Method and device for rapid photo-detection by means of a super-lattice

To detect a temporal variation, in particular an ultrashort pulse, in a beam of electromagnetic radiation, this beam is applied to a super-lattice of type II, along its axis of growth, and the voltage between the opposite sides of the network along the same axis is determined. The super-lattice is preferably a composite super-lattice, in particular, with alternate layers of indium arsenide and of gallium antimonide. The method is, in particular, applied in the infrared range.

FIELD OF THE INVENTION 
The present invention concerns semiconductor super-lattices. 
PRIOR ART 
Semiconductor super-lattices have, in particular, been the object of the 
following publications: 
L. Esaki and R. Tsu IBM Journal of Research and Development, 14, 61 (1970). 
L. Esaki and L. L. Chang, Phys. Rev. Lett. 33, 495 (1974). 
R. Dingle et al., Phys. Rev. Lett. 33, 827 (1974). 
R. Dingle, in Festkorper XV, edited by H. J. Queisser, Pergamon Vieweg, 
1975, p.21. 
L. Esaki and L. L. Chang. Journal of Magnetism and Magnetic Materials 11, 
208 (1979). 
L. Esaki, Journal of Crystal Growth, 52, 2277 (1981) and Surf. Sci., 113, 
No. 1-3 (1982). 
The mathematical tools for their analysis have, moreover, been defined in 
particular in the following publications: 
G. A. Sai Halaz, L. Esaki and W. A. Harrison, Phys.Rev. B 18, 2812 (1978). 
G. Bastard, Phys. Rev. B 24, 5693 (1981) and B 25, 7584 (1982). 
M. Altarelli, Phys. Rev. B, 28, 842 (1983). 
Briefly, a super-lattice is a semiconductor structure wherein there appear 
along one of its axes (termed below the axis of growth), periodic 
variations of the lower limit of the conduction band and of the upper 
limit of the valence band. In other words, a periodic variation is 
produced of the width of the forbidden band along the axis of growth. 
The "waveform" of this periodic variation is most frequently very 
straightforward, at least in theory. Thus one may distinguish: 
super-lattices wherein the periodic variation has a rectangular shape, such 
as the heterostructures obtained by the alternation of gallium arsenide 
(GaAs) and aluminumgallium arsenide (Al.sub.x Ga.sub.1-x As) layers, 
studied in particular by Esaki et al. (1974), Dingle et al. (1975) or also 
heterostructures of indium arsenide and of gallium antimonide (InAs-GaSb) 
studied by Esaki (1978 and 1982); 
the super-lattices where this periodic variation assumes on the whole a 
sinusoidal shape, such as NIPI doped superlattices studied by G. H. Dohler 
et al. Phys. Rev. B 27, 3538 (1983); 
the "saw-tooth" super-lattices studied in particular by Capasso et al., 
Phys. Rev. Lett. 51, 2318 (1983). 
One of the advantageous properties of super-lattices is that they form 
centers of concentration of the charge carriers: electrons in the wells of 
potential of the conduction band, that is to say in the "hollows" of the 
lower limit of the conduction band; holes in the wells of potential of the 
valence band, that is to say, in the "humps" of the upper limit of the 
valence band. 
This has led to a new classification: 
The super-lattices are termed super-networks of type I wherein the hollows 
and the humps subject to the said concentration are found substantially at 
the same points along the axis of growth (GaAs-Al.sub.x Ga.sub.1-x As). 
The super-lattices of type II are, on the contrary, those wherein the 
hollows (concentration of the electrons) and the humps (concentration of 
the holes) appear at different alternate points along the axis of growth 
(InAs-GaSb), doped super-lattices). 
OBJECT OF THE INVENTION 
It is an object of the present invention to provide a new transient 
photovoltaic effect which appears in the Type II super-lattices and which 
is such as to allow the making of a rapid infrared photodetector. 
It is a further object to provide a method for detecting a temporal 
variation, in particular, an ultrashort pulse in a beam of electromagnetic 
radiation. 
