Investigation of Parallel Conduction in GaAs/AlxGal

IEEEJOURNAL
OF QUANTUMELECTRONICS,
VOL. QE-22,NO.
9, SEPTEMBER 1986
1753
Investigation of Parallel Conduction in
GaAs/AlxGal- x As Modulation-Doped
Structures in the Quantum Limit
P. KIRK,
AND
P. S. KOBIELA
The modulation doping technique, while
instrumental
in achieving high electron mobilities, is also responsible
for an effect called persistentphotoconductivity(PPC)
[lo]. This effect is characterized by a light-induced conductivity enhancement that persists for longtimes (in some
systems, 2 lo8 s) at low temperatures. The PPC has been
attributed to the excitation of electrons out of deep donorrelated traps in the AlGaAs, known as DX centers, which
suppress recapture due to large lattice relaxation [ 111. In
I. INTRODUCTION
the
GaAs/Al,Ga, -,As system, these excited electrons are
UANTIZEDHallresistanceandthesimultaneous
able
to maintain quasi-equilibrium with the 2DEG layer
zerodiagonalresistancestateoftwo-dimensional
in the GaAs [ 121, forming a parallel conduction path in
carriers is now a well-documented phenomenon in a numthe Al,Gal -,As.
ber of systems [1]-[3]. This phenomenon, occurring at
ThePPC
in GaAs/AlxGal- x As modulation-doped
low temperature and.high magnetic field,is characterized
structures has been utilized by a number of authors [3],
by the experimental fact of the Hall resistance
pxy becom[ 131-[ 151 to modulate the carrier density when studying
ing quantized in units of h/ie2 where h is Planck’s conquantum transport. Although PPC has been studied in the
stant and e is the electronic charge. When pxy takes on
GaAs/Al,GaI -,As system by a number of workers [ 161quantized values of h / e 2 , the diagonal resistivity pxr ap[18] none of these studies has explored the effects of PPC
0. The quantum number i
proaches zero in the limit T
on the behavior of the 2DEG in the quantum limit. Here
is anintegerfor
integral quantization,whichcanbe
we present a detailed study of PPC effects on the quantum
understood within the framework of an independent partransport coefficients in high-mobility
a
GaAs/
ticle picture [4], [5]. The quantum number can also take
Al, Gal - x As modulation-doped structure. The measureon fractional values [6], [7], which is believed to arise
ments are compared to low field values of the transport
fromthecondensationof
the 2D carriers into a highly
coefficients to derive information concerning density, mocorrelated fluid-like ground state [SI.
bility,
and the distribution of carriers
in the 2DEG and
Since the first observation of the integral quantum Hall
parallel
conduction
path.
effect in the two-dimensional electron gas (2DEG) of a
Abstract-We present a detailed study of the transport in GaAsi
Al,Ga, -,As modulation-doped structures in the low field and high
magnetic field quantum limit for varying amounts of parallel conduction in the AlGaAs region. We observe the apparent breakdown of
quantum Hall effect behavior due to low mobility carriers in the parallel channel. The onset of conduction through the parallel channel by
quantum transport measnrments has been observed, along with a nonlinear dose dependence due to photoexcitation.
Q
-+
[ 11, thephenomenon has
Si-MOSFETinversionlayer
been studied in numerous embodiments of 2D carrier systems. The systems that have attracted the most attention
arethecompoundheterojunctionepilayerstructures,
in
particular the GaAs/AlxGal -,As systems [2], due to the
lattice match of the constituents. The perfection of these
heterojunction systemshasallowedtheachievementof
extremely high carrier mobilities by the modulation doping technique [9]. The quantum Hall effect has been seen
in numerous 111-V compound systems and recently in a
11-VI system [ 3 ] .
Manuscript received December 1, 1985; revised March 10, 1986.
M . A. Reed is with the Central Research Laboratories, Texas Instruments, Inc., Dallas, TX 75265.
W. P. Kirk and P. S . Kobiela are with the Department of Physics, Texas
A&M University, College Station, TX 77843.
IEEE Log Number 8609339.
