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Dopant

A dopant is an impurity atom or ion intentionally introduced into a pure host material, most commonly a semiconductor such as silicon or germanium, to alter its electrical conductivity and other properties by creating either excess electrons or holes as charge carriers.^[1] This process, known as doping, enables the control and enhancement of conductance in semiconductors by introducing excess charge carriers, forming the foundation of modern electronics.^[2] Dopants are classified into two primary types based on their effect on the semiconductor's band structure: n-type dopants, which are typically group V elements like phosphorus, arsenic, or antimony that donate extra electrons to the conduction band, and p-type dopants, which are group III elements such as boron, aluminum, or gallium that create "holes" in the valence band by accepting electrons.^[3] In n-type semiconductors, electrons become the majority charge carriers, while in p-type, holes dominate, allowing for the creation of p-n junctions essential for devices like diodes and transistors.^[4] The concentration of dopants, often ranging from 10^13 to 10^18 atoms per cubic centimeter, precisely controls the material's resistivity and enables tailored performance in applications.^[5] The significance of dopants lies in their role in enabling semiconductor devices that power computing, telecommunications, and renewable energy technologies, with doping techniques having evolved from early diffusion methods in the mid-20th century to advanced ion implantation for nanoscale precision.^[2] By modulating the bandgap and carrier mobility, dopants not only enhance conductivity but also influence optical properties, such as in light-emitting diodes (LEDs) and solar cells, where they improve efficiency and wavelength tuning.^[6] Beyond semiconductors, dopants are employed in optical materials, dielectrics, and superconductors to achieve desired properties such as lasing or enhanced critical temperature. Ongoing research focuses on novel dopants, including rare earth elements, to address challenges in high-speed and low-power electronics.^[7]

Fundamentals

Definition and Purpose

A dopant is a trace impurity element or compound intentionally introduced into a pure host material, such as a semiconductor or crystal lattice, at concentrations typically below 1% to modify its electrical, optical, thermal, or mechanical properties without significantly altering the host's overall structure.^[8]^[9] These impurities, often atoms from group III, V, or rare-earth elements, are added in controlled amounts—usually on the order of parts per million to parts per billion—to tailor the material's functionality for specific technological needs.^[5] The primary purpose of doping is to engineer desirable behaviors in the host material, such as generating charge carriers (free electrons or holes) in semiconductors, inducing color centers for optical absorption, enhancing luminescence efficiency, or fine-tuning the bandgap energy for light emission or detection.^[9]^[10] Dopants achieve this by occupying either substitutional sites (replacing host atoms in the lattice) or interstitial sites (fitting between lattice positions), which introduces localized energy states that interact with the host's electronic structure.^[9] For instance, in silicon semiconductors, phosphorus acts as a donor to increase electron density, while in optical crystals like yttrium aluminum garnet, neodymium ions enable laser action through radiative transitions.^[5]^[11] In terms of general effects, doping shifts the Fermi level—the energy at which the probability of finding an electron is 50%—and introduces donor or acceptor energy levels within the bandgap of the host material.^[5]^[12] For n-type doping, donor levels lie just below the conduction band, facilitating the release of electrons into it and elevating the Fermi level; conversely, p-type doping places acceptor levels above the valence band, promoting holes and lowering the Fermi level. In energy band diagrams, these modifications appear as shallow impurity levels splitting off from the band edges, enabling controlled carrier concentrations that transform insulators or poor conductors into highly functional materials.^[5]^[12] The concept of doping was first recognized in early 20th-century semiconductor research, building on studies of impurity effects in materials like copper oxide and silicon during the 1920s and 1930s.^[13] A pivotal milestone occurred in 1947 at Bell Laboratories, where the invention of the point-contact transistor relied on intentionally doped germanium to achieve amplification, marking the dawn of modern semiconductor technology.^[13]^[14]

