Quantum well structures

By forming quantum well (QW) structures with two different heterojunctions having different band offsets it is possible to form QWs having, when subjected to optical excitation, dipoles. The presence of a dipole in a narrow enough well results in QWs having absorption edges which, unlike those of conventional QWs can be shifted to the blue by application of an electric field of appropriate polarity.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to quantum well structures, and in particular but 
not exclusively to such structures configured for use as optical 
modulators. 
2. Related Art 
In the broad field of optical signal processing there are many applications 
for high performance optical signal encoding and processing elements. For 
example, in high speed optical fiber communications systems, direct 
modulation of laser sources leads to undesirable wavelength shifts, 
"chirp", in the optical output of the laser. One way in which chirp may be 
avoided is to cease modulating the laser directly, optical modulation 
being achieved through use of a modulator in the optical path of the 
laser's output. In the generally less well developed area of optical 
signal processing, components such as logic gates, latches, and signal 
encoders are required. The bandwidth which optical signal processing and 
optical communications potentially offer means that there is a desire for 
components which operate at high speed, typically switchable at GHz rates, 
and preferably switchable at tens of GHz. 
The present invention is concerned with such signal processing components, 
and in particular with modulators, which comprise quantum well structures. 
A quantum well is, in its simplest form, a double heterostructure, with a 
layer of low band-gap material sandwiched between two layers of higher 
band-gap material. Typically the layers all comprise semiconductors, for 
example the double heterostructure may consist of GaAs sandwiched between 
identical layers of AlGaAs. If the layer of low band-gap material is 
sufficiently thin, of the order of 100.ANG. or less, the energy levels in 
the valence and conduction bands becomes quantised, and the structure is 
referred to as a "quantum well". 
While single quantum wells do exhibit measurable quantum effects, the 
intensity or strength of the effects can be increased by increasing the 
number of quantum wells. Several, typically tens or many tens or hundreds 
of quantum wells are formed in a multilayer structure, which structures 
are referred to as "multiple quantum wells", or "multiple quantum well" 
("mqw") structures. 
The basis behind the use of quantum well structures as modulators is that 
they can exhibit large changes in their optical absorption coefficient on 
the application of an electric field. 
In devices such as QW modulators, utilising excitonic effects, the exciton 
of most significance is that involving the n=1 heavy hole. In this 
specification, unless the context clearly requires otherwise, we refer to 
the n=1 heavy hole exciton. 
Our own interpretation of the accepted explanation of this phenomenon will 
now be given with reference to FIG. 19 which shows, schematically, the 
behaviour of a conventional quantum well structure. The structure will be 
assumed to consist of a pair of GaAlAs layers 2, 2' with a GaAs layer 1 
therebetween. Thin solid lines 3 and 4 indicate respectively the valence 
band maximum in bulk GaAlAs and GaAs. Thin solid lines 5 and 6 similarly 
indicate the conduction band minimum in bulk GaAlAs and GaAs respectively. 
However because the GaAs layer is thin enough to provide quantum 
confinement of the electrons and holes there is an increase in minimum 
energy for them both. The new minima, the quantum well minima, for the 
electrons and holes are shown as broken lines 7 and 8 respectively. Note 
that in FIG. 19 electron energy increases towards the top of the Figure 
and hence hole energy increases as one moves down the Figure. With no 
applied field the resultant energy gap 9 is greater than that of the 
equivalent bulk GaAs. Typical probability density distributions of 
electrons and holes in the well are indicated by 10 and 11. The 
probability density distributions are pseudo-Gaussian and centered on the 
mid-point of the well. 
