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Title

High‑temperature electron transport inmetamorphic InGaAs/InAlAs heterostructures

Author(s)Suzuki, T.; Ono, H.; Taniguchi, S.

Citation

Science and Technology of Advanced Materials,
6(5): 400‑405

Issue Date

2005‑07

Type

Journal Article

Text version

author

URL

http://hdl.handle.net/10119/4881

RightsNOTICE: This is the author's version of a work
accepted for publication by Elsevier. T. Suzuki,
H. Ono and S. Taniguchi, Science and Technologyof Advanced Materials, 6(5), 2005, 400‑405,
http://dx.doi.org/10.1016/j.stam.2005.02.024

Description

Japan Advanced Institute of Science and Technology

High-temperature electron transport
in metamorphic InGaAs/InAlAs heterostructures
T. Suzuki1∗, H. Ono2 , and S. Taniguchi2
1

Center for Nano Materials and Technology,
Japan Advanced Institute of Science and Technology
1-1 Asahidai, Nomi-shi, Ishikawa, 923-1292, Japan
2

Advanced Devices R&D Department,
Semiconductor Solutions Network Company, Sony Corporation
4-14-1 Asahi-cho, Atsugi-shi, Kanagawa, 243-0014 Japan

Abstract
We have investigated high-temperature electron transport in metamorphic InGaAs/InAlAs modulationdoped heterostructures with several indium contents. The electron mobility characterizing the low-fieldtransport properties was obtained from the Hall measurements. From room temperature to 400 K,∼ 26 % decrease in the mobility was observed, which is well-explained by the polar-optical-phonon scattering theory. The indium content dependence of the mobility is explained by the theory with the Γ-valley
electron mass. On the other hand, the electron saturation velocity characterizing the high-field transport
properties was studied by means of the delay-time analysis of the transistors with gate length of 0.121.0 µm. We observed ∼ 12 % decrease in the saturation velocity from room temperature to 400 K, whichis smaller than that in the mobility and roughly consistent with the energy relaxation theory. In theindium content dependence of the saturation velocity, the effect of decrease in the electron density in theL- and X-valley is important. The high-frequency performance of the transistors at high temperatures
shows a deterioration according to the decrease in the saturation velocity.
Keywords— metamorphic InGaAs/InAlAs, electron mobility, electron saturation velocity, delay-time
analysis, high-frequency performance∗

Corresponding author. E-mail address: tosikazu@jaist.ac.jp; Phone:+81-761-51-1441; Fax:+81-761-51-1455(T.Suzuki)

1

1

Introduction

Recently, semiconductor devices obtained from lattice-mismatched growth, called metamorphic
growth, have received considerable attention. In the metamorphic growth, the lattice mismatch
between active device layers and the substrate is relaxed by devised buffer layers. Since InGaAs
with high indium content provides high electron mobility and saturation velocity, InGaAs devices obtained from the metamorphic growth on GaAs substrates, such as metamorphic highelectron mobility transistors (MHEMTs)[1,2] and metamorphic heterojunction bipolar transistors (MHBTs)[3,4], are attractive for high-frequency or high-speed applications. In addition
to the fact that the metamorphic InGaAs devices have a cost advantage in comparison withlattice-matched InGaAs devices grown on InP substrates, it is important that the metamorphic
devices offer a freedom of choice of the indium content. As the metamorphic growth enables us
to realize an unstrained InGaAs layer with almost any indium content, the indium content is
considered as a new structure parameter in the device design; high-frequency performance andbreakdown voltage can be balanced by choosing the indium content in device optimization[5,6].
For further development of the narrow-bandgap InGaAs metamorphic devices, deteriorationin the device performance at high temperatures is an important issue for practical use. In
this work, in order to elucidate the deterioration, we have investigated high-temperature electron transport properties in the metamorphic InGaAs/InAlAs heterostructures grown on GaAs
substrates with several indium contents, in comparison with the lattice-matched heterostructures grown on InP substrates. The low-field transport properties have been studied throughcharacterization of the electron mobility obtained from the Hall measurements up to 400 K, in2

comparison with polar-optical-phonon and alloy-disorder scattering theory. On the other hand,
the high-field transport properties have been investigated by means of high-frequency measurements of the transistors with gate length of 0.12-1.0 µm up to 473 K. The high-temperatureelectron saturation velocity obtained from the delay-time analysis is compared with the energy
relaxation theory.