Types and Classification

Dopants are classified primarily by their chemical elements, which determine their valence electron contribution and interaction with the host lattice. Elements from Group III of the periodic table, such as boron and aluminum, act as acceptors in silicon-based semiconductors by providing three valence electrons, creating hole-accepting sites that enhance p-type conductivity.^[2] Similarly, Group V elements like phosphorus and arsenic serve as donors, contributing five valence electrons to introduce excess electrons for n-type doping.^[2] Transition metals, including chromium and iron, are employed for their ability to create deep energy levels that influence recombination processes and optical properties in the host material.^[15] Rare-earth elements, such as neodymium and europium, are notable for inducing luminescence effects through intra-ionic transitions, making them suitable for optical applications.^[16] Classification by valence further distinguishes dopants based on their energy level positions relative to the host's band edges. Shallow dopants, like phosphorus in silicon, have ionization energies close to the conduction band (approximately 0.045 eV), allowing easy thermal ionization and effective carrier generation at room temperature.^[17] In contrast, deep dopants, such as gold in silicon, position their levels near the midgap (around 0.54 eV), acting as efficient recombination centers or traps rather than primary carriers.^[17] Isovalent dopants maintain the same valence as the host atoms, exemplified by germanium in silicon, where they introduce lattice strain without net charge compensation, influencing band structure indirectly.^[18] Aliovalent dopants, differing in valence (e.g., phosphorus in silicon), require charge compensation mechanisms like vacancy formation to maintain lattice neutrality.^[18] Dopants can also be categorized by their functional behavior in the host material. Electrical dopants primarily modify conductivity by introducing free carriers, as seen with group IV-V impurities in elemental semiconductors.^[5] Optical dopants alter absorption and emission spectra, often through rare-earth ions that enable specific wavelength interactions.^[16] Magnetic dopants, typically transition metals, incorporate localized spins to enable quantum effects like spin-dependent transport.^[19] A critical aspect of dopant classification involves their solubility limits and segregation coefficients, which govern incorporation stability during processing. The solubility limit represents the maximum concentration before precipitation occurs; for phosphorus in silicon, this is approximately 3 × 10^{20} cm^{-3} at typical annealing temperatures, beyond which inactive precipitates form, reducing effective doping.^[20] Segregation coefficients, defined as the ratio of dopant concentration in the solid to that in the liquid phase (k = C_s / C_l), quantify partitioning during crystal growth; for phosphorus in silicon, k ≈ 0.3, leading to uneven distribution and potential pile-up at interfaces.^[21] These parameters explain why high concentrations often result in precipitation for many dopants, limiting achievable carrier densities.^[20]

Doping Processes

Common Techniques

Diffusion is a thermal process used to introduce dopants into materials, where dopant atoms spread from regions of high concentration to low concentration, primarily through vacancy or interstitial mechanisms in the crystal lattice.^[22] This method involves heating the material in an atmosphere containing dopant sources, such as gases or doped oxides, allowing atoms to incorporate into the surface and diffuse inward.^[23] The process is governed qualitatively by Fick's laws of diffusion, which describe the flux of dopants; Fick's first law states that the diffusion flux J is proportional to the negative gradient of concentration C, expressed as

J = -D \nabla C,

where D is the diffusion coefficient dependent on temperature and material properties.^[24] Ion implantation introduces dopants by accelerating ions to high energies, typically in the range of 10-500 keV, and directing them into the subsurface of the target material to embed them at controlled depths.^[25] This physical process creates a precise dopant profile but induces lattice damage from ion collisions, necessitating a subsequent annealing step at elevated temperatures (often 500-1300°C) to repair the crystal structure and electrically activate the dopants by placing them on substitutional lattice sites.^[26]^[27] Other techniques include chemical vapor deposition (CVD), which enables epitaxial doping by simultaneously depositing the host material and incorporating dopants from vapor-phase precursors, achieving uniform layers with controlled thickness.^[28] Molecular beam epitaxy (MBE) provides precise control over layer thickness and doping at the atomic scale under ultra-high vacuum, using directed beams of atoms or molecules for sequential deposition.^[29] Neutron transmutation doping offers exceptional uniformity, particularly for phosphorus in silicon, through the nuclear reaction ^{30}\mathrm{Si}(n,\gamma)^{31}\mathrm{Si} \rightarrow ^{31}\mathrm{P} + \beta^-, where thermal neutrons convert stable silicon isotopes into dopants during irradiation in a reactor.^[30] Diffusion excels in achieving uniform bulk doping due to its equilibrium-driven nature, while ion implantation is preferred for shallow junctions with sharp profiles, though it requires additional annealing to mitigate damage. Ion implantation was commercialized in the 1970s, revolutionizing precise doping in semiconductor manufacturing.^[31]

Concentration and Distribution

Dopant concentration is typically expressed in units of atoms per cubic centimeter (cm⁻³) or atomic percent (at%), with the former being more common in semiconductor contexts due to its direct relation to carrier density.^[32] In semiconductors like silicon, typical doping levels range from 10¹⁴ to 10²⁰ cm⁻³, spanning lightly doped regimes for devices requiring low conductivity to heavily doped contacts.^[32] These concentrations are controlled to achieve precise electrical properties, with atomic percent providing a host-lattice-normalized measure (e.g., 10¹⁸ cm⁻³ equates to roughly 0.002 at% in silicon, given its atomic density of ~5 × 10²² cm⁻³).^[17] The spatial distribution of dopants is modeled using specific profiles that reflect the introduction method, enabling prediction and control of concentration gradients. For ion implantation, the as-implanted profile approximates a Gaussian distribution, given by:

C(x) = \frac{Q}{\sqrt{2\pi} \Delta R_p} \exp\left[ -\frac{(x - R_p)^2}{2 \Delta R_p^2} \right]

where Q is the implanted dose (atoms/cm²), R_p is the projected range (mean depth in cm), and \Delta R_p is the straggle (longitudinal spread in cm).^[25] This model arises from statistical scattering during implantation and is valid for amorphous targets at moderate energies. In contrast, thermal diffusion from a constant surface source yields a complementary error function (erfc) profile:

C(x, t) = C_s \operatorname{erfc}\left( \frac{x}{2\sqrt{D t}} \right)

where C_s is the surface concentration, D is the diffusion coefficient, and t is time; this describes the penetration from a fixed boundary condition.^[22] These profiles allow simulation of post-process distributions, with subsequent annealing altering them via diffusion or activation. Dopant concentrations and profiles are measured using techniques that probe depth-resolved composition or electrical activity. Secondary ion mass spectrometry (SIMS) sputters the surface with ions and analyzes ejected species to map atomic concentrations with sub-monolayer sensitivity and ~10 nm depth resolution, ideal for shallow implants.^[33] Rutherford backscattering spectrometry (RBS) uses high-energy ion beams to detect backscattered particles, providing elemental depth profiles up to microns deep via energy loss analysis, though with lower sensitivity for light dopants.^[34] Electrical methods, such as capacitance-voltage (C-V) profiling, apply bias to a Schottky or p-n junction and measure depletion capacitance to infer ionized dopant density, offering non-destructive profiling of active carriers but assuming uniform profiles.^[35] At high concentrations exceeding ~10¹⁹ cm⁻³, doping becomes degenerate, where the Fermi level enters the conduction or valence band, imparting metallic-like conductivity with degenerate electron or hole gases.^[17] Solubility limits—e.g., ~1 × 10²¹ cm⁻³ for phosphorus^[36] and ~5 × 10²⁰ cm⁻³ for boron in silicon—^[37] constrain substitutional incorporation; beyond these, excess dopants form electrically inactive precipitates or clusters, reducing activation efficiency. During high-temperature processing like epitaxy, autodoping occurs as volatile dopants evaporate from the substrate and redistribute into the growing layer, contaminating unintended regions and requiring mitigation via backsealing or low-pressure conditions.^[38]

Applications in Semiconductors

N-type Doping

N-type doping involves the intentional introduction of donor impurities from Group V elements, such as phosphorus (P) or arsenic (As), into a semiconductor host like silicon (Si). These atoms possess five valence electrons, four of which form covalent bonds with the surrounding silicon lattice, leaving the fifth electron loosely bound in a shallow donor energy level approximately 0.045 eV below the conduction band edge.^[17] This shallow level facilitates thermal ionization at room temperature, where thermal energy (kT ≈ 0.026 eV at 300 K) readily excites the extra electron into the conduction band, generating free electrons without requiring external energy input.^[39] The primary effects of n-type doping are a significant increase in the concentration of free electrons (n), making them the majority charge carriers while holes (p) become minority carriers, with n ≫ p. This doping shifts the Fermi level upward toward the conduction band, altering the material's electrical properties to favor n-type conduction. For partial ionization scenarios, particularly at lower temperatures where not all donors are ionized (freeze-out regime), the electron concentration can be approximated as [n](/page/N+) \approx \sqrt{\frac{N_D N_C}{2}} \exp\left( -\frac{E_d}{2kT} \right), where N_D is the donor density, N_C is the effective density of states in the conduction band, E_d is the donor binding energy, k is Boltzmann's constant, and T is temperature (the factor of 2 accounts for donor degeneracy).^[17] A key application of n-type doping is in the fabrication of n-channel metal-oxide-semiconductor field-effect transistors (MOSFETs), where phosphorus-doped silicon forms the source, drain, and channel regions to enable electron flow. Typical doping levels range from 10^{16} to 10^{17} cm^{-3} for low-power devices to minimize power dissipation and ensure high electron mobility, while higher concentrations up to 10^{19} cm^{-3} are used in high-power devices for improved current handling and reduced on-resistance.^[40] Challenges in n-type doping include the formation of thermal donors in oxygen-rich Czochralski-grown silicon, where oxygen interstitials aggregate during annealing at 450°C to create double-donor defects that unpredictably increase carrier concentration and complicate resistivity control.^[41] Additionally, compensation by unintentional acceptors, such as residual boron or carbon impurities, reduces the effective donor concentration by pairing with ionized donors, necessitating precise purification and gettering techniques to achieve desired electrical characteristics.