11. THEORY
Let us first consider single carrier conduction for two
parallel media in the absence of any quantum transport
phenomena.Let us also define the media by theindex
i( = 1, 2). Under theinfluence of a mutually perpendicular
electric field E and magnetic field B , we can express the
conductivity tensor for media i as
where ni is the carrier density, e is the electronic charge,
mT is the effective mass, w,, is the cyclotron frequency,
0018-9197/86/0900-1753$01.00 O 1986 IEEE
1754
JOURNAL
IEEE
and ri is the scattering time. For simplicity, we consider
a single relaxation time ri for the carriers in media i .
Now, the toal conductivity of the two-component system can be expressed as a sum of the individual conductivity tensors:
+
r2
NO. OF
QE-22,
ELECTRONICS,
QUANTUM
VOL.
Here, the low-mobility region dominates the resistivity,
whereastheHallresistanceissimply
the sheetcarrier
density.
Let us now consider transportin this systemin the
n2e2
2
2-
9, SEPTEMBER 1986
-wc,r1
1
1
2
+ w:,r:
+
&+
rnf
r1
n1e2
w:,r: rn?
-%72
1
2
+ w i r i rn?
+ 1 + r2w",;
n2e2
__
(2)
rn;~.
The measured quantities ofinterest are usually the comTo understandtheobservation
of the
ponents of the resistivity tensor. These quantities are the quantumlimit.
quantum Hall effect in the 2DEG, let us initially set n2 =
Hall resistivity p and the magnetoresistance pxx.We can
?
0. In a 2DEG that is void of any imperfections, it can be
find these quantities by inverting (2), whereupon
and
To specialize, let us define media 1 as the 2DEG at the
GaAs/Al, Gal - x As heterojunction interface, and media 2
as the Al, Gal -,As. For this situation, we shall assume
that the mobility of the carriers in the 2DEG, y l , is much
greater than the mobility in the parallel conduction path,
shown (by going to the frame of reference cE X BIB2)
that ox, = nec/B, which does not exhibit a quantized density. To explain the experimentalobservationsofthe
quantum Hall effect requires the existence of localized
states in the tailsof each Landau level subband. When the
cc2.
It is convenient to define the low magnetic field and Fermi level resides in these localized states, which cannot
carry any current at T = 0, the remaining extended states
high magnetic field limits of these general expressions.
of the filled Landau levels automatically adjust to carry
At low magnetic field (wcl r 1 and wc2r2 << 1), we have
the entire Hall current. These current-carrying extended
1
Pxx ( 5 ) states cannot scatter dueto their wide separationin energy
nlePl + n2eP2
from any empty states. Thus, thediagonal resistivity vanishes, i.e., pxx = 0. Since the density of these currentand
carrying states does not change with B as long as the Fermi
level resides in the localized states, the carrier density n l
= in where i isthe(integral)number
offilled Landau
subbands whose density n = eB/h. Substituting this into
where we have made the substitution ri = pirn,?le. Both
(S), the Hall resistivity of the 2DEG in the quantum limit
components of the resistivity tensor in the low field limit
is given by
are dominated by the contribution of the high-mobility region.
pxJ, = h/ie2,
(9)
Similarly, in the high field limit (wc,r l and w0r2 >>
which is the quantized resistance in units of 25, 813 0.
l ) , we have
The experimental result is a step structure in the Hall ren1
n2
sistance versus magnetic field or carrierdensity, normally
controlled by a gate voltage. An alternative to gate modulation of carrier density is to photoexcite carriers intothe
2DEG from traps. The concurrent effect of this modulaand
tion technique is the subject of the present investigation.
Let us now consider the presence of a media
(Al,Gal -.As) parallel to the 2DEG. Prior to any pho-
-+-
REED etCONDUCTION
ai.: PARALLEL
IN MODULATION-DOPED
STRUCTURES
1755
duced strain. Low field values of the mobility and carrier
density were measured at T = 1 K, and were found to be
p = 10m2/V s and n = 2.8 X lOI5 mP2, respectively.
The quantum transport measurements were taken between 20 mK and 7.0 K in a dilution refrigerator using a
7.8 T superconducting solenoid to apply magnetic fields
perpendicular to the sample. Temperature measurements
weremadeusinga3Hemeltingcurvethermometer.
