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Title

Low‑frequency noise in InAs films bonded on low‑k
flexible substrates

Author(s)Le, Son Phuong; Ui, Toshimasa; Suzuki, Toshi‑kazuCitation

Applied Physics Letters, 107(19): 192103‑1‑
192103‑4

Issue Date

2015‑11‑09

Type

Journal Article

Text version

publisher

URL

http://hdl.handle.net/10119/15422

RightsCopyright 2015 American Institute of Physics.
This article may be downloaded for personal use
only. Any other use requires prior permission of
the author and the American Institute of Physics.
The following article appeared in Son Phuong Le,
Toshimasa Ui, and Toshi‑kazu Suzuki, Applied
Physics Letters, 107(19), 192103 (2015) and may
be found at http://dx.doi.org/10.1063/1.4935458

Description

Japan Advanced Institute of Science and Technology

APPLIED PHYSICS LETTERS 107, 192103 (2015)

Low-frequency noise in InAs films bonded on low-k flexible substrates
Son Phuong Le, Toshimasa Ui, and Toshi-kazu Suzukia)
Center for Nano Materials and Technology, Japan Advanced Institute of Science and Technology (JAIST),
1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan(Received 30 August 2015; accepted 27 October 2015; published online 9 November 2015)
We have systematically investigated low-frequency noise (LFN) in InAs films with several thicknesses (’ 10-100 nm) bonded on low-k flexible substrates (InAs/FS), comparing with that in InAs
films epitaxially grown on GaAs(001) substrates (InAs/GaAs). We obtain current LFN spectra
exhibiting approximate 1=f characteristics and consequent effective Hooge parameters a dependingon the thickness, where we find that a in the InAs/FS is larger than that in the InAs/GaAs. The
behavior of a can be attributed to the fluctuation of the electron mobility dominated by surface/
C 2015 AIP Publishing LLC.
interface charge scattering and by thickness fluctuation scattering. V[http://dx.doi.org/10.1063/1.4935458]

A narrow-gap compound semiconductor InAs has attractive properties,1,2 applicable to mid-infrared optical devices,3
ultra-high-speed electron devices,4–6 and also interband tunnel devices.7,8 Moreover, heterogeneous integration of InAs
film devices on host substrates was realized with excellent
device performances.9–11 Previously, we fabricated InAs
films bonded on host low-dielectric-constant (low-k) flexible
substrates (FS),12–14 by using epitaxial lift-off (ELO) andvan der Waals bonding (VWB) method,15,16 investigating
electron scattering and carrier recombinations in the InAs
films. As a result, we found important roles of surface/interface charge scattering and thickness fluctuation scattering in
the InAs films bonded on low-k FS.13 Such specific scattering mechanisms might be responsible for electronic noisecharacteristics through fluctuations of both the electron number and the mobility in the InAs films, especially for lowfrequency noise (LFN) according to slow dynamics of trapping/detrapping of surface/interface charges. Even though
the DC electronic properties are elucidated, the LFN in the
InAs films bonded on low-k FS remains an issue. Although
there were several studies on LFN in InAs devices based on
the 6.1 Å family heterostructures,17–21 InAs devices on hostsubstrates are different in the formation method and also in
the electron scattering mechanisms. Moreover, it was often
difficult to elucidate the underlying mechanisms behind the
LFN. In this work, we carried out a systematic investigation
on LFN in the InAs films bonded on low-k FS (InAs/FS)
with the film thicknesses d ’ 10-100 nm, comparing withthat in InAs films epitaxially grown on GaAs(001) substrate(InAs/GaAs); this can illustrate insights into InAs devices onhost substrates.
Using the InAs(thickness ’ 500 nm)/FS and theInAs(thickness ’ 500 nm)/GaAs, Hall-bars and two-terminal(2T) devices were fabricated. The fabrication process is thesame as the previous report;12,13 we employed the ELO and“inverted” VWB process shown in Fig. 1 for the InAs/FS, inwhich the InAs device layer was “inverted” and bonded ontoa host low-k FS, polyethylene terephthalate coated bya)Author to whom correspondence should be addressed. Electronic mail:tosikazu@jaist.ac.jp0003-6951/2015/107(19)/192103/4/$30.00

