Intersubband transitions from the ground state to the first and second excited states in pseudomorphic AlGaAs/InGaAs/GaAs/AlGaAs multiple step quantum wells have been observed. The step well structure has a configuration of two AlGaAs barriers confining an InGaAs/GaAs step. Multiple step wells were grown on GaAs substrate with each InGaAs layer compressively strained. During the growth, a uniform growth condition was adopted so that inconvenient long growth interruptions and fast temperature ramps when switching the materials were eliminated. The sample was examined by cross‐sectional transmission electron microscopy, an x‐ray rocking curve technique, and the results show good crystal quality using this simple growth method. Theoretical calculations were performed to fit the intersubband absorption spectrum. The calculated energies are in good agreement with the observed peak positions for both the 1→2 and 1→3 transitions

Chen, Y. W.

Li, H. S.

Lie, D. Y. C.

Wang, K. L.

English

Caltech Authors - Main

lntersubband transitions in pseudomorphic lnGaAs/GaAs/ AIGaAs multiple 
step quantum wells 
H. S. Li, Y. W. Chen, and K. L. Wang 
Device Research Laboratory, 66-/47B Engineering IV. Department of Electrical Engineering, 
University of Cal!fornia at Los Angeles, Los Angeles, California 90024-1594 
D. Y.C. Lie 
Department of Electrical Engineering, MIS I/6-8/, Caltech, Pasadena, California 9I/25 
(Received 29 January 1993; accepted 8 July 1993) 
Intersubband transitions from the ground state to the first and second excited states in 
pseudomorphic AlGaAs/lnGaAs/GaAs/ AlGaAs multiple step quantum wells have been 
observed. The step well structure has a configuration of two A1GaAs barriers confining an 
InGaAs/GaAs step. Multiple step wells were grown on GaAs substrate with each InGaAs layer 
compressively strained. During the growth, a uniform growth condition was adopted so that 
inconvenient long growth interruptions and fast temperature ramps when switching the 
materials were eliminated. The sample was examined by cross-sectional transmission electron 
microscopy, an x-ray rocking curve technique, and the results show good crystal quality using 
this simple growth method. Theoretical calculations were performed to fit the intersubband 
absorption spectrum. The calculated energies are in good agreement with the observed peak 
positions for both the 1 ___, 2 and 1 ___, 3 transitions. 
I. INTRODUCTION 
Intersubband transitions in multiple quantum wells 1 
have received a great deal of interest for their applications 
of novel optoelectronic devices, for example, infrared 
detectors2•3 and modulators.4•5 In Ref. 5, infrared modula-
tion was demonstrated utilizing the enhanced Stark shift in 
multiple AlxGa1_xAs/GaAs/ AlyGa 1_ yAs step quantum 
well structures. 6 The device operated at 77 K because of a 
large leakage current from thermionic emission. If a higher 
operation temperature is desired, not only a thicker but 
also a higher barrier has to be used to block this excessive 
leakage. However, for the GaAs/ AlxGa 1_xAs material 
system, the maximum direct gap barrier height is only 336 
meV with x=0.45. For x greater than 0.45, the 
AlxGa1_xAs becomes indirect with the X points lower 
than the 1 point. In that case there can be leakage due to 
the intervalley scattering into the X valleys in the barriers. 
For the step well, an alternative approach is to use strained 
InGaAs/GaAs/ AlGaAs material combinations since the 
InGaAs/ AlGaAs interface has a larger barrier height. 
The strained InGaAs/GaAs/ AlGaAs system has been 
extensively studied in the area of modulation-doped field-
