PRL 98, 026802 (2007)

PHYSICAL REVIEW LETTERS

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Microscopic Basis for the Mechanism of Carrier Dynamics in an Operating p-n Junction
Examined by Using Light-Modulated Scanning Tunneling Spectroscopy
Shoji Yoshida, Yuya Kanitani, Ryuji Oshima, Yoshitaka Okada, Osamu Takeuchi, and Hidemi Shigekawa*
Institute of Applied Physics, CREST-JST, 21st COE, University of Tsukuba, Tsukuba 305-8573 Japan(Received 7 July 2006; published 10 January 2007)
The doping characteristics and carrier transport in a GaAs p-n junction were visualized with a 10 nm
spatial resolution, using light-modulated scanning tunneling spectroscopy. The dynamics of minority
carriers under operating conditions, such as recombination, diffusion, and electric field induced drift,
which had previously been analyzed on the basis of empirical electric properties, were successfully
examined on the nanoscale. These results provide a solid basis for elucidating the mechanism of thecarrier transport properties predicted by using the macroscopic analysis.
DOI: 10.1103/PhysRevLett.98.026802

PACS numbers: 87.64.Dz, 73.40.Kp, 73.43.Fj

The dynamics of the doped minor carriers plays anessential role in the functional materials and devices.
With the miniaturization of semiconductor devices, forexample, the difference in such electronic properties ofeach element has an evermore crucial influence on macroscopic functions. However, the electronic properties havebeen, in general, analyzed using the macroscopic behavior
obtained by the data averaged over the operating area.
Thus, direct observation of the characteristics, which provides us with the basis of the results of the macroscopic
analysis, is of great importance and there has been agrowing desire to obtain nanoscale characterization techniques to probe various electrical properties in semiconductor devices. For this purpose, advanced microscopy,
which enables us to investigate nanoscale electrostatic
potential distributions and doping profiles, has been developed [1– 4]. However, the measurement of carrier transport
in operating devices has rarely been performed [5,6] inspite of its fundamental and practical importance.
In this Letter, we present the results of real-space mapping of the doping characteristics and carrier transport inan operating semiconductor device, a GaAs p-n junction,using light-modulated scanning tunneling spectroscopy(LM-STS) [7]. The characteristics of the minority-carrier
flow into the neutral region were successfully visualized,
providing the solid basis for elucidating the mechanism of
the carrier transport properties predicted by using themacroscopic analysis.
LM-STS was employed to measure the surface photovoltage (SPV) of a semiconductor material below thescanning tunneling microscopy (STM) tip. SPV is definedas the change in the surface potential of the semiconductormaterial induced by super-band-gap illumination[Fig. 1(c)], which provides information about the polarityand magnitude of the surface band bending under the dark
condition [8,9]. In STM measurement, since the bias voltage applied between the tip and the sample modifies theamount of surface band bending, the obtained SPV includes bias-dependent characteristics [10]. This phenomenon is called tip-induced band bending (TIBB), the value
0031-9007=07=98(2)=026802(4)of which is governed by the doping characteristics [11] andthe dynamical behavior of the excess carriers injected, forexample, by the external bias voltage and optical excitations. By taking advantage of these characteristics, wequantitatively determined the doping profile across a p-njunction interface with a 10 nm resolution, and succeeded in examining the minority-carrier dynamics on
the nanoscale under an operating condition.
The experimental setup is illustrated in Fig. 1(a). A p-njunction was prepared by growing n-(Si-doped, 2:0 1018 cm3 , 500 nm) and p-type (Be-doped, 2:0 1018 cm3 , 500 nm) GaAs layers on an n -GaAs(001)

FIG. 1 (color). (a) Experimental setup. (b) I-V curve (left axis)
and SPV spectrum (right axis) obtained on the n-type area (setpoint: VS  3:0 V, I  0:10 nA). (c) 1D energy diagrams ofthe tunnel junction for an n-type semiconductor with a positive
sample bias voltage under dark (left) and illuminated (right)
conditions. When electron (blue circles)-hole (red circles) pairs
are produced by super-band-gap illumination, holes flow towards
the surface due to the electric field affecting the area, resulting in
the reduction of band bending. (d) Light-intensity dependence of
SPV measured on an n-type area (VS  2:5 V).