SUMMARY OF THE INVENTION 
The invention provides a method for detecting a temporal variation, in 
particular, in an ultrashort pulse in a beam of electromagnetic radiation, 
characterized by the operations of (a) applying the beam to a type II 
super-lattice along its axis of growth; and (b) determining the voltage 
between the opposite sides of the super-lattice along the same axis. 
The invention applies, in particular, when the super-network is a composite 
super-lattice. 
At present, such super-lattices are formed by compounds of semiconductors 
III-V, or alloys of the latter. 
In practice, the composite super-lattices are periodic laminates of the 
layers of two different compounds. 
It is advantageous to choose these compounds so that the lower limit of the 
conduction band of one of the compounds should be lower than the upper 
limit of the valence band of the other compound, which makes it possible 
to choose the width of the forbidden band of the super-lattice by way of 
design, as will be seen below. 
In a particularly advantageous mode of the embodiment, one of the compounds 
is indium arsenide (In As) and the other, gallium antimonide (Gs Sb). One 
may also envisage using alloys of such compounds. 
For its part, the thickness of the layer is, in principle, less than 
approximately 300 angstroms, and preferably less than approximately 200 
angstroms, in particular, for the InAs-GaSb super-lattices. 
As a general rule, the thicknesses of the one compound and of the other are 
substantially equal to within an approximate factor of 2. Thus, the method 
may be implemented with a layer thickness of approximately 30 anstroms for 
the indium arsenide and 50 angstroms for the gallium antimonide. 
Although doping does not play a direct part, it is desirable that it should 
remain at as low a level as possible. In practice, the indium arsenide and 
the gallium antimonide contain residual n and p type dopants, 
respectively. 
The laminate constituting a super-lattice may comprise approximately 100 
pairs of layers for a total thickness of one or several micrometers along 
its axis of growth. 
As a variant, the super-lattice can also be a doped lattice of the type 
termed "NIPI", that is to say, comprising an alternation of heavily doped 
n zones and heavily doped p zones with or without interposition of 
intrinsic semicondutor layers attaching originally to the term "NIPI". 
In accordance with another aspect of the invention, the super-lattice is 
given an overall asymmetry of reflection along the direction of growth in 
relation to the incident beam of electromagnetic radiation. 
This overall asymmetry of reflection may be at least partly geometrical in 
origin, for instance, in that the super-lattice exacty comprises an 
integral number of spatial periods (pairs of layers). 
The overall asymmetry of reflection may also be in part due to the 
absorption of light in the layers of the super-lattice. 
The invention also concerns a device for detecting a temporal variation, in 
particular an ultrashort pulse in a beam of electromagnetic radiation. The 
device comprises a type II super-lattice, such as defined above, means for 
focussing the incident beam, so that it is produced substantially along 
the axis of growth of the super-lattice and measuring means sensitive to 
the potential difference obtaining between the opposite sides of the 
lattice along its axis of growth. 
The super-lattice is, for instance, formed on a substrate rendered 
conductive by strong doping and obtained by the technique called molecular 
beam epitaxy. 
A super-lattice in accordance with the invention has a rapid response to 
the rising front of a light pulse. The photoelectric signal then decreases 
more slowly. The time constant of the decrease may, moreover, vary 
slightly according to whether the transition which has produced it is a 
transition from a non-illuminated state to an illuminated state, or, on 
the contrary, from an illuminated to a non-illuminated state. 
Moreover, the impedance created by the measuring means between the opposite 
sides of the super-lattice may be adjusted to define the time constant of 
the decrease in response of the device to the transitions of 
electromagnetic radiation, of course insofar as it is desired to shorten 
this time constant. 
According to another aspect of the invention, where one uses a 
super-lattice such as those of an of InAs/GaSb composition, the periodic 
arrangement of the laminating of the super-lattice may be chosen so as to 
render it sensitive to a predetermined wavelengths band of the incident 
radiation. 
Finally, the invention concerns any application of a type II super-lattice, 
in particular of a composite In As/Ga Sb super-lattice, to transient 
photovoltaic measurements, in particular of ultra short pulses in the 
infrared range.