effect transistors7 and lasers.8 It is known that, to achieve 
high electron mobility and sharp photoluminescence peak 
for this type of structures, different optimum growth con-
ditions have to be employed when growing the InGaAs 
and AlGaAs compounds. The AlGaAs growth requires a 
higher substrate temperature plus a lower V to III flux 
ratio, whereas the InGaAs needs a lower temperature and 
a larger flux ratio. One additional consideration in the 
growth is the possible formation of misfit dislocations, due 
to the large lattice mismatch between the InGaAs and 
GaAs/ AlGaAs, once the epitaxial layer exceeds the critical 
layer thickness. 9•10 The fast As flux change when switching 
the materials can be obtained by installing two As guns or 
a valved As cell in the growth chamber. To change the 
substrate temperature, it is a common practice to insert a 
long growth interruption (about 2 min) or a fast temper-
ature ramp in the growth procedure, with only a few ex-
ceptions in which a uniform growth temperature is used. 
For studying doped multiple quantum well structures 
(with many periods), the repeated temperature changes 
are inconvenient for the growth. Besides, impurity incor-
poration during the long interruption may cause doping 
and contamination problems. It is desired therefore to use 
a uniform growth condition to grow the entire structure. In 
this article, we report the growth of pseudomorphic 
InGaAs/GaAs/ AlGaAs multiple step quantum wells on 
GaAs substrate using this growth condition. The sample 
was characterized by cross-sectional transmission electron 
microscopy (TEM) and an x-ray rocking curve technique, 
and intersubband transitions were demonstrated for the 
grown sample. The results suggest high quality quantum 
wells with this simple growth method. 
II. EXPERIMENT 
Samples were grown by a computer controlled Perkin-
Elmer 430 molecular-beam epitaxy (MBE). A 5000 A 
GaAs buffer layer, doped with Si to 2.4X 1018 cm- 3, was 
first grown to obtain a smooth starting surface for the sub-
sequent growth of multiple quantum wells. The multiple 
quantum well structure contains ten periods of step quan-
tum wells. Each period consists of a 60 A In0.22Gao.78As 
well, a 85 A GaAs step, and a 267 A Alo.37Gao.63As barrier. 
The quantum well was doped with Si to a total two-
dimensional (2D) doping level of 5X 1012 cm- 2 for each 
period. The growth was carried out at a substrate temper-
ature of 530 •c and with a constant As flux, which gives a 
V to III flux ratio of about 4 during the lnGaAs growth. 
The multiple quantum wells were capped with a 3000 A 
1840 J. Vac. Sci. Techno!. B 11(5), Sep/Oct 1993 0734-211X/93/11(5)/1840/4/$1.00 ©1993 American Vacuum Society 1840 
1841 Ll et al.: Pseudomorphlc lnGaAs/GaAs/AIGaAs multiple step quantum wells 1841 
E~ 
! .....! 
GaA:laAs 
··-AIG~ 
FIG. l. Cross-sectional TEM micrograph of the sample structure, show-
ing ten periods of the step well, with each InGaAs layer coherently 
strained on the GaAs buffer. The band diagram is shown inset. 
GaAs cap layer, also doped to 2.4 X 1018 em - 3• Intersub-
band absorption was measured with a Nicolet-740 Fourier-
transform infrared spectrometer ( FTIR) at 300 K using a 
waveguide scheme. 5 
Ill. RESULTS AND DISCUSSION 
Figure 1 shows the cross-sectional TEM micrograph of 
the multiple step quantum well structure. As one can see, 
there are a total number of ten period step wells in this 
structure, with each consisting of three layers, namely the 
InGaAs, GaAs, and AlGaAs. The band diagram is shown 
inset. As shown by this picture, no misfit dislocation is 
observed throughout the quantum well region, indicating 