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PHYSICAL REVIEW LETTERS

substrate (Si-doped, 8:3  1018 cm3 ) using molecularbeam epitaxy [12]. Au-Zn Ohmic-contact electrodes wereformed on both sides of the samples. LM-STS measurements were performed on a cleaved clean (110) surface atroom temperature in ultrahigh-vacuum (<1  108 Pa).
Mechanically chopped illumination from a laser diode(635 nm, 100 Hz), 60 off-normal to the surface, was focused onto the tunnel junction area with a spot diameter of
0.02 mm. A tungsten STM tip was used for measurement.
Figure 1(b) shows a typical current-voltage spectrum(I-V curve) acquired on the n-type area. Here, both theelectrodes were shorted, and sample bias voltage VS wasapplied via the two electrodes, as shown in Fig. 1(a) (STM
tip is grounded). For the positive-sample-bias-voltage region, the tunneling current oscillates due to the chopped
laser illumination, and the two virtual I-V curves, whichcorrespond to those under dark (blue) and illuminated (red)conditions, can be simultaneously obtained. The SPV spectrum (green circles) is obtained by calculating the lateralshift of the two I-V curves with respect to the bias voltage
for the I-V curve under the dark condition. The central partof the spectrum with the tunneling current below 3 pA is
missing due to the difficulty in calculating the shift of thetwo I-V curves in that region.
Since the GaAs(110) surface has no surface state
within the bulk band gap, TIBB easily occurs for the
positive VS . In contrast, for the negative sample bias voltage condition, the SPV is small because the Fermi level isclose to the valence band edge, as shown in the onedimensional (1D) energy diagram of the tunneling junction, which has a metal-insulator-semiconductor (MIS)

FIG. 2 (color). (a) SPV mapping at VS  2:5 V (1000 nm 1000 nm, 80lateral  20vertical LM-STS spectra). (b) A plotof the cross-section along the blue line marked in (a). (c), (d) are
SPV mappings of the same area at VS  2:5 V and VS 
2:5 V, respectively (500 nm  500 nm, 67  17 LM-STS
spectra). (e) Cross sections of the SPV images along the redlines in (c)—red dots, (d)—blue dots. Green bar represents thespace charge region (SCR) at the interface. (f) SPV spectra
obtained by averaging all data in each region (blue: n-type
region, green: space charge region, red: p-type region).

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structure [Fig. 1(c)]. For the measurement on the p-type
area, the opposite bias dependence occurs.
In order to obtain the flat band condition during photoillumination, we illuminated the sample with light of theintensity indicated by the dashed line in Fig. 1(d). By
making the light spot small, the thermal expansion [9]effect was reduced, which was ascertained by confirmingthat there was no photoresponse in the tunneling current on
the n-type area under the negative VS , where no SPV is
expected as mentioned earlier. Under these conditions, themeasured SPV is equivalent to the amount of TIBB existing under the dark condition.
Spatially resolved LM-STS measurements were performed simultaneously with topographic imaging. The
feedback loop of STM was opened at equally spaced
measurement points during topographic imaging to fix
the tip position and an I-V curve was acquired underchopped light at each point. As explained using Fig. 1(b),the SPV was calculated from the I-V curves for the chosenbias voltages and shown with a color scale in Figs. 2(a),2(c), 2(d), and 3(b).
Before demonstrating the visualized carrier dynamics
under operating conditions, we first show the potential ofthis method by presenting the results obtained under the

FIG. 3 (color). (a) Experimental setup. (b) A series of SPV
mappings as a function of the applied forward-bias voltage(KS  2:5 V). (c) A current-voltage relation macroscopicallyobtained for the p-n junction. (d) (upper) Band diagram of a p-njunction with the distribution of minority electrons (blue circles)
and holes (red circles) under a forward-biased voltage condition.
Fh and Fe denote the Fermi levels for holes and electrons;(lower) 1D band diagrams of the STM tunnel junction with
the STM tip placed at the positions indicated by the two green
dashed lines. (e) Cross sections of SPV images in (b) across theinterface of the p-n junction.