bisazide-rubber. To obtain several InAs film channel thicknesses d ’ 10-100 nm, the recess thinning process was carriedout, where the “inverted” VWB process is advantageous toobtain a high crystal quality after the recess thinning according to the growth-direction dislocation distribution.22 The top
InAs surfaces for both the InAs/FS and the InAs/GaAs are notcovered by anything. The 2T devices have InAs channel width
W ¼ 20-100 lm and length L ¼ 5-400 lm.
From Hall-bar measurements at room temperature, we
obtain the electron mobility l and the sheet electron concentration ns as functions of the InAs film thickness d, as shownin Fig. 2, where the error bars come from the thickness measurements by laser scanning microscope as described in Ref.
13. Although ns exhibits a variation, l shows systematic
behaviors well-fitted by 1=l ¼ 1=l0 þ 1=lC þ 1=lTF , wherel0 is a thickness-independent constant mobility, lC is a mobility due to Coulomb scattering by surface/interface
charges, and lTF is a mobility due to thickness fluctuation
scattering, each given by the following.13 The thicknessindependent constant mobility is l0 ’ 14 000 cm2 =V-s,owing to polar optical phonon scattering giving a mobility oflph ’ 25 000 cm2 =V-s23 and to possible additional scattering
independent of the thickness. The surface/interface charge
scattering mobility24–26 and the thickness fluctuation scattering mobility25–30 are given bylC ¼

4pes 2 h3 kF 3
d ¼ Adnc e3 m2

andlTF ¼ Bd c ðc ’ 5:2Þ; (1)respectively, with constants A and B, the surface/interface
charge density nc , which is the sum of the charge density at
the surface and the InAs-FS or InAs-GaAs interface, thedielectric constant es , the electron effective mass m , and the
Fermi wave vector kF . The fitting gives nc  1  1012 cm2
(InAs/FS) and  9  1013 cm2 (InAs/GaAs), and we obtainc ’ 5:2 experimentally and numerically.13 The obtained nc
for the InAs/GaAs is quite larger than that for the InAs/FS,
indicating the dominance of the InAs-GaAs interface in comparison with the surface. For the InAs/FS, since the thickness
fluctuation scattering is dominant in the regime ofd ⱗ 15 nm, we can obtain the value of B by fitting, while wecannot for the InAs/GaAs, which does not show such regime

107, 192103-1

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192103-2

Le, Ui, and Suzuki

Appl. Phys. Lett. 107, 192103 (2015)

FIG. 1. Schematic of the formation of
InAs films on low-k flexible substrates.
The InAs device layer is “inverted”
and bonded.

because of low surface/interface charge scattering mobilities.
However, the InAs/FS exhibits a smaller B than the InAs/
GaAs, indicating a larger thickness fluctuation (maybe shortrange one relevant to quantum scattering).
We carried out LFN characterization of the 2T devices,which show Ohmic I-V characteristics, by using the samemeasurement system as Ref. 31. Figures 3(a) and 3(b) show
examples of measurement results of current noise power
spectrum density SI for the Ohmic regime of the InAs/FS andthe InAs/GaAs devices, respectively, with the InAs film
thickness d ’ 10; 30; 100 nm, W ¼ 50 lm, L ¼ 350 lm(InAs/FS), and L ¼ 400 lm (InAs/GaAs). We obtain approximate 1=f spectra satisfying SI =I 2 ’ K=f b ; with b  1 and aconstant factor K, where the DC current I is varied by changing the noiseless 2T bias voltage V. As shown in the insets ofFigs. 3(a) and 3(b), plotting SI f at f ¼ 1 Hz as a function ofI, where SI f / I 2 is confirmed, we evaluate the factor
K ¼ SI f =I2 . In order to check the channel size (width andlength) dependence of K, in Fig. 4, we plot the factor K as afunction of the total electron number in the InAs channel
N ¼ LWns . We obtain the relation K / 1=N, indicating the
LFN dominated by the InAs channel with a negligible contribution from the contact and electrode. The effective Hooge
parameters32 a ¼ SI fN=I2 ¼ KN, obtained by fitting of K as
a function of N, are shown in Fig. 5(a) as a function of the
InAs film thickness d. We observe that a in the InAs/FS islarger than that in the InAs/GaAs. Figures 5(b) and 5(c)FIG. 2. The electron mobility l as a function of the InAs film thickness dwith fitting curves. The inset shows the sheet electron concentration ns as afunction of d.

