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Four-dimensional imaging of carrier interface dynamics in p-n junctions

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Science  09 Jan 2015:
Vol. 347, Issue 6218, pp. 164-167
DOI: 10.1126/science.aaa0217

Traveling a long way past the junction

Diodes are central components of modern electronic circuits. They essentially consist of two semiconductors sandwiched together, with one deficient in electrons (p), the other enriched (n). Najafi et al. used ultrafast electron microscopy to study the dynamics in a silicon diode on a time scale of trillionths of a second. They discovered that when light excites the diode's charge carriers, those carriers migrate much farther past the p-n junction than standard models would imply. The authors explain the results using a ballistic transport model.

Science, this issue p. 164

Abstract

The dynamics of charge transfer at interfaces are fundamental to the understanding of many processes, including light conversion to chemical energy. Here, we report imaging of charge carrier excitation, transport, and recombination in a silicon p-n junction, where the interface is well defined on the nanoscale. The recorded images elucidate the spatiotemporal behavior of carrier density after optical excitation. We show that carrier separation in the p-n junction extends far beyond the depletion layer, contrary to the expected results from the widely accepted drift-diffusion model, and that localization of carrier density across the junction takes place for up to tens of nanoseconds, depending on the laser fluence. The observations reveal a ballistic-type motion, and we provide a model that accounts for the spatiotemporal density localization across the junction.

Multiple spectroscopic techniques have enhanced the understanding of charge carrier dynamics in semiconductors (13). However, as the size approaches the critical limit of the nanoscale (4), it becomes necessary to investigate the behavior of carriers at a high spatiotemporal resolution to elucidate the extent of spatial and density localizations at these scales. In semiconductors, carrier excitation, transport, and recombination occur on time scales that span a wide range, from a few femtoseconds to hundreds of microseconds (5), and these processes are dramatically altered in nanostructures due to their low dimensionality and the large surface-to-volume ratio (6, 7). Although a large body of literature exists on carrier dynamics in bulk semiconductors, studies of surfaces and interfaces demand the resolution of the dynamics in both space and time with high enough sensitivity. Recently developed scanning electron-probe microscopies, which combine the spatial resolution of electron microscopy and the temporal resolution of laser spectroscopy, make such studies possible (8).

Here, we report direct imaging of carrier interfacial dynamics in the silicon p-n junction by scanning ultrafast electron microscopy (SUEM). We image the spatiotemporal evolution of carrier density after excitation and follow the behavior of transport and recombination of carriers. It is shown, with the spatial resolution of the electron probe, that optically induced long-range carrier transport can span tens of micrometers. Snapshots of the carrier density on the picosecond time scale indicate the localization of excess carriers and the associated electric field across the junction. The displaced carriers remain localized in both space and time (up to tens of nanoseconds) until they cross the junction and recombine. With high excitation fluence, carrier localization distorts the effective junction potential and acts as a locally time-dependent field, providing an energetically favorable pathway to recombination. These observations were accounted for by developing a model that describes both the ballistic-type carrier transport and the decay of energy to the lattice.

The p-n junction diodes were purchased as wafers from EL-CAT Inc. and used without further modifications. The wafers consisted of phosphorus-doped n-type silicon (1.4 × 1014 cm−3) epitaxially grown on boron-doped p-type silicon (9.4 × 1018 cm−3) with (111) crystal orientation; this results in an intrinsic potential (Vintrinsic) of 0.79 V (fig. S1). No external field was applied to the junction. The samples were cleaved and immediately transferred into the SUEM chamber, where the pressure was maintained at 1.2 × 10−6 torr. Surfaces with the root mean square (RMS) roughness of less than 100 nm [orders of magnitude smaller than the estimated diffusion length in silicon (9)] were selected for this experiment to minimize interruptions of carrier diffusion. As shown below, the ballistic coherence length of carriers is tens of micrometers, a much larger value than the roughness scale, and thus it is relatively irrelevant on the picosecond time scale. Images of a typical surface studied statically—i.e., without time resolution—are provided in Fig. 1 and fig. S2.

Fig. 1 Schematic of SUEM and imaging of the junction.