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PHYSICAL REVIEW LETTERS

static condition. Figure 2(a) shows an SPV image of VS 
2:5 V, obtained over a 1000 nm  1000 nm area that
includes n -, n-, and p-type layers, as indicated inFig. 2(b). Since TIBB under positive VS is large (negligible) for the n-type (p-type) region, the change in SPV
across the p-n junction is clear. Furthermore, the difference in the SPV between n - and n-type layers due to thedifference in the dopant concentration is also clear. A line
profile of the blue line in Fig. 2(a) is plotted in Fig. 2(b),where the averaged values of SPV are 0.50 V for then -GaAs region and 0.85 V for the n-GaAs region, respectively. To examine the validity of these values, we
calculated the electrostatic potential beneath the STM tip
in the three-dimensional geometry, assuming a parabolic
tip [11,13]. The calculated values are 0.58 and 0.82 V forn -GaAs and n-GaAs, respectively, which are in excellent
agreement with the values obtained experimentally.
Figures 2(c) and 2(d) are the SPV images obtained at the
p-n junction interface with positive [(c) 2:5 V] andnegative [(d) 2:5 V] VS , respectively. The SPV in thespace charge region (p-n junction interface) is almost zeroas shown using the line profiles of these SPV images inFig. 2(e). Zero SPV in the space charge region appears to
be anomalous because TIBB should be induced under bothpolarities of the VS at the p-n interface [14].
In general, the electric field between the tip and thesemiconductor surface modifies the electrostatic potential
in the semiconductor sample. Because of the modified
potential field, photoexcited carriers drift and accumulate
on the sample surface beneath the STM tip, resulting in
nonequilibrium carrier distribution that reduces the electrostatic potential field. However, in the space charge region, photoexcited carriers flow across the area due to thebuilt-in electric field formed by the p-n junction and do notaccumulate under the STM tip, resulting in the observed
zero SPV. The SPV spectra obtained at different sample
bias voltages were averaged in each area and summarized
in Fig. 2(f). The difference between SPV spectra of thethree different areas is clear, and the SPV spectrum for the
space charge region is zero for all sample bias voltages.
By taking advantage of the above phenomenon, we canidentify the position of the space charge region [green bar
in Fig. 2(e)]. The experimental value of the width is 50 nm,
which is in good agreement with the calculated value,
45 nm [15]. As has been seen, nanoscale characteristicsof the local band structure of the semiconductor material
can be quantitatively determined using LM-STS.
Now, we employed this method to examine the mechanism of the carrier transport properties, of which a prediction was made from the results of the macroscopic scale forthis sample. The relationship between the p-n diode current IF and the forward-bias voltage VF determined fromthe macroscopic current-voltage characteristics is expressed as


