METHOD AND DEVICE FOR ADDRESSING QUBITS, AND METHOD FOR PRODUCING THE DEVICE
20250245541 ยท 2025-07-31
Assignee
Inventors
Cpc classification
H10D48/3835
ELECTRICITY
G06N10/40
PHYSICS
G06N10/00
PHYSICS
G06N10/20
PHYSICS
B82Y10/00
PERFORMING OPERATIONS; TRANSPORTING
H10D64/01
ELECTRICITY
International classification
G06N10/40
PHYSICS
Abstract
A method of addressing at least one qubit to be addressed in a set of two or more qubits in diamond, comprises; exposing the qubit to be addressed to an electromagnetic field; and at the same time exposing another qubit of the set of two or more qubits to an electromagnetic counter field in such a way that the electromagnetic field has no effect on the other qubit or that the electromagnetic field has a different effect on the other qubit than on the qubit to be addressed.
Claims
1. A method of addressing at least one qubit to be addressed in a set of two or more qubits in diamond, comprising: exposing the qubit to be addressed to an electromagnetic field; and at a same time exposing another qubit of the set of two or more qubits to an electromagnetic counter field in such a way that the electromagnetic field has no effect on the other qubit or that the electromagnetic field has a different effect on the other qubit than on the qubit to be addressed.
2. The method according to claim 1, wherein: the qubits in the set of two or more qubits comprise nuclear spins of nitrogen atoms in NV centers; readout and coupling with the qubit of the two or more qubits takes place via an electronic spin of the respective NV center; and coupling between qubits takes place through magnetic dipole interaction.
3. The method according to claim 2, wherein the two or more qubits are arranged in a two-dimensional grid.
4. The method according to claim 2, wherein the two or more qubits are NV centers created in synthetic diamonds.
5. The method according to claim 2, wherein a distance between each qubit of the two or more qubits and at least one other qubit of the two or more qubits is sufficiently small to support direct coupling between the qubit and the at least one other qubit.
6. The method according to claim 2, wherein a distance between each qubit of the two or more qubits and at least one other qubit of the two or more qubits is 30 nm or less.
7. The method according to claim 1, wherein addressing each of the qubits of the two or more qubits is achieved by an electric field via a Stark effect or by a semi-static magnetic field via a Zeeman effect.
8. The method according to claim 7, wherein the addressing is realized by the electric field via the Stark effect.
9. The method according to claim 7, wherein the addressing is realized by the semi-static magnetic field via the Zeeman effect.
10. The method according to claim 7, wherein the two or more qubits are arranged in a line and a conductor for addressing the qubits runs parallel to the line.
11. The method according to claim 7, wherein the two or more qubits are arranged in a two-dimensional orthogonal X*Y grid; and a respective conductor for addressing the qubits runs in parallel with each row of qubits along an X axis of the two-dimensional orthogonal X*Y grid; and a respective conductor for addressing the qubits runs in parallel with each column of qubits along a Y axis in the two-dimensional orthogonal X*Y grid.
12. The method according to claim 1, wherein: the qubits comprise NV centers, each NV center having a nuclear spin and an electron spin; the nuclear spins of the NV centers are addressed using electromagnetic fields in a range of 1 kilohertz to 100 megahertz; and electron spins are addressed using electromagnetic fields in a microwave range from 500 MHz to 50 GHz. (see paragraph [0022].)
13. The method according to claim 12, wherein the electron spins are addressed using a (magnetic, electromagnetic, electric?) field of 2.87 GHz.
14. The method according to claim 10, wherein conductive structures assigned to individual qubits are used to provide the electromagnetic fields and electromagnetic counter fields, and the conductive structures have a smaller dimension than a distance between adjacent qubits.
15. A device for quantum computing comprising: a set of two or more qubits; and two or more electromagnetic sources; wherein: the two or more qubits are NV centers in diamond; two qubits of the two or more qubits are arranged to be directly entangled by dipole-dipole interaction; at least one of the electromagnetic sources of the one or more electromagnetic sources is arranged to interact with a nuclear spin of the NV centers at a frequency range of 1 KHz to 100 MHz; and at least another one of the electromagnetic sources of the one or more electromagnetic sources is arranged to interact with an electron spin of the NV centers at a frequency of 500 MHz to 50 GHz.
16. The device according to claim 15, wherein a distance between each qubit of the two or more qubits and at least one other qubit of the two or more qubits is sufficiently small to support direct entanglement between the qubit and the at least one other qubit.
17. The device according to claim 15, wherein a distance between each qubit of the two or more qubits and at least one other qubit of the two or more qubits is 30 nm or less.