FIG. 1b shows, schematically, the effect of applying an electric field 
across the layers of the well of FIG. 1a. With the field applied, the 
shape of the potential energy well seen by the electrons and holes changes 
dramatically. As a result of the changed band edge variation the 
probability density distribution of electrons follows the drop in minimum 
conduction band energy and hence moves to the right (the positive 
potential side) in FIG. 1b. Similarly, the hole distribution follows the 
fall in valence band minimum (hole) energy and hence moves to the left 
(the negative potential side) in FIG. 1b. The result is that the band gap 
shrinks. This is the so-called quantum-confined Stark effect. The change 
in band gap of course causes a shift in the absorption band edge, 
increasing absorption at lower photon energies (a red shift). Thus a 
quantum well device can be used as a modulator for wavelengths in the 
region of the band edge. 
Unfortunately, in addition to the desired band edge shift there is a 
significant reduction in the absorption coefficient when a field is 
applied. In U.S. Pat. No. 4,826,295 the absorption coefficient for photon 
energies greater than the no-field band gap is estimated in one example to 
fall from about 2000 cm.sup.-1 in the no-field case to about 300 cm.sup.-1 
in the with-field case. For photon energies just below the no-field band 
gap, but above the relevant with-field band gap, the absorption 
coefficient is estimated in U.S. Pat. No. 4,826,295 to rise from less than 
10 cm.sup.-1 with no field to about 300 cm.sup.-1 with an applied field. 
While not preventing the use of quantum well structures in practical 
modulators, the fact that an absorption coefficient drop is associated 
with the desired field-induced band edge shift is nevertheless a 
disadvantage of known quantum well optical devices. 
In European patent application 0324505 there is described a second-harmonic 
generator or frequency doubler which comprises a quantum well structure. 
According to 0324505, the conversion of radiation of angular frequency 
.omega. to radiation having an angular frequency 2.omega., in a non-linear 
material, has an efficiency proportional to the square of that material's 
non-linear receptivity .psi..sup.(2). In EP 0324505, a dipole moment is 
induced in a quantum well structure, .psi..sup.(2) of that structure being 
proportional to the size of the dipole moment. In the first embodiment in 
'505, the well comprises 120.ANG. of GaAs sandwiched between AlAs barrier 
layers. Several such wells, together with thicker, charge,,separating 
layers of AlAs, form the intrinsic region of a p-i-n structure. By 
applying an electric field across the layers, the centers of gravity of 
the wave functions of the electrons and holes in the well shift, creating 
a dipole moment. With an applied field of unspecified strength, 
.psi..sup.(2) of the aforementioned structure is said to be 400 times as 
large as that of LiNbO.sub.3, and 5000 times as large as that of KDP. 
The angular frequency, .omega., of the radiation to be up-converted is 
chosen to satisfy the relation 2h.omega..congruent.Eg, where Eg is the 
bandgap of the well material (here GaAs, whose bandgap is 1.42 Ev at 
300K). 
In place of the AlAs in the barrier layers, Al.sub.x Ga.sub.1-x As can be 
used, and this permits the construction of a waveguiding quantum well 
structure, further increasing the efficiency of conversion. 
As an alternative to the formation of a dipole as the result of an applied 
field, an embodiment is proposed in which a dipole is formed by varying 
the composition of the well from (InAs).sub.1-x (GaAs).sub.x to 
(GaSb).sub.1-y (GaAs)y across the well width, AlAs barrier layers being 
used. This structure is suggested to give second harmonic generation with 
an efficiency as high as that in the first embodiment described above. 
Also it is stated that this graded structure allows one to dispense with 
the electrodes and power source used in the first embodiment, since the 
application of an electric field is no longer necessary. 
Further embodiments in '505 include a modulator for modulating the bias 
electric field, thereby modulating .psi..sup.(2) and hence modulating the 
harmonic wave. 
In a further embodiment a filter is provided at the optical output of the 
qw structure, the filter passing the second harmonic wave ant blocking the 
low frequency input signal. This embodiment is also proposed for use in 
combination with the modulator or the graded-composition well. 
Nowhere in '505 is there any suggestion that any advantage is to be 
obtained for applications other than second-harmonic generation by having 
a quantum well structure having a compositionally induced dipole. 
