Lithography using quantum entangled particles

A system of etching using quantum entangled particles to get shorter interference fringes. An interferometer is used to obtain an interference fringe. N entangled photons are input to the interferometer. This reduces the distance between interference fringes by n, where again n is the number of entangled photons.

FIELD OF INVENTION
 The present application describes a technique of using quantum-entangled
 particles, e.g. photons, for lithography for etching features on a
 computer chip that are smaller than the wavelength of light used in the
 etching process, by some fraction related to the number of entangled
 particles.
 BACKGROUND
 Quantum mechanics tells us that certain unobserved physical systems can
 have odd behavior. A particle which is decoupled from its environment and
 which has two possible states will not necessarily be in either of those
 states, until observed. Putting this in quantum mechanical terms, the
 particle is simultaneously in a "superposition" of both of those states.
 However, this only applies while the particle is in certain
 conditions--decoupled from its environment. Any attempt to actually
 observe the particle couples the particle to its environment, and hence
 causes the particle to default into one or the other of the eigenstates of
 the observable operator.
 This behavior is part of the superposition principle. The "superposition
 principle" is illustrated by a famous hypothetical experiment, called the
 cat paradox. a cat in a box with a vial of poison. The vial containing the
 poison could equally likely be opened or not opened. If the box/cat/poison
 is decoupled from its environment, then the cat achieves a state where it
 is simultaneously dead and not dead. However, any attempt to observe the
 cat, causes the system to default to dead or alive.
 The theory of quantum mechanics predicts that N particles can also exist in
 such superposition states.
 Lithography is a process of etching features on a substrate.
 Photolithography uses light to etch these features. Each spot can be
 etched, or not etched, to form a desired feature. In general, it is
 desirable to make the features as small as possible.
 In the prior art, called Classical Optical Interferometric Lithography, a
 lithographic pattern is etched on a photosensitive material using a
 combination of phase shifters, substrate rotators, and a Mach-Zehnder or
 other optical interferometer. The minimum sized feature that can be
 produced in this fashion is on the order of one-quarter of the optical
 wavelength [Brueck 98]. The only way to improve on this resolution
 classically is to decrease the physical wavelength of the light used in
 the etching process.
 This can come at a tremendous commercial expense. Optical sources and
 imaging elements are not readily available at very short wavelengths, such
 as hard UV or soft x ray.
 SUMMARY
 The present system uses a plurality of entangled particles, e.g., photons,
 in a lithographic system to change the lithographic effect of the photons.
 The multiple entangled photons can etch features whose size is similar to
 that which could only be achieved by using light having a wavelength that
 is a small fraction of the actual light wavelength that is used.
 In one disclosed embodiment, two entangled photons can be used a form an
 interference pattern that is double the frequency, or half the size, of
 the actual optical frequency that is used. This operation goes against the
 established teaching and understanding in the art that the wavelength of
 the illuminating light forms a limit on the size of features that can be
 etched. Usually, these features could not be made smaller than one-quarter
 or one-half of the wavelength of the light used to carry out the etching.
 The present system enables forming features that are smaller than
 one-quarter of the wavelength of the light that is used, by some multiple
 related to the number of entangled particles that are used.
 The present system for quantum lithography uses an interferometer that
 forms an interference pattern whose fringe spacing depends on both the
 number of entangled photons entering the device as well as their
 wavelength. Multiple entangled photons are used within the interferometer.
 These n entangled photons experience a phase shift that is greater, by a
 factor of n, than the normal phase shift that would be experienced by a
 single photon of the same wavelength in the same device. The changed phase
 shift forms a changed interference pattern in the output to achieve a
 changed frequency of interference fringes. By so doing, finer features can
 be etched.
 An n-fold improvement in linear resolution is obtained by using n entangled
 particles, e.g. photons. A two dimensional lithographic operation
 effectively squares the improvement to density (n.sup.2). As such, the
 entangled quantum lithography system makes it possible to etch features,
 for example, that are 1 to 10 nanometers apart, using radiation that has a
 wavelength .lambda., of 100 nanometers or more.
 Another important use of this system is to retrofit an existing system.
