Taking Measurement Technology to the Quantum Level
Nanoscale dimensions produce new materials properties that challenge measurement technology. Metrology must become more capable of imaging at atomic dimensions and measuring new materials with quantum-level properties.
Alain C. Diebold, College of Nanoscale Science and Engineering, Albany, N.Y., www.cnse.albany.edu -- Semiconductor International, 8/1/2009
Quantum phenomena are present in every device that uses semiconductor materials, from ICs to photovoltaics to solid-state lighting. The nanoscale dimensions of current and future ICs are driving measurement science and technology into quantum-level metrology (QLM). The term "nanoelectronics" has applied to ICs for several generations, and it is readily apparent when one reviews the search for nanoelectronics that is "Beyond CMOS." The goal of photovoltaics research is typically to increase the quantum efficiency of turning light into electricity. With solid-state lighting, the goal is improving the efficiency of producing light; i.e., using less electricity.
The 2009 International Technology Roadmap for Semiconductors (ITRS) will be completed and available on the Internet by year's end.1 The ITRS provides an overview of the latest information about future transistor and metrology technology. Rapid advances in IC technology are the result of nanoscale materials properties. Transistors use stress enhancement of carrier mobility and new higher-dielectric-constant materials, while future transistors are expected to use new materials in the nanoscale channels. The gate length is so short that we are approaching transistors that operate in the manner described by Lundstrom's nanotransistor, where the drive current is a function of carrier velocity and not gate length.2 The higher the drive current, the faster the IC switches. The measurement of film thickness and transistor gate length (i.e., critical dimension or CD) is required to measure features with atomic-level precision. Sidewall roughness requirements for the transistor gate are also driven to atomic levels by their impact on device properties. New processes also drive metrology, and processes such as dual patterning will be considered. Phenomena such as quantum confinement change materials properties for new substrate materials such as ultrathin SOI.
The semiconductor industry also provides a guide to the research needs for Emerging Research Materials and Devices in the ITRS.1 Potential new materials and devices for the switch that replaces the transistor when it can no longer be scaled are described as being "Beyond CMOS." New materials such as graphene provide insight into the challenges associated with QLM R&D. Many of the faculty at the College of Nanoscale Science and Engineering (CNSE) of the University at Albany are working in the area of QLM. This is highlighted by the nanoelectronics-associated centers led by the college. One of the Nanoelectronics Research Initiative (NRI) Centers, the Institute for Nanoelectronics Discovery and Exploration (INDEX) is headquartered at CNSE. QML R&D requires the most advanced measurement and process capability, which makes CNSE the perfect location, since we have all of the most advanced immersion, e-beam and imprint lithography, as well as process capability to fabricate working devices at the most leading-edge feature sizes.
Advanced CMOS examples
CD measurement requirements are challenged by the need for line shape measurement at increasingly small linewidths. CD measurement is approaching atomic dimensions. When the DRAM half-pitch reaches 20 nm, CD measurement uncertainty must be ~0.3 nm. The requirement to control linewidth roughness comes from the need to control leakage current. The recent introduction of dual patterning makes a difficult situation worse, due to the two sets of linewidths and line shapes. The process steps associated with dual patterning (for a positive resist) are shown in Figure 1, and spacer-based dual patterning in Figure 2.
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2. Spacer-based dual patterning creates matching linewidths and line shapes. |
Future generations of transistors will continue to use stress enhancement of carrier mobility. Several methods are being investigated at CNSE Engineering, including Raman microscopy, photoreflectance and X-ray diffraction (XRD). Stress changes silicon's crystal lattice (strain), changing its electronic band structure, phonon dispersion, and thus its optical response. The stress in a silicon or SiGe structure can be determined from the shift in the optical phonons measured by Raman microscopy. Professor Robert Geer's group at CNSE is pushing the spatial resolution of scanning Raman microscopy for local strain metrology through the use of so-called "tip-enhanced" Raman or nano-Raman. X-ray diffraction is widely recognized as a means of measuring the strain in silicon and SiGe. Professor Richard Matyi's group at CNSE is investigating the use of in-plane XRD. When this is combined with traditional XRD, the full 3-D lattice strain can be measured. My group is investigating photoreflectance. This method measures the change in the energy of the critical points in the optical response of silicon. One can calculate the stress in the silicon lattice using the energy shift. The optical response is directly related to the electronic band structure of silicon.
