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InGaAs metamorphic high-electron mobility transistor structures with tensile and compressive strain
TSF-30465; No of Pages 5 Thin Solid Films xxx (2012) xxx–xxx
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Optical characterization of InAlAs/InGaAs metamorphic high-electron mobility transistor structures with tensile and compressive strain Ching-Hsiang Chan b, Ching-Hwa Ho a, b,⁎, Ming-Kai Chen c, Yu-Shyan Lin c, Ying-Sheng Huang b, Wei-Chou Hsu d a
Graduate Institute of Applied Science and Technology, National Taiwan University of Science and Technology, Taipei 106, Taiwan Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan Institute of Optoelectronic Engineering, National Dong Hwa University, Hualien 974, Taiwan d Institute of Microelectronics, Department of Electrical Engineering, National Cheng Kung University, Tainan 701, Taiwan b c
a r t i c l e
i n f o
Available online xxxx Keywords: Optical property Metamorphic high-electron mobility transistor Two dimensional electron gas Photoreflectance Photoluminescence
a b s t r a c t We have measured surface photovoltage (SPV), photoreflectance (PR), and photoluminescence (PL) spectra of two InAlAs/InxGa1 − xAs/InAlAs metamorphic high-electron mobility transistor (MHEMT) structures. One possesses a V-shaped InxGa1 − xAs (x= 0.3–0.5–0.3) tensile-strained channel in In0.5Al0.5As/InxGa1 − xAs/In0.5Al0.5As heterostructures, and the other is an In0.42Al0.58As/In0.53Ga0.47As/In0.42Al0.58As MHEMT structures with InxGa1 − xAs (x = 0.53) compressively-strained channel grown on GaAs by molecular beam epitaxy. The comparison of SPV, PR, and PL spectra facilitates the identification of channel-well transitions in the MHEMT structures with different InxGa1 − xAs channels. Inter-subband transitions, Fermi-level energies, and built-in electric field of the two MHEMT structures with dissimilar InxGa1 − xAs channel are evaluated and discussed from the experimental analyses of SPV, PR and PL measurements. The results showed that the design of tensile-strained MHEMT structure enhances sheet-carrier density and avoids surface-roughness scattering by increasing V-shape electric field between the two channel interfaces. The electron mobility of the tensile-strained MHEMT structure is hence being promoted. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The InAlAs/InGaAs based metamorphic high-electron-mobility transistors (MHEMTs) grown on GaAs possess high speed, low noise and wide bandwidth which avoid drawbacks of using InP as a substrate including fragility, smallness of wafer size and high cost [1–3]. For the HEMT devices, the main differences between the MHEMTs and pseudomorphic HEMTs (PHEMTs) are the MHEMTs contain an extra metamorphic buffer layer (e.g. InxAl1 − xAs) in between the GaAs substrate and the InAlAs/InGaAs device layers to accommodate stress-induced dislocations caused by lattice mismatch [4]. The indium content in the channel layer is also an important factor for determination of device performance in the MHEMTs. The In-rich channels have larger mobility but lower breakdown voltage whereas the lower-In-content channels posses high break-down voltage but low speed. It exists a tradeoff between the operation power and speed in the InAlAs/InGaAs MHEMT structures grown on GaAs [5,6]. Therefore, optical studies on the channel properties of the MHEMT structures including channelwell transition energies, two-dimension-electron gas (2DEG), Fermi
⁎ Corresponding author. Tel.: + 886 227303772; fax: + 886 227303733. E-mail address: [email protected] (C.-H. Ho).
level, mobility, current density, strain type, band diagram, as well as built-in electric field in the device structures are crucial and essential, which need to be explored. Photoreflectance (PR) and photoluminescence (PL) are powerful tools for optical characterization of semiconductor device structures [7,8]. The PL and PR techniques had been proven to be effective, contactless and nondestructive methods for optical characterization of pseudomorphic HEMT structures [9]. Surface photovoltage (SPV) spectroscopy is also a useful technique for characterization of semiconductor and device structures [10]. Different kinds of optical information can be respectively obtained from PL, PR and SPV measurements. In comparison with the optical information, the channel and device properties of the MHEMTs can be realized. In this paper, we characterize two MHEMT structures of one In0.5Al0.5As/InxGa1 − xAs/In0.5Al0.5As with a V-shaped InxGa1 − xAs (x = 0.3–0.5–0.3) tensile-strained (TS) channel and the other is an In0.42Al0.58As/In0.53Ga0.47As/In0.42Al0.58As MHEMT with InxGa1 − xAs (x = 0.53) compressively-strained (CS) channel grown on GaAs by molecular beam epitaxy (MBE). The optical methods for probing the MHEMT structures are PL, PR, and SPV measurements. The SPV spectra revealed interband transition features for the epitaxial layers consisted in the TS- and CS-MHEMT structures. Analyses of the PL and PR spectra identified that sheet carriers of 2DEG are introduced in the TS and CS channels for the MHEMTs. The high-density 2DEG also lifts up the
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C.-H. Chan et al. / Thin Solid Films xxx (2012) xxx–xxx
2. Experimental details Two MHEMT structures with tensile-strained and compressivelystrained channels were respectively grown by MBE. Fig. 1 shows the layer structures of the two MHEMTs. The TS-MHEMT consisted of a 500-nm In1 − yAlyAs (y = 1–0.5) metamorphic buffer layer, a 200nm In0.5Al0.5As undoped barrier, a 20-nm undoped symmetrically graded V-shaped InxGa1 − xAs channel (x = 0.3–0.5–0.3), a 3-nm undoped In0.5Al0.5As spacer layer, a δ(n +)-In0.5Al0.5As layer with n = 2 × 10 12 cm − 2, a 2-nm undoped In0.5Al0.5As spacer, a δ(n +)In0.5Al0.5As layer, a 25-nm undoped In0.5Al0.5As layer, and finally a 20-nm n + InGaAs cap layer. The CS-MHEMT structure included a 500-nm In1 − yAlyAs (y = 1–0.58) metamorphic buffer layer, a 200nm In0.42Al0.58As undoped barrier, a 20-nm In0.53 Ga0.47As channel, a 3-nm undoped In0.42Al0.58As spacer layer, a δ(n +)-In0.42Al0.58As layer with n = 2 × 10 12 cm − 2, a 2-nm undoped In0.42Al0.58As spacer layer, a δ(n +)-In0.42Al0.58As layer with n = 2 × 10 12 cm − 2, a 25-nm undoped In0.42Al0.58As layer, and finally a 20-nm n + InGaAs cap layer. The fabrication processes of the MHEMTs were described elsewhere [11]. Before the progress of optical measurements, the cap layers of the device structures were removed by chemical etching. The PL experiments were performed in an integrated spectral measurement system, where a Triax 320 imaging spectrometer equipped with three gratings of 600, 1200, and 2400 groves/mm acted as the optical dispersion units [8]. A 532-nm laser acted as the pumping light source. A TE-cooled InGaAs detector attached at the outside slit of the spectrometer was employed for optical detection. AC phase-sensitive detection (PSD) was implemented by using a lock-in amplifier to improve the signal-to-noise ratio. The pumping laser was chopped at a frequency of 200 Hz. For PR measurements, an 150 W halogen lamp dispersed by a PTI 0.2 m monochromator (1200 grooves/mm grating inside) provide the monochromatic light. The incident monochromatic light was focused onto the sample with a spot size of about hundred μm 2. The reflected light from the MHEMT sample surface was collected and detected by a Si diode
InGaAs cap layer i-In0.5Al0.5As
CS-MHEMT
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
(b)
In0.42Al0.58As
CS-MHEMT 0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.7
1.8
1.9
2.0
Fig. 2. (a) Surface photovoltage (SPV) and (b) DSPV spectra of the TS- and CS-MHEMTs at 300 K.