 Interferometric lithography systems are already known and used. This
 system makes it possible to re-use those existing lithographic systems to
 obtain Better etching results. The established techniques of improving
 lithographic technology is by requiring owners to buy or build totally new
 semiconductor fabrication equipment that use shorter wavelength light.
 This system improves the resolved output of the same equipment. This
 allows existing interferometric lithography equipment to be effectively
 retrofitted.
 Also, previous attempts to reduce feature size have used shorter wavelength
 light to reduce the feature size. That shorter wavelength light is always
 more energetic. Hence it can cause damage to the substrate.
 In contrast, the present system reduces the etched feature size without
 requiring more energetic particles.

DESCRIPTION OF THE PREFERRED EMBODIMENTS
 The present system replaces the classic "analog" optics of a lithographic
 system that has new "digital" optics that use a number of
 quantum-entangled particles, e.g. photons, electrons, atoms or the like.
 This will obtain the increased resolution, and reduction of feature size
 without shortening the physical wavelength. This system uses quantum
 entanglement effects to produce the same result as that previously
 obtained by using a shorter wavelength.
 For example, if the uncorrrelated classical stream of photons is replaced
 by sets of n entangled photons, then the interference pattern has the form
 (1+(2n.phi.)) with .phi. =kx being the phase shift in one arm of the
 interferometer, and k =2.pi./.lambda. being the wave number. Consequently,
 the peak to peak distance in the interference pattern now becomes
 .lambda./(2n). This is substantially smaller than the original peak to
 peak spacing of .lambda./2 and, in fact, increases the linear solution by
 a factor of n. So even though the optical source and imaging is done with
 a relatively long wavelength (.lambda.), the effective wavelength of the
 interference pattern is .lambda./n. Therefore, the resolution increases by
 a factor of n.
 Analog classical optics operates according to the so-called Rayleigh
 diffraction limit which imposes a restriction on minimum feature size that
 can be etched by a photon or other particle. This minimum feature size
 cannot be smaller than half a wavelength. The minimum size lines are on
 the order of .lambda./2, where .lambda. is the optical wavelength used for
 the exposure. This limit on line sizes generally holds whenever classical
 optics and lenses are used for interferometric lithographic etching.
 Put mathematically, the prior art classical device lays down a series of
 interferometrically-produced lines which obey the function form
 1+cos(2.phi.) where k =2.pi./.lambda. is the wave number, and .lambda. is
 the optical wavelength, where I is the optical intensity and
 k=2.pi./.lambda. is the wave number, and .lambda. is the optical
 wavelength.
 Quantum entangled photons are used in this application for reducing the
 size of the features. In a classical stream of photons used for
 interferometric lithography, the minimum size feature is on the order of
 one-half the optical wavelength. For a stream of n entangled photons, the
 interference pattern has the form (1+cos(2n.phi.)) with .phi. kx
 =2.pi./.lambda., resulting in an effective resolution of the interference
 pattern that scales linearly with n. The size of the feature is a function
 of the number of entangled photons n. Thus, for a given wavelength of
 photon, the resolution for entangled photons increases by n over the
 non-entangled classical system along one dimension. Etching in two
 dimensions can increase the resolution by n.sup.2.
 A single photon can be downconverted into two photons of lower wavelength.
 The polarization, energy and position of the resulting two photons are
 correlated because of conservation principles. In this particular case,
 the position correlation provides scaling properties. The ability to
 produce these entangled photons is well understood.
 The present system uses particle beams which are quantum in nature to carry
 out this operation. These beams are composed of streams of single photons,
 each of which is an individual quantum particle that is decoupled from the
 system around it. The correlated particles are made to behave in a way
 that is non-locally correlated. In accordance with quantum mechanical
 theory, the position, direction of motion, and frequency of each photon
 depends on the other photon(s).