show a as the functions of l and ns , respectively. The Hooge
parameters a are negatively correlated with l as well as d,whereas uncorrelated with ns , suggesting that the mobility
fluctuation is more important.
We consider a ¼ al þ aN  ðdlÞ2 =l2 þ ðdNÞ2 =N basedon the Burgess theorem,31–36 where dl and dN are the fluctuations of the mobility l and the electron number N relevant
to 1=f noise, respectively. If the electron number fluctuation
is dominant, a ’ aN  ðdNÞ2 =N: The electron number fluctuation caused by trapping/detrapping at the surface/interface
states with a density Di gives a  Di kB T=ns / 1=ns ,37 which
is not the case as in Fig. 5(c). We hence consider that the mobility fluctuation is dominant, a ’ al  ðdlÞ2 =l2 ; where

FIG. 3. SI =I2 as a function of f for (a) InAs/FS and (b) InAs/GaAs. The
insets show SI f at 1 Hz as a function of I, confirming SI f / I2 .

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192103-3

Le, Ui, and Suzuki

Appl. Phys. Lett. 107, 192103 (2015)

FIG. 4. The factor K as a function of the total electron number N, exhibiting
K / 1=N.

dl dl0 dlC dlTF’þþ
l2 l0 2 lC 2 lTF 2(2)

with obvious notations. We consider that the fluctuations oflC / d=nc and lTF / dc are related to spatial randomness38,39 based on the following picture. The surface/interface charges are distributed randomly and fluctuate slowly,
making a time-dependent random potential with slow dynamics. In addition, while the InAs film thickness d means
the spatially averaged one, there is a spatial thickness inhomogeneity (fluctuation), making a random potential throughthe spatial fluctuation of quantum levels. The surface/interface charges and the spatial thickness fluctuation uncorrelatedly make a slowly time-dependent total random potential.

FIG. 6. a=l2 as a function of the InAs film thickness d.

Under the time-dependent random potential, an electron
wave function tends to be localized, whose position slowly
fluctuates, leading to a slow fluctuation of the film thickness
at the electron position. Therefore, the temporal fluctuationof lC / d=nc and lTF / d c will reflect the spatial fluctuation
dd (maybe long-range one). Also, while nc is the spatiallyaveraged surface/interface charge density, there is a spatial
density inhomogeneity (fluctuation). Thus, the slow fluctuation of the electron position leads to a slow fluctuation of thesurface/interface charge density at the electron position.
Therefore, the spatial fluctuation dnc will induce the temporal fluctuation of lC / d=nc . According to the picture, we
assume the order of the fluctuations dlC =lC  ðdd=d 
dnc =nc Þ and dlTF =lTF  cdd=d, leading to
dl dl0
1 dd dnc
c dd
þ


þ
nc
l2 l0 2 lC d
lTF d


dl0
1
c dd
1 dnc
þ c

(3)
¼ 2þ
l0
Ad Bd
d Ad nc
using lC ¼ Ad and lTF ¼ Bd c . As a result, we obtain22
ðdd Þ2ðdlÞ2a1c
1 ðdnc Þðdl0 Þ2
þ


þ
þ
l4
l0 4
d2
l2
Ad Bd cA2 d 2 nc 2
(4)similarly to Ref. 40. The first term including the polar opticalphonon scattering mobility lph should be independent of the
thickness d and consequently is irrelevant to a depending on
d. Moreover, if we assume the Hooge model,32,35 it is plausible that the first term is negligible. Using the Hooge universal constant aH ’ 2  103 (or less for low-dimensional
InAs systems41,42), the contribution from the first term may
be l2 =lph 2  aH  2  103 and negligible in the measureda > 2  103 . Thus, by neglecting the first term of Eq. (4),we expect the relationðdnc Þ2
a
1
2c
c2
2
ð
Þ
dd

þ
þ
þ
: (5)
A2 d2 nc 2
l2
A2 d 4 ABdðcþ3Þ B2 d ð2cþ2Þ

FIG. 5. The Hooge parameter a as the functions of (a) the InAs film thicknessd, (b) the electron mobility l, and (c) the electron sheet concentration ns .