detector. The signal was detected and recorded via EG&G model 7265 lock-in amplifier and a personal computer. For SPV measurements, the same monochromator as PR was used for the monochromatic light source. For sample preparation, a capacitor-like configuration with top-side surface contacts a copper mesh, and the
i-In0.42Al0.58As
2nm
(n )
i-In0.42Al0.58As
3nm
InxGa1-xAs (x=0.53)
20nm
Co m p re s s iv e ly -s t ra in e d c h a n n e l
i-In0.42Al0.58As
200nm
i-In1-yAlyAs (y=1-0.5) Metamorphic buffer layer 500nm
i-In1-yAlyAs (y=1-0.58) Metamorphic buffer layer 500nm
S.I.GaAs Substrate
S.I.GaAs Substrate
TS-MHEMT
1.6
Photon Energy (eV)
+
200nm
2.0
GaAs
25nm
Te n s ile -s t ra in e d c h a n n e l
1.9
300K
(n+)
InxGa1-xAs (x=0.3-0.5-0.3) 20nm
1.8
In0.5Al0.5As
TS-MHEMT
i-In0.42Al0.58As
3nm
1.7
GaAs
25nm
(n )
1.6
Photon Energy (eV)
20nm
2nm
i-In0.5Al0.5As
TS-MHEMT
InGaAs cap layer
+
i-In0.5Al0.5As
300K
20nm
(n+)
i-In0.5Al0.5As
(a) Photovoltage (Arb. Units)
Fermi level (EF) higher above the first E1, and second E2 states (n= 1 and n = 2) in the channel conduction-band well. Device parameters of 2DEG, channel inter-subband transitions, Fermi-level energy, and electric field for the TS and CS MHEMTs are evaluated. The discrepancy in between the performances of the two MHEMT structures is discussed.
DSPV
2
CS-MHEMT
Fig. 1. The device structures of a tensile-strained V-shape MHEMT and a compressive-strained MHEMT.
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C.-H. Chan et al. / Thin Solid Films xxx (2012) xxx–xxx
ΔR/R (Arb. Units) DSPV
(a) TS-MHEMT
300K DSPV
InGaAs 2DEG
GaAs
FK oscillations
In Al As 0.5
0.5
PR
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Photon Energy (eV)
ΔR/R (Arb. Units) DSPV
(b) CS-MHEMT
300K DSPV
GaAs
InGaAs 2DEG
In
In Al As 1-y
0.42
y
Al
0.58
As
(y=1-0.58)
PR
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Photon Energy (eV) Fig. 3. The DSPV and PR spectra of (a) TS-MHEMT and (b) CS-MHEMT structures. The Franz–Keldysh oscillations of the TS V-shape channel are presented in the PR spectrum of the TS-MHEMT.
other side of the MHEMT closely attached on a copper sample holder by silver paste. The photoexcited electron–hole pairs were extracted out from the top and bottom electrodes of the capacitor-like configuration, and then sent to a low-noise amplifier. The incident light was chopped at 200 Hz and an AC PSD detection was employed for the SPV measurement. 3. Results and discussion Fig. 2(a) shows the SPV spectra of the TS- and CS-MHEMT structures at 300 K. The SPV spectrum of the TS-HMEMT shows a smaller broadened peak near 1 eV, which is inferred to come from the intersubband transitions in the InxGa1 − xAs (x = 0.3–0.5–0.3) channel related to 2DEG. The broadened peak near 1 eV was weaker and not clearly detected in the SPV spectrum of the CS-MHEMT sample. Besides, there are also some transition features near 1.4 eV and 1.57 eV for TS-HEMT, and near 1.4 eV and 1.7 eV for CS-MHEMT in Fig. 2(a). The features can be enhanced more clearly by taking the
3
SPV spectra with the first derivative mathematical processing (DSPV). The DSPV results can show many clear features as depicted in Fig. 2(b). The transition features near 1.42 eV for both TS- and CS-samples are originated from the GaAs substrate. The feature near 1.57 eV in the TS-MHEMT comes from the transition of In0.5Al0.5As barrier layer. The DSPV feature of 1.7 eV is caused by the transition in the In0.42Al0.58As barrier layer in the CS-MHEMT sample. In order to identify intersubband and interband transitions of the TS- and CS-MHEMT structures, PR measurements are carried out at 300 K. Fig. 3(a) and (b) shows, respectively, the DSPV and PR spectra of TS- and CS-MHEMT structures from 0.75 to 2.0 eV. In comparison with the DSPV spectrum in Fig. 3(a), the PR result identifies the transitions of 1.42 eV for GaAs and 1.57 eV for the In0.5Al0.5As barrier layer in the TS-MHEMT. Especially, a broadened feature at 0.8–1.0 eV combined with a series of Franz–Keldysh (FK) oscillations was presented at lower energy side of the PR spectrum in Fig. 3(a). The broadened feature closely relates to the 2DEG signal coming from the TS channel well and the FK oscillations correlate with the built-in electric field in the semiconductor device [12]. The PR and DSPV spectra in Fig. 3(b) also verify the transition energies of 1.38 eV for the metamorphic buffer layer In1 − yAlyAs (y = 1–0.58) and 1.7 eV for the In0.42Al0.58As barrier layer in the CS-MHEMT sample. The PR spectrum in Fig. 3(b) also proves the existence of 2DEG in the CS-MHEMT because a broadened feature located near 0.85–1.1 eV was also detected. In the presence of 2DEG, the inter-subband absorption function becomes a broadened two-dimensional density of states multiplied by a Fermi level filling function [9]. Therefore, a 2DEG feature should contain channel-well intersubband transitions and it shows quite broad in the PR spectrum [9]. In order to further analyze 2DEG and channel-well intersubband transition energies for the TS- and CS-MHEMT structures, theoretical quantum-well calculations