BRIEF DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In FIG. 1, the super-lattice SL is constituted by a substrate S whose 
thickness is of the order of a fraction of one millimeter. On this 
substrate, alternate layers of materials A and B are caused to grow, for 
instance, by epitaxy with molecular jets and this along a direction of 
growth marked z. Since the drawing is not to scale, it shall be assumed 
that the super-lattice comprises about one hundred pairs of layers A and B 
forming an overall thickness of one micrometer. 
The fabrication of super-lattices uses advanced techniques and it is very 
delicate since many factors intervene. One of these factors is the 
dimension of the crystal lattices normally comprised in the two materials 
A and B of the laminate. The nature of the materials which can be used is 
still relatively limited, because of the problems of evaporation, adhesion 
and of crystal reconstruction which may occur when epitaxy is used. 
First of all, super-lattices were made whose laminate structure consists 
alternately of layers of gallium arsenide (Ga As) and of a 
gallium/aluminum/arsenide alloy usually designated Ga.sub.1-x Al.sub.x As. 
The expert knows that in such a super-lattice, the limits of the conduction 
band and of the valence band are defined by square wave plots designated 
LBC and LBV in FIG. 2. In FIG. 2, the abscissae represent the z direction 
of the axis of growth, while the ordinates are energies usually measured 
in milli-electron volts (meV). 
In a type I super-lattice as illustrated in FIG. 2, potential wells will be 
observed constituted by the hollows of the LBC limit of the conduction 
band. The charge carriers concerned, that is to say, the electrons, will 
preferentially establish themselves in the potential wells. Thus the 
drawing represents a cloud of electrons GE at the bottom of each one of 
the potential wells. This is a simplification because in a super-lattice, 
quantization of the energy levels which can be taken up by the electron, 
will occur. In other words, one says that there exist "sub-bands" in the 
conduction band. 
Similarly, a cloud of positive charge carriers or holes will be observed in 
each one of the wells of the valence band. These clouds of holes are 
designated GH. And, taking the inversion of the signs into account, the 
quantum wells of the valence band are defined by the humps of the latter 
in a representation such as that of FIG. 2. 
The forbidden band of such a super-lattice is the gap between the basic 
conduction and valence sub-bands. 
The super-lattice of FIG. 2 is type I, because the clouds of electrons GE 
and of the holes GH are at the same points along the direction of growth 
z. 
It is different in a type II super-lattice, as will now be seen with 
reference to FIG. 3. 
The super-lattice of FIG. 3A is an alternate laminate of layers In As and 
Ga Sb, of respective thicknesses d.sub.1 and d.sub.2. The period d of the 
lattice is designated d, with d=d.sub.1 +d.sub.2. The limits of each pair 
of layers will also be given a designation of z.sub.n-1, z.sub.n, and 
z.sub.n+1, which here commences when passing from Ga Sb to In As, thus 
defining the elementary cell of the super-lattice. 
The type II super-lattice of FIG. 3A has two particular features: 
the first, related to its belonging to type II, is that the LBC and LBV 
square wave plots appear "in phase", that is to say, that the hollows of 
the LBC square wave plot (the quantum wells of the conduction band) 
alternate with the humps of the LBV plot (the quantum wells of the valence 
band); 
moreover, the lower extremes LBCE of the limit of the conduction band LBC 
are lower than the upper extremes LBVE of the limit of the valence band 
LBV. It follows therefrom that the LBC and LBV plots overlap. The reading 
of FIG. 3A is facilitated in that the LBV line is marked by regularly 
interspaced points. 
The first observation made above has the result that the privileged 
concentrations of electrons GE alternate with privileged concentrations of 
holes GH along the z axis. In FIG. 3, a schematic illustration has been 
shown of the probability of the presence FOE of electrons along the z axis 
(square modulus of the wave function .psi..sub.e (z)) and similarly FOH 
for the probability of the presence of holes along the z axis (modulus of 
the wave function .psi..sub.h (z), squared). 
It is now recalled that quantization applies, that is to say, there are 
sub-bands in a super-lattice. 
Thus, FIG. 3A shows the level E.sub.1 of the basic state of the electron in 
the quantum wells of the limit LBC of the conduction basnd. 