that the InGaAs layers are coherently strained to the GaAs 
buffer. A higher resolution picture was also obtained (not 
shown) from which the step well was determined to be 66 
A InGaAs, 94 A GaAs, 263 A AlGaAs, and a total period 
of 423 A. Based on these layer thicknesses, the composi-
tions of the two ternary compounds can be calculated. The 
small well is In0.21 Gao. 7.As and the thick barrier is 
Alo.29Gao_71 As. For this sample, the intended indium com-
position for each InGaAs quantum well is 22%, and hence 
the multiple quantum well region equivalently contains an 
average indium content of 3.2%. From a theoretical view-
point, to prevent the generation of misfit dislocations, the 
critical layer thicknesses for the individual InGaAs layer as 
well as the multiple quantum wells have to be considered. 11 
The 60-A-thick In0_22Gao_78As quantum well is thinner 
than the critical layer thickness predicted by either the 
force or energy balance model,9•10 whose calculations give 
roughly a critical layer thickness of 140 and 460 A, respec-
J. Vac. Sci. Technol. B, Vol. 11, No.5, Sep/Oct 1993 
1x101 F-"-----------~, 
Substrate 
+1 
-6 -5 -4 -3 -2 
-1 
1 x1 0-4 '--'---'-LJ..-'--'-L..L.J.-L.L..L....L.J....l--k 
-1.5 
-1 0 -0.5 0.0 0.5 
Delta Theta (degree) 
Fro. 2. (400) double crystal x-ray rocking curve. The quantum well 
periodicity and the indium composition were determined to be 423 A and 
22%, respectively. 
tively. The total thickness of the multiple quantum wells is 
about 4120 A. This thickness is slightly above the critical 
layer thickness of 1400 A according to the force balance 
model, nevertheless is still much lower than the value pre-
dicted by the energy balance model of 4 f-tm. The experi-
mentally determined InGaAs critical layer thickness ver-
sus different indium composition was found to be bounded 
in between these two theoretical predictionsY We believe 
that the total layer thickness for our structure is below the 
critical layer thickness limitation, and therefore the struc-
ture is fully strained. 
The ( 400) double crystal rocking curve of the sample is 
depicted in Fig. 2. Informations on the quantum well pe-
riodicity (p) and perpendicular strain ( (~ ) ) were ob-
tained through 13 
(1) 
and 
(~ ) =- 6.80 /tan 8 B• (2) 
where A. is the x-ray wavelength, rn is the direction cosine 
of the diffracted waves with respect to the inward normal 
to the sample surface, aep is the spacing between the mul-
tiple quantum well peaks, e B is the Bragg angle of the 
substrate, and 6.80 is the spacing between the quantum well 
zeroth-order peak and the substrate peak. It is noted that 
the perpendicular strain in Eq. (2) is defined relative to the 
substrate and averaged over a quantum well period. Using 
Eq. ( 1 ) , the quantum well periodicity was calculated to be 
423 A. The average strain for each period was determined 
to be 0.475% from Eq. (2). This means an actual strain of 
3% for the InGaAs layer, after divided by the fraction of 
the InGaAs layer width over the period. To determine the 
indium composition, the relaxed film lattice mismatch was 
first deduced for the InGaAs using 14 
[AaJ 1-v [AaJ 2v [AaJ 
-;; ,=1+v 7 
1 
+1+v -;; 
11 
• 
(3) 
1842 Ll et a/.: Pseudomorphlc lnGaAs/GaAs/ AIGaAs multiple step quantum wells 1842 
0.24 --·~ ----~ 
0.20 1 --<> 2 
~ 016 
c: 
.e 
0 
~0 12 
1 --<> 3 
008 
004 ~-~· 
4 5 6 7 8 9 10 
Wavelength (micron) 
FIG. 3. The absorption spectrum from the FTIR measurement using a 
waveguide scheme. Both the I - 2 and 1- 3 absorption peaks were ob-
served at 7.6 and 5.3 f£ffi, respectively. 
where v is the Poisson ratio and is 0.311 for the GaAs 
