Observation of a depletion region surrounding metal electrode
on an n-type modulation-doped quantum well
Toshiyuki Ihara1, Hidefumi Akiyama1, Loren N. Pfeiffer2, and Ken W. West2
1
Institute for Solid State Physics, University of Tokyo and CREST, JST, Chiba 2778581, Japan
2
Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, USA
Abstract. We measured low-temperature micro-PL image of dilute two-dimensional electron gas (2DEG) in an n-type
modulation-doped quantum well. We found that annealing of conventional metals, such as Indium and AuGeNi, results
in a formation of depletion region of 2DEG surrounding metal electrode. The difficulty of realization of ohmic contact to
the dilute 2DEG is probably due to the formation of a depletion region separating the metal electrode and 2DEG.
Fabrication of ohmic contact to the electron gas
formed in semiconductor quantum structures is
important for both fundamental and applied physics [1].
In particular, realization of ohmic contact to the twodimensional electron gas (2DEG) in the n-type
modulation doped quantum well is absolutely essential
for the investigation of 2DEG physics at low
temperature [2,3]. One of the contact fabrication
methods is thermal annealing of metal on the top
surface of the sample, as shown in Fig. 1(a). AuGeNi
and Indium are generally used. This method is valid for
high-density 2DEG. For low-density 2DEG, however,
it is difficult to form ohmic contact by this metal
annealing method. As shown in Fig. 1(b), the current
voltage characteristics often exhibits insulating or nonohmic curve at 5K.
Since transport measurement shows all averaged
information, it has not been understood what causes
this problem of difficulty of ohmic contact formation to
the dilute 2DEG. On the contrary, optical measurement
can provide spatially and energetically resolved spectra
of 2DEG. In particular, it has been reported that the
PL-imaging method can be used to make a map of
spatial distribution of 2DEG [4-6]. To the best of our
knowledge, no one has tried to invest the contact
problem of the dilute 2DEG by PL-imaging method.
In this work, we explore to find the origin of the
difficulty of contact problem for the dilute 2DEG by
optical measurements. We measured 2D PL images of
an n-type modulation doped quantum well at 5K
around metal electrode. We found that annealing of
conventional metals, such as Indium and AuGeNi,
results in a formation of depletion region of 2DEG
surrounding metal electrode. In the case of Indium
electrode, we observed a depletion region with a width
of 20 m, which completely separates the 2DEG and
the Indium electrode. In the case of AuGeNi electrode,
the width of the depletion region D is rather small (<
10 m).
Figure 1(a) shows the sample structure grown by
molecular-beam epitaxy, which is consisted of the
following layers grown on a non-doped 001 GaAs
FIG. 1. (a) Sample structure and the geometry of
micro-PL measurement. (b) Typical current-voltage
characteristics at 5K for Indium and AuGeNi
electrode.
substrate: 1-m (GaAs)9 (Al0.33Ga0.67As)71 super-lattice,
6.3 nm GaAs quantum well, 20 nm Al0.33Ga0.67As
spacer, 1x1011 cm-2 Si delta-doping, 450 nm
(GaAs)9(Al0.33Ga0.67As)71 super-lattice, and a 30nm
GaAs cap layer. The electron density was estimated to
be 3 x 1010 cm-2 by Hall measurement at 5 K. On the
top surface of different pieces of the sample, we
fabricated two kinds of metal electrode, Indium and
AuGeNi, and annealed for 30 minutes at 450 C. When
we use Indium, no current was observed at 5 K, as
shown in Fig 1(b). In the case of AuGeNi, it exhibits
non-ohmic curve.
In our micro-PL measurements, we excite the sample
with a cw titanium-sapphire laser in a back-scattering
geometry shown in Fig. 1 (a). The point excitation with
intensity of 40 W and photon energy of 1.612 eV was
focused into 0.8 m. The sample was cooled to liquid
Helium temperature in a cryostat. The position of the
sample was controlled by an automatic stage, which
enabled us to measure 2D PL images.
Figure 2 (a) shows scanning micro-PL spectra
measured in 2 m steps for 100 m in the vertical
direction to the Indium electrode boundary at 0 m. At
80 m, we observed a single peak (Y) at 1.589 eV,
which dominates the PL spectra above 60 m. Below
FIG. 2. (a) Scanning PL spectra measured in 2 m
steps for 100 m to the vertical direction of the
Indium electrode boundary at 0 m. (b) PL and
corresponding PLE spectra at the position of 80, 60,
48 and 20 m. ML peak corresponds to the absorption
of one-monolayer thinner quantum well.
60 m, Y peak loses its intensity and another peak (X)
appears at 1.591 eV. Between 48 m and 0 m, X peak
dominates the PL spectra. Below 0 m, we observed no
PL signal, since there is Indium electrode.
We assigned Y and X peaks to the charged excitons
and the neutral excitons, respectively. The negatively
charged excitons are the bound states of two electrons
and a hole, which appears in the PL spectra in the
presence of dilute electron gas [7]. The neutral excitons
are the bound states of an electron and a hole, which
appear in non-doped quantum wells. We verified these
assignments by measurements of photoluminescenceexcitation (PLE) spectra. Figure 2 (b) shows PL (solid
lines) and corresponding PLE (dotted lines) spectra at
the positions of 80, 60, 48 and 20 m. At 80 m, the
PLE spectrum shows a typical double peak structure at
1 and 2. At 60 m, the 2 peak shows red shifts,
while 1 peak stays at the same energy. At 48 m, the
 peak loses its intensity and the 2 peak exhibits an
asymmetrical lineshape. At 20 m, the 1 peak
disappeared and the 2 peak becomes symmetrical
peak at the same energy of excitons (X) in the PL.
