Bistable Charge Configuration of Donor Systems near the GaAs(110

Aug 15, 2011 - The ionization occurs along a contour line of a constant value of tip-induced band bending (TIBB).(18) The critical TIBB at each donor ...
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LETTER pubs.acs.org/NanoLett

Bistable Charge Configuration of Donor Systems near the GaAs(110) Surfaces K. Teichmann,† M. Wenderoth,*,† S. Loth,† J. K. Garleff,‡ A. P. Wijnheijmer,‡ P. M. Koenraad,‡ and R. G. Ulbrich† † ‡

IV. Physikalisches Institut, University of G€ottingen, Friedrich-Hund-Platz 1, 37077 G€ottingen, Germany COBRA Inter-University Research Institute, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands ABSTRACT: In gated semiconductor devices, the space charge layer that is located under the gate electrode acts as the functional element. With increasing gate voltage, the microscopic process forming this space charge layer involves the subsequent ionization or electron capture of individual dopants within the semiconductor. In this Letter, a scanning tunneling microscope tip is used as a movable gate above the (110) surface of n-doped GaAs. We study the build-up process of the space charge region considering donors and visualize the charge states of individual and multi donor systems. The charge configuration of single donors is determined by the position of the tip and the applied gate voltage. In contrast, a two donor system with interdonor distances smaller than 10 nm shows a more complex behavior. The electrostatic interaction between the donors in combination with the modification of their electronic properties close to the surface results in ionization gaps and bistable charge switching behavior. KEYWORDS: space charge layer, bistability, GaAs, donors, cross-section STM, STS

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he challenge of the ever-shrinking semiconductor devices has been a subject of discussion for decades.1 Already in the 1970s, Keyes and Hoeneisen2,3 predicted that in semiconductor devices below a critical size, doping cannot be described in a homogeneous model anymore: the random distribution of the dopant atoms causes local fluctuations in the doping concentration. Furthermore the discrete nature of the charge bound on a dopant atom in combination with the long-range Coulomb field of the ionized core leads to a complex electrostatic potential landscape. Transport measurements in low-dimensional systems through a given device have shown to be dependent on the arrangement of charges in the potential landscape during the cooldown cycle.4 It has been shown that nanoscale structures have an impact on the ionization energy of single dopant atoms.5 In optical spectroscopy, the influence of charge reversal of defects on the emission spectra has been reported.6,7 For a deeper understanding of the mutual interaction within the donor system, the combined knowledge of the arrangement of dopant atoms including their position in real space r, their charge state and the corresponding electrostatic potential ϕtotal(r,V) as a function of gate voltage V is required. Scanning probe microscopy (SPM) is a suitable tool to provide access to the structural information down to the atomic scale. It has been used to map the electrostatic potential landscape in various systems,8 11 to controll the charge states of molecules on insulating films12 and metal atoms on graphene,13 and to investigate the mutual interaction of doping centers located in a surface monolayer.14 Recently it was shown that the tip of a scanning tunneling microscope (STM) can be used as an ultrasmall movable gate to control the charge state of r 2011 American Chemical Society

individual dopant atoms in a semiconductor15 17 by the use of tip-induced band bending.18 In this Letter, we show that in the case of a multidonor system a complex ionization scenario in the space charge region occurs: donors in different depths below the surface have different ionization thresholds,19 so they can change their charge states at the same applied tip voltage. This results in a bistable behavior of the ionization. We use scanning tunneling spectroscopy (STS) to visualize the different steps of ionization of multidonor systems, to quantify their Coulomb interaction, and to measure their dynamics. Taking a bottom up approach to understand the build-up process of a space charge region, two donors already show interaction and bistable behavior and provide a basic explanation for the origin of telegraph noise.20 For our experimental study, we use GaAs samples with a silicon doping concentration of nSi ≈ 5  1018 cm 3 . The measurements were performed at 5 K on the (110) surface of GaAs. Details of the experimental setup and methods are given in ref 21. We use sharp tips with a radius of less than 5 nm. Figure 1a shows a constant current topography of the GaAs(110) surface including two donors visible in the topographic image. Analyzing topography images on the same donors at different voltages we can conclude that the donor D1 is in an odd layer and the donor D2 is in an even layer counting the surface layer as 1. From the topographic height one can conclude that donor D1 is closer to the surface than D2.22 At every topography Received: March 28, 2011 Revised: July 1, 2011 Published: August 15, 2011 3538

