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InGaAs/InP multiple quantum well modulators in experiment and theory
R. Schwedler, H. Mikkelsen, K. Wolter, D. Laschet, J. Hergeth, H. Kurz
To cite this version:
R. Schwedler, H. Mikkelsen, K. Wolter, D. Laschet, J. Hergeth, et al.. InGaAs/InP multiple quantum well modulators in experiment and theory. Journal de Physique III, EDP Sciences, 1994, 4 (12), pp.2341-2359. �10.1051/jp3:1994281�. �jpa-00249267�
Classification Physics Abstracts
78.65J 7360F 81.10B
InGaAs/InP multiple quantum well modulators in experiment
and theory
R. Schwedler, H. Mikkelsen, K. Wolter, D. Laschet, J. Hergeth (*) and H. Kurz Institut fur Halbleitertechnik, RWTH Aachen Sommerfeldstrasse 24, 52074 Aachen, Germany (Received 8 February1994, accepted 2 May1994)
Abstract. The optoelectronic properties of InGaAs/InP quantum well modulators
are in-
vestigated experimentally~ including transport and recombination processes. The applied experi-
mental techniques are differential electro-transmission, photocurrent and electric field modulated
photoluminescence. In our theoretical treatment we consider the electric field dependence of the confined state energies and of the overlap of electron-hole wavefunctions. From these the di- electric function of the multiple quantum well material is reconstructed. Comparison between
experiment and theory reveals the importance ofspecific material related aspects. Among them,
non intentional background doping and interface degradation are identified as major sources of
discrepancy between theory and experiment.
1. Introduction,
During the past few years multiple-quantum-well (MQW) structures have been extensively investigated. The optoelectronic properties of MQW structures in the presence of electric fields are of particular interest because they can exhibit strong electrooptic effects based on
specific excitonic effects. The red shift of the excitonic electroabsorption peak under an electric field perpendicular to the layers is known as the quantum confined Stark effect (QCSE) [1-3], first observed in the AlGaAs/GaAs heterostructure system [4]. In MQWS, these excitonic
peaks appear even at room temperature in MQWS in contrast to bulk semiconductors, and
persist even when large electric fields are applied. Therefore, the QCSE opened the way to
design a host of novel detectors and modulators which exhibit enhanced performance compared
to bulk semiconductors. Although the greatest effort has been centered on the AlGaAs/GaAs system, other material systems, most notably InGaAs/InP, are of considerable interest [5-7].
The absorption edge of this ternary material system at room temperature is in the 1,550 nm
range, the spectral center of optical fiber communication.
(*) Present Address: Aixtron GmbH, Kackertstrafle 15~ Aachen, Germany.
2342 JOURNAL DE PIiYSIQUE III N°12
Applications of high speed III-V semiconductor light modulators include low chirp external laser modulators, optical logic circuits, and smart pixel arrays (8, 9]. Most of the work on such optical devices for switching and processing applications has concentrated on the use of QCSE [7]. The main advantage of such devices is the inherent capability of optics to transfer large amounts of information in parallel. The most interesting example is the self-electrc-optic-
effect device (SEED) which is an optically bistable logic switching device that combines optics and electronics. Particularly attracting are the very low switching energies 11, 2]. Depending
on whether the opto-electronic feedback is positive or negative, the device can function as a bistable optical switch or a self-linearized modulator [3, 10-12].
The versatility of the SEED concept is exemplified by its many different modes of operation.
SEEDS can be employed as memory elements, optical level shifters, wavelength converters, self-linearized modulators, and oscillators [3, 1i-16]. Recently, the observation of QCSE and the application of the effect to bistable switching devices were reported in InGaAs/InP MQW
structures [5, 17]. Very few bistability experiments have been performed in waveguides in the 1,550 nm region. Bistable switching in semiconductor amplifiers has been achieved using an
electrical bias close to the lasing threshold [18-20].
The technical key characteristics of SEEDS are Ii) the electrical energy, needed to modify
the spectral characteristics of the MQW structure, (it) the speed of the QCSE modulator, and
(iii) the modulation depth of the reflected or transmitted optical signal. The electrical energy is essentially that required to charge up the volume of the device to the operating field. The
speed is basically limited by the time it takes to apply the electric field to the MQW structure.
However, the main disadvantage in such QCSE based SEEDS is the high operating voltage
needed [2ii. High voltages result in very large power dissipation densities when the devices are switched repetitively at high rates. The switching power P isgiven by P
= CV2/2T, with C the capacitance associated with the PIN diode, T the switching time, and V the switching voltage [22]. Therefore, a reduction below 5 V in the operating voltage of such devices is required.
In this case, their dynamic power consumption is reduced and hence their application in high speed dense arrays is permitted. Moreover, this provides their compatibility with silicon CMOS
circuits in hybrid architectures [23].
