity.
We have measured the frequency transfer functions of the non-steady-state photo-EMF amplitude in the as fabricated β-Ga2O3 crystal (Fig. 2). The dependencies contain the growth of the signal at low frequencies ω followed by the frequency independent part. The signal growth at low frequencies is an important manifestation of the adaptivity of space charge formation in photoconductive materials [2,37]. The signal at low ω is small because of the fact, that both the space charge field grating and the grating of free electrons (photoconductivity grating) follow the movement of the interference pattern. The spatial shift between them is nearly equal to π/2, which finally results in small value of the average drift component of the current. The grating with larger relaxation time becomes “frozen-in” at higher frequencies, the spatial shifts between gratings increase, and holographic current reaches its maximum at the frequency-independent region. Since there is no decaying part in the dependence, the space charge formation occurs in the condition of quasi-stationary photoconductivity (ωτ ≪ 1), and the signal behavior is described by an expression [2]
Here ED = (kBT/e)K is the diffusion field, τM = ε0ε/σ0 is the Maxwell relaxation time, LD is the diffusion length of electrons [37]. The growing and frequency-independent regions are separated by the cut-off frequency ω1The dependencies of the signal amplitude and the first cut-off frequency versus illumination level are presented in Fig. 3. The amplitude of the photocurrent in the maximum of frequency transfer function is proportional to the light intensity: Jω ∝ I0. There is, however, a sublinear dependence of the cut-off frequency for K‖[100] and for K‖[010]. This can be due to the corresponding nonlinearity of the photoconductivity. The presence of dark conductivity can contribute in the initial stage of dependence ω1(I0) as well. As seen from Eq. (2) the measurements of the cut-off frequency ω1 at low K provide the estimate of the Maxwell relaxation time and corresponding photoconductivity of the sample. For the chosen intensities I0 = 0.039 – 0.40 W/cm2 of TE-polarized light the photoconductivity equals σ0 = (0.48 – 2.5) × 10−10 Ω−1cm−1 along the [100] axis and σ0 = (0.32 – 1.0) × 10−10 Ω−1cm−1 along the [010] axis.
Fig. 2 Frequency transfer functions of the non-steady-state photo-EMF Jω measured for two crystal orientations.
Fig. 3 Dependencies of the signal amplitude Jω and first cut-off frequency ω1 on the average light intensity I0.
Dependence of the signal amplitude on the spatial frequency of the interference pattern is another characteristic usually measured in the non-steady-state photo-EMF experiments (Fig. 4). The observed behavior of the signal is explained as follows: the growth of the signal at low K is due to the increase of the space charge field amplitude, which is proportional to the diffusion field ED [37]. The decay at high K is caused by the diffusion “blurring” of the photoconductivity grating. The expression for this dependence is known from the theory of the non-steady-state photo-EMF effect [2, 3]:
The maximum of the signal is achieved at , so the electron diffusion length can easily be estimated from the experimental curves: LD = 190 nm for K‖[100] and LD = 200 nm for K‖[010]. Figure 4 also presents the dependencies of the first cut-off frequency versus spatial frequency. These experimental dependencies are fitted using Eq. (2) with LD = 110 nm for K‖[100] and LD = 130 nm for K‖[010]. We should note that increased light reflection at large incident angles leads to the decrease of the light intensity in the crystal volume, and this can affect the signal excitation for K > 10 μm−1. The difference in the estimates of the diffusion length obtained from dependencies Jω(K) and ω1(K) may be associated with the mentioned factor.Fig. 4 Dependencies of the signal amplitude Jω and first cut-off frequency ω1 on the spatial frequency K of the interference pattern.
Looking at Figs. 2–4 one can easily note the anisotropy of the non-steady-state photo-EMF in the monoclinic β-Ga2O3. The fact that the photo-EMF amplitude and cut-off frequency in these figures are larger for the case K, j‖[100] does not make this geometry more effective for the signal excitation. When analyzing the anisotropy of the effect it is necessary to consider the dependence of the signal amplitude on the light polarization as well (Fig. 5). Each of the two curves plotted in Fig. 5 reveals the anisotropy of the photoexcitation processes, while the difference of the maximal (minimal) values points out to the anisotropy of the transport properties along the [100] and [010] directions. As seen from the figure, the maximal amplitudes are achieved in the both orientations, when the light is polarized along the [010] axis. The maxima for the two geometries are observed at angles that differ by 90°, but their magnitudes are nearly equal, which points out to the weak anisotropy of the transport characteristics, e.g. the mobility of electrons. The signal in the case K, j‖[010] and Θ = 0° is even higher by ∼ 10% than that for K, j‖[100] and Θ = 90°. So the optimal geometry for the excitation of the non-steady-state photo-EMF in a β-Ga2O3 crystal is the following: the grating vector K, holographic current j and light polarization should be parallel to the [010] axis.