Nowhere in '505 is there any suggestion that there is any merit in 
providing a quantum well structure having a compositionally induced dipole 
with electrodes. In this connection it should be noted that in '505 it is 
suggested that with a graded structure the dipole is fixed and hence 
.psi..sup.(2) is fixed, while modulating the bias voltage on a non-graded 
well structure--where .psi..sup.(2) is dependent on the size of the 
applied field, results in a desired modulation of the second harmonic 
signal through modulation of .psi..sup.(2). 
In their paper in journal of Applied Physics, Vol. 62, No. 8, pp 3360-3365, 
Hiroshima and Nishi describe a graded-gap quantum well (GGQW) structure in 
which there is an effective `internal` electric field which concentrates 
the carriers on the same side of the well in both the conduction and 
valence bands. The authors note that such a structure can be realized by 
varying the alloy composition in the well layer so that the band gap 
varies linearly within the well. The paper deals with a theoretical 
analysis of the so-called quantum-confined Stark effect with particular 
attention being paid to excitonic effects. The structure on which their 
theoretical analysis is built is a GGQW comprising an Al.sub.x Ga.sub.1-x 
As well layer, 100.ANG. thick, in which the aluminum content x varies from 
0 to 0.15 along the growth direction, and Al.sub.0.6 Ga.sub.0.4 As barrier 
layers. The authors note that the electron and light-hole envelope 
functions for various applied field conditions are nearly symmetric and 
are less effected than the heavy-hole envelope function by an external 
applied field. 
It is interesting to note that Hiroshima and Nishi are concerned only with 
their linearly-graded gap quantum well structure, which in their words 
"has an effective "internal" electric field which concentrates the carrier 
on the same side of the heterointerface in both the conduction and valence 
bands". Nowhere do they suggest that pushing the electrons and holes to 
the same side of the well with a built-in field is a bad idea or that 
there is anything to be gained by building a structure in which the 
electrons and holes are pushed to opposite sides of the well by a built-in 
field. The authors are not concerned with establishing a structure which 
inherently produces electron-hole pairs as dipoles and do not teach 
towards such a concept. From our own study of the paper, it appears that 
the structure which they describe does produce a small inherent dipole, 
probably with a dipole moment of no more than 5.ANG.. 
BRIEF SUMMARY OF THE INVENTION 
The present invention seeks to provide quantum well structures in which 
field-induced band edge shifts can be achieved without a significant 
accompanying change in absorption coefficient. 
The present invention seeks to provide quantum well devices, and in 
particular quantum well modulators, which have a reduced sensitivity to 
small variations in well width and/or reduced sensitivity to electric 
field nonuniformities within the devices during their operation. 
The present invention also seeks to provide quantum well devices of the 
type described, which devices have operating voltage requirements lower 
than those of comparable prior art devices.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
The invention in its broadest sense is perhaps best explained by reference 
go the behaviour of a conventional quantum well structure such as that 
represented in FIGS. 1(a) and 1(b). The following explanation or 
description of the behaviour of such a conventional quantum well structure 
is unusual, but is believed to make explanation of the present invention 
much easier. The non-expert reader will no doubt be thankful for the 
general absence of calculus! 
Consider an electron-hole pair in its ground state in a conventional 
symmetric square QW. In the absence of an applied or built in field the 
charge density (10 and 11) of both the electron and hole will have its 
`center of gravity` coincident with the center of the well. The energy 
needed to create this ground state, ie the photon energy needed to promote 
the electron from the top of the valence band to the bottom of the 
conduction band, is just the bandgap, 9, of the QW. (We neglect the 
electrostatic attraction between the electron and the hole that gives rise 
to the formation of excitons since this plays only a minor role in the so 
called quantum confined Stark effect). When an electric field is applied 
to the quantum well the energy needed to create the above mentioned 
electron hole pair, the band gap energy, will change; and subsequently 
there will be electroabsorption so all we need to do to understand how the 
QW band gap changes with applied electric field is to understand how the 
minimum energy needed to create an electron hole pair changes in the same 
circumstances. 
