Research ArticleSEMICONDUCTORS

From time-resolved atomic-scale imaging of individual donors to their cooperative dynamics

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Science Advances  10 Mar 2017:
Vol. 3, no. 3, e1601552
DOI: 10.1126/sciadv.1601552

Abstract

The key elements in the steady miniaturization process of cutting-edge semiconductor devices are the understanding and controlling of charge dynamics on the atomic scale. In detail, we address the study of charging processes of individual doping atoms and, especially, the interaction of those atoms with their surroundings. We use pulsed optical excitation in combination with scanning tunneling microscopy at the n-doped gallium arsenide [GaAs(110)] surface to investigate single donor dynamics within a nanoscaled, localized space charge region. Tuning the tunnel rate can drive the system into nonequilibrium conditions, allowing distinction between the decay of optically induced free charge carriers and the decay of donor charge states. The latter process is atomically resolved and discussed with respect to donor-level binding energies and local donor configurations.

Keywords
  • Scanning tunneling microscopy
  • semiconductor
  • GaAs
  • Dopant dynamics
  • nanotechnology

INTRODUCTION

Optical excitation of a semiconductor generates electron-hole pairs. Besides simple recombination, the presence of local fields and structural inhomogeneities can result in complex relaxation pathways (1). This process includes not only field-driven charge transport but also the interaction with local defects. Up to now, access to the correspondent microscopic processes is usually limited to probing a large volume of the host material (2, 3). On the macroscopic scale, a standard indicator, characterizing dynamic properties of charge processes inside a semiconductor, is the surface photo voltage (SPV). SPV describes the change of local potentials due to the presence of photo-generated charge. Microscopically, the buildup of an SPV is linked to various mechanisms such as the dynamics of dopants and the optically excited, freely movable carriers within the semiconductor. Especially, the controlled charging and discharging of individual dopants is the most elementary process in semiconductor electronics. In state-of-the-art device development, switching is already accomplished by a handful of donors (46). In this context, disorder, for example, the specific configuration of doping atoms, is crucial. SPV studies have already reported a significant inhomogeneity of the static properties (7, 8) on the atomic scale. Apart from its relevance in fundamental research, an atomic-level view on charge dynamics is needed for further device miniaturization. In particular, determining the influence of boundaries—for example, surfaces or internal interfaces—will substantially improve our understanding of dynamic properties of semiconductor nanostructures.

Here, we demonstrate the necessity for atomically scaled analysis of locally very inhomogeneous charging dynamics of individual donors, which, up to now, have usually been described by a single decay constant. We have used an optical pump-probe technique combined with scanning tunneling microscopy (STM) (Fig. 1A; for more details, please see Materials and Methods) by applying the shaken-pulse-pair excitation (SPPX) (911) procedure. A periodic modulation of the optically induced tunnel current dI as function of the delay time td between pump and probe pulse represents the time evolution. Our sample system, sketched in Fig. 1A, is the STM tip-induced electrostatic potential (color-coded) (12) in silicon-doped GaAs (gallium arsenide, n-type), including the influence of optically excited electron-hole pairs. Comparable to the situation inside a Schottky contact, the electric field separates free charge resulting, at positive bias voltages, in an accumulation layer of holes at the surface. In return, initially ionized donors capture electrons and become neutral. The shift of the surface potential due to the presence of the photo-generated holes, leading to an increase of the tunnel current at the same bias voltage, is called SPV. The relaxation mechanisms of the donors and the electron-hole pairs plus their mutual interaction define the steady state of the charge configuration (13, 14). Additionally, previous studies have shown that tunneling electrons can address and thereby directly annihilate the photo-generated and accumulated holes at the surface (15, 16). Using the tunnel current I0 as an additional control parameter, we drive the system into different non-equilibrium conditions.

Fig. 1 Charge dynamics at the n-doped GaAs(110) surface.