These spectral evolutions are analogous to the results
for a variable-density 2D electron gas in n-type doped
quantum wells reported by other groups [8-10]. This
supports our interpretations of Y and X peaks to the
charged excitons and the neutral excitons.
Appearance of charged exciton in the spectra
indicates the presence of dilute 2DEG in the quantum
well [4-6]. Thus, the observation of Y peak above 60
m represents the 2DEG in that region far from Indium
electrode. Apparently, this 2DEG is formed by the
modulation doping of Si along the quantum well. On
the contrary, we observed neutral excitons between 0
and 40 m. This indicates that 2DEG is not formed in
this region. There is a depletion region of 2DEG near
FIG. 3. PL-image probed by the intensity of (a) Y
peak and (b) X peak near Indium electrode. Region A,
D and M corresponds to 2DEG, depletion region and
metal electrode, respectively.
Indium electrode.
Now we want to demonstrate that this depletion
region surrounds the whole Indium electrode showing
the results of 2D PL-image measurement. Figure 3(a)
shows 2D PL-image probed by the intensity of Y peak
near Indium electrode. Spatial resolution is 2m and
the image size is 100 x 100 m. Three clear regions
denoted by A, D and M were observed. At the position
in the region A, we observed strong Y emission, which
represents the formation of 2DEG. In the region M, no
PL signal appeared due to the Indium electrode. In the
region D, we observed weak Y emission indicating
depletion of 2DEG. This depletion region completely
separates the 2DEG in region A and Indium electrode
(M). We guess this depletion region surrounding metal
electrode is the origin of insulating character shown in
Fig. 1(b) for Indium electrode.
As to the region D, a more clear PL-image can be
obtained by plotting of X peak intensity, as shown in
Fig. 3(b). The X emission is apparently strong in the
region D. The width of this region D is almost constant
(20 m). This width is quite large compared to the
scale of the quantum well width of 6 nm.
We also measured PL-image of 2DEG near AuGeNi
electrode. Figure 4(a) shows PL-image probed by the
intensity of Y peak near AuGeNi electrode. Spatial
resolution is 2m and the image size is 100 x 100 m.
Four regions denoted by A, B, D and M were observed.
Region A with strong Y emission corresponds to 2DEG
formed by Si modulation doping. Region M with no PL
FIG. 4. PL-image probed by the intensity of (a) Y
peak and (b) X peak near AuGeNi electrode. Region
D corresponds to 2DEG probably resulted from Ge.
signal corresponds to the Au electrode.
In the region of B and D, we observed characteristic
feature. Strong Y emission was observed in the region
B near the Au electrode. In other words, the depletion
region D is sandwiched between 2DEG in the region A
and B. Figure 4(b) shows PL-image probed by X peak
intensities. Strong X emission in the depletion region D
was observed between region A and B. Due to the
formation of 2DEG in the B region near AuGeNi
electrode, the width of the depletion region D is rather
small (< 10 m) compared to the case of Indium
electrode.
We want to focus to the area in the circles in Fig.
4(a) and (b). In this area, the width of depletion region
is almost zero. In other words, the depletion region
does not separate the 2DEG in region A and B. We
guess that current can transport using this channel. This
interpretation can explain the current-voltage character
shown in the Fig. 1(b) for AuGeNi electrode.
Note that 2DEG in the region B was observed only
for the AuGeNi electrode, not for Indium. We guess
this is because Ge works as donor so that 2DEG
appears near the AuGeNi electrode. We have not tried
other kinds of metal such as InSn. This is one of the
subjects of future investigation. Dependence of
quantum well width, spacer width, doping density,
anneal temperature and time are also subjects of future
study.
In summary, we measured PL-image of dilute 2DEG
and found that the annealing of conventional metals
results in a formation of depletion region surrounding
metal electrode. In the case of Indium, the width of the
depletion region is almost 20 m, which completely
separates the 2DEG and the Indium electrode. In the
case of AuGeNi, the width of the depletion region is
rather small (< 10 m). The difficulty of realization of
ohmic contact to the dilute 2DEG is probably due to
the formation of a depletion region separating the metal
electrode and 2DEG.
This work was partly supported by a Grant-in-Aid
from the Ministry of Education, Culture, Sports,
Science, and Technology (MEXT), Japan.
[1] S. M. Sze, Physics of Semiconductor Devices (WileyInterscience, New York, 1981)
[2] D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev.
Lett. 48, 1559 (1982).
[3] T. Chakraborty and P. Pietilainen, The Fractional
Quantum Hall Effect (Springer-Verlag, New York, 1988).
[4] G. Eytan, Y. Yayon, M. Rappaport, H. Shtrikman, and I.
Bar-Joseph, Phys. Rev. Lett. 81, 1666 (1998).
[5] K. Matsuda, T. Saiki, S. Nomura and Y. Aoyagi,
Nanotechnology 15, S345 (2004).
[6] A. Esser, Y. Yayon, I. Bar-Joseph, Phys. Status Solidi B
234, 266 (2002).
[7] K. Kheng, R. T. Cox, Merle Y. d’ Aubigné, Franck
Bassani, K. Saminadayar, and S. Tatarenko, Phys. Rev. Lett.
71, 1752 (1993).
[8] V. Huard, R. T. Cox, and K. Saminadayar, A. Arnoult,
and S. Tatarenko, Phys. Rev. Lett. 84, 187 (1999).
[9] G. Yusa, H. Shtrikman, and I. Bar-Joseph, Phys. Rev. B
62, 15390 (2000).
[10] R. Kaur, A. J. Shields, J. L. Osborne, M. Y. Simmons, D.
A. Ritche, and M. Pepper, Phys. Status Solidi B 178, 465
(2000).