Attempts to reduce the operating voltage have been reported using shallow quantum wells [24] and superlattice (SL) structures [25]. A semiconductor superlattice is a stack of wells and barrier layers thin enough so that the wells are coupled by resonant tunneling. Contrast
ratios of 40:1 at voltages as low as 4 V have been achieved in the AlGaAs/GaAs system [26].
Furthermore, in the transparent substrate and lattice matched InGaAs /InP system superlattice
diodes have been fabricated [27], and photocurrent spectra have been reported [28].
Recently, the successful reduction of the operating voltage in InGaAs/InP PIN modulator diodes by employing the Wannier-Stark effect in a superlattice stack [29] instead of the more
usual QCSE MQW structure has been reported [30]. Placed in a homogeneous electric field, such a modulator changes the absorption spectrum by misaligning the resonant energy levels in adjacent quantum wells. This results in a Wannier localization of the initially delocalized
electrons and holes. The voltage drop between two adjacent wells has to be on the order of the miniband width of the delocalized carriers, which is typically between 20 and 60 mev [29].
Since the SL period is usually only about 5-10 nm, the necessary applied bias across a 1,000 nm stack will be less than 6 V.
in this contribution, we focus on optical and transport properties of MQW modulators.
The theoretical approach we used to model the electronic states and the dielectric function of InGaAs/InP MQW modulators is described in the following section. Chapter 3 describes the experimental methods: sample preparation, transmission, photocurrent, and photolumi-
nescence spectroscopy. Then, the results of our experiments are presented. The influence of
non-ideal material properties on modulator performance are discussed in chapter 5. The paper is concluded by a brief summary of our results.
2. Theory.
The operation of MQW diodes as light modulators is based on the Quantum Confined Stark Effect (QCSE) [4, 31]. A modulated electric bias leads to a modulation of the MQW dielectric
function and consequently of the intensity of the light transmitted through the PIN diode.
A theoretical treatment of the modulation process requires three steps: I) the single particle
electronic states for electrons and holes have to be calculated, taking into account the electric field applied for modulation, it) the absorption strengths of all relevant electronic transitions
have to be calculated, and iii) the dielectric function of the complete modulator structure must be presented.
2.I CALCULATION OF ELECTRONIC STATES. In the framework of the envelope function the- ory [32], the MQWS confined states are obtained from the solutions of a set of one-dimensional Schr0dinger equations, which accounts for both the quantum size effect and for field effects on
the confined states:
Here, m*(E,z) denotes the atially ependend effective mass in kz-direction, Viz) is
the
confining potential, and F(z) is the electric field in
ectrons,
holes, or light holes.
The boundary nditions
~
' dz
must be fulfilled at
~~~~~ ~~~~~E)~i~o) ~~ ~ ~~~~g~/~~~ ~~~
where ho denotes the spin-orbit splitting energy. All material parameters are taken from the literature [36, 37]. While analytical solutions of equation ii) exist for special cases [31, 38],
it is more appropiate to solve it numerically for different electric fields with an electronic transfer-matrix method [39,40] to determine the confined state energies Eq,~ and wavefunctions
~fiq,~. For this purpose, the effective potential Viz) + eF(z)z is split in small (Az m 0.5 nm) slices, approximated by rectangular potential profiles. Solutions for the cases F(z) e 0 and
F(z) = const are derived.
While the field dependence of the wave functions and energy eigenvalues can be obtained easily from the transfer matrix model, it is nevertheless instructive to use a simple, but quite precise variational model depicting the shift AE of the electronic states due to the QCSE. In the simplest realistic approximation, the change of electronic states due to the electric field is
given by [31]:
~ ~ ~
AE =
~~~~'~~
~~~~ ~~F~ (4)
8h
where q is a proportionality constant defined in reference [31]. The ratio AE/F~ is plotted in
figure I for electrons and holes in InGaAs/InP MQWS. Figure I implies a set of restrictions
2344 JOURNAL DE PIiYSIQUE III N°12
m
tR lo ~i
> n
~ ~l
r~
~~-3
>
~
~
~ ~~-~
cq
El
~ /~
~ ~~-5
5 lo 15
L~ I n~
Fig, i. Proportionality factors for the quadratic QCSE (Eq. (4)) in InGaAs/InP quantum wells
depending on well width Lz for electrons, light holes, and heavy holes.
to the design of QCSE modulators: for a useful QCSE shift of some mev electric fields of the order of 50 kV/cm have to applied. Then, the well thickness must be chosen to be substantially greater than 5 nm [41]. As the quantum size effect becomes small for these well widths, the
operating wavelength of QCSE modulators is essentially fixed to the well material's band edge.
It is also obvious from figure i, that, for any reasonable well width, the QCSE is dominated
by the shift of the heavy-hole states.