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Figure 2. The ionization induced by the tip-induced band bending (TIBB, colored areas and black lines) for an electron bound to D1 (a,b) depends on the presence of a second charged donor D2 (c,d). The potential landscape of this configuration, charged donors superimposed on the TIBB, is shown as the green curve (b,d). The ionization level is marked by the short black line. The Coulomb potential of D2 causes a reduction of the TIBB. This increases the ionization threshold by ΔVCoulomb with respect to the Fermi energy (black dashed line).

Figure 1. (a) Constant current topography image taken at a bias voltage of 3 V and set point current of 0.5 nA. (b) Differential conductivity crosssection taken along the yellow line. In order to enhance the contrast, an averaged spectrum taken on the free surface (white rectangle) is subtracted. In (c), the neutral (0) and ionized charge states (+) of the two donors are labeled by 00 = D01,D02, +0 = D+1 ,D02, 0+ = D01,D+2 , and ++ = D+1 ,D+2 , respectively. The solid black lines correspond to the observed enhanced differential conductivity (bright lines in b). The solid lines (red and blue) indicate the ionization curves as expected for a single donor; the dotted lines indicate the shifted ionization curve as expected for a donor in the vicinity of a second charged donor. (The white dashed line in (a) marks the dI/dV - cross section discussed in Figure 3.).

point, an I(V)-spectrum was taken. A spectrum section along the yellow solid line running through the dopants’ positions is shown in Figure 1b. The dominating bright lines of the dI/dV signal show the ionization of donors as a function of the tip position and the bias voltage. The onset of the two ionization curves start at different voltages, as the two donors are in different depth below the surface. Details for the case of single donors are described in refs 16 and 19. The ionization occurs along a contour line of a constant value of tip-induced band bending (TIBB).18 The critical TIBB at each donor position is labeled as TIBBc1 and TIBBc2 for D1 and D2, respectively. The corresponding position dependent bias voltage is labeled as Vc1, Vc2, respectively. The minimum of the contour line is centered at the dopant atom, which is schematically shown

in Figure 1c as the blue solid line for D1 and the red solid line for D2. The thick black lines represent the measured dI/dV signal. If the bias voltage is lower than the solid blue and the solid red curve (i.e., V < Vc1,Vc2), both donors are neutral (D01, D02). Keeping the tip close to D1, the donor behaves as an isolated donor and ionizes at TIBB = TIBBc1. For TIBB > TIBBc1 D1 is ionized while D2 is still neutral (D+1 , D02). The reverse situation (D01, D+2 ) happens when the tip is close to D2. At a certain point both lines intersect. Remarkably, the experimental data show, that those lines do not cross each other unperturbed (e.g., they do not follow the blue and red solid line in Figure 1c), but are continued at a higher bias voltage with an offset of 0.2 V. This means, that in the vicinity of the ionized donor D+2 (D+1 ) the ionization curve of D1 (D2) is shifted to a higher voltage. In Figure 1c (dotted lines), this is schematically shown as an upward shift of the contour line of the constant critical value. The charge state as a function of position and bias voltage is indicated in Figure 1c. To describe the origin of the ionization gap and to estimate the coulomb interaction from the measured voltage shift, we compare a single donor with a double donor system (Figure 2). While the TIBB is considered as a homogeneous contribution to the potential landscape, the discrete nature of the donor charge VD1 Coulomb(r) is taken into account for one (Figure 2a,b) and two D2 donors VD1 Coulomb(r) + VCoulomb(r) (Figure 2c,d), respectively. The potential landscape is described by ϕtotal(r,V) = TIBB(r,V) + D2 VD1 Coulomb(r) + VCoulomb(r) To estimate the shift of the potential of D1 by the influence of a second ionized donor we will consider the pure electrostatic effect. As a first guess, we assume a constant potential shift ΔVCoulomb caused by the potential of D2 at the center of D1. Such a model implies that the critical TIBB value of ionization is shifted to TIBBc* = TIBBc + ΔVCoulomb. We estimate this shift using the Coulomb potential ΔVCoulomb = Q(4πε0εrΔr) 1. The experimentally determined distance between D1 and D2 is Δr = 4.7 nm. The image charge of D2 is taken into account using a dielectric constant εr = 8.16 For Q = 1e, we obtain ΔVCoulomb = 39 mV. In order to compare this value with the measured bias voltage shift 3539