and PL measurements were carried out. For the estimation of strain-induced energy shift in the channel wells of the MHEMTs, a physical model proposed for strained and relaxed InGaAs alloys was used [13]. The strains in the TS-MHEMT and CS-MHEMT calculated from the lattice-constant differences between channel and barrier layers are + 0.014 [tensile: (5.855 Å–5.744 Å)/ 5.744 Å] and −0.0076 [compressive: (5.823 Å–5.868 Å)/5.868 Å], respectively. The differences will result in a red shift for the TS sample but a blue shift for the CS sample. The theoretical quantum-well calculations by taking into account the TS and CS effects on light hole and heavy hole determined the values of intersubband transition energies as listed in Table 1. The 11H defines the transition between E1 (the first electron state) in conduction-band well and HH1 (the first heavy-hole state) in the valence-band well. Because of different strain type, the energy of 11H is slight larger than that of 11L in the TS sample while the energies show a contradict behavior in the CS-MHEMT as those shown in Table 1. Fig. 4 shows the room-temperature PL and PR spectra of (a) TS-MHEMT and (b) CS-MHEMT. The calculated results of intersubband transition energies of 11H, 11L, 21H, and 21L are also indicated with arrows for comparison with the PL and PR features in Fig. 4. The PL intensities in Fig. 4 show that the E1 related peak (including 11H and 11L) is lower than that of E2 related peak (21H and 21L) for both TS- and CS-MHEMT structures. It is an indication that the EF is higher above the E2 state in the channel-conduction
Table 1 C The experimental and calculated inter-subband transition energies of the MHEMT structures. The calculated values of Fermi-level energy (EF–Em ) and 2DEG density for the MHEMTs at 300 K are also included for comparison. Sample
TS CS
Channel composition
In0.3Ga0.7As V-shape x = 0.3–0.5–0.3 In0.5Ga0.5As In0.53Ga0.47As
Tool
Cal. Expt. and Cal. Cal. Expt. and Cal.
Inter-subband transition energy (eV)
Fermi-level energy (meV)
11H
11L
21H
21L
0.847 0.785 0.618 0.797
0.841 0.779 0.610 0.805
0.884 0.824 0.662 0.843
0.878 0.818 0.654 0.851
EF–E1C
EF–E2C
EF–E3C
N2d (1012 cm− 2)
84.9
45.8
− 14.2
3.5
88.9
42.8
− 26.2
3.0
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(a)
(a)
300K
TS-MHEMT
22L 21H (E1 related) 21L (E related) 2 11H 11L 22H
300K
PL
PR 0.7
0.8
0.9
1.0
1.1
Expt.
2DEG FK oscillations
0.8
1.2
1.0
1.2
0.12
300K
CS-MHEMT
(b)
TS-MHEMT
0.10
21L 21H (E related) 2 (E1 related) 11L 11H
PL PR
0.08 0.06 0.04 0.02
FK oscillations fit
0.00 0.7
0.8
0.9
1.4
Photon Energy (eV)
(4/3π) (E-E0)3/2 (eV)3/2
ΔR/R (Arb. Units) Intensity (Arb. Units)
Photon Energy (eV)
(b)
PR
TS-MHEMT
ΔR/R (Arb. Units)
ΔR/R (Arb. Units) Intensity (Arb. Units)
4
1.0
1.1
1.2
0
Photon Energy (eV)
band well for all the MHEMTs [14]. The other evidence to verify this point is the energies of E1 and E2 related peaks (PL) are lower than the broadened 2DEG features in the corresponding PR spectra in Fig. 4(a) and (b). The transition probability for the E1 and E2 states is lower because they are filled with 2DEG to reduce the intensities of PR signal. In the presence of 2DEG, the inter-subband absorption function becomes a broadened two-dimensional density of states multiplied by a Fermi level filling function. The one-electron theory indicates that the imaginary part of the complex dielectric function (ε = ε1 + iε2) can be expressed as [9]
j
ð1Þ
where Dj is the amplitude of the jth feature; E is the photon energy; Γj is the broadening parameter, and Ej(mnH) is the inter-subband enerC V C V gy given by Ej(mnH) = Em, j − En, j(H). Em, j and En, j(H) are the energies
EF
TS-MHEMT
6
8
10
Fig. 6. (a) Decomposition of experimental PR spectrum of the TS-MHEMT into two parts for analyses of 2DEG and FK oscillations in the V-shape channel. (b) The dependence of [4/(3π)](En − E0)3/2 vs. index of extremums in the FK oscillations of TS-MHEMT. The dashed line is the least-square fit to Eq. (3).
of the mth conduction and nth heavy-hole valence subbands, respectively, referred to the jth feature. The mnH denotes a transition from mth conduction subband to nth heavy-hole valence subband. The Fermi function of Eq. (1) can be expressed as 9 > > > = 1 j ; fe ¼ C > > ðλE−λE ð mnH Þ− E −E j F > > m;j > > ; :1 þ exp kT 8 > > > <
In0.53Ga0.47As
E3 E2 E1
ð2Þ
where λ = mh*/(me* + mh*), me* and mh* are the electron and in-plane heavy-hole effective masses, respectively, in units of free electron mass. Eqs. (1) and (2) are also suitable for the analysis of light-hole transitions in the valence subbands. The mnL denotes a transition from mth conduction subband to nth light-hole subband. The broadened PR feature in the PR spectra of Fig. 4(a) and (b) can be analyzed
InxGa1-xAs (X=0.3-0.5-0.3)
4
Index n
Fig. 4. Room-temperature PL and PR spectra of (a) TS-MHEMT and (b) CS-MHEMT device structures.
n h io j ε2 ¼ ∑ Dj Im ln E−Ej ðmnHÞ þ iΓj ⋅ 1−f e ;
2
E3
EF
E2 E1 CS-MHEMT
Fig. 5. The representative schemes for the confined states, Fermi level, and channel conduction-band wells of the TS- and CS-MHEMTs.