18. The device according to claim 15, wherein conductive structures assigned to individual qubits are used to provide electromagnetic fields and electromagnetic counter fields, and the conductive structures have a smaller dimension than a distance between adjacent qubits.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DESCRIPTION
[0081] In
[0082] For making contact, the wires 20, 22, 24 each have corresponding contact areas 26 to which electrical connections (not shown) can be bonded. The first two wires 20, 22, which are used for addressing and reading out the two qubits 14, 16, are spaced approximately 20 nm to 30 nm apart, which thus also corresponds to the spacing between the two qubits 14, 16. As a result, these qubits 14, 16 can easily become entangled.
[0083] The second wire 24, which forms the ground for reading out the qubits 14, 16, is arranged centrally between the two first wires 20, 22 and is thus at a distance of 10 nm to 15 nm from these first wires 20, 22.
[0084] All of the wires 20, 22, 24 are arranged plane-parallel to one another on the surface 18. They have in the straight region (cf.
[0085] The device 10 now functions in such a way that simultaneous formatting of the qubits 14, is given by a suitable LASER pulse through the surface 18, which easily reaches the qubits 14, 16 through the transparent wires 20, 22 made of ITO. A spin polarization takes place due to the laser pulse and all qubits 14, 16 go into the ground state. This gives you a defined and known initial state (formatting).
[0086] Alternatively, the wires 20, 22 could also be formed from silver or gold, for example, with the LASER pulse then being diffracted around these wires 20, 22 due to the very narrow dimensions of the wires 20, 22, so that the LASE R-Pulse reaches qubits 14, 16 for formatting. The qubits 14, 16 can then be addressed individually or together.
[0087] For this purpose, a suitable high-frequency current is applied to the contacts 26 of the respective wires 20, 22, which is in the kilohertz range for addressing the core spins of the qubits 14, 16. The current flowing in the wires 20, 22 induces a magnetic field that acts on the respective qubit 14, 16.
[0088] In the immediate vicinity of the wires 20, 22, a magnetic near field is formed which, due to the Laplace equations, is superelevated in the area of the qubits 14, 16 arranged next to each other and therefore influences particularly good the nuclear spins of these qubits 14, 16. The appropriate magnetic near field is fed to each qubit 14, 16, whereby it is addressed. At the same time, the respective other qubit 16, 14 is fed a counter-magnetic field that compensates for the magnetic field components of the magnetic near fields used to address the qubits 14, 16 at the location of the respective other qubits 16, 14 so that no cross-talk can take place. As a result, on one side both qubits 14, 16 can be addressed differently or identically at the same time, and on the other side addressing of only a single qubit 14, 16 can take place independently of the addressing of the other qubit 16, 14.
[0089] To read out the qubits 14, 16, for example, a suitable uniform LASER irradiation could again take place, whereby photoelectrons are generated in both qubits 14, 16, which are then skimmed off and measured via the respectively assigned first wires 20, 22, whereas the second wire 24 serves as a ground. For this purpose, there are changeover switches, so that the wires 20, 22 can be used once for formatting (i.e. supplying current) and once for reading out (i.e. measuring current).
[0090] Alternatively, suitable LASER pulses could also be fed separately to each qubit 14, 16 by suitable lighting means, so that the qubits 14, 16 can be read out individually.
[0091] The manufacture of the device 10 could, for example, take place as follows: A manufacture of the qubits 14, 16 is carried out with doping of the diamond 12 with subsequent first and second temperature treatment process steps according to DE 10 2019 117 423.6, whereas the steps of contacting the second wire 24 and the masking and contacting the first wires 20, 22 are suitably integrated in this manufacturing process.
[0092] More precisely, a diamond 12 is doped with sulfur or another suitable dopant and subjected to a first tempering step at approximately 1000 C. Subsequently, the second wire 24 made of tungsten is vapor deposited on the surface 18 of the diamond 12 together with the respective contact surfaces 26, for example by means of a removable mask.
[0093] Thereafter, a contact mask (not shown in
[0094] Corresponding mask production methods are familiar to the person skilled in the art, so that they do not have to be discussed in more detail.
[0095] An implantation of nitrogen takes place through this mask in order to generate the qubits 14, 16. As a result, the position of the qubits 14, 16 under the first wires 20, 22 formed later is also precisely specified.
[0096] After a second temperature control step at about 800 C., the first wires 20, 22 are vapor deposited through the mask together with the respective contact surfaces 26 made of ITO and the device 10 is thus finished.
