Classifications

• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10F—INORGANIC SEMICONDUCTOR DEVICES SENSITIVE TO INFRARED RADIATION, LIGHT, ELECTROMAGNETIC RADIATION OF SHORTER WAVELENGTH OR CORPUSCULAR RADIATION
  • H10F19/00—Integrated devices, or assemblies of multiple devices, comprising at least one photovoltaic cell covered by group H10F10/00, e.g. photovoltaic modules
• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10F—INORGANIC SEMICONDUCTOR DEVICES SENSITIVE TO INFRARED RADIATION, LIGHT, ELECTROMAGNETIC RADIATION OF SHORTER WAVELENGTH OR CORPUSCULAR RADIATION
  • H10F77/00—Constructional details of devices covered by this subclass
  • H10F77/10—Semiconductor bodies
  • H10F77/14—Shape of semiconductor bodies; Shapes, relative sizes or dispositions of semiconductor regions within semiconductor bodies
  • H10F77/146—Superlattices; Multiple quantum well structures
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y10/00—Nanotechnology for information processing, storage or transmission, e.g. quantum computing or single electron logic
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y15/00—Nanotechnology for interacting, sensing or actuating, e.g. quantum dots as markers in protein assays or molecular motors
• • B—PERFORMING OPERATIONS; TRANSPORTING
  • B82—NANOTECHNOLOGY
  • B82Y—SPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
  • B82Y20/00—Nanooptics, e.g. quantum optics or photonic crystals
• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10F—INORGANIC SEMICONDUCTOR DEVICES SENSITIVE TO INFRARED RADIATION, LIGHT, ELECTROMAGNETIC RADIATION OF SHORTER WAVELENGTH OR CORPUSCULAR RADIATION
  • H10F30/00—Individual radiation-sensitive semiconductor devices in which radiation controls the flow of current through the devices, e.g. photodetectors
  • H10F30/10—Individual radiation-sensitive semiconductor devices in which radiation controls the flow of current through the devices, e.g. photodetectors the devices being sensitive to infrared radiation, visible or ultraviolet radiation, and having no potential barriers, e.g. photoresistors
• • H—ELECTRICITY
  • H10—SEMICONDUCTOR DEVICES; ELECTRIC SOLID-STATE DEVICES NOT OTHERWISE PROVIDED FOR
  • H10F—INORGANIC SEMICONDUCTOR DEVICES SENSITIVE TO INFRARED RADIATION, LIGHT, ELECTROMAGNETIC RADIATION OF SHORTER WAVELENGTH OR CORPUSCULAR RADIATION
  • H10F71/00—Manufacture or treatment of devices covered by this subclass
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
  • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
  • Y02E10/00—Energy generation through renewable energy sources
  • Y02E10/50—Photovoltaic [PV] energy

Definitions

• the present invention generally relates to photosensitive optoelectronic devices. More specifically, it is directed to intermediate-band photosensitive optoelectronic devices with inorganic quantum dots providing the intermediate band in an inorganic semiconductor matrix.
• Optoelectronic devices rely on the optical and electronic properties of materials to either produce or detect electromagnetic radiation electronically or to generate electricity from ambient electromagnetic radiation.
• Photosensitive optoelectronic devices convert electromagnetic radiation into an electrical signal or electricity.
• Solar cells also called photovoltaic (“PV”) devices, are a type of photosensitive optoelectronic device that is specifically used to generate electrical power.
• PV photovoltaic
• Photoconductor cells are a type of photosensitive optoelectronic device that are used in conjunction with signal detection circuitry which monitors the resistance of the device to detect changes due to absorbed light.
• Photodetectors which may receive an applied bias voltage, are a type of photosensitive optoelectronic device that are used in conjunction with current detecting circuits which measures the current generated when the photodetector is exposed to electromagnetic radiation.
• These three classes of photosensitive optoelectronic devices may be distinguished according to whether a rectifying junction as defined below is present and also according to whether the device is operated with an external applied voltage, also known as a bias or bias voltage.
• a photoconductor cell does not have a rectifying junction and is normally operated with a bias.
• a PV device has at least one rectifying junction and is operated with no bias.
• a photodetector has at least one rectifying junction and is usually but not always operated with a bias.
• the term "rectifying” denotes, inter alia, that an interface has an asymmetric conduction characteristic, i.e., the interface supports electronic charge transport preferably in one direction.
• the term “photoconductive” generally relates to the process in which electromagnetic radiant energy is absorbed and thereby converted to excitation energy of electric charge carriers so that the carriers can conduct ⁇ i.e., transport) electric charge in a material.
• the te ⁇ n "photoconductive material” refers to semiconductor materials which are utilized for their property of absorbing electromagnetic radiation to generate electric charge carriers. When electromagnetic radiation of an appropriate energy is incident upon a photoconductive material, a photon can be absorbed to produce an excited state. There may be intervening layers, unless it is specified that the first layer is "in physical contact with” or "in direct contact with” the second layer.
• the rectifying junction is referred to as a photovoltaic heterojunction.
• the usual method is to juxtapose two layers of material with appropriately selected semi-conductive properties, especially with respect to their Fermi levels and energy band edges.
• Types of inorganic photovoltaic heteroj unctions include a p-n heterojunction formed at an interface of a p-type doped material and an n-type doped material, and a Schottky-barrier heterojunction formed at the interface of an inorganic photoconductive material and a metal.
• n-type denotes that the majority carrier type is the electron. This could be viewed as a material having many electrons in relatively free energy states.
• p-type denotes that the majority carrier type is the hole. Such a material has many holes in relatively free energy states.
• the band gap is the energy difference between the highest energy level filled with electrons and the lowest energy level that is empty. In an inorganic semiconductor or inorganic insulator, this energy difference is the difference between the valence band edge Ev (top of the valence band) and the conduction band edge Ec (bottom of the conduction band).
• Ev top of the valence band
• Ec bottom of the conduction band
• the band gap of a pure material is devoid of energy states where electrons and holes can exist. The only available carriers for conduction are the electrons and holes which have enough energy to be excited across the band gap. In general, semiconductors have a relatively small band gap in comparison to insulators.
• excitation of a valence band electron into the conduction band creates carriers; that is, electrons are charge carriers when on the conduction- band-side of the band gap, and holes are charge carriers when on the valence-band-side of the band gap.
• a first energy level is "above,” “greater than,” or “higher than” a second energy level relative to the positions of the levels on an energy band diagram under equilibrium conditions.
• Energy band diagrams are a workhorse of semiconductor models. As is the convention with inorganic materials, the energy alignment of adjacent doped materials is adjusted to align the Fermi levels (E F ) of the respective materials, bending the vacuum level between doped-doped interfaces and doped-intrinsic interfaces.
