CHINESE JOURNAL OF PHYSICS
VOL. 45 , NO. 6-I
DECEMBER 2007
Weak Localization and Electron-Electron Interaction Effects in
Al0.15 Ga0.85 N/GaN High Electron Mobility Transistor Structures Grown on
p-type Si Substrates
Kuang Yao Chen,1 C.-T. Liang,1, ∗ N. C. Chen,2 P. H. Chang,2 and Chin-An Chang2
1
Department of Physics, National Taiwan University, Taipei 106, Taiwan
2
Department of Electronic Engineering,
Chang Gung University, Tao-Yuan 333, Taiwan
(Received December 18, 2006)
We report on magnetotransport studies of Al0.15 Ga0.85 N/GaN high electron mobility
transistor (HEMT) structures grown on p-type Si(111) substrates. Both weak localization
(WL) and electron-electron interaction (EEI) correction terms to the conductivity of the SiN
treated HEMT are smaller than those of the untreated HEMT. Since both WL and EEL
corrections tend to decrease the conductivity of an AlGaN/GaN HEMT structure, our SiN
treatment is useful for enhancing the performance of GaN-based HEMT structures grown
on Si, which is compatible with the mature Silicon CMOS technology.
PACS numbers: 73.20.Fz, 73.43.Qt
I. INTRODUCTION
AlX Ga1−X N/GaN heterostructures have been a topic of great interest recently because of their applications in optoelectronic and electronic devices, such as blue light emitting diodes [1], laser diodes [2], ultraviolet detectors, high–power microwave devices [3],
high frequency field effect transistors [4], and high electron mobility transistors (HEMTs)
[5, 6]. It is worth mentioning that spontaneous and piezoelectric polarizations effects can
be exploited to design a nominally undoped GaN HEMT [7-9]. The spontaneous polarization is due to the position of the anion and cation in the lattice, and the piezoelectric
polarization is caused by lattice strain and thermal strain between the AlGaN and GaN
layers. The difference of the polarizations between the AlGaN and GaN layers can cause
the formation of a high-density two-dimensional electron system (2DES) near the interface
of an AlGaN/GaN heterostructure.
Quantum corrections to the conductivity of disordered systems at low temperatures
(T ) have been intensively studied [10]. There are two main mechanisms of the quantum corrections: (i) weak localization in a weak magnetic field, which can be understood in terms of
quantum interference between two waves propagating by multiple scatters along the same
path but in opposite directions, and (ii) electron-electron interactions, which can be interpreted as the diffraction of one electron wave by the oscillation in the electrostatic potential
generated by the other electrons [11]. At very low magnetic fields we can observe the suppression of the weak localization effect as a fast decrease in the magnetoresistance. When a
magnetic field is applied it would destroy the phase coherence owing to the Aharonov-Bohm
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616
c 2007 THE PHYSICAL SOCIETY
OF THE REPUBLIC OF CHINA
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KUANG YAO CHEN, C.-T. LIANG et al.
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effect. The weak localization contribution to the magnetoconductivity of a 2D system is
given by [12, 13]
τφ
h̄
h̄
e2
1
1
WL
+ ln
,
(1)
+
+
∆σxx (B) = 2 ψ
−ψ
2π h̄
2 4eDBτφ
2 4eDBτe
τe
where τφ and τe are the phase relaxation and momentum relaxation times, respectively, ψ
is the digamma function, and D is the electronic diffusion constant given byD = 21 VF2 τe .
The longitudinal conductivity at zero magnetic field can be expressed as [14]
ee
WL
σxx = σD + ∆σxx
(T ) + ∆σxx
(T ) ,
(2)
ee (T ) and ∆σ W L (T ) stand for the electronwhere σD is the Drude conductivity and ∆σxx
xx
electron interaction and weak localization quantum corrections, respectively. It has been
W L (T ) one is able to study the electron-electron interaction
shown that by subtracting ∆σxx
effects, since σD is temperature-independent at low T [15].