The 515-nm optical pump initiates carrier excitation to the conduction band. Transport of charges to the junction then takes place in the diode while the scanning electron probe measures the induced changes at different time delays. The inset is an SUEM image of the diode recorded at –­­680 ps; the well-known but unintuitive contrast between n-type and p-type silicon in the diode is due to the energetics of the local bending of the vacuum level (1518) and simply reflects the (±) surface charge involvement in enhancing or suppressing SEs in the p (n) regions.

In SUEM, femtosecond infrared pulses (1030 nm, 300 fs) are split to generate green (515 nm) and ultraviolet (UV) (257 nm) pulses. The green is used to pump the specimen samples, whereas the UV is directed toward the microscope’s photocathode to generate short pulses of electrons from the field emission tip; details of the design and operation were given previously (10). The time delay between the optical pump and electron probe pulses was controlled, covering the range from Embedded Image ps to Embedded Image ns with the snapshot resolution of ~2 ps. The pulsed electrons, accelerated to 30.0 kV by electrostatic lenses, produce secondary electrons (SEs) from the top 1 to 5 nm (11) of the sample’s surface, which are then collected by the SE detector. To generate an image, the electron probe was scanned across the area of interest, which included the image region for carrier transport, typically using a resolution of 200 nm, which is sufficient for a surface scan over tens of micrometers. It has been shown that this spatial resolution can be made better than 10 nm (10). The experimental setup is schematically depicted in Fig. 1.

Under our experimental conditions, the transient surface charge density in the local vacuum is estimated to be less than ~107 cm−2 due to the fluences used (maximum 1.28 mJ/cm2), indicating that surface field transients do not strongly interfere with the electron probe (12). Within a given material, the number of emitted SEs depends on the topography and composition (13), but, in all SUEM experiments presented here, we obtain the change in carrier density by subtracting the image recorded at negative time (reference image recorded at Embedded Image ps) from the image obtained at a given positive time, i.e., Embedded Image, where rx,y is the spatial pixels scanned and t± are the frame times after time zero (t+) and before time zero (t). This results in the so-called “contrast image in which the bright and dark contrasts correspond, respectively, to increases in local electron and hole densities (fig. S3), and the difference image becomes insensitive to collection and other possible fluctuations. Such images provide the snapshots that are used to construct movies S1 to S3.

After optical excitation in the specimen, electrons are promoted to the conduction band, and in this case the junction separates electron-hole (e-h) pairs, with e and h drifting in opposite directions, a process usually described by the drift-diffusion model (14); this locally increases the density of majority carriers in both n-type and p-type. In the absence of additional fields, the charge separation occurs solely in the vicinity of the junction, where excited carriers are influenced by the static junction potential. The inset in Fig. 1 shows the raw SUEM image of the diode recorded at a negative time delay (Embedded Image ps), long before the arrival of the initiating pump pulse. The observed difference in brightness between p-type and n-type regions in the image agrees with previous observations (15, 16) and is attributed to the difference in effective electron affinities between the two regions (17, 18). The pump pulse was guided to symmetrically illuminate n-type and p-type, as highlighted by the dotted ellipse in Fig. 1. A deviation of up to several micrometers in beam placement may occur, although it can be accounted for, as discussed below.

To understand the influence of the junction on the dynamics, we first examined n-type and p-type silicon individually without the junction and with doping levels and crystal orientations similar to their counterparts in the diode. Figure 2, A and B, shows contrast images recorded for n-type and p-type silicon, respectively, at various time delays. The images clearly display a bright contrast in both samples after the optical excitation; the contrast is rather weak in n-type, with a spatial spread comparable to the laser profile on the surface, but is considerably stronger in p-type, with a larger spatial extent. This is attributed to the larger absorption cross section in heavily doped p-type silicon (19). In both samples, the bright contrast gradually decays at long times. Such behavior in lightly doped n-type and heavily doped p-type is independent of laser fluence. If the presence of the junction potential does not alter the dynamics, we would expect to observe the same behaviors in the n-type and p-type regions of the diode as those shown in Fig. 2, A and B.

Fig. 2 Dynamics with and without the junction.

Silicon (A) n-type and (B) p-type samples without a junction were studied as individual wafers. Both n-type (1.4 × 1014 cm−3 P-doped) and p-type (9.4 × 1018 cm−3 B-doped) show a bright signal (increased electron density) under laser illumination, in contrast to the behavior when the junction is present. (C) A series of contrast images in which the bright and dark contrasts correspond to the local electron and hole densities, respectively, relative to the signal at negative time. These frames were chosen to display the unperturbed signal (–470 ps), excitation (6.7 ps), carrier separation after transport (36.7, 80 ps), and relaxation toward equilibrium (653.3 ps, 3.32 ns).