• Carrier mobility is a significant property in inorganic and organic semiconductors.
• Mobility measures the ease with which a charge carrier can move through a conducting material in response to an electric field.
• insulators In comparison to semiconductors, insulators generally provide poor carrier mobility.
• a device comprises a plurality of layers of a first semiconductor material and a plurality of dots-in-a-fence barriers disposed in a stack between a first electrode and a second electrode.
• Each dots-in-a-fence barrier is disposed in the stack between and in direct contact with a respective two of the layers of the first semiconductor material.
• Each dots-in-a-fence barrier consists essentially of a plurality of quantum dots of a second semiconductor material embedded between and in direct contact with two layers of a third semiconductor material.
• Each quantum dot provides at least one quantum state at an energy between a conduction band edge and a valence band edge of the adjacent layers of the first semiconductor material. Wave functions of the at least one quantum state of the plurality of quantum dots overlap as at least one intermediate band.
• the layers of the third semiconductor material are arranged as tunneling barriers to require a first electron and/or a first hole in a layer of the first material to perform quantum mechanical tunneling to reach the second material within a respective quantum dot.
• the layers of the third semiconductor material are also arranged as tunneling barriers to require a second electron and/or a second hole in a layer of the first semiconductor material to perform quantum mechanical tunneling to reach another layer of the first semiconductor material without passing through a quantum dot.
• the lattice constants of the first semiconductor material and the third semiconductor material are preferably sufficiently close to avoid inducing defects (e.g., ⁇ a/a ⁇ ⁇ 1%). More preferably, the third semiconductor material is lattice matched to the first semiconductor material.
• the first semiconductor material is GaAs
• the second semiconductor material is InAs
• the third semiconductor material is Al x Gai_ x As with x > 0.
• each InAs quantum dot has an average lateral cross-section of 2R and a height of €, with 2 nm ⁇ R ⁇ 10 ran
• each Al x Gai -x As layer has a thickness t, with 0.1R ⁇ t ⁇ 0.3R.
• Each GaAs layer disposed between two dots-in-a-fence barriers has a thickness d, with 2 nm ⁇ d ⁇ 10 nm.
• the preferred density of embedded InAs quantum dots in the GaAs bulk is from 10 10 to 10 12 quantum dots per square centimeter.
• the first semiconductor material is InP
• the second semiconductor material is InAs
• the third semiconductor material is AIo 48 In 0 52 As.
• each InAs quantum dot has an average lateral cross-section of 2R and a height of t, with 2 nm ⁇ R ⁇ 12 nm
• each Al 0 ⁇ In 0 52 As layer has a thickness t, with 0. IR ⁇ t ⁇ 0.3R.
• Each InP layer disposed between two dots-in-a-fence barriers has a thickness d, with 2 nm ⁇ d ⁇ 12 nm.
• the device is arranged as a p-i-n heterostructure, a first layer of the plurality of layers of the first material nearest to the first electrode is n-doped, a second layer of the plurality of layers of the first material nearest to the second electrode is p-doped, and the other layers of the plurality of layers of the first material are intrinsic.
• the device can be oriented so that either the n-doped first layer or the p-doped second layer is the layer closer to the substrate/semiconductor wafer.
• one of the n-doped first layer and the p-doped second layer may be the substrate/semiconductor wafer.
• the at least one quantum state in each quantum dot can include a quantum state above a band gap of the second semiconductor material providing an intermediate band and/or can include a quantum state below a band gap of the second semiconductor material providing an intermediate band.
• the quantum dots in the dots-in-a-fence barriers may be arranged in a photosensitive device such as a solar cell.
• FIG. 1 illustrates an intermediate band solar cell.
• FIGS. 2A and 2B are energy-band diagrams for a cross-section of an inorganic quantum dot in an inorganic matrix material, with the lowest quantum state in the conduction band providing the intermediate band.
• FIGS. 3 A and 3B are energy-band diagrams for a cross-section of an inorganic quantum dot in an inorganic matrix material, with the highest quantum state in the valence band providing the intermediate band.
• FIG. 4 is an energy band diagram for the intermediate band solar cell of FIG. 1, with inorganic quantum dots in an inorganic matrix material, and with the lowest quantum state in the conduction band providing the intermediate band.
• FIG. 5 illustrates a cross-section of the array of quantum dots in the device in FlG. 1, as generally idealized and as formed in colloidal solutions.
• FIG. 6 illustrates a cross-section of the array of quantum dots in the device in FIG. 1, if produced using the Stranski-Krastanow method.
• FIG. 7 is an energy band diagram for a cross-section of an inorganic quantum dot in an inorganic matrix material, illustrating de-excitation and trapping of a passing electron.
• FIG. 8 illustrates a cross-section of an array of quantum dots like that shown in FIG. 5, modified to include a tunneling barrier.
• FIGS. 9A and 9B are energy-band diagrams for a cross-section of a quantum dot including tunneling barriers with a lowest quantum state above the band gap providing the intermediate band.
• FIGS. 10 is an energy band diagram for a solar cell based on the design in FIG. 1, with quantum dots modified to include the tunneling barrier, and with the lowest quantum state above the band gap providing the intermediate band.
• FIGS. 1 IA and 1 IB are energy-band diagrams for a cross-section of a quantum dot including tunneling barriers with a highest quantum state below the band gap providing the intermediate band.
• FIG. 12 is an energy band diagram for a solar cell based on the design in FIG. 1, with quantum modified to include the tunneling barrier, and with the highest quantum state below the band gap providing the intermediate band.
• FIG. 13 illustrates a cross-section of the array of quantum dots modified to include the tunneling barrier, if produced using the Stranski-Krastanow method.
• FIGS. 14 and 15 demonstrate tunneling through a rectangular barrier.
• FIG. 16 demonstrates a triangular tunneling barrier.
• FIG. 17 demonstrates a parabolic tunneling barrier.
• FIG. 18 illustrates a structure of GaAs/InAs intermediate band fence barrier (DFENCE) solar cell.
• Path A shows transport along on-dot sites through the GaAs buffer, Al x Gai -x As fences, InAs wetting layers, and InAs quantum dots.
• Path B shows charge transport along off-dot sites through the GaAs buffer, InAs wetting layers and Al x Gai -x As fences.
• FIGS. 19A and 19B are energy-band diagrams for cross-sections of a DFENCE structure from FIG. 18.
• FIG. 19A illustrates an on-dot band diagram (along line “A” in FIG. 18) and
• FIG. 19B illustrates an off-dot band diagram (along line “B” in FIG. 18).
• the thin InAs wetting layer 1832 has negligible impact on tunneling, it is not represented in FIG. 19B.