 In the quantum optics community, it has been known for many years that
 light can exist in an entirely nonclassical state called a number state or
 a Fock state. This is described by Scully. The number state has no
 classical analog, as the coherent state does. In particular, the number
 state .vertline.N&gt; has a precise and fixed number of photons in it. This
 is in contrast to the classical-like coherent state, which can only be
 determined to have a mean number of photons n.sub.mean
 =.vertline..alpha..vertline..sup.2 due to the quantum fluctuation factor
 .DELTA.n. The number state .vertline.N&gt; has no intensity fluctuations,
 .DELTA.N=0. This is a remarkable fact that gives the number state a
 digital quality; one can have either 0, 1, 2, etc., photons in a single
 number-state mode. Particles in number states can be produced en masse by
 a process called parametric downconversion. Number states have, however,
 somewhat paradoxical and non-intuitive properties.
 FIG. 1 shows a block diagram of the overall quantum lithographic etching
 system. A single photon 101 of specified frequency is output from laser
 99. This photon is sent to a downconverter 100.
 A downconverter of this type receives a high-frequency photon into a
 nonlinear optical crystal of a material as KTP. A nonlinear interaction in
 the crystal generates a pair of daughter photons. If the original photon
 has frequency .omega. and vector wave number k, then the daughter photons
 have the very same quantities, .omega..sub.1, .omega..sub.2, k.sub.1,
 k.sub.2. The particles obey the laws of conservation of energy and
 momentum in the form,
EQU .omega.=.omega..sub.1 +.omega..sub.2, (1a)
EQU k=k.sub.1 +k.sub.2, (1b)
 which entangles or correlates the photons in terms of energy and wave
 number. This correlation is the basis for many interesting experiments
 where the two daughter photons can be treated as number states in
 particular photon modes in an interferometer.
 The schematic for the down-conversion process is shown in FIG. 2. Incoming
 high frequency photons from the left are down-converted in a nonlinear
 crystal and produce two daughter photons that are correlated in both
 momentum and frequency. The vector wave number conservation condition, Eq.
 (1b), is logout degenerate in azimuthal angle about the initial photon
 propagation axis, generating a typically circular pattern of photons.
 A typical spectral pattern is shown in FIG. 3. Choosing two points
 equidistant apart, as illustrated by the crosses in the FIG. 3, identifies
 by angular separation a particular down converted pair.
 "Parametric" down conversion imposes the additional restriction that
 .omega..sub.1 =.omega..sub.2 and k.sub.1 =k.sub.2, which selects photon
 pairs symmetrically placed about the center of the spectrum in FIG. 2. By
 choosing appropriate angular deflections in the optics, these particular
 pairs can be captured.
 The correlated photon particles are coupled through a coupler system 110 to
 beam splitter 122. This 122 is the input beam splitter to a partial Mach
 Zehnder interferometer with beam splitter 122, mirrors 126 and 128 and a
 phase shifter 130. The Interferometer produces parallel lines as its
 output. It has been demonstrated in Brueck, 98, "Interferometric
 lithograph--from Periodic Arrays to Arbitrary Patterns", Microelectron Eng
 42: 145-148 March 1998, that etching a series of parallel lines can be
 generalized in the lithographic domain into forming any desired feature.
 The correlations between the photons are quantum in nature, and the angular
 relation allows selection of a particular photon moving in a particular
 path, generating desired nonclassical number states of the form
 .vertline.N&gt;.
 A more detailed schematic of the Mach-Zehnder interferometer (MZI) is shown
 in FIG. 4. First and second correlated input photons 1 and 2 are input to
 both ports A and B.
 Neglecting losses in the interferometer for this discussion, if the input
 optical intensity is some constant I.sub.0, then for a classical
 interferometer-if all the input power enters from input port A-the
 superposition of C and D on the substrate will yield an interference
 pattern in lithographic resist at grazing incidence given by,
EQU I=I.sub.0 (1+cos 2kx)
 where, k=2.pi./.lambda. is the optical wave number, and x is the path
 difference between the first path 400 and the second path 402.
 This result turns out have the same functional form whether or not one uses
 classical input light, quantum coherent (ordinary laser) input light, or
 number-state input light, provided one only uses the one upper input port
 A.