To find how the energy of an electron hole pair changes when an electric 
field is applied we can picture the pair as a polarisable atom. When the 
field is applied, the positively charged hole will move to the down field 
side of the well while the negatively charged electron will move in the 
opposite direction towards the up field side of the well. The `centers of 
gravity` of the two charge distributions will no longer be in the same 
place and consequently an electric dipole moment will have been induced. 
Elementary electrostatics tells us that the energy of an electrically 
neutral system with a dipole moment, p, in a field, F, is just -pF. Hence 
when the dipole moment is in the same direction as the field, as in our 
case, then the system has a lower energy in the presence of the field than 
in its absence. Hence the minimum energy needed to create an electron-hole 
pair, ie the band gap, decreases with increasing applied field. There is 
an associated red shift and decrease in height of the absorption edge. The 
decrease in height comes about because the electron and hole are separated 
by the field and it is more difficult for the light to create spatially 
separated electron hole pairs than electron hole pairs in which the 
carriers have the same charge distributions. 
While the above arguments give a qualitative understanding of the quantum 
confined Stark effect, it is not quantitative. To make the arguments 
quantitative, which is important for an appreciation of some of the 
advantages of the invention, we must include the work done on the electron 
hole pair during its formation. Again elementary electrostatics tells us 
that the work done in creating the dipole is +(.alpha..sub.p F.sup.2)/2, 
where .alpha..sub.p is the polarisability of the electron hole pair. This 
raises the energy of the dipole by the same amount. So the change, 
.alpha.E in the energy of the electron hole pair due to the presence of 
the field is 
EQU .DELTA.E=-pF+(.alpha..sub.p F.sup.2)/2 (1) 
But, by the definition of the dipole moment and the polarisability, 
EQU p=.alpha..sub.p F (2) 
so that 
EQU .DELTA.E=-(.alpha..sub.p F.sup.2)/2. (3) 
Note that the shift in the adsorption edge (which is to the red) is the 
same regardless of the direction in which the field is applied. 
We have seen that the shift in the absorption edge varies as the square of 
the total field experienced by the electron hole pair. This field will in 
general be a combination of built-in and applied fields. Ideally, one 
would want this total field to be the same for all the quantum wells in a 
device such as a modulator so that the adsorption edges of the wells move 
in unison, and an optimum extinction ratio results. However, there will 
inevitably be field nonuniformities and hence corresponding variations in 
the shifts in the absorption band edge. These shifts in the absorption 
band edge throughout the device will be magnified by the quadratic 
dependence on the field, the result being that the fractional variation of 
.DELTA.E from well to well will be double the fractional variation in F 
from well to well. 
Inhomogenities in the electric field are by no means the only problem. 
Variations in well width, L, can also produce problems. When one evaluates 
the polarisability of a conventional quantum well one finds that it varies 
as L.sup.4. Hence any fractional variation in the width of the quantum 
wells in a surface modulator (that is one in which light propagates in a 
direction normal to the planes of the quantum well layers) will give rise 
to a fractional variation in the bandgap 4 times that in the well width. 
This results in a smearing of the absorption edge when an electric field 
is applied additional to the smearing already present due to 
inhomogenities in the applied field. 
It is clear that these properties make the design and fabrication of 
modulators and in particular surface modulators using conventional quantum 
wells particularly demanding. 
The preceding analysis of the operation and deficiencies of conventional 
quantum well structures is the result of our appreciation of the potential 
benefits offered by the present invention. As far as we are aware, no--one 
has previously considered or described the operation of quantum well 
structures in terms of electrostatics. We have realised that the problems 
arise in the conventional quantum well devices such as modulators because 
the electroabsorption is essentially the result of two conflicting 
processes. On the one hand, the turning on of the field raises the energy 
of the system by performing work on it during the creation of the dipole. 