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using Eq. (1), and the analyses extract the values of E1, E2, EF–E1C and EF–E2C listed in Table 1. The peak positions in the PL spectra (11H,L and 21H,L) in Fig. 4 also verified the fitted values of E1 and E2 from PR in the conduction-band well of the CS- and TS-MHEMTs. Fig. 5 shows the representative conduction-band wells for the CS- and TSMHEMTs. The EF is higher than E1 and E2 but is lower than E3. The calculated values of EF–E1C, EF–E2C and EF–E3C for the two MHEMTs are also listed in Table 1 for comparison. The sheet carrier density of 2DEG can be expressed as N2D ¼
" ! !# C C me kT EF −E1 EF −E2 þ exp ⋅ ln 1 þ exp [15], kT kT π⋅ℏ2
⁎ where m⁎ e is the electron effective mass by taking me = 0.058 m0 (electron rest mass) herein for InGaAs [9]. The obtained values of sheet carrier density N2D are 3.5 × 10 12 cm − 2 and 3.0 × 10 12 cm − 2 for the TS- and CS-MHEMTs, which are close to the previous sheet densities obtained by Hall-effect measurements [11]. The higher value of N2D for the TS-MHEMT is inferred to come from a better carrier confinement in the V-shape channel as well as a lower In content than that of CS-MHEMT to render a superior current–voltage characteristic [11]. To further analyze the built-in electric field of the MHEMT structure, the PR spectrum in Fig. 4(a) can be decomposed into two parts for distinct analyses of 2DEG and built-in electric field of the TSMHEMT structure. Fig. 6(a) shows the decomposition of PR spectrum into two parts respectively for 2DEG and FK oscillations. As shown in Fig. 6(a), the position of nth extremum in the FK oscillations can be expressed by: [12] nπ ¼ ð4=3Þ½ðEn −E0 Þ=ℏW
3=2
þ χ;
ð3Þ
where En is the photon energy of the nth extremum; E0 is the band gap, and χ is an arbitrary phase factor. The electro-optic energy ℏW is given by (ℏW) 3 = q 2ℏ 2F 2/2μ, where F is the electric field and μ is 1 1 1 given by ¼ þ . The me* and mh* are the effective masses of μ me mh electrons and holes. Eq. (3) indicates a linear relationship between the [4/(3π)][(En − E0)/ℏW] 3/2 and the index of nth extremum in the FK oscillations, for calculation of built-in electric field of the V-shape channel in the TS-MHEMT. Fig. 6(b) plots [4/(3π)](En − E0) 3/2 vs. the index of extremums in the FK oscillations of Fig. 6(a). The obtained value of built-in electric field was F = 128 ± 6 kV cm − 1 for the graded V-shape channel of the TS-MHEMT. The design of V-shape channel can enhance electron mobility by confining 2DEG localization at the center of the V-shape channel, which avoids surface-roughness scattering with electron transport along the channel interfaces.
5
4. Conclusions In conclusion, optoelectronic properties of two MHEMT structures (InAlAs/InGaAs/InAlAs) with one tensile-strained V-shape channel and one compressive-strained channel have been evaluated by SPV, PR, and PL measurements at 300 K. The SPV measurements identify the interband transitions of the barrier layer and buffer layer in the CS- and TS-MHEMT structures. The results of PL measurements confirmed the energy positions of 11H and 11L for the E1 state, and 21H and 21L for the E2 state, respectively, in the channel conduction-band wells of the two MHEMTs. The analyses of PR spectra by taking into account the Fermi-level filling function determined the Fermi-level energy and the sheet carrier density for the CS- and TS-MHEMTs. The presence of FK oscillations in the PR spectrum of the TS-MHEMT facilitates the evaluation of built-in electric field of the V-shape channel. The experimental analyses show that the design of TS-MHEMT structure enhances 2DEG density and reduces surfaceroughness scattering on the channel interfaces in comparison with the CS-MHEMT structure. Acknowledgments This work was sponsored by the National Science Council of Taiwan under the grant no. NSC-98-2221-E-011-151-MY3. References [1] M. Boudrissa, E. Delos, C. Gaquiere, M. Rousseau, Y. Cordier, D. Theron, J.C. De Jaeger, IEEE Trans. Electron Devices 48 (2001) 1037. [2] W.C. Hsu, Y.J. Chen, C.S. Lee, T.B. Wang, Y.S. Lin, C.L. Wu, IEEE Electron Device Lett. 26 (2005) 59. [3] K. Ouchi, T. Mishima, M. Kudo, H. Ohta, Jpn. J. Appl. Phys. 41 (2002) 1004. [4] W.C. Hsu, Y.J. Chen, C.S. Lee, T.B. Wang, J.C. Huang, D.H. Huang, K.H. Su, Y.S. Lin, C.L. Wu, IEEE Trans. Electron Devices 52 (2005) 1079. [5] M. Zaknoune, B. Bonte, C. Gaquiere, Y. Cordier, Y. Druelle, D. Théron, Y. Crosnier, IEEE Electron Device Lett. 19 (1998) 345. [6] M. Boudrissa, E. Delos, Y. Cordier, D. Théron, J.C. De Jaeger, IEEE Electron Device Lett. 21 (2000) 512. [7] F.H. Pollak, H. Shen, Mater. Sci. Eng. R10 (1993) 275. [8] C.H. Ho, K.W. Huang, Y.S. Lin, D.Y. Lin, Opt. Express 13 (2005) 3951. [9] C.H. Ho, J.S. Li, Y.S. Lin, Semicond. Sci. Technol. 24 (2009) 035013. [10] C.H. Chan, J.D. Wu, Y.S. Huang, Y.K. Su, K.K. Tiong, J. Appl. Phys. 106 (2009) 043523. [11] W.C. Hsu, D.H. Huang, Y.S. Lin, Y.J. Chen, J.C. Huang, C.L. Wu, IEEE Trans. Electron Devices 53 (2006) 406. [12] H. Shen, F.H. Pollak, Phys. Rev. B 42 (1990) 7097. [13] Ch. Köpf, H. Kosina, S. Selberherr, Solid State Electron. 41 (1997) 1139. [14] D.Y. Lin, Y.S. Huang, T.S. Shou, K.K. Tiong, F.H. Pollak, J. Appl. Phys. 90 (2001) 6421. [15] D.Y. Lin, M.C. Wu, H.J. Lin, J.S. Wu, Phys. E 40 (2008) 1757.