• I is the dot length and I - R
• FIG. 21 is a graph of the carrier escape rate versus quantum dot radius for the same structures as in FIG. 20.
• FIG. 23 is a graph of power conversion efficiency versus number of quantum dot layers (N) for quantum dots with a radius of 8 nm when x increases from 0 to 0.2.
• FIG. 24 is a graph of power conversion efficiency versus intermediate band energy level calculated for: (a) the ideal conditions proposed in the paper A. Luque and A. Marti, Phys. Rev. Lett.
• FIG. 25 illustrates a structure of an InP/InAs intermediate band fence barrier (DFENCE) solar cell.
• Path A shows transport along on-dot sites through the InP buffer, Al 048 In 0 52 As fences, InAs wetting layers, and InAs quantum dots.
• Path B shows charge transport along off-dot sites through the InP buffer, InAs wetting layers and Al 048 In 0 52 As fences.
• FIGS. 26 A and 26B are energy-band diagrams for cross-sections of a DFENCE structure from FIG. 25.
• FIG. 26A illustrates an on-dot band diagram (along line “A” in FIG. 25) and
• FIG. 26B illustrates an off-dot band diagram (along line “B” in FIG. 25).
• the thin InAs wetting layer 2532 has negligible impact on tunneling, it is not represented in FIG. 26B. .
• the data is also included for the same structure with no tunneling barriers.
• FIG. 28 is a graph of the carrier escape rate versus quantum dot radius for the structure as in FIG. 25, and an equivalent structure having no tunneling barriers.
• FIG 29 is a graph of the carrier escape rate versus quantum dot radius for the structure as in FIG. 25.
• the y-axis scale in FIG. 29 is adjusted to more clearly show the escape rate for the DFENCE structure.
• FIG. 30 is a graph of power conversion efficiency versus number of quantum dot layers (N) for quantum dots with a radius of 8 nm.
• FIG. 31 is a graph of power conversion efficiency versus intermediate band energy level calculated for: the ideal conditions proposed in the Luque model, the Luque model for InP with the band gap of 1.34 eV, an upper limit of the InP/InAs DFENCE model.
• the labeled data on the ideal Luque model curve is the bulk band gap assumed that corresponds with the intermediate band level on the abscissa to achieve maximum efficiency.
• FIG. 32 illustrates the relationship between lattice constant, peak absorption wavelength, and energy gap for a variety of common compound semiconductors. Ternary and quaternary combinations of these semiconductors (in between the points shown) provide lattice matched materials having different energy gaps.
• Quantum dots confine charge carriers (electrons, holes, and/or excitons) in three-dimensions to discrete quantum energy states.
• the cross-sectional dimension of each quantum dot is typically on the order of hundreds of Angstroms or smaller.
• An intermediate-band structure is distinguishable, among other ways, by the overlapping wave functions between dots.
• the "intermediate" band is the continuous miniband formed by The overlapping wave functions. Although the wave functions overlap, there is no physical contact between adjacent dots.
• FIG. 1 illustrates an example of an intermediate-band device.
• the device comprises a first contact 110, a first transition layer 115, a plurality of quantum dots 130 embedded in a semiconductor bulk matrix material 120, a second transition layer 150, and a second contact 155.
• one transition layer (115, 150) may be p- type, with the other transition layer being n-type.
• the bulk matrix material 120 and the quantum dots 130 may be intrinsic (not doped).
• the interfaces between the transition layers 115, 150 and the bulk matrix material 120 may provide rectification, polarizing current flow within the device.
• current-flow rectification may be provided by the interfaces between the contacts (110, 155) and the transition layers (115, 150).
• the intermediate-band may correspond to a lowest quantum state above the band gap in the dots 130, or a highest quantum state below the band gap in the dots 130.
• FIGS. 2A, 2B, 3A, and 3B are energy-band diagrams for cross-sections through example inorganic quantum dots 130 in an inorganic bulk matrix material 120. Within the dots, the conduction band is divided into quantum states 275, and the valence band is divided into quantum states 265.
• the lowest quantum state (E e ,i) in the conduction band of a dot provides the intermediate band 280.
• Absorption of a first photon having energy h V 1 increases the energy of an electron by EL, exciting the electron from the valence band to the conduction band electron ground state E e>1 of the quantum dot.
• Absorption of a second photon having energy h v ⁇ increases the energy of the electron by EH, exciting the electron from the ground state E e ,i of the quantum dot to the conduction band edge of the bulk semiconductor 120, whereupon the electron is free to contribute to photocurrent.
• Absorption of a third photon having energy h V 4 increases the energy of an electron by EQ, exciting the electron directly from the valence band into the conduction band (which can also occur in the bulk matrix material 120 itself), whereupon the electron is free to contribute to photocurrent.
• the highest quantum state (Eh,i) in the valence band provides the intermediate band 280.
• Absorption of a first photon having energy h v / increases the energy of an electron having an energy E h , i by En, exciting the electron from the valence band side of the band gap into the conduction band, thereby creating an electron-hole pair.
• this can be thought of as exciting a hole in the conduction band by E H , thereby moving the hole into the E hj quantum state.
• Absorption of a second photon having energy h v 2 increases the potential energy of the hole by E L , exciting the electron from the ground state Eh, i of the quantum dot to the valence-band edge of the bulk semiconductor 120, whereupon the hole is free to contribute to photocurrent.
• FIG. 4 illustrates an energy band diagram for the intermediate-band device, using an array of dots having the profile demonstrated in FIGS. 2A and 2B.
• the aggregate of the overlapping wave functions of the E e ,i energy state between adjacent quantum dots provides the intermediate band 280 between the conduction band edge (Ec) and the valence band edge (Ev) of the bulk matrix semiconductor 120.
• Ec conduction band edge
• Ev valence band edge
• the intermediate band 280 allows the absorption of two sub-band gap photons h V 1 and h v 2 , leading to the creation of additional photocurrent.
• FIG. 5 illustrates a cross-section of the device including an array of spherical quantum dots.
• inorganic quantum dots can be formed as semiconductor nanocrystallites in a colloidal solution, such as the "sol-gel" process known in the art. With some other arrangements, even if the actual dots are not true spheres, spheres may nonetheless provide an accurate model.
• an epitaxial method that has been successful in the creation of inorganic quantum dots in an inorganic matrix is the Stranski-Krastanow method (sometimes spelled Stransky-Krastanow in the literature).
• This method efficiently creates a lattice-mismatch strain between the dots and the bulk matrix while minimizing lattice damage and defects.
• Stranski-Krastanow is sometimes referred to as the "self-assembled quantum dot" (SAQD) technique.
• the self-assembled quantum dots appear spontaneously, substantially without defects, during crystal growth with metal-organic chemical vapor deposition (MOCVD) or molecular beam epitaxy (MBE).