[0097] In
[0098] From
[0099] The wires 74, 76, 78 in the first layer 80 are aligned plane-parallel to one another and the wires 86, 88, 90 in the second layer 92 are aligned plane-parallel to one another. The wires 74, 76, 78 of the first layer 80 are oriented orthogonally to the wires 86, 88, 90 of the second layer 92 and all of the wires are electrically isolated from one another. Corresponding contact surfaces have not been shown here to simplify the illustration. These first electrically conductive wires 74, 76, 78, 86, 88, 90 also have a height and width in the range from 1 nm to 10 nm, preferably 5 nm. The length of the straight sections of the wires 74, 76, 78, 86, 88, 90 extends approximately 5 nm to 10 nm beyond the outer qubits 54, 56, 58, 60, 64, 66, 68, 70, respectively.
[0100] These first electrically conductive wires 74, 76, 78, 86, 88, 90 are in turn used for addressing and reading out the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 and are spaced approximately 20 nm apart up to 30 nm in the respective layer 80, 92, which corresponds to the distance of the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 directly arranged below the virtual intersection points of the wires 74, 76, 78, 86, 88, 90 (cf.
[0101] Instead of one or more second electrically conductive wires, as in the device 10 according to
[0102] The device 50 now functions in such a way that simultaneous formatting of the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 through surface 84 is performed by an appropriate LASER pulse which easily reaches the qubits 14, 16 through the transparent wires 74, 76, 78, 86, 88, 90 made of ITO.
[0103] The addressing of the individual qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 can now be done by assigning each qubit 54, 56, 58, 60, 62, 64, 66, 68, 70 two first wires 74, 76, 78, 86, 88, 90, whereby by different suitable signals on the respectively crossing first wires 74, 76, 78, 86, 88, 90 each individual qubit 54, 56, 58, 60, 62, 64, 66, 68, 70 can be addressed individually through the individually developing magnetic near fields. More precisely, the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 are located in the vicinity of intersection points of first wires 74, 76, 78, 86 with respect to a projection onto the layers 80, 92, 88, 90, so that in the crossing wires 74, 76, 78, 86, 88, 90 applied magnetic high frequency fields are superimposed so that for each qubit 54, 56, 58, 60, 62, 64, 66, 68, 70 individual magnetic near fields appear. By means of individually adapted magnetic counter fields in these individual near fields, the influences of the magnetic near fields of the respective remaining qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 are eliminated or sufficiently reduced.
[0104] The crossing wires 74, 76, 78, 86, 88, 90 can generate elliptically or circularly polarized magnetic near fields for each qubit 54, 56, 58, 60, 62, 64, 66, 68, 70 so that Qutrite states can be produced.
[0105] For example, for the purpose of reading out qubits 54, 56, 58, 60, 62, 64, 66, 68, 70, a suitable LASER pulse is used, with first wires 74, 76, 78, 86, 88, 90 being switched from a current supply to a current measurement and the back contact serving as a ground for the generated photoelectrons. By combining the individual measurement signals of the first wires 74, 76, 78, 86, 88, 90, each qubit 54, 56, 58, 60, 62, 64, 66, 68, 70 can be assigned a special measurement signal.
[0106] The fabrication of the device 50 could be done, for example, as follows: A fabrication of the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 is performed with doping of the diamond layer material 52 followed by first and second annealing steps according to DE 10 2019 117 423.6, wherein the steps of contacting with the backside contact 94 and contacting with the first wires 74, 76, 78, 86, 88, 90 are suitably integrated into this fabrication process.
[0107] More precisely, a backside contact 94 of tungsten is produced here on a suitable substrate material 96 by deposition, for example sputtering, and a diamond layer 52 is arranged thereon, for example by gas phase deposition. This diamond layer 52 is doped with sulfur or another dopant in accordance with DE 10 2019 117 423.6 and subjected to a first tempering step at around 1000 C.
[0108] Then nitrogen is implanted to generate the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70, whereby for the precise positioning of the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70 the nitrogen is implanted with an AFM tip. This method is described in principle, for example, in the article Nanoscale Engineering and Optical Addressing of Single Spins in Diamond, S. Pezzagna et al., Small 2010, 6, 19, 2117-2121. For orientation purposes, auxiliary markings in the form of graphite marks or metal wires can be arranged outside the surface area to be provided with the qubits 54, 56, 58, 60, 62, 64, 66, 68, 70.