Similarly, the level HH.sub.1 of the basic state of the holes (heavy, as 
will be seen below), will be observed in the quantum wells of the limit 
LBV of the valence band. 
The second property of the In As-Ga Sb super-lattices will be better 
understood on examining FIG. 4. The latter comprises period d of the 
super-lattice expressed in angstroms along the x axis. Along the y axis, 
it is graduated in energy (electronvolts). The graph corresponds to the 
case where thicknesses d.sub.1 and d.sub.2 are equal. 
In this FIG. 4, the area designated E.sub.1 illustrates the size of the 
basic sub-band of the quantum wells of the conduction band. The area 
E.sub.2, E.sub.3, etc., illustrates the sizes of the higher order 
sub-bands. It will be seen that these areas thin out very rapidly to 
terminate in a single line when period d increases towards 250 angstroms. 
The HH.sub.1 curve illustrates the basic sub-band in the quantum wells of 
the valence band for the heavy holes. The HH.sub.2, etc., areas illustrate 
the higher order sub-bands. 
Finally, the LH.sub.1 area illustrates the first sub-band of the quantum 
wells of the valence band for light holes and the LH.sub.2 and following 
areas illustrate the higher order sub-bands. 
It is not necessary to develop here the difference between heavy and light 
holes. This difference is set out in the articles cited at the beginning 
of the description. 
In point of fact, it suffices to accept that the super-lattice is, in its 
state termed "limite electrique quantique" (in English, Electric quantum 
Limit or EQL) wherein only the basic sub-bands of the conduction band and 
of the valence band are occupied. It is, then, the E.sub.1 and HH.sub.1 
sub-bands which are essential for defining the state of the super-lattice. 
FIG. 4 also shows an advantageous characteristic of the In As-Ga Sb 
lattices related to the fact already noted that LBVE is higher than LBCE. 
In point of fact, by selecting the period d of the lattice, one defines at 
will the distance between the zones HH.sub.1 and E.sub.1, that is to say, 
the width of the forbidden band. 
For instance: 
the width of the forbidden band is a few milli-electronvolts for a period 
of the super-lattice of 150 angstroms; beyond this, it has been 
demonstrated that the forbidden band increases again in spite of the 
apparent crossing of layers E.sub.1 and HH.sub.1 (Altarelli's article 
already cited); 
this width of the forbidden band does, on the contrary, increase to some 
hundreds of milli-electron volts when the period d of the lattice falls to 
approximately 60 angstroms. 
The behavior of such super-lattices is quite astonishing and has already 
formed the object of many studies. 
It has, in particular, been observed that there occurs a periodic curving 
of the bands because of the spatial separation of the charge carries 
(electrons and holes). But it has become apparent that this phenomenon 
could not, on its own, explain all the observations made with the 
super-lattices. Besides, one is here essentially concerned with a 
photo-induced effect which is continuous, contrary to the transient 
photo-electric effect which will be described below. 
Studies effected by the assignees of the present invention have shown, 
first of all, that if a voltage generated in an elementary cell of the 
super-lattice is termed .DELTA.v for instance, between the abscissae 
z.sub.n and z.sub.n+1, there occurs a phenomenon of addition when an 
injection of charge carriers is applied to the super-lattice. That is to 
say, when the voltage .DELTA.V existing at the terminals of the 
super-lattice as a whole is equal to N times the voltage .DELTA.v, as 
recalled in equation (1) in the Annex, N being the number of periods 
comprised in the super-lattice. 
The specialists have taken a rather long time to perceive this situation, 
which is, nevertheless, apparently simple. 
As has already been explained, it will now be considered that the 
super-lattice is in its electric quantum limit state, that is to say, that 
only the conduction and valence sub-bands are occupied. .psi..sub.e (z) 
designates the wave function envelope relating to the electrons which is 
centered in relation to the indium arsenide layer. (The approximations of 
the wave function envelopes have been described in G. Bastard's articles 
cited above). 
It will be observed that the wave functions of the electron extend somewhat 
into the adjacent gallium antimonide layers (see in FIG. 3A the FOE curve 
which represents .vertline..psi..sub.e (z).vertline..sup.2.). 