• MOCVD metal-organic chemical vapor deposition
• MBE molecular beam epitaxy
• SOQD Self-ordered quantum dot
• FIG. 6 illustrates a cross-section of an intermediate-band device as fabricated by the Stranski-Krastanow method.
• a wetting layer 132 ⁇ e.g., one monolayer
• the material ⁇ e.g., InAs) used to form the wetting layer 132 has an intrinsic lattice spacing that is different from the bulk material ⁇ e.g., GaAs), but is grown as a strained layer aligned with the bulk lattice. Thereafter, spontaneous nucleation ( ⁇ 1.5 monolayers) seeds the dots, followed by dot growth, resulting in quantum dot layers 131.
• Bulk 121 overgrowth (over the dots layers 131) is substantially defect free.
• the wetting layer between the dots does not appreciably contribute to the electrical and optical properties of the device, such that the dots produced by the Stranski- Krastanov method are often illustrated as idealized spheres like those illustrated in FlG. 5 in the literature. (The wetting layer between the dots is not considered a "connection" between the dots).
• the high concentration of strained quantum dots introduces a high charge density ( ⁇ l *10 16 cm "3 -- see R. Wetzler, A. Wacker, E. Schll, C. M. A. Kapteyn, R. Heitz and D. Bimberg, Appl. Phys. Lett.77, 1671(2000)) in the dot region, and photoexcited carriers (electron and hole) are rapidly captured by the self-assembled quantum dots. Consequently, the very high efficiencies predicted for quantum dot intermediate band solar cells have not been realized, due in part to non-ideal band structures that result in charge trapping followed by recombination of the photocarriers in the dots. In contrast to laser applications where fast carrier trapping is required (see L. V. Asryan and R. A. Suris, Semicond. Sci. Technol. 11, 554 (1996)), photogenerated carriers must tunnel through, or be transported around the quantum dots to avoid trapping and recombination at these sites.
• Luque, Thin Solid Films 511, 638 (2006) of the host has shown limited success. Although these devices have photoresponse extended to longer wavelengths, they also exhibit a significantly reduced open circuit voltage (V oc ) compared to large bandgap homoj unction cells.
• FIG. 7 illustrates a free electron being trapped by the quantum dot 130 when the charge carrier decays to an excited state E e , 2 (701) or to the ground state E c j (702, 703).
• This de- excitation process reduces photocurrent as the energy is absorbed into the lattice as phonons. Similar carrier deexcitation and trapping also happens with holes. Accordingly, to improve the performance of intermediate-band solar cells, there is a need to reduce charge carrier de- excitation due to charge trapping.
• a solution for reducing de-excitation trapping is to encapsulate each quantum dot in a thin barrier shell to require carriers to perform quantum mechanical tunneling to enter the dot.
• quantum mechanics when an electron impinges a barrier of higher potential, it is completely confined by the potential "wall.”
• the electron can be represented by its wave function. The wave function does not terminate abruptly at a wall of finite potential height, and it can penetrate through the barrier. These same principles also apply to holes.
• the probability T 1 of an electron or hole tunneling through a barrier of finite height is not zero, and can be determined by solving the Schr ⁇ dinger equation.
• FIG. 8 is a generalized cross-section of the array of quantum dots, each quantum dot modified to include a tunneling barrier 140.
• FIGS. 9A and 9B are energy band diagrams demonstrating a quantum dot modified to include a tunneling barrier 140 and having a quantum state above the band gap as the intermediate band 280. Some free electrons will be repelled (901) by the tunneling barrier. Such electrons are still available to contribute to photocurrent. Some free electrons will tunnel through the tunneling barrier (902) into and then out of the dot.
• the probability that a free electron will tunnel through it is the same from either side of the barrier. For example, if a barrier presents a tunneling probability (T t ) of 0.5, there is a 50% chance that an electron (having an energy E) impinging on the barrier will tunnel.
• T t tunneling probability
• E energy
• Electrons below the band gap within the dot are excited into a first quantum state ⁇ e.g., E e , i) providing the intermediate band, by photons having energy h V 1 .
• a photon having energy h V 2 may excite an electron to an energy where it will tunnel through (903) the tunneling barrier 140 to the Ec, bu i k energy level of the bulk matrix material 120.
• a photon having an energy h vj may excite an electron over (904) the barrier 140.
• Electrons excited over the barrier have an excess energy of ⁇ Ei. This excess energy ⁇ Ei is quickly lost as the electrons excited over the barrier decay to Ec. bu i k energy level. This loss of excess energy is relatively minor in comparison to the energy lost to trapping without the tunneling barriers 140, and in general, occurs before the electron can be trapped by an adjacent dot (i.e., entering an adjacent dot over, rather than through, the tunneling barrier 140).
• a photon of energy h v 4 may excite an electron directly from the Ev. bu i k energy level to an energy level where it tunnels through (905) the tunneling barrier 140 into the Ec ,bu i k energy level of the bulk matrix material 120. Further, a photon having an energy h v$ may excite an electron directly from the Ey. bu i k energy level over (906) the barrier 140. [0080] In order to further minimize the probability that a free electron passing (902) into and out of the dot will experience deexcitation, it is preferred that a second quantum state (e.g., E e , 2 ) is substantially equal to the Ec,bui k energy level of the bulk material.
• a second quantum state e.g., E e , 2
• the second quantum state is preferably within ⁇ 5 ⁇ 7 of the Ec ,bu i k energy level (A: being the Boltzmann contant and T being the operating temperature), thereby creating an overlap between the second quantum state and the Ec. bu ik energy level.
• a free electron if entering a dot at an energy corresponding to a forbidden level within the dot is statistically more likely to be trapped due to deexcitation; by positioning the second quantum state in the dot within ⁇ SkT oi the Ec. bu i k energy level, the probability of trapping decreases.
• FIG. 10 is an energy band diagram for a device using the quantum dots from FIGS. 9A and 9B.
• the transition layers 115 and 150 are arranged to create rectification, thereby controlling the direction of current flow.
• the relative proximity between the quantum dots and the transition layer 115 and the time it takes for an electron that escapes a dot over the barrier 140 (904 or 906) to decay to Ec. bu i k energy level it is possible that for some configurations, an electron that escapes a dot over the barrier 140 might have sufficient energy to create a reverse current flow into the transition layer 115.
• ⁇ E 3 is the difference between the conduction band edge (Ec, p -tra ns i t ion) of transition layer 115 and the conduction band edge (Ec, ba ⁇ i er ) peak of the tunneling barrier 140.