Ultrathin SOI and quantum confinement
One interesting example of QLM is that of film thickness measurement for ultrathin SOI. Ultrathin SOI is listed as a material for future ICs in the 2008 ITRS. The changes in materials properties of ultrathin silicon films include quantum confinement. Use of the bulk dielectric function results in as much as a 20% error for 2 nm SOI films, with the origin of film thickness measurement error being the change in silicon's dielectric function as film thickness decreases.3 Dielectric function and refractive index are equivalent expressions of a material's optical response. Dielectric functions are complex, and the dielectric function's imaginary part is an expression of the absorption of light. The values of the dielectric function depend on the wavelength of light. Knowledge of quantum mechanical properties is essential to understanding optical properties.
The dielectric function can be calculated from the band structure. At certain places in the band structure — known as critical points — there is a high probability of light absorption. Two important critical points in the silicon band structure are the E1 and E2 critical points. The E1 CP occurs in the bands along (111) directions in the silicon lattice and the E2 CP occurs along the (100) direction. Although the values of the dielectric function of bulk silicon have been available for some time, the optical properties of nanoscale films, wires and dots are just beginning to be understood. It is the E1 CP that shifts energy due to quantum confinement when the thickness of the silicon film shrinks below 10 nm. The particle in a box problem we encountered in quantum mechanics courses provides a good start at understanding this quantum confinement. The interesting aspect of this phenomenon is that the E1 CP has a strong excitonic character. Excitons are electron-hole pairs. The E2 CP does not have an excitonic character, and does not shift energy for the films we have studied. We are researching the nature of these excitonic transitions and the impact of nanoscale dimensions on bound excitons and optical transitions that experience excitonic enhancement (Fig. 3).
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3. Shift in the dielectric function of silicon with film thickness. |
Beyond CMOS materials
Research into new materials such as graphene, a single layer of graphite, is a striking example of quantum-level metrology.4 The s and two of the three p atomic orbitals of carbon hybridize into an in-plane set of sp2 orbital that strongly bonds to adjacent carbon atoms in a hexagonal arrangement (Fig. 4). The remaining p orbitals form π bands above and below the plane of the graphene layer. The electrons move through the π bands very easily, resulting in a very high mobility for carriers (>100,000 cm2/V-sec) in graphene at low temperatures. Charge carriers in graphene are so different from electrons and holes in semiconductors that they are referred to as Dirac Fermions. The velocity of carriers in graphene is ~1/300 the speed of light, and carriers do not propagate with an effective mass as they do in semiconductors.5 Almost every aspect of graphene research provides an interesting new QLM.
Understanding how to "see" graphene layers requires that we invoke quantum phenomena. It is well known that one can see a single layer of graphene on a 300 nm thick SiO2 layer on silicon. The magic 300 nm thickness gives just the right optical properties to see graphene in white light. Curiously, graphene's optical properties can be modeled with the same wavelength independent complex refractive index as graphite. One can assume that a graphene single-layer thickness is the distance between the above and below plane π orbitals, i.e., thickness = 0.34 nm.6, 7 The wavelength-independent, complex refractive index of graphite is
n = 2.6 - 1.3i
in the wavelength range 400–750 nm.6 Thus the contrast dependence with SiO2 film thickness is a result of the wavelength dependence of the SiO2 reflectivity. The optical properties of graphene are defined solely by the fine structure constant,7
α = e2/hc ≈ 1/137
Frequently, graphene samples have more than one layer of carbon atoms. Although these layers are attached by van der Waals attraction, the electrical properties of the graphene depend on the number of layers. Professor Geer's group uses Raman spectroscopy to determine the number of graphene layers using the 2-D band. The 2-D band is not a typical single phonon transition. The quantum mechanical picture of the 2-D band is that of a two-phonon, resonant Raman process involving the electronic π band. This makes the 2-D band sensitive to the changes in band structure due to an increase in the number of graphene layers.8 The number of graphene layers can also be determined using low-energy electron microscopy (LEEM). The electron reflectivity from graphene shows quantized oscillations due to quantum well (QW) resonances. When the LEEM electron energy matches one of the QW states, the electron transmits through the film, reducing the reflectivity.9,10 In the INDEX Center, Robert Hull's efforts include LEEM of graphene and other Beyond CMOS materials.