Similarly, .psi..sub.h (z) designates the wave function envelope associated 
with the heavy holes. The square of its modulus, that is to say, the FOH 
curve is illustrated negatively in relation to the FOE curves of the 
electron according to a natural convention. it will also be observed that 
the wave function .psi..sub.h (z) is centered on the gallium antimonide 
layer. 
This spatial separation of the wave functions of the electrons and holes 
corresponds to a local polarization which induces an overall potential 
difference .DELTA.v at the terminals of the super-lattice. As set out in 
equation 1, .DELTA.v is equal to the sum of the local potential 
differences .DELTA.v between the planes z=z.sub.n and z=z.sub.n+1 limiting 
the n.sup.th unitary cell. 
The expert will understand that in a unitary cell, the potential difference 
.DELTA.v may be defined by equation 2 given in the annex, where: 
e is the charge of the electron, 
n.sub.s is the number of charge carriers injected per unit of surface, 
(more exactly of electron-hole pairs), 
.epsilon. and .epsilon..sub.0 are the usual dielectric constants, and 
z, z', dz and dz' are the usual symbols of the integration variables. 
Relation (2) defines the integral of the difference between the 
probabilities of the presence of electrons and of holes, firstly over a 
fraction of a unitary cell extending from its up line terminal as far a 
current value z, whereupon a fresh integration is effected for z varying 
from the one to the other limit of the unitary cell. 
Equation (2) implicity brings in the conditions at the limits, which ensure 
that the electric field fades outside a dipolar bi-dimensional charge 
distribution. 
It is now becoming clear that the system may be considered as an assembly 
of capacitors in series, each associated with one period of the 
super-lattice, the positive plate of the said capacitors is situated at 
the level of the mean value at z of the wave function of the holes, and 
whose negative plate is at the mean value at z of the wave function of the 
electrons. This is illustrated in FIG. 3B, where the capacitors designated 
C.sub.n-2 to C.sub.n+2 are shown. 
Work carried out by the assignees of this invention has made it possible to 
verify that, if the wave functions are normalized over the segment 
z.sub.n, z.sub.n+, the double integral of the equation (2) may be written 
in the form of a simple integral which forms the object of equation (3). 
In its turn, this integral may be expressed as the difference between the 
mean value of z.sub.h for the holes and the mean value of z.sub.e for the 
electrons, which is also written in equation (3) using the normal 
graphical convention for illustrating the mean value (&lt; &gt;). 
By inserting the value of the double integral determined by equation (3) 
into Equation (2), one arrives at equation (4). The latter lets moreover 
the surface S of the sample appear perpendicular to its axis of growth. 
The expression .DELTA.v thus obtained in equation (4) is comparable to the 
ratio of one charge Q to one capacitance C, which is a mathematical 
justification of the arguments set out above with reference to FIG. 3B. 
Taking the symmetry of wave functions into consideration, it may also be 
shown that the difference between the mean values of z.sub.h and z.sub.e 
may be defined by the equation (5), where p.sub.e and p.sub.h are, 
respectively, the probability for the electrons to be in the In As layer 
and the probability for the holes to be in the Ga Sb layer. 
Thus, for example, one will consider a super-lattice having N=100 periods, 
for these In As layers whose thickness is 30 angstroms, while that of the 
Ga Sb layers is 50 angstroms. The determination of the wave functions 
yields a probability p.sub.e of approximately 0.7, and a probability 
p.sub.h of approximately 1. If a carrier density of n=n.sub.s /d=10.sup.17 
cm.sup.-3 is injected, the potential difference .DELTA.v at the terminals 
of the super-lattice as a whole is of the order of 200 millivolts. 
The preceding considerations demonstrate the existence of a fresh 
photovoltaic effect, of a quantum origin, which is produced because of the 
localization of the wave functions and the absence of an overall symmetry 
of reflection along the axis of growth of the super-lattice. 
It has, however, been noticed that this effect could not be observed under 
continuous illumination, because of the conductance of the super-lattice 
parallel to its axis of growth. One is thus, in point of fact, concerned 
with a transient effect governed by the time of recombination .tau. of the 
electron-hole pairs and also by the time constant RC of the electric 
circuit. This aspect will be returned to below. 