2

Materials

The modulation-doped metamorphic Inx Ga1−x As/Inx Al1−x As heterostructures (x = 0.36, 0.43,
and 0.53) were grown on semi-insulating (001)GaAs substrates by means of molecular beam
epitaxy. Following the undoped graded InAlAs metamorphic buffer layer, the active layers
incorporated 200 nm undoped InAlAs layer, 15 nm undoped InGaAs quantum-well channel, 6 nm
undoped InAlAs spacer, Si delta-doping plane, 12 nm undoped InAlAs barrier layer, and 50 nm
n+ -InGaAs cap layer. The lattice-matched (LM) In0.53 Ga0.47 As/In0.52 Al0.48 As heterostructures
grown on InP have the same active layers. The indium contents were precisely determined byphotoluminescence measurements taking into account quantized energy levels in the channels,and (004) and (115) X-ray diffraction measurements.
In the metamorphic growth, surface with crosshatch is obtained. Figure 1 shows, as an
example, the atomic force microscope (AFM) image of the heterostructure with the indium
content of 0.43. The root mean square roughness of the metamorphic materials is as large as∼ 2-3 nm. From plan-view transmission electron microscope (PTEM) observation, as shownin Fig. 2, we have found rather high-density crystalline defects, threading dislocations andstacking faults, in the active layers of metamorphic heterostructures. The defect density was3

typically on the order of 108 cm−2 , which is larger than the case of LM structures by threeorders of magnitude. It should be noted that the defect density cannot be estimated from crosssectional TEM (XTEM) observations, especially for the metamorphic materials with defect8−2density <∼ 10 cm [7], because it seems as if almost all dislocations were confined inside thebuffer layer from the XTEM observation. At the present time, even in the best case, we observe
the defects on the order of 107 cm−2 in the active layer of the metamorphic devices. Although
there are some reports which conclude that the defect density in InGaAs MHEMTs or MHBTs
6
−2
is <
∼ 10 cm from XTEM observations, we consider that they are underestimated results. In

spite of the surface roughness and the high-density defects, as shown below, we obtain the same
electron transport properties of the metamorphic structure with x = 0.53 and the LM structure,
which indicates that the effects of the surface roughness and defects on the transport properties
are negligible.

3

Electron mobility

We have carried out Hall measurements (van der Pauw method) of the heterostructures after
recess etching up to 400 K. For all the heterostructures, the sheet carrier (electron) concentrationis ∼ 3.5 × 1012 cm−2 , which is almost constant up to 400 K. Figure 3 shows the temperaturedependence of the electron mobility µ obtained from the Hall measurements. We obtain themobility at room temperature (295 K) of µ = 8100, 8900, and 10300 cm2 /Vs for x = 0.36, 0.43,
and 0.53, respectively. The same temperature dependence is obtained for the metamorphic
structure with x=0.53 and the LM structure. This indicates that the defects do not affect themobility. In the region higher than room temperature, the most dominant mechanism limiting4the low-field mobility is polar-optical-phonon scattering[8], which gives the mobility as a functionof temperature T ,
√
¶
µ
1 −1
3 2π 3 h̄21
exp (Eop /kB T ) − 1−µpop =,
1/2
3/2 exp (E /2k T ) K (E /2k T )
3/2
∗
²
²
(E
/k
T
)
em
Eop
∞
op B
op
1
op
B
B

(1)

where m∗ is the electron effective mass, Eop is the optical phonon energy, ²∞ and ² are the highfrequency and static dielectric constants, and K1 is a modified Bessel function. This formula isoriginally obtained for three-dimensional electron systems. However, in the case of the polaroptical-phonon scattering, the three-dimensional approach is justifiable also for two-dimensional
electron systems as discussed in[9]. Therefore, the formula is valid for our InGaAs quantum-wellchannels. Assuming m∗ = mΓ , where mΓ = (0.067 − 0.0531x + 0.0091x2 )m0 is the InGaAs
42
Γ-valley electron effective mass[10], and Eop ∼ 35 meV, we can estimate µpop <∼ 10 cm /Vs inthe high-temperature region, which is consistent with the measurements. In order to confirm
that this scattering mechanism dominates the measured electron mobility, we investigate thenormalized electron mobility, i.e., the mobility divided by the room-temperature mobility. Figure
4 shows measured temperature dependence of the normalized mobility and the theoretical curve
obtained from (1) assuming Eop = 35 meV. We find universal behavior of the normalized mobility
for every indium contents in quite good agreement with the theory. From room temperature
to 400 K, approximately 26 % decrease in the mobility is observed according to the enhanced
polar-optical-phonon scattering.
The other important scattering mechanism is the alloy-disorder scattering[11], which gives