The temporal behavior of the junction is summarized in Fig. 2C for 1.28 mJ/cm2 fluence; full sets of contrast images can be viewed in movies S1 to S3. The dynamics can qualitatively be described as follows. Immediately after the excitation (the frame at +6.7 ps), both layers are bright, mirroring their individual behaviors in the absence of the junction. After 36.7 ps, charges are transported toward the junction, resulting in excess electron and hole density in n-type and p-type, respectively; the depletion layer at the junction remains dark due to surface patch fields that hinder SE detection (17, 18). After transport across the junction (+80 ps), the density of excess carriers reaches its maximum. The spatial extent of charge separation is estimated to span tens of micrometers within the first ~80 ps. The observed “bending” at the junction is due to the asymmetry in the pump beam placement, as discussed in the supplementary materials. Such drastic difference in contrast behavior, with and without the junction, provides the underpinning for obtaining the density evolution.

At longer times, the diode relaxes toward equilibrium as carriers move back across the junction to recombine. Analysis of images for all regions (fig. S11) indicates that the relaxation toward equilibrium occurs more quickly at higher fluences. In fact, at 0.16 mJ/cm2 fluence, the decays essentially plateau within the experimental time scale of 3.32 ns. The transients suggest that the recombination dynamics are influenced by the number of displaced carriers; specifically, as the system is removed further from equilibrium at larger fluences, recombination is increasingly facilitated. Moreover, the high spatial resolution of SUEM provides a range of apparent dynamics throughout the illuminated region due to the spatial profile of the laser pulse; carriers near the center of the laser profile, where the local fluence is highest, recombine more quickly than regions farther away.

The rapid transport of carriers over tens of micrometers in only ~80 ps is not expected from the conventional drift-diffusion model. According to such a model, carrier drift occurs only within the depletion layer, where the intrinsic electric field is nonzero. The longitudinal diffusion coefficient of electrons in silicon as a function of electric field strength (at 300 K) has been measured (9) and ranges from 10 to 30 cm2/s. It follows that such values for a 50-μm distance will yield dynamics on the microsecond time scale, contrary to our observation. Furthermore, the involvement of lattice phonons at a velocity of 103 m/s cannot account for the observed picosecond time scale behavior. For these reasons, we have developed the following model, illustrated in Fig. 3, A and D, which accounts for the observed results.

Fig. 3 Theoretical modeling of carrier separation and transport.

Shown are the behaviors of isotropically expanding electrons (red) and holes (blue) after the excitation in (A) p-type and (D) n-type; the arrows represent the initial (x) velocity directions. In both layers, the minority carriers are able to cross the junction, whereas the majority carriers are reflected by the junction. This results in net charge separation represented in the figure by the shaded regions. Calculated also are the (B) electron and (C) hole densities originated in p-type and the (E) electron and (F) hole densities originated in n-type. All density calculations reflect the behavior after +20 ps of propagation time. These calculations show the extent of carrier expansion in space and at different times. The scale of the normalized density shown (0 to 2 × 10−4) when multiplied by Np, which is 109 e-h pairs, gives the actual density.

The excitation of the junction with 2.41 eV photons results in carriers with excess energy equivalent to a temperature of ~104 K. In the model, the important point is that these carriers move ballistically at a relatively high speed, on the order of 106 m/s, and on the picosecond time scale the lattice phonons cannot fully quench such motion. In the supplementary materials, we consider the influence of the lattice, which drains the energy (and reduces the speed) as a function of time. It is shown that, even for electron-lattice interaction times on the order of 10 ps, the observed carrier behavior is robust. The initial excited carrier population follows the laser profile. With the junction placed at Embedded Image in the surface (x-y) plane, the initial e-h pair density is determined for p-type (Embedded Image) and n-type (Embedded Image) and takes on a Gaussian profile (see the supplementary materials). The velocities of motion in the x-y plane can similarly be expressed for a given temperature and for the subpicosecond equilibrated carriers.