[0109] After a second tempering step at about 800 C., the first wires 74, 76, 78 of the layer 80, for example made of silver, are drawn with the aid of an AFM tip on the surface 72 of the diamond material 52 and corresponding contact surfaces (not shown) are created. A suitable electrical insulator layer 82, such as, for example, made of SiO2, is then arranged on the surface 72 of the diamond material 52, as a result of which the first wires 74, 76, 78 are covered. Finally, the first wires 86, 88, 90 of the second layer 92 are arranged on the surface 84 of the insulating layer 82, also by drawing with the AFM tip.
[0110] Wire drawing with the AFM tip can be carried out in accordance with the procedure basically described in the publication Atomic force microscope integrated with a scanning electron microscope for correlative nanofabrication and microscopy by I. W. Rangelow et al., J. Vac.Technol. B 36 (6), November/December 2018. In addition, markers or auxiliary wires can be used for orientation. As an alternative to wire drawing with an AFM tip, mask-based methods can again be used to generate the first wires 74, 76, 78, 86, 88, 90, these masks preferably being removed each time to keep the distance between the wires as small as possible 74, 76, 78, 86, 88, 90 and the respectively assigned qubits 54, 56, 58, 60, 62, 64, 66, 68, 70.
[0111] It has become clear from the above illustration that the present disclosure enables qubits 14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70 to be addressed in a simple manner without the risk of crosstalk between different qubits 14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70. From the above description, it is clear that the present disclosure enables addressing of qubits 14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70 in a simple manner without the risk of crosstalk between different qubits 14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70. Addressing can be done individually or collectively for different qubits 14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70. In addition, easy readout n of qubits 14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70 is also possible.
[0112] Unless otherwise stated, all features of the present disclosure can be freely combined with one another. Also, unless otherwise indicated, the features described in the figure description may be freely combined with the other features as features of the disclosure. A restriction of individual features of examples to combination with other features of other examples is thereby expressly not intended. In addition, objective features of the device can also be used as process features in a reformulated form, and process features can be used as objective features of the device in a reformulated form. Such a reformulation is thus automatically disclosed.
[0113] Feature 1 includes a method of addressing at least one qubit (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) in a set of two or more qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70), characterized in that the qubit to be addressed (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) is exposed to an electromagnetic field, while at the same time another qubit of the set of qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) is exposed to an electromagnetic counter field in such a way that the electromagnetic field has no effect on the other qubit (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) or that the electromagnetic field has a different effect on the other qubit (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) than on the qubit to be addressed (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70).
[0114] Feature 2 includes a method according to feature 1, characterized in that electromagnetic near fields are used as the electromagnetic field and as the electromagnetic counter field, the electromagnetic near fields preferably being magnetic near fields which in particular have a frequency in the microwave range and/or or kilohertz range.
[0115] Feature 3 includes a method according to features 1 and 2, characterized in that color
[0116] centers, preferably NV centers in diamond (12, 52), are used as qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70).
[0117] Feature 4 includes a method according to any one of the features 1-3, characterized in that the electromagnetic fields and electromagnetic counter fields are generated by electromagnetic sources (20, 22, 74, 76, 78, 86, 88, 90), preferably electrically conductive structures, in particular lines, metallizations or wires (20, 22, 74, 76, 78, 86, 88, 90) are provided, wherein the electrically conductive structures (20, 22, 74, 76, 78, 86, 91 88, 90) have a smaller dimension than the distance between adjacent qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70).
[0118] Feature 5 includes a method according to anyone of the features 1-4, characterized in that the qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) consist in a transparent material (12; 52), so that a formatting of the qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70), preferably a simultaneous formatting of several, in particular all qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70), can be carried out by means of an optical radiation, preferably a LASER radiation.
[0119] Feature 6 includes a device for addressing at least one qubit (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) in a set of two or more qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70), characterized in that means (20, 22, 74, 76, 78, 86, 88, 90) for generating an electromagnetic field, which are designed in such a way that the qubit (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) to be addressed can be exposed to the electromagnetic field, and in that means (20, 22, 74, 76, 78, 86, 88, 90) exist for generating at least one electromagnetic counter field, which are designed such that at least one other qubit of the set of qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) can be exposed to an electromagnetic counter field in such a way that the electromagnetic field has no effect on the other qubit (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) or that the electromagnetic field has a different effect on the other qubit (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) than on the qubit to be addressed (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70).
[0120] Feature 7 includes a device according to feature 6, characterized in that the device is adapted to carry out the method according to anyone of the features 1-4.
[0121] Feature 8 includes a device according to features 6 or 7, characterized in that electromagnetic sources (20, 22; 74, 76, 78, 86, 88, 90), preferably first electrically conductive structures, in particular lines, wires (20, 22; 74, 76, 78, 86, 88, 90) or metallizations, exist for generating the electron-magnetic fields and electromagnetic counter-fields, each qubit (14, 16; 54, 56, 58, 60, 62, 64, 66, 68, 70) being assigned at least one electromagnetic source.