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Nano Letters of 0.2 V, we calculate the TIBB.18 We varied the parameters, such as tip geometry, tip sample-distance, flat band conditions, and doping concentration within reasonable limits, following the procedure described in ref 16. We find that the difference in TIBB at D1 is 21((7) meV for 1.8 and 2.0 V bias voltage. The denoted uncertainty corresponds to the variation of the parameters for the TIBB calculations. The TIBB value is about a factor of 2 smaller than the estimated value of ΔVCoulomb. Both values ΔVCoulomb and ΔTIBB are based on certain assumptions. ΔVCoulomb will change significantly if the influence of the surface and the metallic tip on the effective εr is taken into account. The homogeneous simulation of TIBB gives ensemble averaged values that can only serve as a qualitative guideline for the dependence of the TIBB on the position. In addition due to the half space geometry the center of mass of the donor wave function might be shifted into the bulk23 which could further reduce the overlap between the wave function of the donor and the TIBB. A quantitative modeling of this configuration is out of the scope of this study, and therefore we defer from a deeper explanation. The trend in our data indicates that the experimentally determined shift of the ionization threshold is smaller than the effect of a bare Coulomb potential. A special configuration occurs directly at the intersection of the ionization curves of the two donors. As soon as one donor ionizes, the second donor level is shifted by ΔVCoulomb and thus is forced into the neutral charge state. This results in two possible stable situations with the same total energy: either D1 is ionized and D2 is neutral or D1 is neutral and D2 is ionized. The actual charge configuration depends on the history of the build-up process of the space charge region. One may therefore expect hysteretic behavior in such a system. When the tip scans from left to right at a bias voltage between 2.1 and 2.3 V (Figure 1b) the result is (D+1 , D02) and when the tip approaches from the right the result it is (D01, D+2 ). The ionization process of each donor cause the same amount of tunneling current enhancement. This means the ionization processes of both donors is indistinguishable and a bistability resulting from an interaction of D01 and D+2 at the intersection of the parabola can in priciple not be observed. Nevertheless, we found a strong indication that bistability of two donors is present in our spectroscopy measurement, as described in the following paragraph. Again we start with Figure 1b showing two obvious features (bright parabolic lines) that we have attributed to the ionization process of two donors. In addition a more subtle spectral feature is found below the onset region of each ionization line. This might look like noise but similar structures have been found in a large number of data sets for different donors Dx. Analyzing the complete spatial and spectral dI/dV information we were able to identify an additional donor (in the following labeled as D3) as the origin in some data sets. These donors are always close to the surface but laterally far away from the donor under investigation. Although their direct signature at Dx in the dI/dV is hardly visible, the Coulomb interaction between Dx and D3 results in a clear shift of the onset of the tunnel current. Additionally, the spectral region between the configuration D0x,D03 and D+x ,D+3 is characterized by an averaged current lying between the current flowing for the D0x, D03 and D+x ,D+3 configuration (results not shown here). We interpret this finding with a fast (within the time resolution of our setup) switching between the configurations D+x ,D03 and D0x, D+3 . For nearly all donor configurations the switching dynamics cannot be observed, however the average current is a strong indication for bistability. From all information, we have so far

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Figure 3. Laterally resolved I(V) spectroscopy section along the white dashed line in Figure 1a is shown in (a). In (b), a selection of single I(V) spectra taken in the vicinity of the D2 show the switching process in the bistable region. As a guide to the eye, the high current configuration (D2 is ionized) are marked by red lines, and the low current one (D2 is neutral) by black lines.

concluded that the spectral feature below the onset is related to interactions between donors. In the following, we like to discuss one special data set showing that special configurations can be stable for several milliseconds, that is, in this case the dynamic of the defect complex can be observed within the temporal resolution of our STM setup. It is fair to mention that in this case the presence of D3 is not proven by any additional spectral feature. But having analyzed a lot of different configurations, the presence of D3 is the highly probable. Figure 3a shows a laterally resolved I(V) section along the white dashed line in the constant current topography in Figure 1a. To enhance the contrast, an averaged spectrum measured on the free surface was subtracted from the data (white rectangle Figure 1a). In a very narrow region (∼ a few nm2) around the donor D2, the current onset characterizing the ionization process starts randomly either at the dominant ionization curve or at a ∼220 mV lower voltage or is even changing during the bias voltage sweep. We exclude an instability of the tips state as a second laterally resolved spectroscopy measurement taken at the same position showed the same instability at the same voltage interval and position. Figure 3b shows a selection of individual current traces taken in the region marked by the white box in Figure 3a. While measuring the I(V) curve the voltage was ramped from high to low values. The average time while acquiring a single current data point was 0.2 ms. The tunnel current is plotted versus voltage (top axis), and additionally a time scale indication the time to acquire a spectrum is shown (bottom axis). In the following, we will show that this experimental observation can be readily explained by the presence of an additional donor D3 located several nanometers below D2. This scenario is 3540

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Figure 4. Panel a shows a schematical view of the potential landscape perpendicular to the surface of two donors plus potential induced by the tip to illustrate the idea that a third donor D3 is located below the donor D2 (in Figure 1). The tip-induced band bending is lower at the position of the donor D3 than for the position of the donor D2 as seen in the inset (1) and (2). Most important is that the binding energy of a donor increases toward the surface which implies that the critical value TIBBc3 to ionize donor D3 is lower, than the critical value TIBBc2 to ionize D2. Thus for an appropriate distance both donors can ionize at the same applied bias voltage. In (b), a contour line of the critical value TIBBc2 and TIBBc3 is plotted for both positions. For the donor D2 the influence of the ionized donor D3 shifts the critical value to a higher amount, it is labeled with TIBB*c2. These lines are compared to the measurements extracted from Figure 3a (black circles).

illustrated in Figure 4a, where the potential landscape perpendicular to the surface is shown. The two insets show the voltage dependent TIBB at the position close to the surface (red curve) and the position of about 8 nm in the surface (blue curve). The TIBB at the position D3 is smaller than the TIBB at the position D2. In combination with an enhanced binding energy for D2 in comparison to D3,19 donors which are in different depths below the surface can have donor levels which cross the Fermi energy at the same applied bias voltage making a bistable behavior possible. In contrast to the case of two donors next to each other in x,y direction, the impact on the tunnel current is different for two donors above each other (z direction). D3 is too far away from the surface to have a direct impact on the tunnel current. Its charge state is only visible by the shift of the ionization curve of D2. A shift occurs due to Coulomb interaction, similar to the case of laterally neighboring donors, as discussed above. Most important is that the ionization state of D2 and D3 are distinguishable within the bistable region. The charge switching of D2 is seen as jumps in the current trace. They are marked with black labels in Figure 3b. A switching of D3 (indicated by red labels in Figure 3b) solely is not visible in the current trace (see above), but can be identified because it modifies the onset voltage of D2. The measured switching points in Figure 4b clearly show an upper and lower limit, which is interpreted as the switching of D2 and D3, respectively. We find that a given charge configuration can be stable for more than 10 ms and that the switching process itself happens on a time scale faster than our time resolution. Note, that we do not

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observe an averaging of the two configurations during a single trace. Trace 1 shows an example that D2 switches first and stays neutral until D3 becomes neutral. Trace 2 demonstrates the reverse switching order. Bistable behavior is observed as multiple switches between the two configurations as shown in the last trace in Figure 3b and the inset of Figure 3a. This observation resembles telegraph noise (which is related to burst or popcorn noise) that occurs in semiconductors where random trapping and release of charge carriers are discussed as possible candidates for a bistable behavior.20 As it scales with kBT, a time constant of milliseconds at room temperature with an activation energy of 0.4 eV found in ref 20 is in reasonable agreement with our system having an activation energy in the order of a few millielectronvolts (the donor binding energy) studied at 6 K. We estimate the Coulomb interaction in a similar way as described for the laterally interacting donors. In Figure 4b, the measured switching points extracted from Figure 3a are compared with the simulated contour line of constant TIBB. The best fit for the lower ionization curve of donor D2 is found with a depth of 0.6 nm and with a critical value of TIBBc2 = 91 mV (solid red line). The shifted ionization curve (dotted red line) corre* = TIBBc2 + ΔVCoulomb = 114 sponds to a contour line of, TIBBc2 mV. Thus the ionization of D3 causes ΔVCoulomb = 23 mV. This value corresponds to a distance of ∼8 nm between D2 and D3. The blue solid line in Figure 4b shows the ionization curve corresponding to this depth and a slight lateral offset (0.4 nm to positive y-direction) of the donor center to the side of D2. We conclude that D3 is not located directly underneath D2. In order to calculate the TIBB contour of D3, we used the same parameter as for the calculations for D1 and D2. The contour line that coincides with TIBBc2 yields TIBBc3 ∼ 1 mV for the depth of D3. This is on the order of the thermal fluctuations. However, the experiment clearly shows well-defined charge states of D3 For voltages lower than the solid red and solid blue line, both D2 and D3 are neutral (D02, D03). If the voltage is higher than the solid blue line, D3 is ionized (D02, D+3 ) and the ionization curve for D2 is shifted to higher voltages (dotted red line). For voltages higher than the dotted red line, both donors are ionized (D+2 , D+3 ). Between the two states (D02, D03) and (D+2 , D+3 ) there is an area where the system is bistable (hatched area). Here the solid red and the solid blue line coincide within the thermal broadening. This means that the critical TIBB values TIBBc2 at D2 and TIBBc3 at D3 are achieved at the same applied voltage. The region of bistability in the experimental data in Figure 3a is in reasonable agreement with the thermal fluctuations at 5 K. In summary, we demonstrate that the ionization behavior of donors is not just the sum of the individual donors. Donors interact via their Coulomb potential creating ionization gaps. Even deeper buried donors can interact with donors close to the surface. Furthermore, the order of ionization is not necessarily well determined. This leads to the interesting phenomenon of bistable ionization configurations. We find typical time scales of milliseconds. Future devices will require larger charge carrier densities realized by higher doping concentrations. This will result in smaller space charge regions and shorter average dopant distance. Comparing our system with the dimension of anticipated devices the mechanism discussed in this paper will become increasingly important.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. 3541

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’ ACKNOWLEDGMENT We thank DFG-SFB 602 A7, DFG-SPP 1285, ASPRINT, NAMASTE (FP7 Grant 214499), STW-VICI Grant 6631, and COBRA for financial support. We gratefully acknowledge U. Kretzer, Freiberger Compound Materials GmbH, for providing the samples. ’ REFERENCES (1) Roy, S.; Asenov, A. Science 2005, 309, 388. (2) Keyes, R. W. Appl. Phys. 1975, 8, 251. (3) Hoeneisen, B.; Mead, C. A. Solid-State Electron. 1972, 15, 819. (4) Heinzel, T.; J€aggi, R.; Ribeiro, E.; v. Waldkirchand, K.; Ensslin, M.; Ulloa, S. E.; Medeiros-Ribeiro, G.; Petroff, P. M. Europhys. Lett. 2003, 61, 674. (5) Pierre, M.; Wacquez, R.; Jehl, X.; Sanquer, M.; Vinet, M.; Cueto, O. Nature Nanotechnol. 2010, 5, 133. (6) Larsen, D. M. Phys. Rev. B 1973, 8, 535. (7) Blome, P. G.; Wenderoth, M.; H€ubner, M.; Ulbrich, R. G.; Porsche, J.; Scholz, F. Phys. Rev. B. 2000, 61, 8382. (8) Ono, M.; Nishigata, Y.; Nishio, T.; Eguchi, T.; Hasegawa, Y. Phys. Rev. Lett. 2006, 96, 016801. (9) J€ager, N. D.; Urban, K.; Weber, E. R.; Ebert, P. Appl. Phys. Lett. 2003, 82, 2700. (10) Reusch, T. C. G.; Wenderoth, M.; Winking, L.; Quaas, N.; Ulbrich, R. G. Phys. Rev. Lett. 2004, 93, 206801. (11) Reusch, T. C. G.; Wenderoth, M.; Winking, L.; Quaas, N.; Ulbrich, R. G. Appl. Phys. Lett. 2005, 87, 093103. (12) Swart, I.; Sonnleitner, T.; Repp, J. Nano Letters 0, 0 (13) Brar, V. W.; Decker, R.; Solowan, H.-M.; Wang, Y.; Lorenzo, M.; Chan, K. T.; Lee, H.; Girit, C. O.; Zettl, A. Z.; Louie, S. G.; Cohen, M. L.; Crommie, M. F. Nature Physics 2011, 7, 43. (14) Nazin, G. V.; Qiu, X. H.; Ho, W. Phys. Rev. Lett. 2005, 95, 166103. (15) Marczinowski, F.; Wiebe, J.; Meier, F.; Hashimoto, K.; Wiesendanger, R. Phys. Rev. B 2008, 77, 115318. (16) Teichmann, K.; Wenderoth, M.; Loth, S.; Ulbrich, R. G.; Garleff, J. K.; Wijnheijmer, A. P.; Koenraad, P. M. Phys. Rev. Lett. 2008, 101, 076103. (17) Lee, D. H.; Gupta, J. A. Science 2010, 330, 1807. (18) Feenstra, R. M. J. Vac. Sci. Technol. B 2003, 21, 2080. (19) Wijnheijmer, A. P.; Garleff, J. K.; Teichmann, K.; Wenderoth, M.; Loth, S.; Ulbrich, R. G.; Maksym, P. A.; Roy, M.; Koenraad, P. M. Phys. Rev. Lett. 2009, 102, 166101. (20) Hsu, S.; Whittier, R. J.; Mead, C. A. Solid-State Electron. 1970, 13, 1055. (21) Loth, S.; Wenderoth, M.; Ulbrich, R. G.; Malzer, S.; Dohler, G. H. Phys. Rev. B 2007, 76, 235318. (22) Depuydt, A.; Haesendonck, C. V.; Savinov, S.; Panov, V. Appl. Phys. A: Mater. Sci. Process. 2001, 72, 209. (23) Hao, Y. L.; Djotyan, A. P.; Avetisyan, A. A.; Peeters, F. M. Phys. Rev. B 2009, 80, 035329.

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