qVF
(1)
IF expkT

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(q: electronic charge, k: Boltzmann constant, T: temperature, : ideality factor).
There are four different voltage regions, as indicated by
the linear fits of the curve with different values of , asshown in Fig. 3(c). The mechanism that explains each of
the four regions was introduced as related to the characteristics of the minority-carrier diffusion properties [16] asfollows: (1)   2 (VF : 0 – 0.4 V, blue line) Recombination
region: minority carriers mostly recombine in the spacecharge area. (2)   1 (VF : 0.4 – 0.6 V, green line) Ideal
diffusion region: minority carriers start to diffuse into theneutral area. (3)   2 (VF : 0.6 – 0.8 V, orange line) High
injection region: injected-minority-carrier density becomes comparable to the majority-carrier density.
(4)   2 (VF : 0.8 V–, red arrow) Series resistance region:
minority-carrier diffusion length apparently becomes longer than those in (2) and (3), because of the electric field by
the VF leaked into the neutral n- and p-type areas.
Although Eq. (1) is the important basis in the analysis ofsemiconductor devices, the mechanism was characterizedfrom the empirically obtained results, that is, macroscopic
current-voltage relationship as shown in Fig. 3(c).
Figures 3(b) are a series of SPV mappings obtained at
the p-n junction with different forward-bias voltages.
Here, the additional bias voltage, VF , was applied to thesample via the n - and p-side electrodes, as illustrated inFig. 3(a). Since the VS is positive (  2:5 V), the SPV islarge for the n-type area. When VF is zero, the SPV imageis the same as that shown in Fig. 2(c), as expected.
However, when the VF is applied, the SPV in the vicinityof the interface is reduced with increasing VF . Since thedecrease in SPV is related to the decrease in TIBB that iscaused by the screening of the electrostatic field below the
STM tip, the observed change is directly related to thechange in the amount of the excess carriers below the STM
tip. This is due to the injection of minority holes into then-type neutral region, as illustrated in Fig. 3(d).
As seen in Fig. 3(b), the SPV image at 0.4 V is similar tothat at 0 V, because only a small number of minority
carriers diffused into the neutral n-type area in the recombination region (0.4 V). In contrast, the SPVat the interface
began to decrease in the ideal diffusion region (0.5 and
0.6 V), and this decrease became prominent in the highinjection region (0:7 V  ), as predicted. This is the first
demonstration of the direct visual observation of carriertransport in a p-n junction.
Let us look into the details of the minority-carrier diffusion. The variation of SPV with VF at a point x, depending on the excess minority-carrier density ex  x; VF ,is generally expressed in a simple logarithmic relationshipofSPV  C lnex =0 ;(2)where C is a constant needed for the conversion of unitsand 0 is an arbitrary carrier density used for normalization[8]. The excess minority-carrier density as a function of the026802-3

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PHYSICAL REVIEW LETTERS

distance from the p-n junction interface is expressed asex  x0 ; VF  exp x  x0 =Lp ;(3)

where x0 is the location of the boundary between theneutral region and the space charge region in the n-typelayer and Lp is the diffusion length of the minority hole inthe direction perpendicular to the interface [17]. By substituting ex in Eq. (3) into Eq. (2), we obtain the variationof SPV as a function of the distance and the minoritycarrier density asx  x0 x0 ; VF 
SPV  C 
 ln
:
Lp
0

(4)

Experimental results can be analyzed using Eq. (4).
Figure 3(e) shows the cross-sectional profiles of the SPV
images in Fig. 3(b). The SPV varies almost linearly withthe distance from the interface and shifts vertically with anincrease in the minority-carrier injection rate as expectedfrom Eq. (4). To obtain LP , we estimated the value of C
using Eq. (2) [17] and analyzed the slopes of the crosssection profiles of SPV by linear fitting [color lines inFig. 3(e)]. The values of LP obtained with different
forward-bias voltages are listed in Table I. LP is insensitive
to the VF up to the high injection region 0:7 V), while anextension of LP is clear for the series resistance region(0:8 V ). In the series resistance region, as the nameindicates, the series resistances formed by the neutral nand p-type regions become comparable to that of the spacecharge region due to the significant reduction of the built-in
potential. Therefore, the voltage drops within the n-type
region; hence, the electric field appearing in the region
induces the drift of minority holes in its direction, resulting
in the apparent extension of LP [16].
Since hole mobility at 300 K is phonon limited, themaximum diffusion length LP in the Si-doped n-GaAs
sample with the same doping concentration [18] is400 nm, and decreases with the influence, for example,of the distribution of dopants and defects. The obtained
values with the VF below 0.7 V (up to the high injection
region) are consistent with the prediction.
In conclusion, the doping characteristics and carriertransport in a GaAs p-n junction were visualized with a
TABLE I. Minority-hole diffusion length Lp obtained from the
SPV measurement [Fig. 3(e)].
Forward-bias voltage (V)
0.5
0.6
0.7
0.8
0.9