Transport measurements were made by pulsing a dc current source and averaging voltages for positive and negative current polarities to eliminate thermal EMF problems. Excitation current amplitudes ranged from10 nA to
5 pA. The pulse sequence consisted of a 650 ms positive
pulse, a 5 ms off period, a 650 ms negative pulse, and a
500 ms settlingperiod.Dependingon
.the temperature
range, the sequence period ranged from5 to 30 s to avoid
any Joule heating of the charge carriers.
Light excitation was made by direct illumination from
a GaAsP/GaAs red LED. Light dose was controlled
by
varying the time the LED was activated by a constant (20
mA) current. Dose quantities reported in this paper refer
to the calculated number of photons arriving at the sample. For our particular experimental configuration, there
wereapproximately 7.8 X 10” photons/s striking the
B
sample surface. The photon dose wasvaried up to an empirically saturated dose value. No attempt has been made
to correct for possible reflection of photons at the sample
surface nor for absorption in the sample; thus, absolute
where the integer i again takes on the appropriate quanintensity figures mustbeviewedcautiously.However,
tized values. These values of the Hall resistivity will derelative dose values reported here were easy to control
viate (specificially, decrease) from thewell-defined quanand are thus highly precise.
tized values upontheonset
of parallel conduction.
IV. RESULTS A N D DISCUSSION
Similarly, we can see from(7) that the diagonalresistivity
will remain vanishingly small in the quantum limit until
QuantumHallresistanceplateauscorresponding
to
carriers populate the parallel conduction band. Thiseffect Landau level filling factors down to i = 2 have been obhas important consequences in the use of quantum Hall
1 showstheHall resisserved in thesestructures.Fig.
effect as a resistance standard or as a method for deter- tance pxy and the diagonal magnetoresistance p.rx at T =
mining the fine structure constant. A high precision mea- 75 mK for a sample cooled under dark conditions and
besurement of p,, simultaneous with the “standard” pxy val- fore anyphotoexcitation by theLEDsource.The
Hall
ues puts a limit on the number of carriers in the parallel plateausagreewiththetheoreticalquantized
values to
conduction path, and thus a limit on the deviation of p x y within the resolution (dynamic range) limitations of
from the standard values.
i = 4plateau, we
theapparatus;specifically,forthe
Q,whereas p,(theohave p,,(experimental) = 645312
111. EXPERIMENTALPROCEDURES
magnetoreretical) = 6453 Q. The minima in the
Thesamples studied weremodulation-dopedGaAs/
sistance could be resolved to within k0.05 Q for p,, valAlo,3Gao,7As heterostructures grown in a Riber 2300 MBE
ues less than 1 Q .
on a Cr-doped GaAs substrate. The epitaxial layers conFig. 2 shows ,oxy as a function of magnetic field as the
sisted of a 1 pm nominally undoped GaAs
buffer layer photoexcitation dose is varied, and Fig. 3 shows p,, as a
followedbya150
Alo,3Gao,7Asspacerlayer and 500 function of magnetic field for the samephoton doses used
of Si-doped Alo,3Gao.7As. The samples were thenfab- in Fig. 2. The measurements were taken sufficiently long
ricated into Hall bridges using standard photolithographic after excitation and at approximately the same time after
techniques.Theminimumchannelwidthused
in these photoexcitation to eliminate possible transient and nonexstudies was 150 pm to exclude any localizationeffects due ponential decay effects of the PPC [ 101. The photon doses
to short channel effects [20]. The samples were mounted
ranged from a minimum of 3.9 X lo9 photons to 2.5 x
onto ceramic flatpacks for lead strain relief.
l O I 3 photons. There was no temperature cycling or temThe samples were cooled slowly ( - 30 h) from room
perature variation between the sets of measurements. We
temperature to low temperature in a light-tight container clearly observe the systematic shift of the quantum Hall
to eliminate residual PPC and to minimize thermally inplateaus (and the accompanying magnetoresistance min-
toexcitation, we shall assume that the Al,Gal -,As is depleted, although it contains deep level complexes known
as DX centers [ 111. Electrons photoexcited from the DX
centers remain in the Al, Ga, -,As conduction band for a
long time because their recapture by theionized donors is
impeded by a microscopic potential barrier. These free
electrons transfer to the 2DEG channel (either by tunneling throughtheinterfacebarrier
or through the ohmic
contacts) and thus add to the 2DEG density [ 161-[18].