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Optical characterization of InAlAs/InGaAs metamorphic high-electron mobility transistor structures with tensile and compressive strain Ching-Hsiang Chan b, Ching-Hwa Ho a, b,⁎, Ming-Kai Chen c, Yu-Shyan Lin c, Ying-Sheng Huang b, Wei-Chou Hsu d a
Graduate Institute of Applied Science and Technology, National Taiwan University of Science and Technology, Taipei 106, Taiwan Department of Electronic Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan Institute of Optoelectronic Engineering, National Dong Hwa University, Hualien 974, Taiwan d Institute of Microelectronics, Department of Electrical Engineering, National Cheng Kung University, Tainan 701, Taiwan b c
a r t i c l e
i n f o
Available online xxxx Keywords: Optical property Metamorphic high-electron mobility transistor Two dimensional electron gas Photoreflectance Photoluminescence
a b s t r a c t We have measured surface photovoltage (SPV), photoreflectance (PR), and photoluminescence (PL) spectra of two InAlAs/InxGa1 − xAs/InAlAs metamorphic high-electron mobility transistor (MHEMT) structures. One possesses a V-shaped InxGa1 − xAs (x= 0.3–0.5–0.3) tensile-strained channel in In0.5Al0.5As/InxGa1 − xAs/In0.5Al0.5As heterostructures, and the other is an In0.42Al0.58As/In0.53Ga0.47As/In0.42Al0.58As MHEMT structures with InxGa1 − xAs (x = 0.53) compressively-strained channel grown on GaAs by molecular beam epitaxy. The comparison of SPV, PR, and PL spectra facilitates the identification of channel-well transitions in the MHEMT structures with different InxGa1 − xAs channels. Inter-subband transitions, Fermi-level energies, and built-in electric field of the two MHEMT structures with dissimilar InxGa1 − xAs channel are evaluated and discussed from the experimental analyses of SPV, PR and PL measurements. The results showed that the design of tensile-strained MHEMT structure enhances sheet-carrier density and avoids surface-roughness scattering by increasing V-shape electric field between the two channel interfaces. The electron mobility of the tensile-strained MHEMT structure is hence being promoted. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The InAlAs/InGaAs based metamorphic high-electron-mobility transistors (MHEMTs) grown on GaAs possess high speed, low noise and wide bandwidth which avoid drawbacks of using InP as a substrate including fragility, smallness of wafer size and high cost [1–3]. For the HEMT devices, the main differences between the MHEMTs and pseudomorphic HEMTs (PHEMTs) are the MHEMTs contain an extra metamorphic buffer layer (e.g. InxAl1 − xAs) in between the GaAs substrate and the InAlAs/InGaAs device layers to accommodate stress-induced dislocations caused by lattice mismatch [4]. The indium content in the channel layer is also an important factor for determination of device performance in the MHEMTs. The In-rich channels have larger mobility but lower breakdown voltage whereas the lower-In-content channels posses high break-down voltage but low speed. It exists a tradeoff between the operation power and speed in the InAlAs/InGaAs MHEMT structures grown on GaAs [5,6]. Therefore, optical studies on the channel properties of the MHEMT structures including channelwell transition energies, two-dimension-electron gas (2DEG), Fermi
⁎ Corresponding author. Tel.: + 886 227303772; fax: + 886 227303733. E-mail address: [email protected] (C.-H. Ho).
level, mobility, current density, strain type, band diagram, as well as built-in electric field in the device structures are crucial and essential, which need to be explored. Photoreflectance (PR) and photoluminescence (PL) are powerful tools for optical characterization of semiconductor device structures [7,8]. The PL and PR techniques had been proven to be effective, contactless and nondestructive methods for optical characterization of pseudomorphic HEMT structures [9]. Surface photovoltage (SPV) spectroscopy is also a useful technique for characterization of semiconductor and device structures [10]. Different kinds of optical information can be respectively obtained from PL, PR and SPV measurements. In comparison with the optical information, the channel and device properties of the MHEMTs can be realized. In this paper, we characterize two MHEMT structures of one In0.5Al0.5As/InxGa1 − xAs/In0.5Al0.5As with a V-shaped InxGa1 − xAs (x = 0.3–0.5–0.3) tensile-strained (TS) channel and the other is an In0.42Al0.58As/In0.53Ga0.47As/In0.42Al0.58As MHEMT with InxGa1 − xAs (x = 0.53) compressively-strained (CS) channel grown on GaAs by molecular beam epitaxy (MBE). The optical methods for probing the MHEMT structures are PL, PR, and SPV measurements. The SPV spectra revealed interband transition features for the epitaxial layers consisted in the TS- and CS-MHEMT structures. Analyses of the PL and PR spectra identified that sheet carriers of 2DEG are introduced in the TS and CS channels for the MHEMTs. The high-density 2DEG also lifts up the
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Please cite this article as: C.-H. Chan, et al., Thin Solid Films (2012), doi:10.1016/j.tsf.2012.03.060
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2. Experimental details Two MHEMT structures with tensile-strained and compressivelystrained channels were respectively grown by MBE. Fig. 1 shows the layer structures of the two MHEMTs. The TS-MHEMT consisted of a 500-nm In1 − yAlyAs (y = 1–0.5) metamorphic buffer layer, a 200nm In0.5Al0.5As undoped barrier, a 20-nm undoped symmetrically graded V-shaped InxGa1 − xAs channel (x = 0.3–0.5–0.3), a 3-nm undoped In0.5Al0.5As spacer layer, a δ(n +)-In0.5Al0.5As layer with n = 2 × 10 12 cm − 2, a 2-nm undoped In0.5Al0.5As spacer, a δ(n +)In0.5Al0.5As layer, a 25-nm undoped In0.5Al0.5As layer, and finally a 20-nm n + InGaAs cap layer. The CS-MHEMT structure included a 500-nm In1 − yAlyAs (y = 1–0.58) metamorphic buffer layer, a 200nm In0.42Al0.58As undoped barrier, a 20-nm In0.53 Ga0.47As channel, a 3-nm undoped In0.42Al0.58As spacer layer, a δ(n +)-In0.42Al0.58As layer with n = 2 × 10 12 cm − 2, a 2-nm undoped In0.42Al0.58As spacer layer, a δ(n +)-In0.42Al0.58As layer with n = 2 × 10 12 cm − 2, a 25-nm undoped In0.42Al0.58As layer, and finally a 20-nm n + InGaAs cap layer. The fabrication processes of the MHEMTs were described elsewhere [11]. Before the progress of optical measurements, the cap layers of the device structures were removed by chemical etching. The PL experiments were performed in an integrated spectral measurement system, where a Triax 320 imaging spectrometer equipped with three gratings of 600, 1200, and 2400 groves/mm acted as the optical dispersion units [8]. A 532-nm laser acted as the pumping light source. A TE-cooled InGaAs detector attached at the outside slit of the spectrometer was employed for optical detection. AC phase-sensitive detection (PSD) was implemented by using a lock-in amplifier to improve the signal-to-noise ratio. The pumping laser was chopped at a frequency of 200 Hz. For PR measurements, an 150 W halogen lamp dispersed by a PTI 0.2 m monochromator (1200 grooves/mm grating inside) provide the monochromatic light. The incident monochromatic light was focused onto the sample with a spot size of about hundred μm 2. The reflected light from the MHEMT sample surface was collected and detected by a Si diode
InGaAs cap layer i-In0.5Al0.5As
CS-MHEMT
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
(b)
In0.42Al0.58As
CS-MHEMT 0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.7
1.8
1.9
2.0
Fig. 2. (a) Surface photovoltage (SPV) and (b) DSPV spectra of the TS- and CS-MHEMTs at 300 K.