• the Ec, p-trans iti o n band gap edge of the p-type transition layer 115 is preferably greater than a conduction band peak of the tunneling barriers (Ec b amer)-
• FIGS. 1 IA and 1 IB are energy band diagrams demonstrating a quantum dot modified to include a tunneling barrier 140 and having a quantum state below the band gap as the intermediate band 280. Some holes will be repelled (1101) by the tunneling barrier. Such holes are still available to contribute to photocurrent. Some holes will tunnel through the tunneling barrier (1 102) into and then out of the dot.
• a photon having an energy h v 3 may excite a hole over (1104) the barrier 140 ("over" being used since holes fall up). Holes excited over the barrier have an excess energy of ⁇ E 2 . This excess energy ⁇ E 2 is quickly lost as the holes excited over the barrier decay to the Ev.b u i k energy level. This loss of excess energy is relatively minor, in comparison to the energy lost to trapping without the tunneling barriers 140, and in general, occurs before the hole can be trapped by an adjacent dot (i.e., entering an adjacent dot over, rather than through, the tunneling barrier 140).
• a photon of energy h v 4 may excite a hole directly from the Ec, bu i k energy level to an energy level where it tunnels through (1 105) the tunneling barrier 140 into the Ev. bu i k energy level of the bulk matrix material 120. Further, a photon having an energy h v$ may excite a hole directly from the Ec. bu i k energy level over (1106) the barrier 140.
• a second quantum state e.g., E h , 2
• E h , 2 a second quantum state of the valence band of the quantum dot is substantially equal to the Ev.
• the second quantum state should be within +5AT of the Ev. bu i k energy level of the bulk material, thereby creating an overlap between the second quantum state and the Ev. bu i k energy level.
• a hole if entering a dot at an energy corresponding to a forbidden level within the dot is statistically more likely to be trapped due to deexcitation; by positioning the second quantum state in the dot within ⁇ 5kT of the Ev. b ui k energy level, the probability of trapping decreases.
• FIG. 12 is an energy band diagram for a device using the quantum dots from FIGS. 1 IA and 1 IB.
• the transition layers 115 and 150 are again arranged to create rectification, thereby controlling the direction of current flow.
• a hole that escapes a dot over the barrier 140 (1 104 or 1106) to decay to Ev. b uik energy level, it is possible that for some configurations, a hole that escapes a dot over the barrier 140 might have sufficient energy to create a reverse current flow into the n-type transition layer 150.
• ⁇ E 4 is the difference between the valence band edge (E v , n - t ran s ition) of transition layer 150 and the valence band edge (Ev . bar ri er ) peak of the tunneling barrier 140.
• the Ev. n - trans i t i on band gap edge of the transition layer 150 is preferably lower than a valence band peak of the tunneling barriers (Ev.ba mer )-
• the "peak" of a barrier for tunneling electrons is the highest energy edge of the Ec.ban ⁇ er of the barrier, whereas the “base” is commensurate with the Ec. bu i k energy level in the bulk matrix material at the interface with the barrier.
• the "peak” of a barrier for tunneling holes is the lowest energy edge of the Ev .barrier of the barrier, whereas the “base” is commensurate with the Ev. bu i k energy level in the bulk matrix material at the interface with the barrier.
• a characteristic of inorganic quantum dots that bears explaining and is apparent in FIGS. 9A and 9B is that in an inorganic quantum dot, the E e ,i quantum state may or may not correspond the conduction band edge (top of the band gap) of the quantum dot material. It is customary to illustrate the band gap of the dot material as though it were a bulk material, even if the band-gap edges of the material as arranged within the quantum dot are not "allowed" quantum states.
• the positions of allowed quantum states within an inorganic quantum dot are dependent on wave functions. As is known in the art, the position of the wave functions/quantum states can be engineered. As illustrated in FIGS.
• a characteristic of the inorganic bulk matrix material 120 may include the formation of a valence band continuum 260 and conduction band continuum 270 above and below the band gap edges of the inorganic bulk matrix material. These continuums are, in essence, a cloud of energy states, with a density of states decreasing with distance from the band gap edge. The presence of the continuums means that a charge carrier escaping a dot over a tunneling barrier may exit the dot into an allowed energy state, which is a consideration when determining how quickly the carrier will fall toward the band gap.
• the deexcitation loss of excess energy ( ⁇ Ei, ⁇ E 2 ) is still likely to cccur before the free electron can be trapped by an adjacent dot (i.e., entering an adjacent dot over, rather than through, the tunneling barrier 140).
• the band continuums 270, 260 over the dot essentially begin at Ec,buik and Ev. bu i k , respectively.
• the presence of the barrier 140 may push the continuum 270 higher directly over the dot in FIGS. 9A and 9B, and may push the continuum 260 lower directly below the dot in FIG. HA and HB.
• FIG. 13 is a cross-section of an array of quantum dots based on the device in FIG. 1, if produced using the Stranski-Krastanow method and modified to include the tunneling barrier 140.
• a thin (e.g., at least one monolayer; for example, 0.1 to 10 run) barrier layer 141 is grown (e.g., MBE, MOCVD), prior to deposition of the wetting layer 132. Then, after growth of the quantum dots 130, another barrier layer 141 is grown, thereby encapsulating each dot.
• the barrier layers 140, 141 are lattice-matched to the bulk matrix material 120, 121.
• a mismatch in strain between the bulk material and the barrier material increases the potential for defects.
• a mismatch may result in an inconsistent lattice spacing within the barrier layer if the thickness of a thin barrier layer varies in places by as little as a monolayer, creating variations during the spontaneous nucleation that seeds the dots.
• lattice matching the barrier to the bulk matrix minimizes the chances of inhomogenieties between successive quantum dot layers and adjacent dots.
• a lattice mismatch between the bulk and the barrier does not induce defects, a small mismatch in lattice constants "a" (e.g.,
• FIGS. 8-13 may be achieved using several different material-type combinations.
• examples of inorganic semiconductor materials include IH-V compound semiconductors such as AlAs, AlSb, AlP, AlN, GaAs, GaSb, GaP, GaN, InAs, InSb, InP, and InN; II- VI compound semiconductors such as CdS, CdSe, CdTe, ZnO, ZnS, ZnSe, and ZnTe; other compound semiconductors such as PbS, PbSe, PbTe, and SiC; and the ternary and quaternary alloys of such compound semiconductors.
• IH-V compound semiconductors such as AlAs, AlSb, AlP, AlN, GaAs, GaSb, GaP, GaN, InAs, InSb, InP, and InN
• II- VI compound semiconductors such as CdS, CdSe, CdTe, ZnO, ZnS, ZnSe, and ZnTe
• other compound semiconductors such as PbS, PbSe
• examples of materials include the aforementioned inorganic semiconductor materials, as well as insulators such as oxides, nitrides, or oxynitrides. How to select materials having appropriate relative energies and how to select materials that lattice-match are well known in the art.