5

almost temperature independent mobilityµalloy = √πeh̄4,2x(1 − x)m∗ 5/2 ΩV 2 EF 1/2(2)

where Ω is the unit cell volume, V is the alloy-disorder potential, and EF is the Fermi energy.
52
We can estimate µalloy >∼ 10 cm /Vs, where we use V ∼ 0.5 eV[12] and EF ∼ 100 meV for

our structures. Although the theory is for the three-dimensional case and should be slightly
modified for the two-dimensional case, the order estimation is unchanged. Therefore, we canconclude that the alloy-disorder scattering gives only small correction of the mobility.
The indium content dependence of the electron mobility should be well-described throughmΓ dependence of the mobility, according to the polar-optical-phonon scattering given by (1).
In fact, as shown in Fig. 5, the measured room-temperature mobility is proportional to 1/mΓ 3/2 .
This clearly shows that the mobility increase with increasing in the indium content is according
to the reduction of mΓ .

4Electron saturation velocity

In order to examine the electron saturation velocity, we fabricated T-gate transistors with gate
length of 0.12-1.0 µm according to the following device process[6,13]. The fabrication was started
with isolation by wet etching. The T-gate structures were realized by tri-layer resist process withelectron-beam lithography. The gate length was precisely measured by using a critical dimension
scanning electron microscope. After the recess etching, Pt/Ti/Pt/Au was deposited and liftedoff for the gate. Then alloyed Ni/AuGe/Au ohmic contacts were formed. Typically, the ohmic
contact resistance was 0.35, 0.3, and 0.2 Ωmm for x=0.36, 0.43, and 0.53, respectively. Finally,6

Ti/Au contact pads were formed. The current gain cut-off frequency fT of the transistors wasmeasured at high temperatures up to 473 K. From the gate length Lg dependence of current
gain cut-off frequency fT at room temperature, Lg × fT of 23, 27, and 32 GHz·µm is obtained
for the x = 0.36, 0.43, and 0.53, respectively.
In order to investigate electron saturation velocity, we performed the delay-time analysis[14].
The total delay time τ = 1/2πfT is divided into two parts, the channel charging time, which
is proportional to the reciprocal drain current density, and the saturation velocity transit time,
during which electrons with the saturation velocity transit under the gate. Therefore, thesaturation velocity transit time can be obtained from the extrapolation of the total delay timeat infinite drain current density. Figure 6 shows the relation between the total delay timeτ and the reciprocal drain current density 1/Id at room temperature, for the 1.0-µm-gatelength transistors. From the linear extrapolation of these plots, we can obtain the saturation
velocity transit time τ0 . Figure 7 shows Lg dependence of τ0 at room temperature. The electron
saturation velocity vsat at high electric fields >∼ 10 kV/cm is evaluated from the slopes ofthese plots. At room temperature, we obtain vsat = 1.8 × 107 , 2.0 × 107 , and 2.5 × 107 cm/s,
for x = 0.36, 0.43, and 0.53, respectively. The same analysis for high temperatures gives theelectron saturation velocity at high temperatures.
Figure 8 shows temperature dependence of the obtained saturation velocity. We obtained
the same temperature dependence for the metamorphic structure with x=0.53 and the LM
structure. This indicates that the defects do not affect the electron velocity at the high electric