P-type Doping

P-type doping introduces acceptor impurities into a semiconductor lattice to increase the concentration of holes, the majority charge carriers, which is crucial for fabricating p-n junctions and bipolar transistor structures in electronic devices. Acceptor impurities are typically elements from group III of the periodic table, such as boron (B) in silicon (Si), aluminum (Al) in silicon (Si), or zinc (Zn) in gallium arsenide (GaAs). These trivalent atoms substitute for the tetravalent host atoms, resulting in one fewer valence electron per dopant atom, which creates an electron deficiency or "hole" in the bonding structure.^[2]^[42] The acceptor atoms establish shallow energy levels near the valence band; for boron in silicon, this level is approximately 0.045 eV above the valence band maximum.^[43] At room temperature, thermal energy readily ionizes these acceptors by capturing electrons from the valence band, thereby generating mobile holes that contribute to p-type conductivity.^[44] For aluminum in silicon, the acceptor level is slightly deeper at about 0.069 eV above the valence band, leading to somewhat less efficient ionization compared to boron.^[45] The primary effect of p-type doping is a substantial increase in hole concentration (p), where p greatly exceeds the intrinsic carrier concentration (n_i) and the electron concentration (n), such that p >> n and p ≈ N_A (with N_A being the acceptor density, assuming full ionization at typical operating temperatures).^[46] In the non-degenerate limit, the minority electron concentration follows n ≈ n_i^2 / N_A from the law of mass action. This doping shifts the Fermi level toward the valence band, closer to the acceptor levels, enhancing the probability of hole occupancy and promoting p-type behavior. For instance, in heavily doped silicon, the Fermi level can lie within 0.1–0.2 eV of the valence band edge, depending on N_A.^[47] A representative example is the use of boron doping in silicon to produce p-type substrates for integrated circuits, where boron concentrations of 10^{15}–10^{18} cm^{-3} are common to achieve desired resistivity levels. In advanced semiconductor nodes below 10 nm, such as those in modern CMOS technology, ultrashallow boron doping is employed to form abrupt p-n junctions with depths under 5–10 nm, often using techniques like plasma doping or monolayer doping followed by low-temperature annealing to minimize diffusion.^[48]^[49] Challenges in p-type doping include boron penetration, where rapid diffusion of boron atoms through thin gate oxides or interfaces occurs during high-temperature processing steps like annealing, potentially shorting devices or altering threshold voltages in MOSFETs.^[50] Another issue is hydrogen passivation of acceptors, in which atomic hydrogen from processing environments (e.g., plasma etching) forms complexes with boron, neutralizing the acceptor levels and temporarily deactivating the dopants until a reactivation anneal is applied.^[51] P-type regions are typically combined with n-type regions to create p-n junctions that enable rectification and amplification in semiconductor devices.

Applications in Optical Materials

Lasing Media

In lasing media, dopants consisting of rare-earth or transition metal ions are incorporated into transparent crystalline hosts, such as oxides or fluorides, to facilitate population inversion and stimulated emission for coherent light generation. These ions introduce discrete energy levels within the bandgap of the host material, enabling selective absorption of pump energy and subsequent emission at specific wavelengths; for instance, Nd³⁺ ions in yttrium aluminum garnet (YAG) create sharp emission lines by promoting electrons between 4f energy levels.^[52]^[53] The foundational achievement in this field was the 1960 demonstration of the first solid-state laser by Theodore Maiman at Hughes Research Laboratories, using a ruby crystal doped with Cr³⁺ ions in Al₂O₃, which produced pulsed output at 694 nm through a three-level system. This milestone shifted laser development from gaseous media to solids, offering enhanced compactness and power handling compared to early gas lasers like helium-neon, while enabling room-temperature operation and rugged designs suitable for practical applications.^[54]^[55] Lasing in these doped crystals relies on a sequence of processes: pump light, typically from flashlamps or diode lasers, is absorbed by the dopant ions, exciting electrons from ground-state to broad upper manifolds; fast non-radiative decay via phonon interactions then relaxes electrons to a metastable upper lasing level, achieving population inversion. In four-level systems, such as those with rare-earth ions like Nd³⁺, the lower lasing level lies above the ground state and remains depopulated at thermal equilibrium, significantly reducing the pump threshold for oscillation compared to three-level systems like ruby. Stimulated emission follows as incoming photons trigger radiative transitions from the upper to lower level, amplifying coherent light while competing with spontaneous emission and losses.^[56]^[57] A widely used example is the Nd:YAG laser, where Nd³⁺ doping in YAG enables efficient lasing at 1064 nm via the four-level scheme, with typical dopant concentrations of about 1 at.% optimized to balance absorption efficiency and avoid concentration quenching from cross-relaxation or energy migration among ions. Quenching becomes prominent above 1-2 at.%, where non-radiative pathways dominate, shortening fluorescence lifetimes and raising thresholds; thus, concentrations in the 0.1-1 at.% range are standard for high-performance devices.^[57]^[58] The Ti:sapphire laser exemplifies transition metal doping, with Ti³⁺ ions in Al₂O₃ providing a broad vibronic emission band for tunability from 650 to 1100 nm, pumped at 488-532 nm to support ultrafast pulse generation. Dopant levels are kept low at 0.05-0.25 at.% to maintain crystal quality and prevent quenching or scattering, while leveraging the ion's d-electron transitions for wide bandwidth.^[59]^[60] These dopant-based solid-state lasers surpass gas lasers in scalability, delivering high output per unit volume in compact, electrically efficient packages that support continuous-wave or high-peak-power operation without the maintenance demands of gas handling.^[61]