On the other hand, the presence of the field lowers the potential energy 
of the system by virtue of the presence of the dipole. Looked at in this 
way it is not surprising, therefore, that the end result, the shift in the 
absorption edge, is sensitive to parameters such as F and L. There is also 
another unsatisfactory aspect. In order to shift the absorption edge one 
must create a dipole. In so doing one makes absorption more difficult and 
so one is in fact degrading the very property one is trying to exploit, 
namely the high band edge absorption! 
Having first realised, with the help of our electrostatic approach, that 
the applied field is changing the band gap as the result of first forming 
a dipole and then acting on the dipole to lower its energy, we further 
realised that we could overcome many of these problems by producing 
asymmetric QW structures which automatically produce electron-hole pairs 
as dipoles. 
If a suitable asymmetric QW is used, then an electron-hole pair will 
already have an intrinsic dipole moment, p.sub.i, and there is no need to 
create one; the `centers of gravity` of the electron and hole charge 
distributions will naturally be in separate places. Additionally, if one 
uses a narrow well then, if the well is narrow and deep enough to bind the 
carriers strongly, the polarisability will be small. To a good 
approximation, the change, .DELTA.E, in the band gap in the presence of a 
field, F, is given by 
EQU .DELTA.E=-p.sub.i F (4) 
ie equation (1) with .alpha..sub.p =0. Equation (4) immediately shows us 
the benefits of QWs which produce electron-hole pairs are dipoles. Because 
p.sub.i is independent of electric field then .DELTA.E depends only 
linearly on the field. Since p.sub.i is essentially a displacement between 
the `centers of gravity` of two charge distributions one expects in to 
vary more nearly linearly with well width, L. We now see than the shift in 
the absorption edge is much less sensitive to variations in electric field 
and well widths than the conventional QW. A much `cleaner` 
electroabsorption characteristic is therefore expected of suitably 
designed QW and MQW structures. 
There is also another advantage in using wells which produce electron-hole 
pairs dipoles which is revealed on closer examination of equations (3) and 
(4). Rewrite (3) in terms of the dipole moment, p.sub.c, induced in the 
conventional QW 
EQU .DELTA.E=-(p.sub.c F)/2 (5. 
We see that for a given .DELTA.E, the dipole p.sub.c induced in the 
conventional QW is twice as large as p.sub.i, the intrinsic dipole needed 
in the asymmetric QW. This means that when the field is applied, the 
intrinsic dipole QW has a superior absorbance per well, because the 
electron and hole charge distributions have more overlap. The absorbance 
per micron of material is further increased if one uses narrow wells 
because one can fit more narrow wells per micron than those of 
conventional thickness. Additionally, for fixed .DELTA.E, and p(=p.sub.c 
=p.sub.i) the field (and thus the voltage) required with a fixed dipole 
structure is half that needed for a conventional structure. 
The arguments presented above show that the desirable features of the 
electroabsorption characteristics of modulators and in particular surface 
modulators containing conventional symmetric quantum wells are inherently 
vulnerable to nonuniformities in well widths and applied fields. As such 
the engineering of modulators using such quantum wells is difficult. 
Simple arguments suggest that asymmetric quantum wells which produce 
electron-hole pairs or dipoles provide (1) a way of reducing modulator 
susceptibility to these nonuniformities and (2) an enhanced extinction 
ratio, or alternatively the same extinction ratio as in the conventional 
device but with lower voltages. 
For optimum results where one is not constrained to use very low (i.e. 1 to 
5 volts) operating voltages we believe that the well width, that is the 
width of the region which will hold both electrons and holes, should be no 
more than about 50.ANG.. This region will of course be made up of at least 
two materials, since at least two offset bandgaps are needed to ensure the 
spatial separation of the carriers needed for the creation of the 
intrinsic dipole moment. The different materials for the well region will, 
in many cases, be ternaries or quaternaries, or one or more of each, 
formed from essentially the same elements. 