detector. The signal was detected and recorded via EG&G model 7265 lock-in amplifier and a personal computer. For SPV measurements, the same monochromator as PR was used for the monochromatic light source. For sample preparation, a capacitor-like configuration with top-side surface contacts a copper mesh, and the
i-In0.42Al0.58As
2nm
(n )
i-In0.42Al0.58As
3nm
InxGa1-xAs (x=0.53)
20nm
Co m p re s s iv e ly -s t ra in e d c h a n n e l
i-In0.42Al0.58As
200nm
i-In1-yAlyAs (y=1-0.5) Metamorphic buffer layer 500nm
i-In1-yAlyAs (y=1-0.58) Metamorphic buffer layer 500nm
S.I.GaAs Substrate
S.I.GaAs Substrate
TS-MHEMT
1.6
Photon Energy (eV)
+
200nm
2.0
GaAs
25nm
Te n s ile -s t ra in e d c h a n n e l
1.9
300K
(n+)
InxGa1-xAs (x=0.3-0.5-0.3) 20nm
1.8
In0.5Al0.5As
TS-MHEMT
i-In0.42Al0.58As
3nm
1.7
GaAs
25nm
(n )
1.6
Photon Energy (eV)
20nm
2nm
i-In0.5Al0.5As
TS-MHEMT
InGaAs cap layer
+
i-In0.5Al0.5As
300K
20nm
(n+)
i-In0.5Al0.5As
(a) Photovoltage (Arb. Units)
Fermi level (EF) higher above the first E1, and second E2 states (n= 1 and n = 2) in the channel conduction-band well. Device parameters of 2DEG, channel inter-subband transitions, Fermi-level energy, and electric field for the TS and CS MHEMTs are evaluated. The discrepancy in between the performances of the two MHEMT structures is discussed.
DSPV
2
CS-MHEMT
Fig. 1. The device structures of a tensile-strained V-shape MHEMT and a compressive-strained MHEMT.
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ΔR/R (Arb. Units) DSPV
(a) TS-MHEMT
300K DSPV
InGaAs 2DEG
GaAs
FK oscillations
In Al As 0.5
0.5
PR
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Photon Energy (eV)
ΔR/R (Arb. Units) DSPV
(b) CS-MHEMT
300K DSPV
GaAs
InGaAs 2DEG
In
In Al As 1-y
0.42
y
Al
0.58
As
(y=1-0.58)
PR
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Photon Energy (eV) Fig. 3. The DSPV and PR spectra of (a) TS-MHEMT and (b) CS-MHEMT structures. The Franz–Keldysh oscillations of the TS V-shape channel are presented in the PR spectrum of the TS-MHEMT.
other side of the MHEMT closely attached on a copper sample holder by silver paste. The photoexcited electron–hole pairs were extracted out from the top and bottom electrodes of the capacitor-like configuration, and then sent to a low-noise amplifier. The incident light was chopped at 200 Hz and an AC PSD detection was employed for the SPV measurement. 3. Results and discussion Fig. 2(a) shows the SPV spectra of the TS- and CS-MHEMT structures at 300 K. The SPV spectrum of the TS-HMEMT shows a smaller broadened peak near 1 eV, which is inferred to come from the intersubband transitions in the InxGa1 − xAs (x = 0.3–0.5–0.3) channel related to 2DEG. The broadened peak near 1 eV was weaker and not clearly detected in the SPV spectrum of the CS-MHEMT sample. Besides, there are also some transition features near 1.4 eV and 1.57 eV for TS-HEMT, and near 1.4 eV and 1.7 eV for CS-MHEMT in Fig. 2(a). The features can be enhanced more clearly by taking the
3
SPV spectra with the first derivative mathematical processing (DSPV). The DSPV results can show many clear features as depicted in Fig. 2(b). The transition features near 1.42 eV for both TS- and CS-samples are originated from the GaAs substrate. The feature near 1.57 eV in the TS-MHEMT comes from the transition of In0.5Al0.5As barrier layer. The DSPV feature of 1.7 eV is caused by the transition in the In0.42Al0.58As barrier layer in the CS-MHEMT sample. In order to identify intersubband and interband transitions of the TS- and CS-MHEMT structures, PR measurements are carried out at 300 K. Fig. 3(a) and (b) shows, respectively, the DSPV and PR spectra of TS- and CS-MHEMT structures from 0.75 to 2.0 eV. In comparison with the DSPV spectrum in Fig. 3(a), the PR result identifies the transitions of 1.42 eV for GaAs and 1.57 eV for the In0.5Al0.5As barrier layer in the TS-MHEMT. Especially, a broadened feature at 0.8–1.0 eV combined with a series of Franz–Keldysh (FK) oscillations was presented at lower energy side of the PR spectrum in Fig. 3(a). The broadened feature closely relates to the 2DEG signal coming from the TS channel well and the FK oscillations correlate with the built-in electric field in the semiconductor device [12]. The PR and DSPV spectra in Fig. 3(b) also verify the transition energies of 1.38 eV for the metamorphic buffer layer In1 − yAlyAs (y = 1–0.58) and 1.7 eV for the In0.42Al0.58As barrier layer in the CS-MHEMT sample. The PR spectrum in Fig. 3(b) also proves the existence of 2DEG in the CS-MHEMT because a broadened feature located near 0.85–1.1 eV was also detected. In the presence of 2DEG, the inter-subband absorption function becomes a broadened two-dimensional density of states multiplied by a Fermi level filling function [9]. Therefore, a 2DEG feature should contain channel-well intersubband transitions and it shows quite broad in the PR spectrum [9]. In order to further analyze 2DEG and channel-well intersubband transition energies for the TS- and CS-MHEMT structures, theoretical quantum-well calculations and PL measurements were