Alx Ga1−x N/GaN HEMTs are usually grown on sapphire substrates. However Si can
also be considered as an alternative to commercial sapphire substrates for nitride-based
devices due to its low cost and large wafer size [16, 17]. Nevertheless it is well known that,
as a result of the large lattice mismatch (about 17%) and thermal mismatch (about 54%)
between GaN and Si, high-quality GaN films on Si are very difficult to grow. It is worth
mentioning that having an AlN layer as an intermediate and nucleation layer can greatly
improve the quality of the GaN film grown on Si [18]. Moreover a delta doping of Si [19]
can reduce the dislocation density of a GaN film, improving the quality of the GaN layer.
Recently we have shown that, by introducing an ultra-thin SiN film during the crystal
growth, the Hall mobility of an Alx Ga1−x N/GaN HEMT on Si can be greatly increased
(> 3 times) [20]. The aim of this paper is to investigate and compare weak localization
and electron-electron interaction effects in untreated and SiN treated GaN/AlGaN HEMT
structures grown on Si. We shall show that inserting an ultra thin SiN layer reduces both the
weak localization and the electron-electron interaction correction terms. Such fundamental
understanding and technique are highly desirable since they can be used to enhance the
performance of an AlGaN/GaN HEMT structure on Si, which is compatible with the Silicon
CMOS technology.
II. THE EXPERIMENT
Two samples, A and B, are studied in this work. These two samples were grown by
metal-organic vapor phase epitaxy (MOVPE) using an Aixtron RF-S system and have an
almost identical structure except that sample B has been SiN treated. The details and
growth of these two samples have been reported elsewhere [20]. We believe that the SiN
treatment helps to reduce the dislocation density in the GaN layer, improving both the
quality of the GaN layer [21] and the mobility of the two dimensional electron systems.
The carrier density of sample A is 9.2 × 1012 cm−2 with a Hall mobility of ∼700 cm2 /Vs,
618
WEAK LOCALIZATION AND ELECTRON-ELECTRON . . .
(a)
VOL. 45
(b)
FIG. 1: (a) Magnetoconductivity, σxx (B) − σxx (0), at low magnetic field for sample A. From top
to bottom: T =4, 5, 6, 8, 10, 14, and 17 K. The solid curves are the theoretical fits to Eq. (2). The
inset shows the magnetoresistivity measurements as a function of the magnetic field for sample A.
(b) Magnetoconductivity, σxx (B) − σxx (0), at low magnetic field for sample B. From top to bottom:
T =4, 6, 8, 10, 12, 14, 16, and 18 K. The solid curves are the theoretical fits to Eq. (2). The inset
shows the magnetoresistivity measurements as a function of the magnetic field for sample B.
FIG. 2: Phase-breaking rate, 1/τφ , vs temperature. The straight line fit is discussed in the text.
whereas the carries density of sample B is 9.4 × 1012 cm−2 with a Hall mobility of ∼2500
cm2 /Vs at T ∼4 K. Four-terminal resistivity and Hall measurements were performed using
standard phase-sensitive ac lock-in techniques.
III. RESULTS AND DISCUSSION
The insets to Fig. 1(a) and Fig. 1(b) show the magnetoresistivity measurements on
sample A and sample B, respectively. We can see that the zero-field resistivity of sample A
is considerably larger than that of sample B. Therefore the mobility and quality of sample
A are lower than those of sample B. As shown in the inset of Fig. 1(a)–(b), the negative
magnetoresistances exhibit a fast decrease in low magnetic field. The fast decrease is
caused by suppression of the weak localization. We analyze the negative magnetoresistance
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KUANG YAO CHEN, C.-T. LIANG et al.
619
at B < Btr [22], where Btr = h̄/(2el2 ) is the so-called transport magnetic field and l is the
elastic mean free path. We obtain σxx by matrix inversion of ρxx and ρxy ,
σxx =
ρxx
,
ρ2xx + ρ2xy
(3)
W L = σ (B) − σ (0) is shown in Fig. 1(a)–(b).
as a function of the magnetic field. ∆σxx
xx
xx
We use Eq. (1) to fit the magnetoconductivity in a magnetic field B < Btr , where the Btr
of sample A is 0.27 T and that of sample B is 0.02 T. The τφ of the two samples found
from the fit is shown in Fig. 2, and the fit of the experimental data is well described by
the temperature dependence of the phase breaking rate, 1/τφ , being consistent with the
theoretical prediction [23, 24]. Figure 2 shows that the τφ for sample A is considerably
larger than that for sample B. At zero magnetic field, the correction term due to weak
localization is given by [10, 15]
∆σ W L (0) = (e2 /2π 2 h̄) ln(τφ /τ + 1) .