In order to confirm this relation, measured a=l2 as a functionof d is plotted in Fig. 6, with a fitting curve according to Eq.
(5), where the fitting parameters are dnc and dd (InAs/FS) or
dd2 =B2 (InAs/GaAs). We confirm that the measurement data

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192103-4

Le, Ui, and Suzuki

Appl. Phys. Lett. 107, 192103 (2015)

TABLE I. The parameters of the InAs/FS and the InAs/GaAs.

dd ðnmÞ
dnc ðcm2 Þ
nc ðcm2 Þpﬃﬃﬃﬃﬃ
nc =dnc (nm)InAs/FS

InAs/GaAs

2
 5  1011
 1  1012
 20…
 4  1012
 9  1013
 20

are well-fitted for both the InAs/FS and the InAs/GaAs. We
find a=l2 / 1=dð2cþ2Þ ’ 1=d 12:4 dominated by the third term
for small d, while a=l2 / 1=d 2 dominated by the fourth term
for large d. It should be noted that dlTF giving the third term
is important for dl, even though we do not observe l dominated by lTF for the InAs/GaAs.
The fitting parameters and other parameters are summarized in Table I. We obtain a large dd  2 nm for the InAs/
FS, while dd for the InAs/GaAs cannot be estimated because
we do not obtain the value of B. However, from the regimeof a=l2 / 1=dð2cþ2Þ , we find that dd 2 =B2 is larger for the
InAs/FS than for the InAs/GaAs owing to the smaller B and/or larger dd, both meaning larger thickness fluctuations; theformer may be short-range one, while the latter may be longrange one. Therefore, we consider that such larger thickness
fluctuation is a reason of the fact that a in the InAs/FS islarger than that in the InAs/GaAs. This larger thickness fluctuation can be attributed to process inhomogeneity over thelarge channel area, owing to the relatively complicated fabrication process of the InAs/FS. On the other hand, we obtaindnc  5  1011 cm2 (InAs/FS) and  4  1012 cm2 (InAs/
GaAs), where the InAs/FS exhibits a quite smaller value.
This can be attributed to the difference of nc in the InAs/FS
and the InAs/GaAs shown in Table I. If the surface/interface
charges obey the Poisson distribution spatially, dnc in thearea S relevant to Coulomb scattering by the surface/interpﬃﬃﬃﬃﬃﬃﬃﬃﬃ
face charges satisfies S2 dnc 2 ’ Snc and hence dnc ’ nc =S,
to smaller nc . In fact, wesuggesting thatpﬃﬃﬃsmaller dnc is due
pﬃﬃﬃﬃﬃ
can estimate S by evaluatingncpﬃﬃﬃ =dnc as shown in Table I,
giving a common length of S  20 nm for both the InAs/
FS and the InAs/GaAs. This should be a relevant length of
Coulomb scattering by the surface/interface charges, which
is similar to the Fermi wavelength, the two-dimensional
screening length, or the phase coherence length.
In summary, we systematically investigated LFN in the
InAs/FS, comparing with that in the InAs/GaAs. From thecurrent LFN spectra exhibiting approximate 1=f characteristics, we obtained the effective Hooge parameters a depending on the InAs thickness, where we find that a in the InAs/
FS is larger than that in the InAs/GaAs. The behavior of the
Hooge parameters was analyzed and attributed to the fluctuation of the electron mobility dominated by surface/interface
charge scattering and by thickness fluctuation scattering. The
analysis gives an estimation of the thickness fluctuation,
which is large for the InAs/FS, being a reason of the large
Hooge parameter. Also, an estimation of the fluctuation of
the surface/interface charge density is given, suggesting a
relevant length of Coulomb scattering by the surface/interface charges.

This work was supported by JSPS KAKENHI Grant
Nos. 26249046 and 15K13348.
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