Reference is now made to FIG. 5 illustrating the results of luminescence 
obtained in an In As/Ga Sb super-lattice subjected to strong photonic 
pulsed excitation. 
An In As/Ga Sb super-lattice (30 angstroms and 50 angstroms) has been 
excited by a continuous wave krypton laser, then by an argon laser fitted 
with an acoustic-optic modulator and providing short pulses of 
approximately 20 nanoseconds at 150 nanojoules per pulse. 
The excitation is effected far above the forbidden band of the sample and 
the dimension of the excited region on the super-lattice is typically 50 
micrometers. 
After various processing operations and corrections, one obtains the curves 
illustrated in FIG. 5, where the x-axis corresponds to the energy of the 
photons emitted in millielectronvolts (meV), while the y-axis defines the 
intensity of luminenscence in arbitrary units. 
For the laser with a continuous wave (Curve CW) the luminescence spectrum 
consists of a single line centered on approximately 270 meV and comprising 
a low energy flank which tends to be saturated when the excitation level 
is increased. 
The energy position of this line (as well as the dependence in relation to 
the excitation level, on the one hand, and the temperature of this 
luminescence line, on the other hand), does altogether favor an 
interpretation based on the band to band recombination of the 
electron-hole carriers. In other words, the dependence on temperature and 
the inventors' other observations tend to show that the luminescence 
observed is essentially of an intrinsic nature, in contrast to the more 
complex luminescence effects which can be due to impurities or other 
interference phenomena which are responsible for the low energy flank. 
In comparison therewith, the high energy flank is relatively gentle, which 
indicates that the charge carriers have an effective temperature 
substantially higher than the temperature of the latice itself. The expert 
knows, in point of fact, that an analysis of quantum phenomena frequently 
leads to attributing a temperature to the charge carriers which is 
different from that of the crystal lattice containing them. 
Now the PE curve will be observed which corresponds to the excitation of 
the super-lattice by short pulses as indicated above. Two observations 
were made at the time: 
the luminescence line widens as the excitation level increases, which 
reflects the increase of the carrier density; 
but, and this above all, this line is shifted as a whole towards the higher 
energies as will be seen by comparing the PE curve drawn in a solid line 
and the CW curve in dots and dashes. 
It has thus been able to show that the gap of the forbidden band does 
effectively increase as the carrier density increases under pulsed 
excitation. 
The shape of the band to band recombination line is that defined by 
equation (6) given in the Annex where: 
h is Planck's constant 
.upsilon. is the frequency, h.sub..upsilon. being the energy of the 
photons; 
q and dq are, respectively, the component of the wave vector of the 
super-lattice in direction z and its differential; 
f.sub.e and f.sub.h are the Fermi distributions respectively relating to 
the electrons and the holes; 
.mu. is the reduced mass of the electron-hole pair; 
m*.sub.e m*.sub.h are, respectively, the effective masses of the electrons 
and of the heavy holes; 
E.sub.g is the value of the gap of the forbidden band; 
.epsilon..sub.z defining the profile of the basic conduction sub-band is 
equal to: 0,5 .DELTA.E (1+cos qd); and 
.DELTA.E here has the value of 60 meV. 
It has also been observed that at a low temperature and at a high injection 
rate, the distribution of the electrons is degenerate. The theoretical 
profile of the line form is then very sensitive to the Fermi quasi-levels 
of the electrons, or which is tantamount to it, the carrier density. It is 
also very sensitive to the effective temperature of the carrier T.sub.e. 
Apart from that, the low energy cut off value of the line form gives the 
value of the gap of the forbidden band E.sub.g of the super-lattice. 
We then proceeded to a adaptation of this function on the spectrum obtained 
with a continuous excitation at 80 milliwatts (curve CW of FIG. 5). This 
gives a carrier density n of approximately 1.2 10.sup.17 cm.sup.-3, an 
effective temperature of 43.degree. K., and a forbidden band gap E.sub.g 
of 262 meV. 