However,asthenumber
of photoexcitedcarriers
increases, the effective doping concentration increases [ 161.
As a consequence, the depletion widthsat the surface and
at the heterojunction interface, which are inversely proportional to the effective doping concentration, become
smaller upon photoexcitation. Preliminary investigations
of this effect have been reported [16], [ 191. However, the
transition from a depleted to a conducting barrier region
has not been investigated in detail.
To consider the case of parallel conduction through
this
barrier region, we will assume that media 2 cannot support a2DEG.Substituting
(9) into (8) forthecase of
mixed condunction, we have for theHall resistivity in the
high field and quantum limit
A
1756
JOURNAL
IEEE
OF ELECTRONICS,
QUANTUM
VOL.
NO. QE-22,
9, SEPTEMBER 1986
12.
no light
I
i = 3
x
I
I
I
I
I
0.0
1.0
2.0
3.0
4.0
B
T
I
5.0
=
75 mK
I
I
6.0
7.0
[TI
Fig. 1. (a) Hall resistance versus magnetic field at T = 75 mK for a GaAs/
A1,,,Gan,,As heterojunction with a carrier concentration
of 2.8 X 10"
m-2, cooled in dark conditions and before the application of any photoexcitationtothesample.
Is,, is the source-drain current.(b)Magnetoresistance versus magnetic field for the sample described in (a).
I
12.
I
I
I
I
1
I
T = 75 mK
10.
-5
u
x
8.
6.
h
4.
2.
0.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
B [TI
Fig. 2. Hall resistance versus magnetic field at T = 75 mK for the sample
described in Fig. I after varying amounts of (cumulative) photon dose.
The photondosesare: (a) 0, (b) 3.9 X IO9, (c) 7.8 X IO9, (d) 1.2 X
IO'', (e) 1.6 x IO", ( f ) 3.1 x IO1', (g) 3.9 x IO", (h) 7.8 x IO", (i)
1.6 X I O i 2 , (k) 3.1 X IO", ( I ) 6.2 X lo",(m) 1.3 X lo", (n) 2.5 X
lot3.
ima) toward higher magnetic field as the density of carriers in the 2DEG increases. We observe the full development of some less-developed plateaus that were weak
(i = 5 ) or nonexistent (i = 7) at lower magnetic fields.
The effect is more apparent for the odd-integer plateaus
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
B [TI
Fig. 3. Magnetoresistanceversusmagnetic
field at T = 75 mK for the
sample described in Fig. 1 after varying amounts of (cumulative)
photon
dose The photon doses are: (a) 0. (b) 3.9 X IO9, (c) 7.8 X lo9, (d) 1.2
X lo'', (e) 1.6 X IO", (f) 3.1 X lo",(g)
3.9 X IO", (h) 7.8 X lo",
(i) 1.6 X 10l2, (k) 3.1 X 10l2, ( 1 ) 6.2 X lo", (m) 1.3 X IO", (n) 2.5
x IO".
since the spin energy is smaller than the Landau energy
at these field values. Upon reaching a critical photon dose
( > 7 . 8 X lo"), quantumtransportapparently
breaks
down, and the plateaus deviate from the expected values.
At the same time, the magnetoresistance minima rise significantly above zero.
The density of carriers as a function of light dose was
determined in two ways: by the high field values of the
(n = B/ep,), either by extrapolating
Hallresistance
through the apparent Hall plateau centers or choosing the
value at a single plateau center, and by the periodicity of
the Shubnikov-deHaas (SdH) oscillations
in pxx [i.e., n
= 2e/hA(l/B)]. This is shown in Fig. 4(a). The departure
of these two methods of determining
the carrier density
becomes apparent at a dose of 1.6 x lo", which is the
samedoseatwhichthequantumtransportclearlydeviates.
Referring to (S), we see that the high field Hall resistance method gives the combined carrier density in both
the 2DEG and the Al,Gal - x A s , whereas the oscillations
in pxx are essentially measuring the 2DEG carrier density.