• FIG. 32 illustrates lattice constants, wavelengths, and energy gaps for a variety III-V compound semiconductors. As is known in the art, ternary and quaternary alloys of these compounds can be grown to lattice match binary III-V compounds.
• the ternary compound Al x Gai -x As can be grown to very closely lattice match GaAs (within approximately 0.1%) for most any value of x.
• the quaternary compound Ga x In i -x As i- y P y can be lattice matched to both GaAs and InP by adjusting x and y (e.g., Gao. 8 lno. 2 As o 65 Po. 35 lattice matches InP).
• ternary and quaternary compounds can be lattice matched to each other.
• the wave function ⁇ has to be determined from the Schr ⁇ dinger equation: where m r is the reduced effective mass of the charge carrier (in this case, an electron), h is the reduced Planck constant, and q is electron charge.
• the reduced effective mass of the charge carrier is:
• m QD is the effective mass of the charge carrier in the quantum dot
• m b * amer is the effective mass of the charge carrier in the barrier material
• Equation (1) can be simplified using the Wentzel-Kramers-Brillouin approximation and integrated to determine the wave function:
• the tunneling probability T 1 is given by:
• Equation (4) For the case of the rectangular barrier illustrated in FIG. 14, solving Equation (4) for the tunneling probability is given by:
• Equation (5) Adapting Equation (5) to also apply to hole tunneling, as illustrated in FIG. 15 (in addition to electron tunneling illustrated in FIG. 14) by taking the absolute value of ⁇ b , and then rearranging the equation to solve for the thickness ( ⁇ x) of the barrier at the energy level of the carrier gives: where m * is the reduced effective mass of the charge carrier (electron or hole).
• the thickness ⁇ x of the barrier is preferably selected based on the energy level at the base of the tunneling barrier. If the bulk matrix is an inorganic material having the conduction band continuum 270 and valence band continuum 260, the density of states generally suggests that a charge carrier having the energy level at the base of barrier will be the dominant carrier energy.
• the energy E of the charge carrier equals the energy level at the base of the tunneling barrier
• ⁇ t , ⁇ equals the absolute value of the height of the barrier, which is the difference between the energy levels at the peak and the base of the tunneling barrier.
• These energy levels are physical characteristics of the materials used for the bulk matrix material 120 and the barrier material 140.
• the barrier height equals the Ec. bamer of the barrier material minus the Ec, bu i k of the bulk matrix material
• the barrier height equals the Ey . barr i er of the barrier material minus the Ev. bu ik of the bulk matrix material.
• the effective mass of the charge carrier in the barrier material rn barrier and in the quantum dot material rn Q0 are also physical characteristics of the respective materials.
• the thickness Ax at the base of the tunneling barrier equals the physical thickness of the tunneling barrier layer 140, 141.
• Equation (6) Equation (6)
• Equation (6) Equation (6)
• the preferred thickness Ax of the barrier layer 140 can be determined for any tunneling probability T 1 .
• the potential profile U(x) of the tunneling barrier can almost always be approximated as rectangular.
• the thickness needed for the barrier layer is directly proportional to the negative of the natural log of the tunneling probability in accordance with:
• Equation (7) An equation to calculate barrier thickness can be derived for any function U(x). Without regard to the potential profile U(x) of the tunneling barrier, Equation (7) holds true.
• FIG. 16 illustrates a triangular barrier
• FIG. 17 illustrates a parabolic barrier.
• Equation (9) Adapting Equation (9) to also apply to hole tunneling by taking the absolute value of ⁇ b , and then rearranging the equation to solve for the thickness (Ax) of the barrier at the energy level of the carrier gives:
• Equation (12) Adapting Equation (12) to also apply to hole tunneling by taking the absolute value of ⁇ b , and then rearranging the equation to solve for the thickness (Ax) of the barrier at the energy level of the carrier gives:
• Equation (7) holds true, without regard to the potential profile U(x) of the barrier.
• the tunneling probability T, for barrier 140 is preferably between 0.1 and 0.9.
• a more precise probability T 1 may be determined experimentally for any design by measuring the photocurrent output, thereby determining the efficiency to be gained.
• the more preferred range for T t is between 0.2 and 0.5.
• barrier height and barrier thickness For any given tunneling probability T 1 . It may seem that making the barrier lower would increase efficiency by lessening the energy lost to deexcitation of carriers that hop out of a dot over the barrier, rather than tunneling out. However, this introduces another inefficiency since the barrier layer would need to be thicker for a same tunneling probability T 1 , reducing the volume- percentage bf the device dedicated to generating photocurrent. Even if the barriers are made of photoconductive materials, they would not be expected to appreciably contribute to photocurrent generation (due to their relatively large band gap). The end result is that thicker barriers take up space that would otherwise be composed of photoconductive materials, lowering photocurrent generation and efficiency.
• the preferred thickness limit for a tunneling barrier is between 0.1 to 10 nanometers. Within the range of 0.1 to 10 nanometers, the thickness of the tunneling barrier is preferably no more than 10% of the average cross-sectional thickness of a quantum dot, through a center of a quantum dot.
• the energy levels of the opposite side of the band gap not create a trap for the opposite carrier.
• the Ev. bamer of the barrier layer 140 is preferably within ⁇ SkTof the Ev. bu i k of the bulk matrix 120. This general ⁇ 5kT difference is also preferred between Ec,bamer and Ec.buik on the conduction band side of the quantum dots in FIGS. 1 IA and 1 IB.
• the quantum dot material may be chosen to minimize the depth of the potential "trap" for the opposite carrier.
• an energy state within the potential "trap" for the opposite side of the band gap is preferably positioned to keep an outermost quantum state within the trap within ⁇ 5/e7Of the energy levels of the adjacent barrier layers 140, somewhat improving the probability that a passing electron or hole will pass right by without deexcitation.
• the number of energy levels shown in the drawings within the quantum dots are simply examples.
• On the tunneling side while there are preferably at least two quantum states (one forming the inte ⁇ nediate band and one positioned to overlap the energy level of the adjacent bulk matrix material), there may only be a single quantum state providing the intermediate band.
• the intermediate band is preferably formed by the quantum states closest to the band gap, a higher order energy state could be used. So long as the wave functions between adjacent dots overlap, a deciding factor as to whether a quantum state can function as an intermediate band is whether the two wavelengths required to pump a carrier by E L and E H will be incident on the dots.
• a band cannot function as an intermediate band if two wavelengths needed to pump the carrier through the band will never be incident on the quantum dots. For example, if one of the wavelengths needed for pumping either E 1 , or EH is absorbed by the bulk matrix material, the barrier material, etc., it will not be incident on the quantum dots, even if the wavelength is incident on the photosensitive device itself. For many materials, this same problem limits the practicality of inter-band pumping through two quantum states (e.g., pumping from the valence band to an E e j state, then to an E e , 2 state, and then into the conduction band).