As shown in the supplementary materials, the initial density profile at t = 0 moves (x – vt) with velocity v. By integrating over all velocities of the product of density and the Maxwell-Boltzmann velocity distribution, and considering the carrier density asymmetry at the interface, we can express the spatiotemporal evolution of the density in the x-y plane. For p-type, we haveEmbedded Image (1)Embedded Image (2)where Np is the total number of photoexcited e-h pairs; σ is the RMS half-width of the laser focus; ve and vh are the average thermal velocities of electrons and holes, respectively; and η(–x) is the Heaviside step function. Similar analysis for n-type is presented in the supplementary materials.

Figure 3 displays the density distributions in space as a snapshot at t = +20 ps; adding up the distributions for carriers originating in p-type (Fig. 3, B and C) and n-type (Fig. 3, E and F) affords the net carrier density. The net electron (red) and hole (blue) densities at t = +20 ps (from Eqs. 1 and 2) in Fig. 3, A and D, are shown as dotted curves. Taking p-type as an example, electrons with initial velocity toward the junction are transported to n-type, whereas holes moving toward the junction face an impassable barrier. This gating behavior is illustrated in Fig. 3A (charges initially from p-type) and Fig. 3D (charges initially from n-type). The net charge separation leads to localization of electrons on one side and holes on the other, shown as shaded regions. This creates a long-range electric field, the potential of which is given in Fig. 4.

Fig. 4 Comparison between experiment and theory.

Shown are comparisons between experimental charge density and electric potential and those predicted by the theoretical model following transport. (A) The net theoretical charge density at +20 ps (the asymmetry of excitation is included). The presence of long-range transport, up to tens of micrometers, is evident. The scale of the normalized density shown (–0.16 × 10−5 to 4.1 × 10−5) when multiplied by Np, which is 109 e-h pairs, gives the actual density. (B) The landscape calculated directly from the Coulomb interactions between separated carriers. The dynamic potential (due to net charge localization) reaches more than 300 meV, which is of the same order of magnitude as the junction potential (0.79 eV). This influences charge localization and carrier recombination. (C) Experimental contrast image of the junction that mirrors charge densities in n-type and p-type after charge separation. (D) The dynamic potential map calculated directly from the experimental data after charge separation by considering each pixel of the net electrons and holes corresponding to bright and dark contrast and calculating the Coulomb potential. The apparent tilt in the figure is due to the inclined angle of the incident laser beam, which is about 15° with respect to the junction.

The sum of these four images, weighted to reflect the increased absorption in p-type, is presented in Fig. 4A. The figure depicts the long-range separation of carriers in agreement with the experimental observations. Separation due to the gating effect creates a net carrier distribution localized across the junction. The resultant Coulomb interactions distort the electric potential landscape as illustrated in Fig. 4B. For comparison, we present an experimental contrast image (Fig. 4C), which mirrors the net carrier distribution, and a potential map (Fig. 4D) calculated directly from the experimental data. Comparison between simulation and experiment shows agreement on the spatial extent of the distortions; this agreement validates the ballistic expansion of carriers as the underlying mechanism. The resulting electric potential, which opposes the intrinsic built-in junction potential, acts as spatiotemporally isolated “forward bias.” At high fluences, this distortion induces a larger restoring force, which explains the fluence-dependent recombination rates observed in fig. S11.

Four-dimensional space-time imaging of carrier dynamics at interfaces, using SUEM, has the potential of unraveling in other complex structures the mechanism of charge transport, with ultrafast time resolution and nanometer-scale scanning capability. The unexpected ballistic carrier velocity (toward the junction) and the gated localization of charges (at the junction) are not predicted by the widely accepted drift-diffusion model, and these features may be characteristics of other materials when examined with the spatiotemporal resolutions of SUEM. At interfaces, the created transient density and electric field are dependent on the optical excitation, and it should be possible to control the properties of nano-to-micrometer–scale heterojunctions using the temporal, spatial, and pulse-shape characteristics of applied light fields.

Supplementary Materials

www.sciencemag.org/content/347/6218/164/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S11

Movies S1 to S3

References (2024)

References and Notes

  1. Acknowledgments: This work was supported by NSF grant DMR-0964886 and Air Force Office of Scientific Research grant FA9550-11-1-0055 in the Physical Biology Center for Ultrafast Science and Technology at California Institute of Technology, which is supported by the Gordon and Betty Moore Foundation.
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