(4)
According to Eq. (4), we can calculate the weak localization contribution to the conductivity
at zero magnetic field from τφ . As shown in Fig. 3, the weak-localization effect of sample
A is greater than that of sample B over approximately the same range of temperatures,
because the τφ /τ of sample A is greater than that of sample B. It is in low-temperature
and low-quality samples where the phase relaxation time is longer than the momentum
relaxation time (τφ /τ >> 1) [25]. Thus the quality of sample A is lower than that of
sample B.
According to Eq. (2), after subtraction of the weak localization, only the electronelectron interaction term and the classical Drude conductivity remain. At low temperatures the classical term is temperature-independent; therefore we can observe the electronelectron interactions at different temperatures [15, 26]. As shown in Fig. 4, the correction
ee , is proportional to ln[(k T τ )/h̄] in
term due to the electron-electron interaction, ∆σxx
B
the diffusion regime [10, 27, 28]. In the diffusive limit the theoretical electron-electron
interaction correction term is given by [27, 28]
ln(1 + F0σ )
kB T τ
e2
ee
),
(5)
3 1−
+ 1 ln(
δσxx =
πh
F0σ
h̄
where F0σ is the interaction constant. The F0σ are calculated to be -0.26963 and -0.26868
using the effective mass in GaN (0.23m0 ) and carrier densities in sample A and sample
B, respectively. Since the carrier densities for sample A and sample B are approximately
the same, the F0σ are almost the same for both samples. Figure 4 shows the zero-field
W L (0)]
conductivity after subtraction of the weak localization contribution [σxx (0) − ∆σxx
as a function of ln[(KB T τ )/h̄] for sample A and sample B over approximately the same
range of T. Since the τ of sample A is ∼3 times shorter than that of sample B, the value
ln[(KB T τ )/h̄] of sample A is ∼2 times smaller than that of sample B. The slope of the
linear fit for sample A (5.4 × 10−5 ) is ∼7 times larger than that for sample B (7.9 × 10−6 ).
According to Eq. (2) and Eq. (5), we can conclude that the electron-electron interaction
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WEAK LOCALIZATION AND ELECTRON-ELECTRON . . .
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FIG. 3: Zero-field weak-localization term measurements as a function of temperature T.
FIG. 4: Zero-field conductivity vs ln(2πkB T τ /h), after subtraction of the weak-localization term.
The straight line fit is discussed in the text.
correction for sample A is considerably larger than that for sample B. The slope of the linear
fit for sample B is close to the theoretical value (6.23 × 10−6 ) using Eq. (5). However, the
slope of the linear fit for sample A is considerably larger than the expected value. We note
that according to Eq. (5) the slopes of the linear fits for the two samples are approximately
the same, since F0σ for sample A is approximately the same as that for sample B. It may be
possible that more charged dislocations exist in sample A [30], leading to a much stronger
electron-electron interaction correction term in sample A. Our experimental results clearly
show that the electron-electron interaction correction of sample A is much larger than that
of sample B.
IV. CONCLUSIONS
In conclusion, the contribution of the quantum corrections to the conductivity of
Al0.15 Ga0.85 N/GaN HEMT structures grown on Si (111) substrates have been studied at
different temperatures. We have demonstrated that both weak localization and electronelectron interaction quantum correction terms can be greatly reduced in the SiN treated
HEMT. Therefore our SiN treatment technique is very useful in improving the performance
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KUANG YAO CHEN, C.-T. LIANG et al.
621
of GaN/AlGaN HEMT structures grown on Si, which is compatible with the mature Silicon
Complementary Metal Oxide Semiconductor technology.
Acknowledgments
This work was funded by the NSC, Taiwan. We thank Y. H. Chang, S. C. Chen, W.
C. Lien, C. F. Shih, K.-T. Wu, and Y. H. Wu for their invaluable help at the early stage of
this work.
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