carried out. For the estimation of strain-induced energy shift in the channel wells of the MHEMTs, a physical model proposed for strained and relaxed InGaAs alloys was used [13]. The strains in the TS-MHEMT and CS-MHEMT calculated from the lattice-constant differences between channel and barrier layers are + 0.014 [tensile: (5.855 Å–5.744 Å)/ 5.744 Å] and −0.0076 [compressive: (5.823 Å–5.868 Å)/5.868 Å], respectively. The differences will result in a red shift for the TS sample but a blue shift for the CS sample. The theoretical quantum-well calculations by taking into account the TS and CS effects on light hole and heavy hole determined the values of intersubband transition energies as listed in Table 1. The 11H defines the transition between E1 (the first electron state) in conduction-band well and HH1 (the first heavy-hole state) in the valence-band well. Because of different strain type, the energy of 11H is slight larger than that of 11L in the TS sample while the energies show a contradict behavior in the CS-MHEMT as those shown in Table 1. Fig. 4 shows the room-temperature PL and PR spectra of (a) TS-MHEMT and (b) CS-MHEMT. The calculated results of intersubband transition energies of 11H, 11L, 21H, and 21L are also indicated with arrows for comparison with the PL and PR features in Fig. 4. The PL intensities in Fig. 4 show that the E1 related peak (including 11H and 11L) is lower than that of E2 related peak (21H and 21L) for both TS- and CS-MHEMT structures. It is an indication that the EF is higher above the E2 state in the channel-conduction
Table 1 C The experimental and calculated inter-subband transition energies of the MHEMT structures. The calculated values of Fermi-level energy (EF–Em ) and 2DEG density for the MHEMTs at 300 K are also included for comparison. Sample
TS CS
Channel composition
In0.3Ga0.7As V-shape x = 0.3–0.5–0.3 In0.5Ga0.5As In0.53Ga0.47As
Tool
Cal. Expt. and Cal. Cal. Expt. and Cal.
Inter-subband transition energy (eV)
Fermi-level energy (meV)
11H
11L
21H
21L
0.847 0.785 0.618 0.797
0.841 0.779 0.610 0.805
0.884 0.824 0.662 0.843
0.878 0.818 0.654 0.851
EF–E1C
EF–E2C
EF–E3C
N2d (1012 cm− 2)
84.9
45.8
− 14.2
3.5
88.9
42.8
− 26.2
3.0
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(a)
(a)
300K
TS-MHEMT
22L 21H (E1 related) 21L (E related) 2 11H 11L 22H
300K
PL
PR 0.7
0.8
0.9
1.0
1.1
Expt.
2DEG FK oscillations
0.8
1.2
1.0
1.2
0.12
300K
CS-MHEMT
(b)
TS-MHEMT
0.10
21L 21H (E related) 2 (E1 related) 11L 11H
PL PR
0.08 0.06 0.04 0.02
FK oscillations fit
0.00 0.7
0.8
0.9
1.4
Photon Energy (eV)
(4/3π) (E-E0)3/2 (eV)3/2
ΔR/R (Arb. Units) Intensity (Arb. Units)
Photon Energy (eV)
(b)
PR
TS-MHEMT
ΔR/R (Arb. Units)
ΔR/R (Arb. Units) Intensity (Arb. Units)
4
1.0
1.1
1.2
0
Photon Energy (eV)
band well for all the MHEMTs [14]. The other evidence to verify this point is the energies of E1 and E2 related peaks (PL) are lower than the broadened 2DEG features in the corresponding PR spectra in Fig. 4(a) and (b). The transition probability for the E1 and E2 states is lower because they are filled with 2DEG to reduce the intensities of PR signal. In the presence of 2DEG, the inter-subband absorption function becomes a broadened two-dimensional density of states multiplied by a Fermi level filling function. The one-electron theory indicates that the imaginary part of the complex dielectric function (ε = ε1 + iε2) can be expressed as [9]
j
ð1Þ
where Dj is the amplitude of the jth feature; E is the photon energy; Γj is the broadening parameter, and Ej(mnH) is the inter-subband enerC V C V gy given by Ej(mnH) = Em, j − En, j(H). Em, j and En, j(H) are the energies
EF
TS-MHEMT
6
8
10
Fig. 6. (a) Decomposition of experimental PR spectrum of the TS-MHEMT into two parts for analyses of 2DEG and FK oscillations in the V-shape channel. (b) The dependence of [4/(3π)](En − E0)3/2 vs. index of extremums in the FK oscillations of TS-MHEMT. The dashed line is the least-square fit to Eq. (3).
of the mth conduction and nth heavy-hole valence subbands, respectively, referred to the jth feature. The mnH denotes a transition from mth conduction subband to nth heavy-hole valence subband. The Fermi function of Eq. (1) can be expressed as 9 > > > = 1 j ; fe ¼ C > > ðλE−λE ð mnH Þ− E −E j F > > m;j > > ; :1 þ exp kT 8 > > > <
In0.53Ga0.47As
E3 E2 E1
ð2Þ
where λ = mh*/(me* + mh*), me* and mh* are the electron and in-plane heavy-hole effective masses, respectively, in units of free electron mass. Eqs. (1) and (2) are also suitable for the analysis of light-hole transitions in the valence subbands. The mnL denotes a transition from mth conduction subband to nth light-hole subband. The broadened PR feature in the PR spectra of Fig. 4(a) and (b) can be analyzed
InxGa1-xAs (X=0.3-0.5-0.3)
4
Index n
Fig. 4. Room-temperature PL and PR spectra of (a) TS-MHEMT and (b) CS-MHEMT device structures.
n h io j ε2 ¼ ∑ Dj Im ln E−Ej ðmnHÞ þ iΓj ⋅ 1−f e ;
2
E3
EF
E2 E1 CS-MHEMT
Fig. 5. The representative schemes for the confined states, Fermi level, and channel conduction-band wells of the TS- and CS-MHEMTs.