Hole diffusion length (nm)
181
183
180
222
429

28
15
9
12
32

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10 nm spatial resolution, using LM-STS. The empirically obtained I-V characteristic properties were successfully examined, for the first time, on the nanoscale. These
results provide a solid basis for elucidating the mechanismof the carrier transport properties predicted by using themacroscopic analysis. Combining this visualization
method with the atomic-scale structural analyses will offer
further insight into the behavior of semiconductor devices
under operating conditions.
This work was supported in part by a Grant-in-Aid forscientific research from the Ministry of Education, Culture,
Sports, Science, and Technology of Japan. We thank Ms.
Rie Yamashita, in our group at University of Tsukuba, for
her help in preparing this Letter.

*Electronic address: http://dora.bk.tsukuba.ac.jp/[1] W. D. Rau, P. Schwander, F. H. Baumann, W. Hoppner,and A. Ourmazd, Phys. Rev. Lett. 82, 2614 (1999).
[2] V. V. Zavyalov, J. S. McMurray, and C. C. Williams,
J. Appl. Phys. 85, 7774 (1999).
[3] R. Shikler, T. Meoded, N. Fried, and Y. Rosenwaks, Appl.
Phys. Lett. 74, 2972 (1999).
[4] N. Duhayon et al., J. Vac. Sci. Technol. B 22, 385 (2004).
[5] D. Ban, E. H. Sargent, S. Dixon-Warren, IEEE J. Quantum
Electron. 40, 865 (2004).
[6] M. A. Topinka et al., Nature (London) 410, 183 (2001).
[7] O. Takeuchi, S. Yoshida, and H. Shigekawa, Appl. Phys.
Lett. 84, 3645 (2004).
[8] L. Kronik and Y. Shapira, Surf. Sci. Rep. 37, 1 (1999).
[9] S. Grafström, J. Appl. Phys. 91, 1717 (2002).
[10] M. McEllistrem, G. Haase, D. Chen, R. J. Hamers, Phys.
Rev. Lett. 70, 2471 (1993).
[11] R. M. Feenstra, J. Vac. Sci. Technol. B 21, 2080 (2003).
[12] Dopant concentration of each layer is confirmed by secondary ion mass spectrometer (SIMS).
[13] Calculations were performed using the SEMITIP program,developed by R. M. Feenstra [11]. Parameters used: work
function of W tip  4:6 eV, applied bias voltage 2:5 V, radius of tip  20 nm, tip-sample distance 
1 nm, T  300 K, tip shank opening angle   90.
[14] N. D. Jäger et al., Phys. Rev. B 67, 165307 (2003).
[15] The width of the space chargeqregion
W was calculated
2"s NA ND
using the equation [16] W  q NA ND Vbi , where NA
and ND are acceptor and donor doping densities, respectively. "s is the dielectric constant of GaAs, and Vbi is thebuilt-in potential of the p-n junction.
[16] S. M. Sze, Physics of Semiconductor Devices (Wiley,
New York, 1981), 2nd ed.
[17] C was derived by subtraction of the two SPV values (0.6 V
and 0.7 V) using Eq. (2): SPVx0 ; 0:7 V 
SPVx0 ; 0:6 V  C ln x0 ; 0:7 V=x0 ; 0:6 V .
Provided that x; VF  is proportional to the macroscopic
p-n diode current with the forward-bias voltage VF , IV ,and x0 ; 0:7 V=x0 ; 0:6 V is equal to I0:7 V =I0:6 V ,these values can be obtained from Fig. 3(c).
[18] B. Sieber, Mater. Sci. Eng. B 24, 35 (1994).

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