Phosphors and Scintillators

In phosphors, dopants serve as activator ions that enable fluorescence by facilitating energy transfer and emission in host lattices, commonly used for down-conversion in lighting and display applications. For instance, Eu^{2+} ions doped into CaF_2 produce efficient blue emission around 425 nm upon near-UV excitation, attributed to 5d-4f transitions in the europium activator, making it suitable for LED backlighting in televisions and displays. The host lattice, such as CaF_2, plays a crucial role in phonon management by minimizing non-radiative relaxation through its low phonon energy, which reduces thermal quenching and enhances emission efficiency at ambient temperatures.^[62]^[63] Scintillators rely on dopants to convert ionizing radiation, like gamma rays, into visible light via prompt emission, essential for radiation detection in medical imaging and security. A classic example is Tl^{+} doping in NaI crystals at concentrations around 0.1-0.3 mol%, where thallium acts as an activator trap, enabling high light yield (up to 38 photons per keV) for gamma detection through efficient electron-hole recombination. In this process, gamma rays create electron-hole pairs in the NaI host, which migrate to Tl^{+} sites, leading to rapid de-excitation and blue-green emission peaking at 415 nm with a decay time of about 230 ns.^[64]^[65]^[66] The underlying mechanisms in both phosphors and scintillators involve band-to-band excitation or impurity-trapped recombination, where dopants create localized states within the host's bandgap to capture excitons or charge carriers. In impurity-trapped recombination, electrons and holes are captured by dopant levels, followed by radiative decay, often accompanied by a Stokes shift—the energy difference between absorption and emission wavelengths—to prevent self-absorption and improve light extraction. Efficiency is quantified by quantum yield, with high-performance materials achieving values exceeding 80%, as seen in optimized activator-host systems where minimal phonon interactions preserve excited-state population.^[67]^[68]^[69] Prominent examples include Ce^{3+}-doped Y_3Al_5O_{12} (YAG:Ce), a yellow-emitting phosphor widely used in white LEDs for down-conversion of blue light from InGaN chips, achieving quantum yields near 90%. This garnet host provides robust phonon management, enabling stable performance in high-power displays and general lighting. For white LEDs using YAG:Ce, luminous efficacy up to 123 lm/W has been reported under typical operating conditions.^[70] For scintillators, Bi_4Ge_3O_{12} (BGO) serves as an intrinsic material but benefits from doped variants, such as Ce-doped BGO, which improves radiation resistance and timing resolution (faster decay time) but reduces light output, in positron emission tomography (PET) scanners for improved image quality in cancer detection.^[71] Development of such phosphors traces back to the 1950s, when rare-earth and transition-metal dopants were introduced in halophosphate hosts like Ca_5(PO_4)_3(F,Cl):Sb^{3+},Mn^{2+} for efficient white emission in fluorescent lamps, marking a shift toward energy-efficient lighting.^[72]^[73]^[74]