(A) The STM tip induces a space charge region below the GaAs(110) surface, leading to the separation of photo-generated electron-hole pairs. The presence of holes beneath the tip modifies the charge configuration at the surface. (B) The optically induced current dI as a function of the delay time td reveals an altering sign from positive to negative values going from low to high tunnel currents (bias voltage, 1.0 V; excitation parameters: repetition cycle, 8 μs; pulse width, 40 ns; average power, 10 μW). The lines are intended as a guide to the eye. (C) Band tunneling scheme for t < τhole. At low tunnel currents, dI(td) is dominated by the hole annihilation process at the surface via IV. (D) Band tunneling scheme for τhole < t < τdon. For high currents, holes at the surface are annihilated fast, whereas surface-near donors still have to emit their electrons into the conduction band to ionize (green arrow). Nearly no net charge at the surface is present, leading to a vanishing IC. Note that in (C) and (D), the same bias voltage is applied. (E) Decay constant τ plotted against current I0 in case of positive and negative dI. The dashed lines are intended as a guide to the eye.

RESULTS

Figure 1B shows a multitude of dI(td) spectra (bias voltage UB = 1.0 V) for increasing tunnel currents I0. As a unique feature, and in contrast to previous studies (10, 11), we applied low laser intensities PL, resulting in a positive optically induced current dI. The correlation between PL and dI and the measuring process of dI itself are explained in detail in Materials and Methods. dI under pulsed excitation consists of the increase of conduction band tunneling dIC due to the buildup of the SPV and the tunneling into valence band states IV due to the presence of the accumulated photo-generated holes at the surface (Fig. 1C). Our study on continuous excitation has shown that the change dIC is likely to be the dominant effect (15). However, the percentages of dIC and IV on dI depend in detail on parameters such as STM tip shape, bias voltage, tunnel current, and excitation intensity. At I0 smaller than 250 pA, we observe an exponential decay of dI(td) = I0⋅exp[−(1/τ)⋅td] with a decay constant τ decreasing with increasing I0 (Fig. 1E, red dots). We attribute this I0 dependency of τ to the tunnel process IV into photo-generated holes inside the valence band. Note that the size of the space charge region changes when decreasing the tip-sample distance for increasing I0. However, for a tip movement of 1 to 2 Å (current range in Fig. 1B for a usual tunnel barrier height of 4 eV), this effect is negligible (see fig. S1). Consequently, the decay of dI(td) is determined by the annihilation process of the accumulated holes at the surface. By adjusting I0, we are able to actively control this decay, in the following termed as τhole.

At I0 = 450 pA, the line shape of dI(td) changes notably. Although dI remains positive for a small td and decays fast, it alters its sign for a larger td. This effect gets even more pronounced for higher currents (500 pA) until a completely negative and exponentially decaying dI(td) is observed (1000 and 1500 pA). We explain the line shape of dI(td) at higher currents with a crossover between two relaxation processes. The hole annihilation dominates at low and medium I0 (Fig. 1C). The negative dI can be identified as the signature of donor ionization by electron emission from the donor level into the conduction band (Fig. 1D, green arrow). During the relaxation to the ground state, dI(td) < 0 reflects a special nonequilibrium condition. For high I0, holes are annihilated rapidly, whereas donors remain neutral (for more details on the nonequilibrium conditions, see fig. S2). Consequently, at the surface, nearly no net charge is found, the potential difference between the tip and the sample at the vacuum barrier vanishes, and the tunnel current drops to almost zero (Fig. 1D). The relaxation of the system (at τhole < t < τdon) is solely determined by the ionization of the donors. As expected for this mechanism, the related decay constant τdon is significantly less dependent on I0 in comparison to τhole (Fig. 1E, yellow dots; exemplary fitting results can be found in figs. S3 and S4).