• the tunneling barrier 140 and bulk matrix material 120 need to be substantially transparent to photons having energy E L and E H -
• Another consideration to balance in selecting materials is the efficiency and contribution to photocurrent of the transition of carriers directly across the bulk matrix band gap E G (without passing into the intermediate band) in both the bulk matrix 120 and in the dots 130 themselves.
• a tunneling barrier 140 is added to dots 130 in, for instance, a colloidal solution, and the coated dots are interspersed within a bulk-material matrix, charge carriers in the bulk 120 can transit through the structure without necessarily tunneling through a barrier 140.
• the dots are formed by the Stranski-Krastanow technique discussed above and illustrated in FIG. 13, carriers will tunnel through barrier layers 141 to transit between bulk layers 121.
• DFENCE diots-in-a-fence
• FIG. 18 An example GaAs/InAs dots-in-fence structure is illustrated in FlG. 18.
• the structure includes a p-GaAs layer 1815, a plurality of dots-in-fence barriers, and an n-GaAs layer 1850.
• a GaAs bulk layer 1821 is grown between each dots-in-fence barrier.
• a GaAs bulk layer 1821 is also provided on the p-GaAs layer 1815 to promote consistent growth of the first dots-in- fence barrier.
• Each dots-in-fence barrier includes an Al x Gai_ x As energy barrier "fence" 1841 surrounding InAs quantum dots 1830 and wetting layers 1832 embedded in the GaAs homojuncti ⁇ n.
• FIG. 19 A is an energy diagram through a dot along line "A" in FIG. 18, and FIG. 19B is an energy diagram off-dot along line "B" in FIG. 18.
• the thin InAs wetting layer 1832 is not believed to be particularly consequential to off-dot tunneling and is omitted as a feature from FIG. 19B.
• the maximum solar power conversion efficiency under AMI .5 spectral radiation of the example GaAs-based photovoltaic cell employing 10-20 layers of InAs quantum dots surrounded by Al x Gai -x As barriers in the junction built-in depletion region can be as high as 45%. Higher efficiencies were anticipated for InP-based cells. This represents a significant improvement over GaAs homojunction cells with maximum efficiencies of ⁇ 25%.
• the structure of the DFENCE heterostructure in FIG. 18 includes multiple layers of quantum dots 1830 in the intrinsic region of a GaAs p + -i-n + structure.
• the InAs dots 1830 are sandwiched between two thin, high band- gap Al x Ga] -x As barrier layers 1841 , which are, in turn, embedded in GaAs 1821 (and between 1821 and 1850 for the topmost dots-in-fence layer).
• the spatial distribution of InAs dots 1830 in the GaAs /Al x Gai- x As barriers is treated as a dense, periodically arranged array of cylinders with length, -6, and radius, R.
• the thickness, t, of the Al x Gai -x As fence barrier is assumed to be 0. Ii?, and the thickness of the surrounding GaAs layer is d.
• the conduction band offset between the strained InAs dot and GaAs buffer is 70% of their difference in band gaps ( ⁇ E 3 in FIG. 19A), and the conduction band offset between Al x Gai -x As and GaAs is 67% of their band gap difference ( ⁇ Ei in FIG. 19A).
• ⁇ E 3 in FIG. 19A the conduction band offset between the strained InAs dot and GaAs buffer is 70% of their difference in band gaps
• the conduction band offset between Al x Gai -x As and GaAs is 67% of their band gap difference ( ⁇ Ei in FIG. 19A).
• the ground state photon transition energies decrease due to reduced confinement for the GaAs/InAs quantum dot structure with or without the Al x Ga ⁇ -x As fences, as shown in FIG. 20.
• R - S nm the lowest transition energy in the absence of a fence is 1.06 eV, consistent with the absorption peak at 1.05 ⁇ 0.05 eV observed in the luminescence of similar sized structures. See J. Y. Marzin, J. M. Gerard, A. Izrae, D. Barrier and G. Bastard, Phys. Rev. Lett. 73, 716 (1994).
• the photocurrent density from the quantum dots is:
• e is the elementary charge
• G(E, z) is the photocarrier generation rate in the quantum dots within the /-region (for background see V. Aroutiounian, S. Petrosyan and A. Khachatryan, J. Appl. Phys. 89, 2268 (2001))
• Ei and E 2 are the lower and upper energies for absorption in the quantum dots, respectively.
• z is the position in the /-region (of total width, z,) as measured from the metallurgical p-n junction, j ' ofz) is the incremental photocurrent generated at position z
• Jr > is the total photocurrent collected from the N quantum dot layers.
• the absorption coefficient of a quantum dot is calculated based on the dipole transition matrix element between the conduction and valance band edge states using Fermi's Golden Rule (see S. Datta, Quantum Phenomena (Addison Wesley, New York, 1989), P. 233). Inhomogeneous Gaussian broadening of the photon transition energy contributes a width of approximately 50 meV to the absorption spectrum (see J. Y. Marzin, J. M. Gerard, A. Izrae, D. Barrier and G. Bastard, Phys. Rev. Lett. 73, 716 (1994)).
• the radiative recombination time is typically ⁇ rec ⁇ 1 ns (see W. H. Chang, T. M. Hsu, C. C. Huang, S. L. Hsu and C. Y. Lai, Phys. Rev. B 62, 6959 (2000)), as will be used in the subsequent analysis.
• ⁇ T> The average transmission coefficient, ⁇ T>, characterizes the electron and hole tunneling efficiency through the fence without trapping into the discrete quantum dot energy levels.
• the current is then equal to the number of carriers that tunnel along the on-dot paths, which, in turn equals the product of the tunneling probability and the number of carriers at that energy in the GaAs layers.
• ⁇ T> can be expressed as:
• N C (E) is the GaAs conduction band density of states,/( ⁇ j is the Fermi-Dirac distribution, and T(E) is the transmission coefficient at incident electron energy, E.
• ⁇ T> decreases from 24% (no fence barrier) to 12%.
• Nj 01 is the area density of quantum dots (typically between 4.7 x lO 10 and 5 ⁇ l0 12 c/w ⁇ 2 for this material system - see T. S. Yeoh, C. P. Liu, R. B. Swint, A. E. Huber, S. D. Roh, C. Y. Woo, K. E ' . Lee, J. J. Coleman, Appl. Phys. Lett.