 However, if both input ports A and B are used, then the results are
 different. In the case of dual-input-port entangled number states,
 (.vertline.N&gt;.vertline.0&gt;+.vertline.0&gt;.vertline.N&gt;)/2, such as those
 produced in parametric photon down conversion, then the functional form of
 the two-photon absorption intensity changes to,
EQU I=I.sub.0 (1+cos 2Nkx) (3)
 where the correlated photons enter the two ports entangled N at a time.
 Note that the N-photon interference pattern in that case oscillates N
 times as fast as before. Since the fringe intensity is proportional to the
 exposure rate, the minimal etchable feature size .DELTA.x determined by
 the Rayleigh Criterion is given by the intensity minimum-to-maximum
 condition Nk.DELTA.x=.pi., or equivalently .DELTA.x=.lambda./(2N), as
 noted above. This is a factor of N below the usual limit of
 .DELTA.x=.lambda./2.
 In particular, using correlated photon pairs (i.e., N=2) it is possible to
 etch features on the order of size .DELTA.x=.lambda./4. With correlated
 photon triplets (i.e., N =3) it is possible to obtain features on the
 order of .DELTA.x=.lambda./6, and so on. Hence, using light of wavelength
 .lambda.=200 nm, features of size .DELTA.x=50 nm can be etched using a
 stream of photons correlated two at a time (i.e., a stream of photons such
 that N=2).
 The physics can be understood with reference to the case of N=2, for
 example. If the photons were not entangled or correlated, then at the
 first beam splitter in FIG. 4 would have a 50--50 chance of each photon
 taking the upper or lower path, independent of each other. The two photons
 behave independently, and in this case the result of Eq. (2) is obtained.
 However, if the two input photons are entangled in number and position,
 which can be obtained from the down-conversion process using the
 downconverter 100 of FIG. 2, then the entangled photon pair move as a
 single unit. At the first beam splitter, both photons either take the
 upper path together, or they both take the lower path together. Quantum
 mechanically, this is written as,
 ##EQU1##
 where a 2 represents a bi-photon in the upper or lower branch mode, and the
 first state vector corresponds to one of the correlated photons, and the
 second to the other. We say that the bi-photon state is entangled in
 number and position. There are only two possibilities: they both take the
 high road (the pathe via mirror 128 in FIG. 1), or they both take the low
 road (the pathe via mirror 126 in FIG,. 1). Since it is impossible to
 distinguish, even in principle, which of these possibilities
 occurred-quantum mechanics demands that the probability amplitudes
 associated with these two paths be added to create an interference
 pattern.
 Taking the phase differential .DELTA..phi.=kx to be associated with an
 extra distance x in the upper path only, for convenience. Then after
 propagating across the MZI, the state now has the form,
 ##EQU2##
 where each photon in the correlated pair contributes one factor of kx for a
 total of 2kx phase shift. When the state is interfered and recombined by
 focusing the photons on the substrate, the interference pattern has the
 form of Eq. (3) with N=2. This gives physical insight into how this
 sub-wavelength diffraction comes about.
 The physical mechanism for the sub-wavelength interference effect arises
 then from the quantum digital nature of entangled photons. The number
 entanglement of the down-converted photon pair causes the photons to
 "talk" to each other in a nonlocal way. There is nothing at all like this
 in classical theory, where there are no photons-only "analog"
 electromagnetic waves. In a sense, the correlated photon pair behaves like
 a single entity, which is why it is referred to as a bi-photon.
 This digital quantum mechanical object accumulates phase in the
 interferometer in a very nonstandard fashion. In particular, since both
 photons in the di-photon pair take the same interferometer path together,
 this object accumulates phase twice as fast as a single photon or a pair
 of un-entangled photons would. Since the phase shift is proportional to
 the path difference divided by the wavelength, and the wavelength is
 fixed, this means that the same path differential .DELTA.x provides double
 the phase shift. This gives rise to two-photon interference fringes that
 have half the spacing as before.
 Interferometers have been used in lithography to produce an interference
 pattern based on a phase shift that causes an interference pattern. FIG. 1
 shows a two-input port interferometer 120 whose output gives the desired
 photon interference pattern. This is used to write an arbitrary pattern
 142 on a photographically sensitive material resist 145. This is similar
 to the standard set up for state of the art classical optical
 interferometric lithography schemes. The present invention replaces the
 classical electromagnetic fields with the appropriate quantum photon
 creation and annihilation operators corresponding to the various ports.