Other Applications

In Dielectrics

Dopants play a crucial role in modifying the dielectric properties of insulators, particularly in ferroelectric materials like barium titanate (BaTiO₃), where ions such as titanium at the B-site or aliovalent substitutions tune the permittivity and Curie temperature. In BaTiO₃, adjusting the Ti content or introducing similar transition metal ions shifts the phase transition temperature, enabling optimization for capacitor applications by enhancing the ferroelectric-paraelectric transition behavior. For instance, off-stoichiometric Ti incorporation can elevate the Curie temperature from approximately 120°C, improving thermal stability in high-temperature dielectrics.^[75] Rare-earth ions, such as yttrium or lanthanum, are also employed as dopants in BaTiO₃ to refine these properties, substituting at A- or B-sites to achieve higher permittivity values suitable for multilayer ceramic capacitors.^[76]^[77] In high-k dielectrics for complementary metal-oxide-semiconductor (CMOS) devices, rare-earth dopants like gadolinium, erbium, or ytterbium are incorporated into oxides such as hafnium oxide (HfO₂) to boost the dielectric constant and maintain stability at scaled dimensions. These dopants increase the effective permittivity from typical values around 20 for pure HfO₂ to over 30, while suppressing crystallization that could degrade performance in gate stacks. The enhancement arises from lattice distortion and improved band alignment, reducing interface traps in thin films. Additionally, in broader dielectric contexts, doping can elevate the relative permittivity dramatically; for example, undoped ceramics may exhibit k ≈ 10, whereas doped ferroelectrics like BaTiO₃ reach k > 1000 near the Curie point due to enhanced polarizability.^[78]^[79]^[80] Key effects of doping include polarization enhancement through local structural modifications and the creation of defects that enable charge trapping for memory applications. In HfO₂-based dielectrics, dopants like titanium introduce oxygen vacancies that facilitate electron trapping, improving charge retention in non-volatile memories without significantly increasing leakage. Polarization is amplified in ferroelectrics via dopant-induced dipole moments, as seen in yttrium-doped BaTiO₃, where the dielectric response strengthens due to altered ionic displacements. Specific examples illustrate these benefits: manganese doping in piezoelectric materials such as Pb(Mg₁/₃Nb₂/₃)O₃-PbZrO₃-PbTiO₃ ceramics enhances mechanical stability and temperature resilience of the dielectric properties, maintaining high electromechanical coupling up to elevated temperatures. In dynamic random-access memory (DRAM) gates, zirconium doping in HfO₂ stabilizes the tetragonal phase, yielding higher permittivity (k ≈ 40) and reduced leakage currents in ultrathin films (below 10 nm), critical for scaling beyond 10 nm nodes.^[81]^[76]^[82] Despite these advantages, challenges persist, particularly dopant segregation at grain boundaries, which leads to nonuniform dielectric performance in polycrystalline films. In oxide ceramics, segregating dopants like rare-earth ions create local variations in permittivity and increase scattering sites, potentially degrading overall capacitance uniformity. This phenomenon is pronounced in high-temperature processing, where diffusion drives accumulation at boundaries, necessitating controlled deposition techniques like atomic layer deposition to mitigate inhomogeneities.^[83]^[84]

In Superconductors

In high-temperature superconductors, particularly cuprates, chemical doping plays a crucial role in inducing and optimizing superconductivity by adjusting the carrier density in the CuO₂ planes. For instance, substituting strontium (Sr) for barium (Ba) in yttrium barium copper oxide (YBCO) modifies the hole concentration, which can enhance the critical temperature (T_c) by reducing Cu-O bond lengths and increasing covalency.^[85] This doping strategy shifts the electronic structure from an antiferromagnetic Mott insulator to a metallic state capable of superconductivity, with the optimal doping level occurring at approximately 0.16 holes per copper atom, where T_c reaches its maximum of up to 133 K.^[86] The carrier doping mechanism in cuprates involves introducing charge carriers that disrupt the antiferromagnetic order of the undoped parent compounds, enabling Cooper pair formation and zero-resistance transport. At underdoping levels below 0.16 holes per Cu, a pseudogap phase emerges, while overdoping suppresses T_c by increasing disorder and pair-breaking scattering.^[87] A seminal example is the discovery of superconductivity in La_{2-x}Sr_xCuO_4 by Bednorz and Müller in 1986, where Sr doping at x ≈ 0.15 yielded T_c ≈ 38 K, marking the breakthrough in high-T_c materials and earning the 1987 Nobel Prize in Physics.^[88] Beyond cuprates, doping enhances performance in other superconductors, such as magnesium diboride (MgB_2). Carbon doping introduces nanoscale impurities and defects that improve flux pinning, allowing the material to sustain higher magnetic fields and currents essential for practical applications, with critical current densities exceeding 10^5 A/cm² at 20 K.^[89] However, achieving effective doping faces challenges, including maintaining phase purity to avoid secondary non-superconducting phases and precise control of oxygen stoichiometry, which acts as an intrinsic dopant influencing carrier density and T_c.^[90] Post-1986 advancements have extended doping strategies to iron-based pnictide superconductors, discovered in 2008, where chemical substitutions like fluorine for oxygen in LaFeAsO or cobalt for iron in BaFe₂As₂ suppress magnetic order and induce superconductivity with T_c up to 55 K, offering new insights into multi-orbital mechanisms.^[91] These materials highlight the versatility of doping in tuning electronic correlations across diverse superconducting families.