substrate. By assuming zero parallel strain (i.e., coherently 
strained), the relaxed film mismatch was calculated to be 
1.6%, from which the indium composition was determined 
via Vegard's law to be 22%. Both the quantum well peri-
odicity and indium composition agree reasonably with the 
TEM data and calibrations done before the growth. 
Depicted in Fig. 3 is the infrared absorption data. Two 
absorption peaks at 7.6 ( 164 meV) and 5.3 J.!m (232 meV) 
were resolved, and, respectively, assigned to be the 1-.2 
and 1 ... 3 transitions in the step well. For convenience, the 
energy states in the well are sequentially numbered as 
1,2,3, etc. In contrast to the square well case, where the 
1 -. 3 transition is forbidden by the intersubband sdection 
rule, this transition was also observed since the symmetry 
has been broken by the insert of the step in the well. 15 Both 
absorption peaks are sensitive to the incident light polar-
ization, and disappear when the polarization is perpendic-
ular to the growth direction. The absorption peak width is 
28 meV for the 1-.2 transition and 36 meV for the 1-.3 
transition. The peaks are broader than those in the case of 
GaAs/ AIGaAs step quantum well, in which they are about 
20 meV. 5 The reason may be the higher doping level used 
in this case. 
Using the known structural parameters, the ebserved 
intersubband absorption spectrum was fitted with theoret-
ical predictions to determine the InGaAs/GaAs conduc-
tion band offset. Structures with various step heights were 
used to fit the intersubband transition energies. In the cal-
culations, a one-band transfer matrix program 16•17 was 
used to calculate the energy states, transition energies, and 
oscillator strength. The best fitting was obtained for both 
the 1 - 2 and l ..... 3 transitions by the least square method, 
with a step height (i.e., the conduction band offset) of 238 
meV. The calculated transition energies are 169 meV for 
the 1 ..... 2 and 229 meV for the l_. 3 transition. Both values 
are close to the experimental data, which are 164 and 232 
meV, respectively. Along with the transition energies, the 
oscillator strengths for the 1 ..... 2 and 1 _. 3 transitions were 
J. Vac. Sci. Technol. 8, Vol. 11, No.5, Sep/Oct 1993 
also calculated to be 0.90 and 0.21. The 2D carrier con-
centration for each period Ps was then determined from 18 
e2h cos2 () 
IA=p.Nr 4 * J-;--8 cos
2 cp, (4) 
Eo m cnr sm 
where I A is the integration of the absorption strength, NT 
is the total number of periods that the infrared beam goes 
through due to the multiple reflections in the waveguide, f 
is the oscillator strength, ()is the angle of incidence, and nr 
is the refractive index. For the structure we used N r= 80, 
IA=65.75 cm- 1, 8=45•, c/J=O·, Ps was calculated to be 
5.47X 1011 cm- 2, which is about 0.11 of the dopant level. 
The discrepancy between the carrier concentration and the 
dopant level may be due to the strain effect or the AlGaAs 
related deep levels because the barrier was grown at a low 
substrate temperature (530 ·c). Despite of the fact that the 
InGaAs/GaAs band offset ratio has been closely investi-
gated by many authors, 19 as an initial attempt, we esti-
mated the conduction band offset ratio for our sample. 
Photoluminescence of the sample was performed at 4 K. 
An excitonic transition from the electron ground state to 
the lowest heavy hole state was observed at 1.21 eV. As-
suming an increase of the InGaAs/GaAs conduction band 
offset by 10 meV (aEc=248 meV) for the reduced tem-
perature, the conduction band ground state energy was 
recalculated. The valence band offset was then varied to fit 