Similarly, the spectrum PE obtained with ultra-short pulses of 150 
nanojoules has formed the object of an adaptation giving n=2.1 10.sup.17 
cm.sup.-3, T.sub.e =55.degree. K. and E.sub.g of 267 meV. 
In a linear approximation, the variation of the forbidden band gap, 
depending on the carrier density under pulsed excitation, is obtained as: 
.DELTA.E.sub.g (in meV)=(4.+-.1.5) 10.sup.-17 .n (in cm.sup.-3). 
The present invention thus makes it possible to explain a variation which 
is much more important than that deriving from the known phenomenon of the 
periodic curving of the bands which is itself also associated with the 
spatial separation of the carriers. This latter effect, which also exists 
under continuous luminous excitation, may be evaluated by a perturbation 
method. For the example here considered, one would obtain a variation of 
the order of 9.10.sup.-18.n in the same measurement units. 
The experiments carried out by the assignees of this invention thus clearly 
demonstrate the existence of a transient photovoltaic effect which is 
substantially of the same order as the voltage .DELTA.v which is observed 
from layer to layer in the super-lattice. 
Although the phenomena are not yet completely explored, it does indeed seem 
that this modification of the forbidden band under pulsed excitation is 
due to a modification of the shape of the quantum wells and of the tunnel 
effect produced between them under the electric field effect produced by 
the photo-voltaic voltage. As a consequence, the confinement energies, on 
the one hand, and the width of the conduction band are affected and 
therefore the band structure of the super-lattice. 
The preceding considerations suppose that two conditions have been met in 
the super-lattice: 
the first is that there exists a spatial separation of the charge carriers, 
which is true as regards all type II super-lattices; 
the second stipulates the existence of an overall assymmetry in direction z 
of the axis of growth. 
This second condition may be met in that the overall structure is 
non-symmetrical, that is to say, that it possesses the same number N of In 
As and Ga Sb layers. One may apply the simple approximation of the 
capacitances as illustrated in FIG. 3B. The symmetry of the basic states 
of the wave functions of the electrons [and] of the holes implies that the 
mean values of z.sub.e and of z.sub.h are, respectively, at the centers of 
the In As and Ga Sb layers. One may then write the relation (7). 
This relation is also obtained by combining the equations (1), (4) and (5). 
But in reality, because of the absorption of light, the density of the 
injected carriers is not homogeneous along the axis of growth of the 
super-lattice. This absorption effect may be described in a simple way: 
the intensity of the incident beam decreases by a factor exp(-.alpha.d) at 
each super-lattice period, and the density of the injected carriers is 
proportional to this absorbed intensity. There follows therefrom the new 
expression of equation (8). For an absorption of photons whose energy is 
close to the absorption threshold (forbidden band), and for the above 
mentioned sample (In As-Ga Sb; 30-50 A), the coefficient .alpha.d is 
approximately 10.sup.-3. As a result, the photovoltaic effect will 
normally be saturated when the number of periods of the super-lattice 
reaches a value of the order of 1,000. 
However, the spatial separation of the charges and the absorption 
coefficient counteract each other. At low values of the forbidden band, 
the absorption coefficient is much smaller. 
Moreover, this absorption effect may contribute, by way of supplementing 
the asymmetry already noted, or by replacing the latter, to providing the 
overall asymmetry of inversion (or of reflection) which is necessary, as 
has already been mentioned. 
We shall now return, referring to FIGS. 6A and 6B to the time parameters of 
the transient photovoltaic effect. 
The surface carrier density n.sub.s and the overall photovoltaic voltage 
.DELTA.v are governed by the operation of two dynamic equations (9) and 
(10). 
In these equations, G designates the generation rate of the electron-hole 
pairs, .tau. designates the time of recombination of the electron-hole 
pairs, and RC designates a time constant of the electric circuit to which 
reference will be made below. 
The recombination time .tau. (which is typically less than one nanosecond 
in the case of the sample considered), governs the concentration of the 
carriers in the mass of the super-lattice sample. Conversely, the time 
constant RC describes the relaxation of the photo-voltaic voltage, which 
corresponds to a net transfer of charges between the end planes of the 
super-lattice in relation to the z axis. 