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using Eq. (1), and the analyses extract the values of E1, E2, EF–E1C and EF–E2C listed in Table 1. The peak positions in the PL spectra (11H,L and 21H,L) in Fig. 4 also verified the fitted values of E1 and E2 from PR in the conduction-band well of the CS- and TS-MHEMTs. Fig. 5 shows the representative conduction-band wells for the CS- and TSMHEMTs. The EF is higher than E1 and E2 but is lower than E3. The calculated values of EF–E1C, EF–E2C and EF–E3C for the two MHEMTs are also listed in Table 1 for comparison. The sheet carrier density of 2DEG can be expressed as N2D ¼
" ! !# C C me kT EF −E1 EF −E2 þ exp ⋅ ln 1 þ exp [15], kT kT π⋅ℏ2
⁎ where m⁎ e is the electron effective mass by taking me = 0.058 m0 (electron rest mass) herein for InGaAs [9]. The obtained values of sheet carrier density N2D are 3.5 × 10 12 cm − 2 and 3.0 × 10 12 cm − 2 for the TS- and CS-MHEMTs, which are close to the previous sheet densities obtained by Hall-effect measurements [11]. The higher value of N2D for the TS-MHEMT is inferred to come from a better carrier confinement in the V-shape channel as well as a lower In content than that of CS-MHEMT to render a superior current–voltage characteristic [11]. To further analyze the built-in electric field of the MHEMT structure, the PR spectrum in Fig. 4(a) can be decomposed into two parts for distinct analyses of 2DEG and built-in electric field of the TSMHEMT structure. Fig. 6(a) shows the decomposition of PR spectrum into two parts respectively for 2DEG and FK oscillations. As shown in Fig. 6(a), the position of nth extremum in the FK oscillations can be expressed by: [12] nπ ¼ ð4=3Þ½ðEn −E0 Þ=ℏW
3=2
þ χ;
ð3Þ
where En is the photon energy of the nth extremum; E0 is the band gap, and χ is an arbitrary phase factor. The electro-optic energy ℏW is given by (ℏW) 3 = q 2ℏ 2F 2/2μ, where F is the electric field and μ is 1 1 1 given by ¼ þ . The me* and mh* are the effective masses of μ me mh electrons and holes. Eq. (3) indicates a linear relationship between the [4/(3π)][(En − E0)/ℏW] 3/2 and the index of nth extremum in the FK oscillations, for calculation of built-in electric field of the V-shape channel in the TS-MHEMT. Fig. 6(b) plots [4/(3π)](En − E0) 3/2 vs. the index of extremums in the FK oscillations of Fig. 6(a). The obtained value of built-in electric field was F = 128 ± 6 kV cm − 1 for the graded V-shape channel of the TS-MHEMT. The design of V-shape channel can enhance electron mobility by confining 2DEG localization at the center of the V-shape channel, which avoids surface-roughness scattering with electron transport along the channel interfaces.
5
4. Conclusions In conclusion, optoelectronic properties of two MHEMT structures (InAlAs/InGaAs/InAlAs) with one tensile-strained V-shape channel and one compressive-strained channel have been evaluated by SPV, PR, and PL measurements at 300 K. The SPV measurements identify the interband transitions of the barrier layer and buffer layer in the CS- and TS-MHEMT structures. The results of PL measurements confirmed the energy positions of 11H and 11L for the E1 state, and 21H and 21L for the E2 state, respectively, in the channel conduction-band wells of the two MHEMTs. The analyses of PR spectra by taking into account the Fermi-level filling function determined the Fermi-level energy and the sheet carrier density for the CS- and TS-MHEMTs. The presence of FK oscillations in the PR spectrum of the TS-MHEMT facilitates the evaluation of built-in electric field of the V-shape channel. The experimental analyses show that the design of TS-MHEMT structure enhances 2DEG density and reduces surfaceroughness scattering on the channel interfaces in comparison with the CS-MHEMT structure. Acknowledgments This work was sponsored by the National Science Council of Taiwan under the grant no. NSC-98-2221-E-011-151-MY3. References [1] M. Boudrissa, E. Delos, C. Gaquiere, M. Rousseau, Y. Cordier, D. Theron, J.C. De Jaeger, IEEE Trans. Electron Devices 48 (2001) 1037. [2] W.C. Hsu, Y.J. Chen, C.S. Lee, T.B. Wang, Y.S. Lin, C.L. Wu, IEEE Electron Device Lett. 26 (2005) 59. [3] K. Ouchi, T. Mishima, M. Kudo, H. Ohta, Jpn. J. Appl. Phys. 41 (2002) 1004. [4] W.C. Hsu, Y.J. Chen, C.S. Lee, T.B. Wang, J.C. Huang, D.H. Huang, K.H. Su, Y.S. Lin, C.L. Wu, IEEE Trans. Electron Devices 52 (2005) 1079. [5] M. Zaknoune, B. Bonte, C. Gaquiere, Y. Cordier, Y. Druelle, D. Théron, Y. Crosnier, IEEE Electron Device Lett. 19 (1998) 345. [6] M. Boudrissa, E. Delos, Y. Cordier, D. Théron, J.C. De Jaeger, IEEE Electron Device Lett. 21 (2000) 512. [7] F.H. Pollak, H. Shen, Mater. Sci. Eng. R10 (1993) 275. [8] C.H. Ho, K.W. Huang, Y.S. Lin, D.Y. Lin, Opt. Express 13 (2005) 3951. [9] C.H. Ho, J.S. Li, Y.S. Lin, Semicond. Sci. Technol. 24 (2009) 035013. [10] C.H. Chan, J.D. Wu, Y.S. Huang, Y.K. Su, K.K. Tiong, J. Appl. Phys. 106 (2009) 043523. [11] W.C. Hsu, D.H. Huang, Y.S. Lin, Y.J. Chen, J.C. Huang, C.L. Wu, IEEE Trans. Electron Devices 53 (2006) 406. [12] H. Shen, F.H. Pollak, Phys. Rev. B 42 (1990) 7097. [13] Ch. Köpf, H. Kosina, S. Selberherr, Solid State Electron. 41 (1997) 1139. [14] D.Y. Lin, Y.S. Huang, T.S. Shou, K.K. Tiong, F.H. Pollak, J. Appl. Phys. 90 (2001) 6421. [15] D.Y. Lin, M.C. Wu, H.J. Lin, J.S. Wu, Phys. E 40 (2008) 1757.
Please cite this article as: C.-H. Chan, et al., Thin Solid Films (2012), doi:10.1016/j.tsf.2012.03.060