• N cm and N vm are the effective densities of electron and hole states in GaAs
• E c and E x are the conduction and valence band energies of GaAs
• E e and E h are the energy eigenvalue for electrons and holes in the InAs quantum dots (referenced to the conduction band edge of the InAs quantum dots)
• v is the thermal velocity of electrons
• ⁇ e and ⁇ ⁇ are the electron and hole capture cross sections, respectively
• ⁇ E 2 is the valence band offset between Al x Gai -x As and GaAs.
• the reverse saturation current, Jo is reduced with an increase in band gap offset energy, ⁇ E, between GaAs and Al x Gai -x As layers.
• Incorporating generation and recombination currents in both the GaAs layers and Al x Ga ]-x As fence barriers yields: where r # is the fractional increase in the net /-region recombination at equilibrium due to the incorporation of the fence barrier, ⁇ is the ratio of the recombination current in the /-region at equilibrium to the reverse drift current resulting from minority carrier extraction, and J NR is the nonradiative recombination current in the intrinsic GaAs regions ⁇ see N. G. Anderson, J. Appl. Phys.
• J S ⁇ N is the interface recombination current at the off-dot sites (see J. C. Rimada, L. Hernandez, J. P. Connolly and K. W. J. Barnham, Phys. Stat. Sol. (b) 242, 1842 (2005)), and J sc is the short-circuit current density under illumination.
• the maximum ⁇ p of GaAs-based intermediate band solar cells is 52%, with the intermediate band energy of between 0.6 eV and 0.7 eV, referenced to the valence band edge of GaAs.
• an average lateral cross-section of each quantum dot preferably satisfies 2 nm ⁇ R ⁇ 10 nm, with each Al x Gai -x As layer having a thickness (t) satisfying 0. IR ⁇ t ⁇ 0.3R, and each GaAs layer disposed between two dots-in-a-fence barriers having a thickness (d) satisfying 2 nm ⁇ d ⁇ 10 nm.
• the average lateral cross-section of each dot should preferably satisfies 6 nm ⁇ R ⁇ 10 nm.
• a period of a quantum dot unit cell within a respective dots-in-a-fence barrier (L) preferably satisfies 2R ⁇ L ⁇ 2R + 2 nm.
• the density of InAs quantum dots is preferably 10 1 to 10 12 quantum dots per square centimeter.
• Including the thin fence barriers surrounding quantum dots opens a new opportunity for narrowing the performance gap between high performance multijunction solar cells and ideal intermediate band quantum dot solar cells.
• DFENCE energy barrier structure There are several advantages of incorporating the DFENCE energy barrier structure: (i) Resonant tunneling through on-dot and off-dot sites becomes possible by adjusting the height (via semiconductor alloy composition) and the thickness of the fence barrier without trapping in the quantum dots or wetting layers; (ii) The fences allow the quantum dots to function primarily as sub-band gap photocarrier generation centers rather than as sites for undesirable recombination, without affecting V 00 ; and (iii) The reverse saturation current due to thermally generated minority carriers at the depletion layer edges and in the interior of the InAs layers is considerably reduced by the band gap offset between the fence and the narrow bandgap host layers. With these properties, GaAs-based quantum dot intermediate band DFENCE solar cells promise power conversion efficiencies as high as 45%.
• Heterostructures employing an energy fence can also be exploited in the InP-based materials system.
• An InP/InAs system has approximately a 3% lattice mismatch in comparison to the 6% to 7% mismatch with GaAs/InAs, such that the optimal dot size in the InP/InAs system tends to be smaller.
• the minimum transition energies in the InAs quantum dots can be as low as 0.65 eV (see M. Holm, M. E. Pistol and C. Pryor, J. Appl. Phys. 92, 932 (2002)), corresponding to the energy that yields the maximum power conversion efficiency of nearly 55%, as shown in FIG. 24.
• FIG. 25 illustrates an InP/InAs DFENCE structure.
• the structure includes a p-lnP layer 2515, a plurality of dots-in-fence barriers, and an n-InP layer 2550.
• a InP bulk layer 2521 is grown between each dots-in-fence barrier.
• a InP bulk layer 2521 is also provided on the p-InP layer 2515 to promote consistent growth of the first dots-in-fence barrier.
• Each dots-in-fence barrier includes an AIo 4sl n o 52 AS energy barrier "fence" 2541 surrounding InAs quantum dots 2530 and wetting layers 2532 embedded in the InP homojunction.
• FIG. 26A is an energy diagram through a dot along line "A" in FIG. 25, and FIG. 26B is an energy diagram off-dot along line "B" in FIG. 25.
• the thin InAs wetting layer 2532 is not believed to be particularly consequential to off-dot tunneling and is omitted as a feature from FIG. 26B.
• L the distance between quantum dots in the plane of the substrate surface and L - I nm + 2R.
• the data is also included for the same structure with no tunneling barriers.
• the ground state photon transition energies decrease due to reduced confinement for the InP/InAs quantum dot structure with or without the Alo . 4elno. 5 2 As fences.
• the escape rate was calculated, as described above for GaAs, for the InP/InAs structure both with and without the Alo .4 sIno .52 As fences as shown in FIG. 28. hi view of the escape rate in FIG. 28 appearing to be zero, the y-axis scale in FIG. 29 is adjusted to more clearly show the escape rate for the DFENCE structure.
• FIG. 30 is a graph of power conversion efficiency versus number of quantum dot layers (N) for quantum dots with a radius of 8 nm.
• FIG. 31 is a graph of power conversion efficiency versus intermediate band energy level calculated for: the ideal conditions proposed in the Luque model, the Luque model for InP with the band gap of 1.34 eV, an upper limit of the InP/InAs DFENCE model.
• the labeled data on the ideal Luque model curve is the bulk band gap assumed that corresponds with the intermediate band level on the abscissa to achieve maximum efficiency.
• an average lateral cross-section of each quantum dot (2R) preferably satisfies 2 ran ⁇ R ⁇ 12 nm, with each Alo .4 shio .52 As layer having a thickness (t) satisfying 0.1R ⁇ t ⁇ 0.3R, and each InP layer disposed between two dots-in-a-fence barriers having a thickness (d) satisfying 2 nm ⁇ d ⁇ 12 nm.
• a period of a quantum dot unit cell within a respective dots-in-a-fence barrier (L) preferably satisfies 2R ⁇ L ⁇ 2R + 2 nm.
• the barrier materials for the dots-in-a-fence structure used in the experiments were lattice matched to the bulk material, a small mismatch in lattice constants (e.g.,
• organic photosensitive devices of the present invention may be used to generate electrical power from incident electromagnetic radiation (e.g., photovoltaic devices).
• the device may be used to detect incident electromagnetic radiation (e.g., a photodetector or photoconductor cell). If used as a photoconductor cell, the transition layers 115/1815/2515 and 150/1850/2550 may be omitted.

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