Expecting a great influence of different atomically scaled donor configurations at the GaAs surface, we studied locally resolved τdon. The constant current topography in Fig. 2A shows the signatures of three donors positioned at different depths beneath the surface. To suppress the contribution of the hole dynamics, we used high tunnel currents (I0 = 1 nA) while recording dI(td) spectra at each raster scan point of the topography in Fig. 2A. Additionally, we chose a sample voltage (UB = 1.3 V) where lateral interaction between donors can be neglected (17). Single, time-resolved spectra, taken directly at the marked dots, show significantly different decay constants for each donor (for logarithmic scale analysis of Fig. 2B, see fig. S5). Although it has already been shown that local defects have an impact on the relaxation process (10, 11), the considerable variation in the dynamics of individual defects has not yet been resolved. To explore these dynamics, we plot τdon spatially resolved in Fig. 2C [the supplementary material includes a movie showing the spatiotemporally resolved decay of dI(td)]. A local enhancement of τdon clearly visible at the donor position. Moreover, τdon changes from donor to donor with the highest τdon for donors closest to the surface. Compared to the free surface (that is, far away from a visible donor) showing a τdon ~100 ns, a donor in layer 1 below the surface (for depth evaluation, see fig. S6) exhibits a τdon of 530 ns. Obviously, the surrounding of the defects plays a crucial role, for example, the presence of the surface and/or the influence of other donors. In this sense, the absolute values of τdon will depend on the local dopant configuration. To elucidate the variation in τdon in Fig. 2C, we analyzed the emission mechanism of the ionization process in detail. By performing a temperature-dependent study, thermal emission can be ruled out (fig. S7). Previous results by Wijnheijmer et al. (18) have shown that EB monotonically increases with decreasing depth of the donor (Fig. 2D and fig. S6). On the basis of these findings, we propose a field-driven tunneling process of electrons from the donor level to the conduction band (Fig. 2E) to explain the correlation between EB and τdon (Fig. 2D).

Fig. 2 Spatially resolved charging dynamics of donors at different depths below the GaAs surface.

(A) Topography of the GaAs(110) surface with three donors (marked as red, green, and blue dots) positioned at different depths below the surface (bias voltage, 1.3 V; tunnel current, 1 nA). (B) Locally resolved time spectra (bias voltage, 1.3 V; tunnel current, 1 nA; excitation parameters: repetition cycle, 8 μs; pulse width, 40 ns; average power, 16 μW) recorded at the positions marked in (A). (C) Spatially resolved decay time τdon. (D) Donor binding energies EB plotted versus depths. Adapted from Wijnheijmer et al. (18). τdon of the corresponding donors in (B) is assigned respectively. (E) Model of field ionization. In this case, electrons tunnel from the donor level into the conduction band.

The binding energy EB and the local field E at the donor position determine the electron emission rate for this tunneling process. To cross-check this EB dependency, we compare the experimental τdon quantitatively with the ionization times τhydro calculated for hydrogen atoms in an electric field (19) with adapted parameters for silicon donors in bulk GaAs (Fig. 3A and fig. S8). For comparison, the found pairs of EB and τdon for the three different dopant depths below the surface in Fig. 2A are included in Fig. 3A. Nearly no charge and hence a weak electric field at the surface characterize the relaxation from the nonequilibrium conditions at high currents I0 (Fig. 1D). Charge fluctuations of donors and thereby field fluctuations take place (17, 20), triggering further field-driven ionizations. We model an electrostatic potential in a cross section at the GaAs surface (Fig. 3, B and C), including random donor positions in charged (blue dots) or neutral (green dots) state, according to the doping density of our sample (3 × 1018 cm−3, 7 nm average distance between two donors). To estimate the probability of charging events, we calculated exemplary Coulomb potentials of ionized donors in this half-space geometry.

Fig. 3 Comparison of donor dynamics: Theory versus experiment.

(A) Calculated field-driven ionization time τhydro for a hydrogen model with adapted parameters plotted against the binding energy EB and compared with experimental pairs of EB and τdon. (B and C) Calculated snapshots of the electric field |E| induced by an exemplary ionized donor in cross-sectional geometry at the GaAs surface based on a random distribution of donors (charged, blue; noncharged, green). The color scale is cut at 5 mV/nm. The volume, marked by the white contour lines, gives the maximum distance for a charged donor in which the donor is able to trigger further ionization of surface-donors with EB = 10 meV/τdon = 237 ns (B, blue/white dot) or EB = 45 meV/τdon = 530 ns (C, red/white dot).