This time constant RC may be due solely to the conduction of the 
super-lattice parallel to its axis of growth; it may also be imposed by an 
external circuit, if the latter provides a discharge gap whose own time 
constant is smaller. It may also vary from the range of values below a 
nanosecond to that of the values comprised between a microsecond and a 
millisecond. 
Two cases may then arise: 
FIG. 6A illustrates the excitation of the super-lattice by a very short 
light pulse (of duration T), comprising successively an ascending 
transition and a descending transition, both being very abrupt. This is 
defined by the curve G (RC&gt;.tau.&gt;T). 
The density of the injected carriers n.sub.s follows the shape of the curve 
G but taking the recombination time .tau. of the carriers into account. 
This also applies to the photo-voltaic voltage .DELTA.V generated at the 
terminals of the lattice since no macroscopic relaxation effect had time 
to materialize. 
In FIG. 6B, the photonic pulse excitation assumes a crenellated shape as 
illustrated by curve G with the condition of T&gt;RC&gt;.tau.. The density of 
the injected carriers n.sub.s then follows the ascending transition with a 
time constant related to the recombination time .tau.. This density 
n.sub.s then follows its maximum to redescend with the same time constant 
.tau. during the descending transition of the curve G. For its part, the 
overall photo-voltaic voltage .DELTA.V will also have a rising front which 
is related to that of the carrier density n.sub.s by an exponential law. 
While n.sub.s is at its maximum, .DELTA.V redescends with an exponential 
time constant RC as far as zero. As the n.sub.s redescends, .DELTA.V then 
assumes negative values, defined as the symmetrical value of its initial 
rise. Finally, .DELTA.V returns to the zero value with a time constant RC' 
which may be different from RC. 
The two time constants are somewhat different when they are solely due to 
the super-lattice itself. It will, in point of fact, be understood that 
the super-lattice is not conductive in the same way when it contains a 
high density of carriers as with hardly any. 
But, as has already been noted, it is possible to shorten the two time 
constants RC and RC' which then become substantially equal if the 
discharge of the overall capacitor present at the terminals of the 
super-lattice is linked with shorter time constants appertaining to an 
external circuit. 
Of course, in the completely opposite situation where the time constant RC 
would be far lower than the recombination time .tau., there would not 
appear any photo-voltaic voltage whatsoever with the illumination 
conditions, because the system would then substantially assume a 
conducting mode. 
The transient photo-voltaic phenomenon, in accordance with the present 
invention, may be observed by means of the experimental device illustrated 
in FIG. 7, by way of example. 
A laser with ultra short pulses LIR operating in the infrared range, 
illuminates an optical device focussing the beam on the super-lattice SL 
obtained by growth on a substrate N+ of gallium arsenide, the direction of 
growth being designated as above. 
A contact device DC is placed on the upper face of the super-lattice, for 
instance, in the form of a silver base lacquer. A lower contact is then 
effected on the substrate N+. A device MV measuring the voltage pulses may 
then be connected between these two contacts. 
With an In As super-lattice having 100 periods with layer thicknesses of 30 
angstroms, and 50 angstroms respectively, and a density of injected 
carriers n=n.sub.s /d of approximately 10.sup.17 cm.sup.-3, there is 
obtained a photo-voltaic voltage which can reach a few hundreds of 
millivolts, e.g. about 0.2 V, depending upon the electricl characteristics 
of the device (including the measuring instrument). It has been observed 
that the electrical characteristics of the substrate, notably its 
conductivity, have a major influence on the amplitude of the measured 
signal. 
Another experiment has been made with a superlattice InAs/GaSb (thickness 
30 angstroms for both). At the temperature of liquid helium, the overall 
resistance, substrate+sample, was about 1500 ohms. A signal of about 5 mV 
has been obtained across a load resistance of 50 Ohms. 
The super-lattices of the type termed "nipi" also have the property of an 
alternate spatial localization of the electrons and holes along their axis 
of growth. Although it has not yet been possible to verify this 
completely, it is considered that such type II super-lattices also possess 
the transient photovoltaic effect in accordance with the invention.