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This chapter discusses epitaxial deposition by chemical vapor deposition (CVD) in which the silicon and dopant atoms are brought to the single crystal surface ...
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Molecular beam epitaxy growth and doping modulation of ...
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Neutron transmutation doping of silicon. I. Electrical parameters ...
Jul 1, 1980 · Thermal‐neutron transmutation doping of silicon produces phosphorus donors by the nuclear reaction 30Si(n,γ)31Si →31P+β−.
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[PDF] Chapter 8 Ion Implantation
Ion implantation, introduced in the mid-1970s, allows independent control of dopant profile and concentration, and is used for doping and other applications.
[32]
[PDF] Electrons and holes in pure Silicon
Jun 4, 2012 · Typical doping level ranges from 10. 14. /cm. 3 to. 10. 21. /cm. 3 ... Doped Semiconductors solid Page 78. Page 79. Note that the total doping ...
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[PDF] Doping Profiling - Georgia Institute of Technology
▫ SIMS is the most common doping profiling technique. ▫ Incident ions ... ▫ Capacitance-voltage measurements used for. ◇Doping profiling. ◇Flatband ...
[34]
[PDF] Chapter 11 Dopant profiling in semiconductor nanoelectronics 11.1 ...
In practice, separate p-doped and n-doped samples of this type have been utilized for calibration of dopant profiles. Fig. 11.5 shows an SCM image of a variably ...
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[PDF] C-V measurement for semiconductor junctions - arXiv
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[PDF] Achieving High Dopant Concentrations in Si - OSTI
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Autodoping Effects in Silicon Epitaxy - IOP Science
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N-Type Semiconductor - an overview | ScienceDirect Topics
Group III–V semiconductors are based on application of group VI atoms as donors and group II atoms as acceptors, while in such system group, IV atoms can act as ...
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Thermal donors in silicon-rich SiGe - AIP Publishing
We have investigated thermal donor formation at 450 °C in oxygen-rich SiGe with more than 1% Ge content by Hall measurements and infrared spectroscopy.
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p-type Semiconductor | Toshiba Electronic Devices & Storage ...
A p-type semiconductor is a group IV intrinsic semiconductor such as silicon (Si) doped with group III boron (B) or indium (In) as an impurity.
[41]
[PDF] NASA TN 0-7517
dp/dT _ -dpp/dT. (4). P. Mp. The ionization energy of boron in silicon is 0.045 eV, and most of the boron is ionized at temperatures well below room temperature ...
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Effect of local strain on single acceptors in Si | Phys. Rev. B
Jul 16, 2007 · Ry * = 0.045 eV is the effective Rydberg for a boron impurity in silicon. The last two terms represent the position of the resonance level ...
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Why aren't aluminum and nitrogen used as dopants in ...
Nov 27, 2021 · From an electrical standpoint, Boron is about 50% lower (0.045eV vs 0.067eV for Al) ionization energy than Aluminum in Silicon so makes a better ...
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[PDF] Equilibrium Carrier Concentrations Lesson - nanoHUB
The equations for the carrier concentrations for an n-type semiconductor, ND >> ni and NA = 0, can be simplified. Since ND >> ni , we can neglect ni in the ...Missing: partial | Show results with:partial
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Behaviour of the Fermi Energy - DoITPoMS
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Wafer-Scale, Sub-5 nm Junction Formation by Monolayer Doping ...
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Boron Doping in Next-Generation Materials for Semiconductor Device
Boron is one of the essential dopants for shallow doping in silicon because of its good diffusivity [3]. Boron doping has grabbed attention for several decades.
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Method to suppress boron penetration in P+ mosfets - Google Patents
With the growing practice of doping gates for MOSFETs with boron, problems have been encountered due to later diffusion of the boron into the active region.
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Hydrogen passivation of shallow-acceptor impurities in p-type GaAs
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Doped Insulator Lasers – solid-state lasers - RP Photonics
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[PDF] solid state lasers
The rare earth ions are natural candidates to serve as active ions in solid-state laser materials because they exhibit a wealth of sharp fluorescent transitions ...
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[PDF] Laser Basics - U.S. Particle Accelerator School
Jun 27, 2008 · The historic ruby laser. Invented in 1960 by Ted Maiman at Hughes Research Labs, it was the first laser. Ruby is a three-level system, so you ...
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[PDF] Chapter 7 Lasers
The first laser was indeed a solid-state laser: Ruby emitting at 694.3nm. [5]. Ruby consists of the naturally formed crystal of aluminum oxide (Al2O3) called ...
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Four-level and Three-level Laser Gain Media - RP Photonics
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Study of Nd 3+ ion as a Dopant in YAG and Glass Laser
The Nd laser incorporates a four-level system and consequently has a much lower pumping threshold than that of the ruby and other lasers. The upper laser ...
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https://www.rp-photonics.com/four_level_and_three_level_laser_gain_media.html
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Titanium–sapphire Lasers - RP Photonics
titanium–sapphire lasers are lasers based on a Ti:sapphire gain medium. They can be widely wavelength-tunable and/or generate femtosecond light pulses.What are Titanium–sapphire... · Pumping Options for Ti:sapphire
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Titanium-doped Laser Gain Media - RP Photonics
The Ti3+ doping concentration has to be kept low (typically 0.05% to 0.25%) because otherwise no good crystal quality is achievable.