Regarding the ionization process of donors with a binding energy EB of 10 meV and a τdon of 237 ns (Fig. 3B, blue/white dot), the required field E of 0.2 mV/nm will already be given if any of the donors in a spherical volume marked by the white contour line in Fig. 3B ionizes. In contrast, to charge a donor with a binding energy EB of 45 meV and a τdon of 530 ns (Fig. 3C, red/white dot), a field E of 2.5 mV/nm is needed. The radius of the correspondent volume reduces to 8 nm (Fig. 3C, white contour line), and consequently, the number of possible donor candidates decreases, making the ionization process unlikely. We deduce that the variation in EB cannot be the only reason for the variation of τdon. In fact, we expect a considerable increase of the ionization probability when more than one donor is involved. From this deduction, we propose a relaxation to the ground state as a stepwise buildup of the electric field, starting with the ionization of donors positioned in the bulk material and continuing to donors near the surface. Hence, the donor dynamics cannot be treated as individual charging and discharging processes connected to a dedicated decay constant τdon. Instead, they have to be regarded as a stochastically distributed ensemble of linked subsequent charging events triggered by random charge fluctuations. Thus, the actual relaxation dynamics will vary from one local donor configuration to another.

DISCUSSION

We are convinced that this coupled charging dynamics of individual donors, including the influence of surfaces and interfaces, can have a massive impact on the functionality of semiconductor devices. Bistabilities in the charge state of coupled donors have already been observed in the millisecond time regime (17). The map for the relaxation time of individual donors in Fig. 2C shows nonisotropic local enhancements of τdon, indicating the interaction among themselves. Continuous charging and discharging events are responsible for shot noise in semiconductor devices (21), but are not yet experimentally resolved on the local scale. Even quantum computer approaches discuss single donors as isolated qubits (2224). Ultimately, in all these subjects, only an atomic-scale characterization can provide a detailed understanding. In this context, pulsed optical excitation combined with STM opens up an exciting research field with a myriad of applications.

MATERIALS AND METHODS

Experimental setup and sample system

All data were recorded in a home-built low-temperature, ultrahigh vacuum STM at a base pressure of 1 × 10−10 mbar and at base temperatures of 77 and 6 K. The bias voltage was defined as the sample voltage. The silicon n-doped GaAs (3 × 1018/cm3) crystals were chemically thinned down to 100 μm and cleaved inside the vacuum chamber exposing the (110) surface. The optical setup, implemented in the STM, is shown in Fig. 4. The laser beam of a continuous-wave laser diode (Toptica, 785 nm) was processed into a pulsed shape by a fiber-coupled EOM (EOSpace). We used the SPPX (10), conceived by Terada et al. at the University of Tsukuba. A high-frequency arbitrary waveform generator (AWG; Keysight A81160) produced the SPPX in an all-electronic method. The shortness of the pulses is restricted by the bandwidth of the AWG to ~1 ns. The pulsed laser beam was focused into the tunnel junction with a focus diameter of less than 20 μm. The periodically modulated, laser-induced tunnel signal dI(td) was measured by a lock-in amplification.

Fig. 4 Optical pulse generation for STM operation.

The laser beam of a low-noise diode laser [continuous wave (cw), 785 nm] is processed into a pulse shape with the help of an electro-optic modulator (EOM), controlled by a high-frequency pulse generator. After focusing the pulses into the tunnel junction, the optically induced signal is extracted by lock-in amplification.

Excitation state–dependent sign of the optically induced current dI(td)

The quantity dI(td) is the difference in the tunnel current induced by a sequence of two shortly separated pulses compared to the current induced by a train of two well-separated pulses. In comparison to other pump-probe experiments, the pump and the probe pulse have identical intensities and both trigger the same mechanism: a change in the tunnel current. In contrast to our studies, dI in previous optical pump-probe SPV measurements had a negative sign (911). We show that different excitation states after the pump pulse (t = tPW) determine the sign of dI. Figure 5 schematically shows two shortly separated optical pulses (Fig. 5A, green), discusses a saturated (Fig. 5B, blue) and a nonsaturated excitation case (Fig. 5C, red), and compares this with the excitation induced by two well-separated double pulses (Fig. 5D).

Fig. 5 Sign reversal in dI dependent on the excitation state of the system after the pump pulse.