FIG. 3 illustrates schematically the insensitivity of carrier probability 
density distribution with respect to minimum energy level. The presence of 
the deed wells in the conduction and valence bands skews the carrier 
distributions even though the minimum energy levels are "above" the energy 
ranges of the deep wells. 
As mentioned above, to ensure low polarisability, deep wells are necessary 
for the electrons and holes. 
Where the QW structure is to be driven with low applied voltages, for 
example less than about 5 volts, optimum performance will generally be 
achieved with somewhat wider wells, for example up to about 100.ANG.. 
Materials 
As will by now be clear, the quantum well structures according to the 
invention have conduction band profiles which tend to push the electrons 
in the well to one side of the well and valence band profiles which tend 
to push the holes in the well towards the opposite side of the well. One 
suitable materials system uses aluminum antimonide (AlSb) barriers with 
quantum wells formed of gallium antimonide (GaSh), for hole confinement, 
and indium arsenide (InAs), for electron confinement. A schematic energy 
level diagram of such a quantum well structure is shown in FIG. 4. The 
solid lines in FIG. 4 represent the conduction and valence band levels for 
the bulk semiconductors and illustrate the overlap between the conduction 
band in InAs and the valance band in GaSb. However, as explained 
previously, quantisation of the energy levels when there is `quantum 
confinement` leads to an increase in the minimum allowable energies for 
electrons and holes in the well, and hence the overlap disappears. In 
particular electrons in InAs are very light and hence are easily 
quantised. Typical energy levels for the quantum well are indicated by the 
broken lines. 
Of course the constituent compounds, and elements, of this system can 
readily be alloyed, and hence device characteristics can be tailored, for 
example by selecting alloy compositions for the quantum well layers which 
give the desired bandgap. In particular there are advantages in forming 
the hole confining region from an InAs rich alloy of InAs and GaSh. 
Of course, as those skilled in the art will appreciate, while quantum well 
structures according to the present invention are preferably based on the 
above described materials system, there are other materials systems which 
could be used. One such system which is capable of providing quantum well 
structures according to the invention is that comprising indium antimonide 
(InSb), cadmium telluride (CdTe) and mercury telluride (HgTe). It is known 
to use HgTe and CdTe alone in quantum well structures, for example see the 
paper by Guldner et al, in Physics Review Letters, Vol. 51, p907, 1983, 
but not in combination with InSb. Fortunately InSb is lattice matched to 
CdTe, so its incorporation into the known two component system is 
possible. CdTe would provide the barrier layers. Bulk InSb has only a 
small band gap, 0.2 eV, and bulk HgTe has no band gap. Quantum confinement 
gives rise to a band gap in HgTe, and causes the band gap of InSb to 
increase. 
Preferably, with the proposed GaSb/InAs/AlSb quantum well structures a GaSb 
substrate is used. The reason for this choice is that both InAs and AlSb 
are slightly imperfectly lattice matched to GaSb, but in opposite senses. 
If appropriately dimensioned InAs and AlSb layers are grown alternately on 
GaSb, the strains tend to cancel each other out, with the result that 
greater overall thicknesses can be grown. 
Also, it should be noted that FIG. 4 illustrates what is in effect the 
simplest realisation of the invention: there are just two regions in the 
quantum well, one for confinement of holes, the other for confinement of 
electrons. While of course it is generally preferable, from the point of 
view of crystal growth, to keep the number of components and the number of 
different layer types to a minimum, it may still be found worthwhile to 
incorporate more components and/or more different layer types to enable 
the use of different alloy systems or to permit the production of more 
complex structures which have good electron and hole confinement and 
separation. Barrier widths of 50.ANG.-100.ANG. are typical. 
Normally the barrier layers will comprise a simple semiconductor, but there 
may be applications where it is advantageous to use alloyed semiconductors 
or even near insulators for the barrier layers. The advantage of using 
simple semiconductors is that they are easier to grow well. 