[0122] Feature 9 includes a device according to feature 8, characterized in that a plurality of electromagnetic sources (20, 22, 74, 76, 78, 86, 88, 90) are arranged in a layer, the qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) having a distance perpendicular to this layer from the respectively associated electromagnetic source of at most 30 nm, preferably of at most 20 nm, in particular in the range 0 nm to 10 nm, and/or the qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) projected onto this layer have a distance from the respectively associated electromagnetic source (20, 22; 74, 76, 78, 86, 88, 90) of at most 20 nm, preferably of at most 10 nm, in particular in the range 0 nm to 5 nm.
[0123] Feature 10 includes a device according to one of features 8 and 9, characterized in that at least one first electrically conductive structure (20, 22; 74, 76, 78, 86, 88, 90) can optionally be connected to an electromagnetic excitation and a photoelectron detection.
[0124] Feature 11 includes a device according to any one of features 8-10, characterized in that at least a second electrically conductive structure (24, 94), preferably a second electrically conductive wire (24), consists of a line or metallization or an electrode (94), which forms the ground for reading out the qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70), the second electrically conductive structure (24) preferably being arranged adjacent to a first electromagnetic source (20, 22), in particular at a distance in a plane of at most 40 nm, preferably at most 30 nm, in particular in a range from 10 nm to 20 nm.
[0125] Feature 12 includes a device according to any one of features 8-11, characterized in that the first electrically conductive structures (20, 22; 74, 76, 78, 86, 88, 90) and/or the second electrically conductive structures (24) i) have a cross-section with a longitudinal dimension of less than 50 nm, preferably of less than 20 nm, in particular in the range 1 nm to 10 nm, and/or ii) have a length of less than 50 nm, preferably of less than 30 nm, in particular of 5 nm to 20 nm.
[0126] Feature 13 includes a device according to any one of features 6-12, characterized in that the qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) are arranged one-, two- or three-dimensions and/or in that the electrically conductive structures (20, 22, 74, 76, 78, 86, 88, 90) are arranged in one, two or three dimensions, there preferably being two or more layers (80, 92) in which electrically conductive structures (74, 76, 78, 86, 88, 90) are arranged, in particular parallel to one another, the electrically conductive structures (74, 76, 78, 86, 88, 90) of different layers (80, 92) being arranged differently, whereby an electrical insulator (82) preferably being arranged between two layers (80, 92).
[0127] Feature 14 includes a method of manufacturing a device according to any one of features 6-13, characterized in that two or more qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70) are created in a surrounding material and first electrically conductive wires (20, 22, 74, 76, 78, 86, 88, 90) are arranged on the surrounding material.
[0128] Feature 15 includes a method according to feature 14, characterized in that one of the following steps is carried out: [0129] Selection of a diamond layer (12; 52) as the surrounding material; [0130] Doping of the surrounding material with a dopant, preferably sulfur, phosphorus or oxygen; [0131] Carrying out a first annealing step after doping; [0132] Carrying out a second annealing step after the generation of the qubits (14, 54, 56, 58, 60, 62, 64, 66, 68, 70); and [0133] Applying second electrically conductive wires (24) for reading out the qubits (14, 16, 54, 56, 58, 60, 62, 64, 66, 68, 70).
LIST OF REFERENCE SYMBOLS
[0134] 10 an example of the device according to the disclosure [0135] 12 diamond bulk material [0136] 14, 16 qubits [0137] 18 surface of the diamond material 12 [0138] 20, 22 first electrically conductive wires made of ITO (Indium-Tin-Oxide) [0139] 24 second electrically conductive wire made of tungsten [0140] 26 contact surfaces of wires 20, 22, 24 [0141] 50 an example of the device according to the disclosure [0142] 52 diamond layer material [0143] 54, 56, 58 qubits [0144] 60, 62, 64 qubits [0145] 66, 68, 70 qubits [0146] 72 surface of diamond material 52 [0147] 74, 76, 78 first electrically conductive wires made of ITO (indium-tin-oxide) [0148] 80 first layer in which the wires 74, 76, 78 are arranged [0149] 82 insulator layer [0150] 84 surface of the insulator layer 82 [0151] 86, 88, 90 first electrically conductive wires made of ITO (indium-tin-oxide) [0152] 92 second layer in which the wires 86, 88, 90 are arranged [0153] 94 back side contact made of tungsten [0154] 96 substrate