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Difference between gas lasers, solid-state lasers, and ... - Keyence
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Modification of luminescence spectra of CaF2:Eu2+ - PubMed
CaF2:Eu(2+) is a well known phosphor having efficient excitation in the near ultraviolet (NUV) range. Phosphors with NUV excitation are required in newly ...
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Europium (II)-Doped CaF2 Nanocrystals in Sol-Gel Derived Glass ...
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[PDF] Validated Models for Radiation Response and Signal Generation in ...
mechanism for light emission is STE capture by a Tl dopant. (activator) followed ... doped NaI to investigate whether Tl doping can affect the electron ...
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[PDF] Scintillation Counters - MSU chemistry
Core-valence transition,. & conduction-valence trans. NaI – transition by Tl dopant. Note that the amount of excitation energy will be random, the energy ...<|separator|>
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Scintillator detectors for gamma-ray detection - Book chapter
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[PDF] Stable Down-Conversion Phosphors that Exploit a Large Stokes ...
May 8, 2012 · The well-known Ce3+ doped Y3Al5O12. (YAG:Ce) achieves high quantum efficiencies (∼90%) but affords broad yellow emission that must be combined ...
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[PDF] Impact of Stokes Shift on the Performance of Near-Infrared ...
However, reabsorption of emitted photons combined with non-unity quantum yield (QY) of the luminophores act as the main loss mechanism that can dramatically ...
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[PDF] Week 6: Ch. 8 Scintillation Counters - MSU chemistry
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Toward scatter-free phosphors in white phosphor-converted light ...
The luminous efficacy and packaging efficiency of the Y3Al5O12:Ce3+ large micro-size cube phosphor-based pc-LEDs were 123.0 lm/W and 0.87 at 4300 K under 300 mA ...
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Ce 3+ phosphors for white LEDs via efficient chemical vapor ...
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Positron Emission Tomography: Current Challenges and ... - NIH
Modern scintillators produce shorter and more intense light pulses compared with earlier crystals, such as BGO (bismuth germanate), which used to dominate PET- ...
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[PDF] Basic Research Needs for Solid-State Lighting - DOE Office of Science
Photon conversion materials themselves have a long history. One common set of photon conversion materials is phosphors used for fluorescent lighting or displays ...
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Insights into the Impact of Yttrium Doping at the Ba and Ti Sites of ...
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Fabrication of La3+ doped Ba1−xLaxTiO3 ceramics with improved ...
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Design of Higher-k and More Stable Rare Earth Oxides as Gate ...
High permittivity (k) gate dielectric films are widely studied to substitute SiO2 as gate oxides to suppress the unacceptable gate leakage current when the ...
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Solution processed rare-earth doped high-k dielectrics for low ...
Aug 15, 2023 · In this work, we present a universal strategy by using rare-earth (RE) elements (Y, Er and Yb) as dopants to improve the dielectric properties ...
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[PDF] Structural and electrical properties of Barium Titanate (BaTiO3) and ...
Permittivity at Tc was remarkedly decreased for Nd-doped BaTiO3 as compared to undoped BaTiO3. Maximum permittivity for pure BaTiO3 about 8500, at curie ...
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Ab initio study of charge trapping and dielectric properties of Ti-doped
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Piezoelectric properties and temperature stability of Mn-doped Pb ...
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Dopant-segregation to grain boundaries controls electrical ...
Sep 15, 2021 · Our work showcases the correlation between microstructure and electrical conductivity, providing opportunities for future microstructural optimization.
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Grain boundary structural transformation induced by co-segregation ...
Sep 15, 2022 · In insulating materials, the dopant solubility limit is considerably low in general, and the dopants often segregate to grain boundaries (GBs) ...Missing: dielectrics | Show results with:dielectrics
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[PDF] Extremely Overdoped Superconducting Cuprates via High ... - HAL
Dec 2, 2021 · The higher Tc that often, but not always, occurs with Sr is understood as the decrease in Cu-O bond lengths (i.e., covalency) resulting from the ...
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Cuprate high-Tc superconductors - ScienceDirect.com
The maximum critical temperatures (Tc) of up to 145 K occur at an optimal hole-doping near p ∼ 0.16 where p is the number of doped holes per Cu atom.
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Unusual behavior of cuprates explained by heterogeneous charge ...
Jan 25, 2019 · The superconducting transition temperature is highest at an optimal level of p ≈ 0.16 doped holes per planar CuO2 unit, and therefore, the phase ...
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[PDF] J. Georg Bednorz and K. Alex Müller - Nobel Lecture
In our Lecture, we take the opportunity to describe the guiding ideas and our effort in the search for high-T, superconductivity. They directed the way from.
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High Trapped Fields in C-doped MgB2 Bulk Superconductors ...
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Manipulating high-temperature superconductivity by oxygen doping ...
May 11, 2022 · The loss of oxygen in the Bi-2212 flake under positive gate voltages can lead to a depletion of the hole concentration, resulting in a rapid ...
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Recent advances in iron-based superconductors toward applications
This article reviews recent progress in the technical applications (bulk magnets, thin films, and wires) of IBSCs in addition to their fundamental material ...