(A) Two shortly separated optical pulses. (B) Response in the tunnel current when the system has reached its local equilibrium after the pump pulse. (C) Response in the tunnel current when local equilibrium is not reached. (D) System response in case of well-separated pulses. The dashed lines mark the average current for each pulse configuration.

If the pump pulse has induced the maximum change in the tunnel current IT (Fig. 5B), the effect of the probe pulse on the tunnel current will be at maximum of the same order. Because of the overlap in the decay (deep blue shading), the average current was less than the average current (black dashed lines) induced by two well-separated pulses (Fig. 5D). As per definition, this leads to a negative dI. If the first pulse does not induce the maximum effect, the shape of the system response, triggered by the second pulse, can change considerably. Figure 5C shows the configuration for which the excitation by the probe pulse leads to more tunnel current (light red shading) in comparison to one single, isolated pulse. In the differential measuring method of the averaged signal (black dashed line), this may lead to a positive dI.

Experimentally, saturation (Fig. 5B) or nonsaturation (Fig. 5C) in the excitation state can be investigated by applying different laser intensities PL [Fig. 6A, red (low excitation intensity) and blue (high excitation intensity)]. The time to obtain saturation for the charge configuration at the surface is connected to the time it takes for a donor to capture one of the photo-generated electrons and to become neutral subsequently. At higher PL, the electron density at the surface is denser and, consequently, the SPV builds up faster during the pump pulse. The current dependency of the decay constants extracted from dI(td) spectra is identical for high and low excitation intensity (Fig. 6B). This is a clear indication that in each case, the same relaxation mechanism is probed, namely, the annihilation of the holes via tunneling. The only difference in both cases is the excitation state of the charge configuration at the surface after the pump pulse, resulting in the sign alteration of dI.

Fig. 6 dI(td) spectra for low and high optical excitation intensity.

(A) Red curves: At low optical excitation intensity PL (10 μW average power), saturation of the SPV during the pump pulse is not obtained, resulting in a positive dI. Blue curves: At high PL (70 μW average power), saturation of the SPV is obtained after the pump pulse. Consequently, the dI becomes negative. (B) Decay constant τ plotted against the set point current for high (blue) and low (red) excitation densities. The current dependency of τ in both cases is identical.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/3/e1601552/DC1

section S1. Evolution of the space charge region when varying the z-height of the STM tip

section S2. Detecting the donor ionization process

section S3. Exemplary fitting results of dI(td) curves of Fig. 1E

section S4. Logarithmic analysis of the decay spectra of Fig. 2B

section S5. Determining the donor depth

section S6. Temperature-dependent analysis of the dopant charging

section S7. Field-driven tunnel ionization from the donor level into the conduction band

section S8. Making a movie of dI(td), spatially resolved

fig. S1. Calculation (Poisson solver) of the tip-induced potential for varying tip heights above the GaAs surface.

fig. S2. Real-time evolutions of experimental parameters (hole density, ionized dopant density, and conduction band tunneling) at high tunnel currents and the corresponding screening configurations sketched in band schemes.

fig. S3. Two exemplary fitting results of the dI(td) spectra of Fig. 1E.

fig. S4. Exemplary fitting results of the dI(td) spectra of Fig. 1E in the transition region.

fig. S5. Decay spectra of Fig. 2B of the main manuscript plotted on normal and logarithmic scale.

fig. S6. Extracting the dopant depth from STM topographies.

fig. S7. Dopant relaxations, given in dI, plotted against the delay time td, for different temperatures.

fig. S8. Schematic for field-driven tunnel ionization.

movie S1. Spatiotemporally resolved decay of dI(td) at the dopants in Fig. 2A.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

REFERENCES AND NOTES

Acknowledgments: We thank G. Herink, P. M. Koenraad, S. Loth, C. Ropers, and A. Weismann for proofreading of the manuscript and constructive remarks. Funding: This work was financially supported by the Deutsche Forschungsgemeinschaft via CRC1073 TP C04. Author contributions: P.K. performed the measurements. P.K. and M.W. analyzed the data and wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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