While barrier widths will normally be in the range 50.ANG. to 100.ANG., the 
optimum width for any particular application should be determined by 
routine experimentation. The barrier width should be sufficient to at 
least substantially prevent tunnelling between wells when the working 
potential is applied, the object being for adjacent wells to be unaffected 
by each other. Because the probability of tunnelling is determined by the 
effective barrier height, thinner wells will in general need thicker 
barrier layers, all other things being equal. Likewise in materials 
systems where the effective barrier heights are necessarily low, it will 
generally be necessary to use barrier layers thicker than those required 
in the GaSb/InAs/AlSb system. It is undesirable so use barrier layers 
which are thicker than necessary, since excess barrier thickness will 
reduce the field intensity 'seen` by the quantum wells for any particular 
applied voltage. An additional and significant disadvantage of excess 
barrier thickness is that it is wasteful of epitaxial growing time and 
ability--generally it would be more useful to grow a multiple quantum well 
structure comprising a greater number of wells. 
The following examples based on the InP/GaInAsP/InGaAs system are included 
to show how it is possible to create significant and useful dipole moments 
even with materials which do not provide very deep wells. In terms of the 
invention, this materials system is very much non-optimum, but 
nevertheless applying the invention to this `everyday` materials system 
does give appreciable advantages. Well widths of 60.ANG. are assumed in 
these examples, but this is not critical. 
EXAMPLES 
For two-part quantum wells of GaInAsP and InGaAs between InP barriers, 
calculations of dipole moments for electrons and holes for different 
phosphorus contents in GaInAsP. An InP substrate was used, the InGaAs 
being lattice matched to InP. 
______________________________________ 
1. For InGaAs sub-well of width 25.ANG., with a GaInAsP.sub.y 
sub-well of width 25.ANG.. 
Hole Electron Difference 
Molar concentration 
Dipole Dipole Dipole 
of P Moment .ANG. 
Moment .ANG. 
Moment .ANG. 
______________________________________ 
0.05 2.59 0.54 2.05 
0.10 4.85 1.10 3.75 
0.15 6.63 1.68 4.95 
0.20 7.95 2.28 5.67 
0.25 8.91 2.90 6.01 
0.30 9.62 3.52 6.10 
0.35 10.17 4.17 6.00 
0.40 10.59 4.82 5.77 
0.45 10.92 5.49 5.43 
0.50 11.20 6.15 5.05 
0.55 11.42 6.82 4.60 
0.60 11.61 7.49 4.12 
0.70 11.92 8.82 3.10 
0.80 12.15 10.10 2.05 
0.90 12.34 11.34 1.00 
______________________________________ 
2. For 50.ANG. sub-well widths: 50.ANG. InGaAs, 50.ANG.GaInAsPy. 
Concentration Dipole Moment 
of phosphorus Difference .ANG. 
______________________________________ 
0.02 5.499 
0.04 9.614 
0.06 12.140 
0.08 13.521 
0.10 14.187 
0.12 14.417 
0.14 14.374 
0.16 14.156 
0.18 13.821 
0.20 13.409 
0.22 12.943 
0.24 12.442 
0.26 11.920 
0.28 11.386 
0.30 10.846 
______________________________________ 
3. For sub-wells of 17.58.ANG. (6 mono-layers) GaInAs, and 
41.02.ANG. (14 mono-layers) GaInAsP. 
Dipole 
Molar Moment 
Concentration Difference 
phosphorus .ANG. 
______________________________________ 
0.2 10.352 
0.25 11.602 
0.30 12.139 
0.35 12.189 
0.40 11.909 
0.45 11.397 
______________________________________ 
FIG. 6 shows the band-gap and notional probability density distributions 
for electrons and holes for this structure with a molar concentration of 
phosphorus of 0.40. The notional displacements of the `centers of gravity` 
of the hole and electron distributions are shown as stars. 