 According to the present system, the classical optical beam is replaced by
 a quantum stream of n entangled photons. We have shown that this makes it
 possible to generate a simple linear matrix relationship between the
 photon operators at the input ports and those at the output ports [Dowling
 98]. The details of the transfer matrix depends on the optical elements
 that make up the interferometer. More phase shifters, beam splitters,
 mirrors, etc., make a more complex matrix. Nevertheless, it is still
 linear and it is a straightforward problem to translate any arbitrary
 two-port interferometric system into an appropriate two-by-two transfer
 matrix. This matrix, can also include complex terms that account for noise
 sources in the interferometer. These noise sources could otherwise lead to
 photon loss or the loss of the quantum correlations.
 One can think of the entire interferometer as a simple quantum circuit with
 two inputs and two outputs. This allows the interferometer to be handled
 in the recently well-developed formalism of quantum circuit theory.
 Additional photon circuits can be added in parallel to the lithographic
 circuit in order to apply fault-tolerant quantum error correction
 techniques in order to minimize the effect of noise sources, allowing
 maximum resolution and contrast in the lithographic exposure.
 Once the quantum operator transfer matrix is in place, a complete
 description of how an arbitrary photon state propagates through the
 interferometer and images interferometric lines at the output ports
 exists. Now an additional degree of freedom is obtained by the wide range
 of photon input states. For example, choosing a coherent state in only one
 input port gives the standard classical results, which can then be used as
 a control. Then combinations of number states for the quantum input state
 can be used to image the sub-wavelength image at the output. The number of
 states can be chosen to be entangled or correlated in a large number of
 different ways in the simulation. Some of these choices are the natural
 output of a nonlinear photon down converter or a parametric oscillator,
 and others can be generated in preprocessing step with linear optical
 elements.
 For example, it is well known that a simple optical beam splitter can take
 an unentangled number direct-product state and convert it into a
 nonseparable entangled number-state output, of the form of Eq. (4), needed
 for this device.
 According to a first disclosed mode, correlated photon pairs (N=2) are
 used. This makes it possible to etch features on the order of size
 x=.lambda./4. For example, light of wavelength 200 nanometers could be
 used to etch features of size x=50 nanometers using a stream of two
 entangled photons correlated photons. These photons are relatively easy to
 produce using the optical process of photon down conversion. Moreover,
 these photons produce the surface damage of a 200 nm photon, even though
 they have the resolution of a 100 nm photon.
 Another mode uses correlated photon triplets (N=3). This etches features on
 the order of x=.lambda./6 in three-photon absorption.
 In fact, there is no theoretical limit on the number of correlated photons
 that could be produced, and hence no limit the amount of division below
 the Rayleigh-limited value.
 Another important advantage is beating the damage criterion that is caused
 by etching in classical physics. Each photon carries an energy e=.lambda.
 which =hc/.lambda. per photon. Hence the energy of the photons rise
 inversely with decreasing wavelengths.
 This can cause undesired resist damage to the material being etched. In
 addition, statistical fluctuations, called shot noise, can cause clumping
 of the arriving high frequency photons and hence lead to irregularities in
 the etch. This system allows etching features that have a better
 resolution without correspondingly increasing the damage potential.
 Specifically classical systems have a linear ratio of energy (damage
 potential) to feature size. The present system improves this ratio by a
 factor of the number of entangled particles.
 The laser used herein is a titanium sapphire laser, producing an output
 wave on the order of 100 to 200 nanometers. The optically nonlinear
 crystal is a KDP crystal doped with LiIO.sub.3.
 Any kind of interferometer could be used. While the present specification
 describes a Mach Zehnder Interferometer, any other kind can be used with
 these teachings.
 Although only a few embodiments have been disclosed in detail above, those
 with ordinary skill in the art certainly understand that modifications are
 possible in the preferred embodiment and that such modifications are
 intended to be encompassed within the following claims, in which: