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
  • 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.

  • 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.

  • 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).

  • 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.

  • 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.

  • 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.

  • Supplementary Materials

    This PDF file includes:

    • 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.

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mp4 format). Spatiotemporally resolved decay of dI(td) at the dopants in Fig. 2A.

    Files in this Data Supplement:

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