As with other QW modulators, modulators according to the present invention 
will routinely be in the form of a PIN structure with the quantum wells in 
the intrinsic region. Also conventional is the use of charge separating 
layers of intrinsic material to each side of the QWs, to ensure uniformity 
of field. The charge separating layers are conveniently formed of the 
material used in the barrier layers of the QWs, and anyway are chosen to 
have a bandgap greater than that of the low gap material in the QWs on 
either side of the intrinsic region there are respectively provided a p 
and an n region to which the device's electrodes are connected. Typically, 
metal electrodes forming ohmic contacts with the p and n regions are used. 
In a further embodiment the invention provides a tuneable Bragg reflector 
comprising multiple multiple-quantum-well stacks, each mqw stack 
comprising quantum well structures according to the invention and grown in 
one sense, alternate mqw stacks having the growth sense reversed. By 
growing each mqw stack of quantum wells grown in one sense, than is with 
their intrinsic electron-hole dipoles disposed in the same sense (poled), 
and then growing the next mqw stack with the intrinsic electron-hole 
dipoles poled in the opposite sense, and so on, a structure is created in 
which, on application of a suitable potential thereacross, the refractive 
indices of alternate layers can be varied in opposite directions. 
An example of such a structure is shown schematically in FIG. 5. Such 
structures are useable as tuneable Bragg reflectors in either waveguide or 
surface configuration, the latter configuration being illustrated in FIG. 
5. In the structure illustrated, which is designed for normal light 
incidence, the mqw stacks are each of a thickness approximately equal to 
one quarter of the device's operating wavelength--that is, each layer has 
a thickness of .lambda./4n, where n is the refractive index of the layer 
at the wavelength .lambda.. The operating wavelength can be near the 
band-gap--equivalent wavelength, in which case there can be strong 
refraction but with the possibility of absorption, or longer wavelengths 
can be used with correspondingly reduced refraction. An electric field is 
applied, normal to the planes of the layers, by means of electrodes on the 
end faces 50, 51 of the structure. A material such as indium tin oxide 
ITO, which is electrically conductive and which transmits light, may be 
applied to the end faces of the structure for use as electrodes. More 
generally, metallic contacts will be applied to the end faces. The number 
of layers in each stack and the number of stacks in the structure are not 
critical and the optimum numbers for any particular application may be 
determined by routine experimentation. The upper limit on both numbers 
will in general be set by the maximum thicknesses which can be grown while 
maintaining good epitaxial growth, by the operating wavelength range, and 
by the requirements for the driving field and for optical performance. 
As those skilled in the art will be aware, in order to ensure electric 
field uniformity, it is desirable to provide charge separating layers of 
intrinsic material between the electrodes and the mqw stacks. Conveniently 
this intrinsic material may have the same composition as the barrier 
layers in the MQWs. Schottkey contacts can be provided to the structure 
using appropriate contacts. Alternatively, a PIN structure may be used, 
the mqw and charge separating layers constituting the intrinsic region 
thereof. 
Typically each mqw stack would comprise between 10 and 100 quantum wells, 
more typically 25 to 50, for example 40. Typically there will be between 3 
and 50 stacks in total, more typically between 10 and 40, for example 30. 
Tuneable Bragg reflectors in waveguide configurations can readily be 
constructed, although of course the layer thicknesses and numbers and 
number of stacks will in general differ from those used in the above 
described surface configuration. 
Tuneable Bragg reflectors according to the invention may conveniently be 
produced using the InP, InGaAs, GaInAsP material system. By selecting 
GaInAsP compositions with phosphorus contents which give the largest 
dipole moments for the well widths chosen, good optical performance can be 
obtained. Examples 1, 2 and 3 above give an indication of suitable 
well-widths, compositions and phosphorus contents. 
Bragg reflectors comprising QWs formed from the other materials systems set 
out above can be expected to provide performance significantly improved 
over that obtained with the InP, InGaAs, GaInAsP system.