Excitonic effects on the optical spectra are most important at cryogenic temperatures. Ex- citon binding energies depend on both QW width and electric field. Theoretical approaches
to calculate the exciton binding energy in heterostructures have been developed by several authors [42, 43]. Within the scope of this contribution, we use the zero-field values calculated
by Grundmann and Bimberg [43], which have been verified experimentally [44]. The electric field induced change of the exciton binding energy is negligible for the quantum well widths and electric fields discussed in this paper [45].
2.2 DIELECTRIC FUNCTION OF lnGaAs/lnP MQWS. in order to model the optical response
of the PIN diode modulator, the field dependent complex dielectric function e
= ei + ie~ of the
MQW material is calculated [46].
The quantized energies and the wavefunctions for electrons, heavy holes and light holes, respectively, are obtained with the transfer matrix solution of the Schr6dinger equation. These
wavefunctions define the electron-hole overlap integral. The excitonic transition energies are composed by the InGaAs bandgap, electron and hole quantization energies minus the exciton
binding energy.
In the case of the excitonic transition, the quantized states are connected to the dielectric function by a simple oscillator model (47, 48] with a Gaussian lineshape G(E) due to inhomo- geneous broadening with halfwidth energy a. The imaginary part of the dielectric function e~
of the well material [47, 48] can be expressed as:
~2(~iLd) ~/~j~2~ j~Bj~~~ / e,n(Z)i~h,m(~)dZ~
0
o~w
~~~
~
xMjE"
= o)GjjEo,~,~ + E~~~ J~w),,) is)
with the exciton binding energy Eexc
= 6 mev and the radius 1
= 150 h, Eo,n,m
= E~ +
Een + Ehm, and G(Eo E,a) = i/(aft)e~l~~~°)~l'~ For the continuum absorption, I-e- for energies above the exciton peaks, e2 is described by the following polarization dependent
expression [48, 47]:
~2(liW) = ~~ ~j j2
/leh ~ j~°° 2
~°~~~~~w ~ ~rfi2
_~
~e,n(Z)ilh,n(Z)dZ~
x /~°° MjE")Gj(E" + Eo,~,~ Au),,)dE" j6)
with the Bloch state matrix element MB defined as
and the reduced electron hole effective mass
~~~~j~
~~~ ~~l ~ ~~h ~~~
The polarization dependence of the M(E") matrix originates from the s and p orbital sym- metry of the conduction and valence band, respectively [47]. Due to the wave quantization, the contributions to M(E") differ strongly between the two possible polarizations of the electric field E of the light:
3/4 (1 + cos~(8)) for SH. Ejjz
Mj E"~ 3/2 II cos~jB)) for SH( E iz
~/~ IS 3Cos~jB)) for E-L; Ejjz 19)
1/2 11 + 3cos2(8)) for &L. E iz where
cos~(B)
= ~ ~~~j ~~~
~,, (10)
en + hm +
and 8 is the angle of the electron wave vector relative to the surface normal (z-axis).
The dielectric function of the MQW stack is modelled as an effective dielectric mixture of bulk InP and quantized InGaAs. The data for the dielectric function of the bulk material InP
are taken from Palik [49]. The data for bulk InGaAs were retrieved from measurements of reflection and transmission on a thin InGaAs film [50].
For energies larger than the InP bandedge, where no quantization effects occur, e~ was assumed to be equal to e2 of bulk InGaAs. The ei spectra are derived by Kramers-Kronig
transformation. In a final step, the contribution to ei from the high energy oscillators for bulk
2346 JOURNAL DE PHYSIQUE III N°12
0.15 12.0
+t~+t~W W m
XX~XX X ~
~~~i~~ ~ ~
ii.5 o.io
~j
,
~ ll.0 ~
o.05
io.5
0.00 10.0
0.7 0.8 0.9 1.0 1.I 1.2
Energy eV
Fig. 2. Calculated real (El and imaginary (e2) part of the dielectric function of the InGaAs/InP MQW material at 0 kV/cm (solid lines) and 70 kV/cm (dashed lines).
InGaAs is added to ei of the well material. These transitions have negligible contributions to e2 in the interval of 0.7 to 1.2 eV studied in this work. Since the layer thicknesses in consideration
are small compared to the light wavelengths, the dielectric constant of the multiple quantum well material can be calculated in an effective medium [51] approach by weighing the respective
constants for well (see above) and barrier (bulk) materials with their relative thicknesses. The total dielectric function eMQw for electric fields polarized along the quantum well plane reads:
eMQw "
~~
ew +
~~
eb Ill
Lz + Lb Lz + Lb
where Lz and Lb are the well and barrier width, respectively.