7

fields. The saturation velocity is given by"#1/2√
2 2Eop 1/2 exp (Eop /kB T ) − 1
vsat = √3πm∗ 1/2 exp (Eop /kB T ) + 1(3)

from the energy relaxation theory[15]. Since the theory is based on the polar-optical-phonon
scattering, it is valid for both two- and three-dimensional electron systems. In order to compare the measured results and the theory, we plot the normalized saturation velocity, i.e., thesaturation velocity divided by the room-temperature saturation velocity, in Fig. 9. The solid
curve is the theoretical value obtained from (3) assuming Eop of 35 meV. Although vsat forhigher indium contents exhibits deviations from theoretical values at higher temperatures, wefind the measurements are roughly consistent with the theory. We observe approximately 12 %decrease in the saturation velocity from room temperature to 400 K, in contrast with the 26 %decrease in the mobility. From room temperature to 473 K, we observe ∼ 19 % decrease in thesaturation velocity for x = 0.36, which is in agreement with the theory. However, for x = 0.43
and x = 0.53, ∼ 23 % decrease in the saturation velocity is observed, which is slightly larger
than the theoretical value.
It should be noted that, the electron effective mass m∗ in (3) is the average electron effective
mass based on the electron distribution in several valleys contributing the high-field transport.
From the measured saturation velocity, we can estimate the average electron effective mass. In
Fig. 10, we show the average electron effective mass estimated from the measurements comparing
with mΓ . Although the average electron effective mass is rather large in the lower indium content
region, it decreases rapidly with the increase in the indium content. As the energy separation
between the Γ-valley and the upper (L- and X-) valleys increases with the increase in the indium
8contents, the electron density in the upper valleys decreases and the velocity overshoot effects
become important.
The high-frequency performance of the transistors at high temperatures shows a deteriorationaccording to the decrease in the saturation velocity. Figure 11 shows the temperature dependenceof Lg × fT . The decrease in the Lg × fT is mainly due to the decrease in the saturation velocity.

5

Summary

In summary, we investigated electron transport properties in the InGaAs/InAlAs heterostructures at high temperatures. The low-field mobility and the high-field saturation velocity werediscussed comparing with a theory. From room temperature to 400 K, we obtain approximately
26 % and 12 % decrease in the mobility and the saturation velocity, respectively. The highfrequency performance of the transistors at high temperatures shows a deterioration mainly due
to the decrease in the saturation velocity.

Acknowledgments
The authors are grateful to Dr. S. Tomiya for analysis of the metamorphic materials. This
work was supported by Center for Nano Materials and Technology (CNMT), Japan Advanced
Institute of Science and Technology (JAIST).

9References[1] H. Masato, T. Matsuno, and K. Inoue, Jpn. J. Appl. Phys. 30 (1991) 3850.
[2] T. Mishima, K. Higuchi, M. Mori, and M. Kudo, J. Cryst. Growth 150 (1995) 1230.
[3] H. Q. Zheng, K. Radhakrishnan, H. Wang, K. H. Yuan, S. F. Yoon, and G. I. Ng, Appl.
Phys. Lett. 77 (2000) 869.
[4] W. K. Liu, D. Lubyshev, Y. Wu, X. M. Fang, T. Yurasits, A. B. Cornfeld, D. Mensa ,S. Jaganathan, R. Pullela, M. Dahlstrom, P. K. Sundararajan, T. Mathew, and M. Rodwell,Proc. 13th Int. Conf. on InP and Related Materials (2001) 284.
[5] Y. Cordier, S. Bollaert, M. Zaknoune, J. diPersio, and D. Ferre, Proc. 10th Int. Conf. on
InP and Related Materials (1998) 211.
[6] H. Ono, S. Taniguchi, and T. Suzuki, Jpn. J. Appl. Phys. 43 (2004) 2259.
[7] M. T. Bulsara, C. Leitz, and E. A. Fitzgerald, Appl. Phys. Lett. 72 (1998) 1608.
[8] K. Seeger, Semiconductor Physics (Springer-Verlag, 1999) p. 208.
[9] W. Walukiewicz, H. E. Ruda, J. Lagowski, and H. C. Gatos, Phys. Rev. B30, (1984) 4571.
[10] I. Vurgaftman, J. R. Meyer, and L. R Ram-Mohan, J. Appl. Phys. 89 (2001) 5815.
[11] B. K. Ridley, Quantum Process in Semiconductors (Oxford Univ. Press, 1999) p. 181.
[12] S. Adachi, Physical Properties of III-V Semiconductor Compounds (John Wiley & Sons,
1992) p. 230.
10

[13] H. Ono, S. Taniguchi, and T. Suzuki, Proc. 16th Int. Conf. on InP and Related Materials(2004) 288.
[14] T. Enoki, K. Arai, and Y. Ishii, IEEE Electron Device Lett. 11 (1990) 502.
[15] P. A. Houston and A. G. R. Evans, Solid-State Electron. 20 (1977) 197.