Fig. 5 Dependencies of the non-steady-state photo-EMF amplitude Jω on the angle between the incidence and polarization planes.
In order to find out the origin of the polarization dependence (photoexcitation anisotropy) we have measured the sample’s transmittance for the laser radiation and estimated the absorption coefficient for the two polarization states, i.e. along the [100] and [010] axes. The obtained values α[100] ≃ 1.1 cm−1 and α[010] ≃ 1.3 cm−1 differ by only 20%, while the maxima in Fig. 5 exceed corresponding minima by 280%. It should be noted here, that we have taken into account the reflection from the two crystal’s interfaces for the both polarization states with n[100] = 1.9201 and n[010] = 1.9523 [38]. The calculated absolute values of α are still very rough estimates, since the sample’s surfaces are not polished, and the volume has some optical inhomogeneity. So the polarization dependence of the absorption coefficient is not the primary source of the photoexcitation anisotropy. There is another factor that defines the generation rates of the electrons, namely, the quantum efficiency of the photoconductivity. The anisotropy of this parameter β[100]/β[010] ≃ 2.3 originates the observed polarization dependence of the detected signal.
3.2. Space-charge waves
An external dc voltage can be utilized for increasing the amplitude of the non-steady-state photo-EMF [3, 39–41]. The signal enhancement is not the only change arising in the dc field, the frequency dependence becomes resonant (Fig. 6). The appearance of the resonant maximum is due to the excitation of space-charge waves, which are the eigenmodes of space-charge evolution in semiconductors placed in an external dc field [37]. The theory of the effect provides the following expression for the signal amplitude [40]:
where L0 = μτE0 is the drift length of electrons in the dc electric field E0. The approximation of the experimental curves in Fig. 6 allows us to estimate the μτ-product of electrons μτ ≃ 5.3 × 10−10 cm2/V along the [010] axis and the Maxwell relaxation time τM ≃ 16 ms, which corresponds to the average photoconductivity σ0 ≃ 1.0 × 10−10 Ω−1cm−1 (I0 = 3.5 W/cm2).Fig. 6 Frequency transfer functions of the nonstationary holographic current Jω excited in an external dc electric field.
The space-charge waves run along the applied electric field and have an unusual dispersive law, i.e. dependence ωscw(K):
Such a decrease of the resonant frequency is observed in the experiment (Fig. 7). The resonant amplitude of the signal depends on the spatial frequency as well. It was shown earlier [3], that this amplitude should reach maximum at . This can also be used for estimation of the diffusion length LD ≃ 200 nm (μτ ≃ 1.6 × 10−8 cm2/V).Fig. 7 Dependencies of the resonant signal amplitude Jω(ωr) and resonant frequency ωr on the spatial frequency K of the interference pattern.
As seen from Fig. 6 and Eq. (5) the resonant frequency depends on the value of applied dc field, and the increase of E0 shifts the resonant maximum to lower frequencies. The amplitude of the resonance grows versus applied field nearly quadratically, which is another intrinsic feature of the non-steady-state photo-EMF excited in the regime with space-charge waves [3, 40].
The dependencies of the resonant frequency and signal amplitude on the light intensity were also observed experimentally. They demonstrated nearly linear dependencies in the range I0 = 0.88 – 3.5 W/cm2, which is well expected since and Jω ∝ σ0 ∝ I0.
Reviewing the experimental dependencies ωr(I0, K, E0) and Jω(I0, K, E0) described in this section we can conclude, that the observed resonance results primarily from the excitation of space-charge waves, but not some other modes, e.g. drift waves [3, 40].
4. Discussion
We have started our investigation of the non-steady-state photo-EMF in β-Ga2O3 using the light with the wavelength λ = 532 nm and photon energy hν = 2.33 eV, while the crystal’s band gap is of 4.8 eV. The origin of the photoeffect at chosen wavelength is not evident to date. The dark conductivity of Ga2O3 is usually attributed to the presence of oxygen vacancies, which are shallow donors [42]. The photoexcitation of these donors seems the most plausible explanation of the photoconductivity.