In figure 2 the calculated dielectric functions ei and e2 for a InGaAs/InP MQW are displayed
for two different electric fields applied along the z-axis- With increasing field the strengths of
the allowed transitions decrease and the peaks are shifted to lower energy. For example, the allowed ElHi transition exhibits this behavior. The EiLi transition reacts similarly, although
the absorption is less for all fields due to the light-hole character. The allowed E2H2 transition exhibits a negligible energy shift but a large change in amplitude, while E2L2 is hardly affected in energy or amplitude. The forbidden transitions become stronger for higher fields. For
instance, the El H2 transition increases in strength for higher fields due to the increasing overlap of electron-hole wavefunctions.
3. Experimental.
The samples are sketched in figure 3. They are grown by Low Pressure Metal Organic Vapour Phase Epitaxy (MOVPE) on a n+-InP substrate followed by a 300 nm n-InP buffer layer. The
MQW section is embedded between two 100 nm I-InP layers acting as diffusion stops for the dopants. The MQW nominally consists of io0 periods of 7 nm InGaAs wells lattice matched
on InP and 20 nm InP barriers. On top of this, 700 nm p+-InP and finally a contact layer of100 nm p+-InGaAs is grown. The thick top p+-InP layer is necessary to ensure lateral
130 nm NilAuZn/Ni loo nm p++-lnGaAs
700 nm p-lnP loo nm I-lnP
loo Periods:
j 7nm I-lnGaAs j
20nm I-lnP
100 nm I.lnP 320nm n-lnP
300pm n-lnPsubst.
Fig. 3. Schematic representation of the MQW PIN diode vertical modulator.
homogeneity of the electric field. All layer thicknesses have been interpolated from the growth
times. Ohmic contacts are prepared on both the p+-InGaAs and the substrate and alloyed. The top p+-InGaAs layer is removed selectively with a wet chemical etchant for optical windows,
and the MQW PIN diode devices are separated by a MESA etch process. The breakdown
voltage of the PIN diodes is M~60 V.
Optical measurements have been carried out at room temperature and at 2 K in a He bath cryostat. Photoluminescence (PL) was excited by either the 633 nm- or the 1,150 nm-line from a HeNe laser. The excitation intensity was below i W/cm~ in all PL experiments. The
luminescence was spectrally dispersed by an 0.5 m monochromator (resolution better than i nm in the entire spectral range) and detected by a cooled germanium PIN-diode. Spectra have been recorded using a lock-in amplifier and a computer controlled data acquisition sys-
tem. For transmission measurements, the samples were irradiated with light from a tungsten halogen lamp, and the transmitted light was analyzed as described above. Differential electro- transmission spectra have been obtained using a pulse generator synchronized with the lock-in amplifier. All spectra have been corrected for detector sensitivity.
4. Results and discussion.
Our PL and transmission experiments are divided in two categories: low temperature charac- terization has been performed to check precisely the structure and composition of the sample.
They lead to an understanding of the rather complicated microscopic interface structure of the MQW. Room temperature spectroscopy yields information on device performance in the
desired operating range: transmission allows quantification of the QCSE modulation, while PL contains information on the field-assisted transport of photogenerated carriers out of the
modulator.
4.I Low TEMPERATURE CHARACTERIZATION. Low temperature PL and absorption spectra
taken at zero bias are depicted in figures 4 and 5, respectively. The 633 nm laser irradiation excites exclusively the InP cap layers of the heterostructure. As shown in the main graph
in figure 4, the PL is, however, dominated by the emission from the MQW EHI transition at 852 mev. The experimental EHI linewidth of 5.6 mev FWHM agrees well with models
assuming an interface roughness of one monolayer [52-56]. A weak LO-phonon satellite line is
2348 JOURNAL DE PHYSIQUE III N°12
6
fl/s
C14
~
~i
~~ QlC~
(
~ C~
125 13 135 IA 0
0.775 0.8 0.825 0.85 0.875 0.9
Energy (eV)
Fig. 4. Luminescence spectra of the MQW PIN diode taken at 2 K. The InP bandedge PL is
displayed in the inset.
f c
~
uJ c O z
~
~
©
~
085 9 095
Fig. 5. Low temperature (2 K) absorption spectrum of the InGaAs/InP MQW PIN diode.
observed at the low energy tail of the EHI-luminescence [57]. The PL from the InP cap layers
is shown in the inset in figure 4. This emission is by two orders of magnitude lower than the QW luminescence due to the very efficient capture of photogenerated carriers into the MQW [58-63].
More details on the MQW band structure are obtained from low temperature transmission spectroscopy as shown in figure 5. Three spectral features are clearly observed and attributed to the EHI, ELI, and EH2 optical transitions. The weak bump at 950 mev may be due to the parity forbidden ElH3 transition. These experimental results are compared to theoretical data summarized in table I. For the calculation, a widely accepted exciton binding energy of 6 mev