the photoluminescence (PL) peak, and a best fitting was 
obtained with a valence band offset of 131 meV. From 
these conduction and valence band offset values, the con-
duction band offset ratio for the InGaAs/GaAs interface 
was estimated to be 65%. 
IV. SUMMARY 
In summary, the growth of pseudomorphic InGaAs/ 
GaAs/ AlGaAs multiple step quantum wells on GaAs sub-
strate has been demonstrated using a single uniform 
growth procedure. The growth was conducted under a uni-
form growth condition so that inconvenient long growth 
interruptions and fast temperature ramps when switching 
the materials were avoided. lntersubband transitions from 
both the 1 _. 2 and 1 -. 3 in the step well were observed, due 
to the asymmetric shape of the well. The sample structure 
was also examined by TEM and with x-ray rocking curve. 
The results reveal the step well structure and show good 
crystal quality. The observed intersubband absorption 
spectrum was fitted with theoretical calculations. The cal-
culated energies are in good agreement with the observed 
transition peaks, and the InGaAs/GaAs conduction band 
offset was deduced. Finally, as an initial attempt, an 
InGaAs/GaAs conduction band offset ratio was estimated. 
ACKNOWLEDGMENTS 
The authors would like to thank Dr. J. M. Tijero for 
helping the PL mesurements, and Dr. T. W. Kang for 
providing the TEM data. This work was, in part, sup-
ported by DARPA through NCIPT, and by Joint Services 
Electronics Program. 
1843 Ll et sl.: Pseudomorphlc lnGaAs/GaAs/ AIGaAs multiple step quantum wells 1843 
1L.C. West and S. J. Eglas, Appl. Phys. Lett. 46, 1156 (1985). 
28. F. Levine, C. G. Bethea, G. Hasnain, J. Walker, and R. J. Malik, 
Appl. Phys. Lett. 53, 296 (1988). 
3C. Hasnain, G. F. Levine, C. G. Bethea, R. As. Logan, J. Walker, and 
R. J. Malik, Appl. Phys. Lett. 54, 2515 ( 1989). 
4A. Harwit and J. S. Harris, Appl. Phys. Lett. 50, 685 ( 1987). 
5R. P. G. Karunasiri, Y. J. Mii, and K. L. Wang, IEEE Electron Device 
Lett. EDI.-11, 227 ( 1990). 
6Y. J. Mii, R. P. G. Karunasiri, K. L. Wang, and P. F. Yuh, Appl. Phys. 
Lett. 56, 1986 (1990). 
7M. V. Baeta Moreira, M.A. Py, M. Gailhanou, and M. Ilegems, J. Vac. 
Sci. Techno!. B 10, 103 (1992), and references therein. 
8Stephen D. Offsey, W. J. Schaff, Luke F. Lester, L. F. Eastman, and S. 
K. Mckernan, IEEE J. Quantum Electron. QE-27, 1455 (1991), and 
references therein. 
9J. W. Mathews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974). 
J. Vac. Sci. Techno!. B, Vol. 11, No.5, Sep/Oct 1993 
10R. People and J. C. Bean, Appl. Phys. Lett. 47, 322 (1986). 
11 R. Hull, J. C. Bean, F. Cerdeira, A. T. Fiory, and J. M. Gibson, Appl. 
Phys. Lett. 48, 56 ( 1986). 
12Y. C. Chen, P. K. Bhattacharya, and J. Singh, J. Vac. Technol. B 10, 
769 ( 1992). 
13V. S. Speriosu and T. Vreeland, Jr., J. Appl. Phys. 56, 1591 ( 1984). 
'4g. N. G. Chu, A. T. Macrander, K. E. Strege, and W. D. Johnston, Jr., 
J. Appl. Phys. 57, 249 (1985). 
15P. F. Yuh and K. L. Wang, J. Appl. Phys. 65, 4377 ( 1989). 
16R. Tsu and L. Esaki, Appl. Phys. Lett. 22, 562 (1973). 
17M. 0. Vassell, J. Lee, and H. F. Lockwood, J. Appl. Phys. 54, 5206 
(1983). 
18R. P. G. Karunasiri, J. S. Park, Y. J. Mii, and K. L. Wang, Appl. Phys. 
Lett. 57, 2585 ( 1990). 
198. Jogai, Appl. Phys. Lett. 59, 1329 ( 1991 ), and references therein. 


Intersubband transitions in pseudomorphic InGaAs/GaAs/AlGaAs multiple step quantum wells

http://authors.library.caltech.edu/29663/1/LIHjvstb93.pdf

Intersubband transitions in pseudomorphic InGaAs/GaAs/AlGaAs multiple step quantum wells

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main