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5. High-resolution TEM imaging of differences in tri-layer graphene stacking patterns. (Source: Florence Nelson, CNSE) |
Another challenge is determining the capabilities of transmission electron microscopy (TEM). Simulations provide a key means of understanding TEM. Graduate student Florence Nelson has shown that high-resolution TEM is capable of imaging differences in the stacking patterns of tri-layer graphene (Fig. 5).
Electrical measurements reflect the unusual quantum properties of graphene. Graphene exhibits a quantum Hall effect and the very unusual Berry phase correction to the semi-classical description of carrier transport. Standard metrology of carrier dynamics includes measurement of the mobility and conductance of graphene. The method used for measuring carrier density, electrical resistivity (inverse of conductance), and the mobility of carriers in semiconductors and graphene is the Hall effect. The Hall effect is a small transverse voltage that occurs when a magnetic field is applied to a semiconductor layer carrying a current (Fig. 6). This method allows independent determination of carrier density and mobility.11 The standard theoretical description of carrier dynamics is a semi-classical, quantum mechanical description.
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6. Depiction of the Hall effect, showing the small transverse voltage produced when a semiconductor layer carrying a current is exposed to a magnetic field. |
An important discovery was that two-dimensional quantum wells in semiconductor structures exhibit a quantum Hall effect.12 The quantum Hall conductivity, σ, takes on either integer or rational fractional values at very low temperature and high magnetic field. The fractional Hall effect in semiconductors has been attributed to electron-electron interactions in the 2-D electron gas of semiconductor structures. Thus, the carrier density plays an important role in the quantum Hall effect. Philip Kim, Horst Stormer and co-workers at Columbia University have shown that graphene has a half-integer dependence to its quantum Hall effect. It also has the Berry phase correction to the semi-classical quantum mechanical description to its carrier transport.11 Berry first described a geometric phase factor as a correction to semi-classical quantum mechanics.12 The unusual 2-D nature of single-layer graphene and its honeycomb arrangement of carbon atoms with sp2 hybridized orbital results in an ideal system for observation of nanoscale quantum phenomena. Kim is a member of the INDEX Center.
Wei Wang, a professor at CNSE and member of the INDEX Center, has reviewed the conductance of multilayer and ribbon-shaped graphene and described the contributions to the electron mean free path.13 One key message is that the graphene's properties depend on the substrate below it. It is also clear that the nanoribbon shape of real pieces of graphene alter the properties associated with large pieces of graphene. Some of these changes come from phonon scattering. For example, the mean free path of carriers in graphene is reduced by phonon scattering. There are two types of phonon scattering, acoustic phonon scattering (AP) and remote interfacial phonon (RIP) scattering in nanoribbons. The RIP contribution comes from the substrate below the graphene.
Similar to many of the functional materials used in modern nanoelectronic devices, graphene's properties are extremely sensitive to process conditions and history. This represents an additional metrology challenge where the functional integrity of a graphene device or interconnect component must be confirmed throughout multiple process or integration steps. Lee and Geer have shown recently that substrate processing (e.g., plasma cleaning) can induce electrostatic doping of subsequently deposited graphene via Raman microscopy. Geer's group has also shown that sequential exposure of graphene to electron irradiation and oxygen can lead to substantial electrostatic doping (indicated by a substantial narrowing of the Raman G-band). This is consistent with other INDEX research at Columbia (Kim and Heinz) and highlights the ever-increasing role played by QLM for post-CMOS devices and architectures.
The extension of CMOS, and R&D of Beyond CMOS technology, provides many examples of QLM. Nanoscale dimensions result in new materials properties that challenge measurement technology. Metrology methods must become more capable of imaging at atomic dimensions and measuring new materials with quantum-level properties.
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Quoting from yr article 'Charge carriers in graphene are so different from electrons and holes in semiconductors that they are referred to as Dirac Fermions'.
Are you serious! you allude to this but where's the references. it's 'airey fairey' - just conjecture.
vincent jakomin - 8/26/2009 2:49:02 PM CDT
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