If true, the carrier density determined from the low field
Hall resistance values as predicted from (6) should agree
REED et al.: PARALLELCONDUCTIONINMODULATION-DOPEDSTRUCTURES
19.0 -
-
N
16.0
I
E
I
I
10.0
/..
-
....
*,-.
(a)
-
-N
16.0
-
./'
13.0
-
I
I
I
__--,/-..-.
I
I
I
I
I
I
5.0
u
2
4.0
30
I
I
1
I
I
........
from low fieldlimit
-
from SdH oscillations
I
1 .o
(0 t o 0.3 T)
0
2
I
0
fl
I
I
E
I
.
.
.
.
.
.
I
.
, _ d
19.0 -
0
,z.'
7.0 -
-
-s
__..-_._---
..-.
x
4.0
I
from SdH oscillations
13.0 -
0
I
6.0
-
0
-
I
...... from high field limit (at i = 4)
-
I
-
I
-5
0.7
dl
0.3
Y
10.0
-
7.0
-
(b)
..............
+.
....+......-..
0.0
4.0 0.0
,
I
I
I
I
I
I
I
I
I
I
5.0
10.0
15.0
20.0
25.C
0.0
5.0
10.0
15.0
20.0
25.C
number of photons x 10l2
Fig. 4. (a) Carrier density versus photon dose, determined from SdH oscillations between 0.5 and 1.0 T andtheHallresistanceatthe
i = 4
plateau (thehigh field limit).(b)Carrierdensityversus
photon dose,
determined from SdHoscillationsbetween 0.5 and 1.0 Tandaleast
squares fit of the pxj data between 0 and 0.3 T (the low low field limit).
well with the method using the SdH oscillations
in ,ox,.
The comparison in Fig. 4(b) shows excellent agreement.
It should be noted that magnetic freeze-out
effects [21],
6 T , are not evident since both
which would occur at
the low andthe high field densities are the same [Fig. 4(a)
versus Fig. 4(b)] until the onset of parallel conduction.
Once we have determined the electron distribution
in
the two regions, we can also determine the
mobility of the
electrons in the Al,Gal -,As. Choosing a photon dose of
wehave nl (2DEG) = 5.5 X l O I 5 m-2and
2.5 X
n2 (Al,Gal-,As)
= 7.5 X IOl5 mP2. Using (7) in the
quantum limit, we get p 2 = 0.19 m2/V s. It should be
noted that the condition w , ~>> 1 is not yet completely
satisfied in the Al,Gal -,As since the magnetoresistance
background is stillincreasing, so the mobility may be
slightly higher than this value.
A sensitive test to determine when conduction starts in
the Al, Gal -,As region is to observe the deviations of the
pxy values from the quantized values, as predicted by (8).
Fig. 5(a) shows the values of the i = 4 plateau as a function of photon dose. The onset of parallel conduction is
> 7.8 X 10". We can define the
again clear for a dose
limits of conduction in the Al,Gal -,As by observing the
minima in pxx, as shown in Fig. 5(b). Using the value for
the mobility in the Al,Gal -,As derived above and our
resolution limit of 0.05 Q,the carrier concentration in the
Al,Gal -,As region for photon doses up to 7.8 X 10" is
found from (7) to be < 4 X 10" mW2.Bridge techniques
used by other workers [22] have measured minimum resistances in these regions to be < lop7Q. From this, it is
possible to put an upper limit on the number of carriers
number of photons x 10"
Fig. 5. (a) Hall resistance versus photon dose taken at the i = 4 plateau.
The inset shows an expanded scale between 0 and 2 X IO" photons. (b)
Magnetoresistance versus photon dose taken
at the i = 4 minima. The
insets shows an expanded scale between 0 and 2 -X 10" photons.
o '
I
-
-
2.0
22.0
24.0
26.0
28.0
30.0
In (number of photons)
Fig. 6. Carrier density in the 2DEG determined by Shubnikov-deHaas oscillations versus 111 (photon dose) at 75 mK.
( < 1 X lo5 mP2) in the Al,Gal -,As region if no deviation is observed (in fact, structure at the edges of theHall
plateaus seen in [22], especially pronounced at high photon doses in our present work, could be due to parallel
conduction). Using (lo), this would imply a deviation of
1 part in 2 X lo9 on the quantized Hall resistance values due to parallel conduction.