The necessity of crystal characterization in different spectral ranges is not the only reason of our choice of the green light instead of the commonly used UV. It seems sensible to begin investigation of a new material for the simplest case. Analyzing the experimental results we can confine ourselves to the case of monopolar photoconductivity for cw laser radiation with λ = 532 nm, but we would have to consider the bipolar one and estimate much more parameters, if the photon energy was sufficient for the interband transitions. Besides, the high energy photons would absorb in the thin surface layer making the problem to be two-dimensional with the rather bulky formulae and more complex fitting procedure [43]. Nevertheless, the excitation by the UV light is very promising, since the larger signal amplitude is expected.
It was noted above that the amplitude of the non-steady-state photo-EMF in Ga2O3 is inferior to that observed in sillenite crystals (Eg = 3.15 – 3.47 eV [37]) for the same experimental conditions. It is resulted essentially from the low photoconductivity in the visible light range. There are several parameters, that determine the value of the photoconductivity and the resulting signal amplitude, namely, the mobility and lifetime of charge carriers, absorption coefficient and quantum efficiency. The rather high value of the mobility μ = 46 – 83 cm2V−1s−1 [33,34] partially compensates the low lifetime in the Ga2O3 crystal. The estimation of the absorption coefficient of 1.1 – 1.3 cm−1 is comparable with the values reported earlier for Ga2O3 [35] and nearly coincide with the typical values for Bi12SiO20 at λ = 532 nm [37].
The studied Ga2O3 crystal has some advantages over the mentioned Bi12SiO20 crystal. The frequency transfer function of the former is flat in the range of 0.1 – 100 kHz, while the signal in the latter decays over 10 kHz. Moreover, the additional measurements of the photoconductivity relaxation in the Ga2O3 crystal allow us to state that the frequency dependence should be flat up to 600 kHz. This means that the photoconductivity relaxation time, which is equal to the electron lifetime in the simplest case, should not exceed 0.26 μs. No influence of shallow traps has been revealed (compare Fig. 2 with those in Refs. [9, 10]). The material has a moderate static dielectric constant ε ≃ 10, which is about 5 times lower than that in sillenite crystals, and this allows to achieve the appropriate cut-off frequency at low illumination levels.
Our investigations reveal the small difference of electrical properties along the [100] and [010] directions. The stronger anisotropy can be present for the other pairs of axes. For example, the difference of the conductivity and mobility along the [010] and [001] axes exceeding an order of magnitude was reported earlier in [33]. The larger conductivity and mobility along the [010] axis was attributed there to the crystal structure with the rutile chains arranged along [010], which results in substantial interaction among gallium 4s orbitals in the octahedral sites. However, the experiments in [34] suggest that the electrical conductivity almost does not depend on the crystallographic direction. In any case, the observation of the non-steady-state photo-EMF for all crystal orientations is considered as a task for the further studies.
The estimates of the material parameters obtained in the space-charge wave excitation regime should be considered as very rough. The resonant maxima have the shape different from the theoretically predicted, which can result from the nonuniformity of the dc electric field distribution. This nonuniformity arises in its turn from the voltage drop near the blocking electrode and from the inhomogeneous light distribution.
As it was mentioned above, gallium oxide grown with the oxygen deficiency demonstrates switching behavior, i.e. electrical nonlinearity [23]. The observation of the nonlinear optical phenomena such as second harmonic generation and photorefractive effect is prohibited in Ga2O3, since the crystal is centrosymmetric, and the third range tensors responsible for these effects vanish. Nevertheless, the nonlinear optical effects of higher orders are possible of course, e.g. the third harmonic generation and photorefractive effect via Kerr nonlinearity. Generally speaking, the studied non-steady-state photo-EMF effect is also a nonlinear phenomenon [10]. It appears as a product of joint action of the photoconductivity and space charge field effects, both of which arise under illumination.
5. Conclusion
In conclusion, we have demonstrated the capabilities of the non-steady-state photo-EMF technique in characterization of the wide-bandgap monoclinic Ga2O3 crystal. The signal was studied in the absence and in the presence of an external dc electric field. The photoelectric parameters such as photoconductivity and diffusion length of electrons are estimated. There is a weak anisotropy of the photo-EMF and electric parameters along the [100] and [010] axes and a pronounced polarization dependence of the quantum efficiency and resulting signal. The rather high amplitude of the signal and flatness of the frequency response in Ga2O3 makes this crystal a potential candidate for the fabrication of adaptive sensors of phase- and frequency-modulated optical signals.
Acknowledgments
This work was supported by the Russian Science Foundation, research grant No. 15-12-00027.
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