11

Figure Captions
Figure 1
Atomic force microscope image of the surface of the metamorphic structure with indium content
of 0.43. A surface with crosshatch is observed.

Figure 2
Plan-view transmission electron microscope image for the metamorphic structure with indium
content of 0.43. High-density crystalline defects, threading dislocations and stacking faults, inthe active layer are observed.

Figure 3
Temperature dependence of the electron mobility in the metamorphic InGaAs/InAlAs heterostructures.

Figure 4
Temperature dependence of the normalized electron mobility in comparison with the theory of
the polar-optical-phonon scattering.

Figure 5
Relation between the room-temperature mobility and Γ-valley electron effective mass mΓ . The
mobility is proportional to 1/mΓ 3/2 .

Figure 6
The total delay time τ = 1/2πfT as a function of the reciprocal drain current density 1/Id atroom temperature for the 1.0-µm-gate-length transistors.
12Figure 7
Saturation velocity transit time τ0 as a function of the gate length Lg at room temperature.

Figure 8
Temperature dependence of the electron saturation velocity obtained from the delay-time analysis.

Figure 9
Temperature dependence of the normalized electron saturation velocity in comparison with theenergy relaxation theory.

Figure 10
Indium content dependence of the average electron effective mass estimated from the saturation
velocity, in comparison with the Γ-valley electron effective mass.

Figure 11
Temperature dependence of the Lg × fT . The high-frequency performance of the transistors at
high temperatures shows a deterioration mainly due to the decrease in the saturation velocity.

13Fig. 1. T.Suzuki et al.

Fig. 2. T.Suzuki et al.

Fig. 3. T.Suzuki et al.

Electron mobility [cm2/Vs]

5000
280

6000

7000

8000

9000

10000

11000

12000

300

340

360
Temperature [K]320Indium content 0.36
0.43
0.53
LM0.53380

400

Fig. 4. T.Suzuki et al.

Normalized mobility

0

0.2

0.4

0.6

0.8

1

1.2

300

400
Temperature [K]

350

450

TheoryIndium content 0.36
0.43
0.53
LM0.53500

Fig. 5. T.Suzuki et al.

Room-temperature mobility [cm2/Vs]

0

2000

4000

6000

8000

10000

12000

14000

16000

0

20

40

80 100 120 140 160(m0/mΓ)3/2

60

Fig. 6. T.Suzuki et al.

Total delay time τ [ps]

0

2

4

6

8

10

12

14

16

0

10

15

Reciprocal drain current density 1/Id [mm/A]

5

Lg=1.0 µm
Room temperature

Indium content 0.36
0.43
0.53
LM0.5320

Fig. 7. T.Suzuki et al.

Saturation velocity transit time τ0 [ps]

0

2

4

6

8

10

0

0.2

0.6

0.8
Gate length Lg [µm]0.41Room temperature

Indium content 0.36
0.43
0.53
LM0.53

1.2

Fig. 8. T.Suzuki et al.

Electron saturation velocity [107cm/s]

0.5
200

1

1.5

2

2.5

3

3.5

250

350

400

450
Temperature [K]300

Indium content 0.36
0.43
0.53
LM0.53500

550

Fig. 9. T.Suzuki et al.

Normalized saturation velocity

0

0.2

0.4

0.6

0.8

1

1.2

300

400
Temperature [K]

350

450

TheoryIndium content 0.36
0.43
0.53
LM0.53500

Fig. 10. T.Suzuki et al.

Electron mass

0
0.2

0.02

0.04

0.06

0.08

0.1

0.3

0.5

0.6
Indium content

0.4

average effective mass m∗/m0
mΓ/m0

0.7

0.8

Fig. 11. T.Suzuki et al.

Lg x fT [GHz ⋅ µm]

10
200

15

20

25

30

35

40

250

300

400
Temperature [K]

350

450

Indium content 0.36
0.43
0.53
LM0.53500550