An area that deserves further attention in this study is
the nonlinear photon dose versus 2DEG carrier
density
behavior that can be seen in Fig. 2. This is replotted and
shown in further detail in Fig. 6. The sharp transition at
a dose of 1.6 X lO"\does not appear to have any effect,
other than on the carrier density, on the quantum
transport
coefficients. We can rule out conduction through the next
higher conduction subband because of the well-behaved
oscillations in ,ox,. We as yet do not have an explanation
of
for this photoexcitation phenomenon.Thedynamics
-
1758
IEEE JOURNAL
NO. OF
QE-22,
ELECTRONICS,
QUANTUM
VOL.
this process clearly deviates from present understandings
[3], [ 2 3 ] of the detailed photoexcitation mechanisms, imHowplying a morecomplicatedrateequationmodel.
ever, the microscopic model interpretation of DX centers
as the responsible traps [ l l ] in the Al,Ga, -,rAs is still
consistent with our results.
V. SUMMARY
We have done a systematic study of the low field and
quantumtransport coefficients in a GaAs/Al,Gal -,As
modulation-doped heterostmcture. We find that the onset
of conduction through a parallel path in the Al, Gal -,As
isreadilyobservableviaquantumtransportmeasureallow us todeterminethe
ments.Thesemeasurements
distribution of carriers in the 2DEG and in a parallel path.
We can also use the measurements to put limits on the
perturbation of the quantized resistance values due to
a
parallel conduction path.
ACKNOWLEDGMENT
We are indebted to H. D. Shih for growth of the MBE
sample, to R . T. Bate, W. R. Frensley, and P. A. Penz
for helpful discussions, and toJ . Williams for sample fabrication.
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REED etCONDUCTION
al.: PARALLEL
IN MODULATION-DOPED
STRUCTURES
W. P. Kirk was born in Joplin, MO, in 1942. He
received the B.A. degree in physics from WashingtonUniversity,St.Louis,
MO, in1964, and
the M.A. and Ph.D. degrees in physics from the
State University of New York at Stony Brook in
1967 and 1970, respectively.
From 1970 to 1975 he held Postdoctoral Fellow and Assistant Professor positions at the University of Florida, Gainesville. In 1975 he joined
the Physics Faculty of Texas A&M University,
College Station, as an Assistant Professor and became an Associate Professor in 1978. Since 1983 he has been a Professor
of Physics. He has been Director of the Campus Helium Liquefaction Facility since 1976. Dr. Kirk’s research interests in experimental low-temperature physics include the quantum Hall effect, transport properties of
metals and semiconductors, macroscopic quantum effects, and many-body
effects. In support of this work Dr. Kirk has developed extensive low-temperature, high-magnetic-field laboratories where transport studies down to
0.0003 K have been made and measurements in applied fields up to 14
T
can be made at very low temperatures. He has authored approximately 80
journal articles and conference papers and one book chapter.
He has received a Brookhaven National Laboratory Summer Fellowship (1967) and
an NSF Postdoctoral Fellowship (1970-1972). He was a Visiting Scientist
at M.I.T. Cambridge, during the Summer of 1973.
Dr. Kirk is a member of the American Physical Society, the American
1759
Association for the Advancement of Science, Sigma XI, the Texas Academy of Science, the American Vacuum Society, and the Materials Research
Society. He is listed in Who’s Who in American Men and Women ofscience
and Who’s Who in Technology Today.
P. S. Kobiela wasborn in Krakow, Poland, in
1951. He received theM.S. degree in physics from
the Jagiellonian University in 1974.
From 1974 to 1981 he was a member of the
Low Temperature Laboratory at the Institute
of
Nuclear Physics, Krakow. Since 1971 he has
undertakengraduatestudiesinphysicsatTexas
A&M University, College Station, where he currently holds a Research Associate position. His
special fields of interest include plastic and liquid
crystals,transportinsemiconductors,lowtemperature calorimetry, the absolute low-temperature scale, and applications
of cryogenics in medical and veterinary sciences. He holds two patents for
cryogenic devices and is co-author of 17 journals and conference reports.
Mr. Kobiela is a member of the American Physical Society.