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SEM

A (SEM) is a type of that forms images of a specimen's surface by raster scanning it with a finely focused beam of high-energy electrons, detecting signals such as for topographic detail and backscattered electrons for compositional contrast. Unlike transmission electron microscopes, SEMs excel at providing three-dimensional-like images with resolutions down to a few nanometers and exceptional , enabling visualization of surface features that optical microscopes cannot resolve. The foundational principles of SEM were developed in the 1930s, with Max Knoll demonstrating the scanning concept in and advancing early prototypes, though practical instruments emerged postwar under Charles Oatley at Cambridge University, culminating in the first commercial model, the Stereoscan, in 1965. These instruments revolutionized materials characterization by allowing non-destructive surface analysis across scales from micrometers to nanometers, integrating techniques like () for elemental mapping. SEM finds broad application in fields including for fracture analysis and microstructure examination, for uncoated or low-vacuum imaging of hydrated samples, and forensics for identification, with ongoing advancements in variable-pressure modes and automation enhancing accessibility and throughput.

Science and Technology

Scanning Electron Microscopy

Scanning electron microscopy (SEM) produces high-resolution images of a sample's surface by scanning a focused of s across it, detecting signals such as for topographic detail and backscattered electrons for compositional contrast. The technique achieves resolutions typically from 1 to 10 nanometers, surpassing optical microscopy limits due to the shorter of s compared to visible . Interaction volumes range from 0.1 to 5 micrometers in depth, depending on (usually 0.5–30 keV) and sample material, enabling three-dimensional-like imaging through signal intensity variations. The foundational concept emerged in 1935 when Max Knoll demonstrated an electron beam scanner for contrast in materials. In 1937, constructed an early scanning prototype aimed at high-resolution atomic , though limited by then-available technology. Significant advancements occurred in the at the , where Dennis McMullan and colleagues developed instruments yielding usable images by 1960, leading to the first commercial SEM from Cambridge Scientific Instruments in 1965. Commercialization accelerated in the 1960s, with ongoing refinements in electron sources (e.g., field emission guns since the 1970s) improving beam brightness and resolution to sub-nanometer levels in modern systems. Instrumentation includes an (tungsten filament, LaB6, or field emission) to generate electrons, electromagnetic lenses for focusing into a fine probe (down to 1 nm diameter), deflection coils for raster scanning, and detectors such as Everhart-Thornley for or solid-state for backscattered electrons. Operation requires high vacuum (10^{-5} to 10^{-7} ) to minimize by residual gas, though variable pressure or environmental SEMs allow imaging at 0.1–10 for hydrated or insulating samples by reducing charging artifacts. Stage accommodates samples up to several centimeters, with precise control for tilt and translation to capture varied perspectives. Sample preparation ensures conductivity and stability under vacuum and beam exposure. Non-conductive specimens, common in and , receive thin conductive s (e.g., 5–20 nm or carbon via ) to prevent charging and enhance emission. Biological samples undergo fixation, , critical point , and to preserve structure without collapse. Beam-sensitive materials like polymers may require low-voltage imaging (0.5–3 keV) or cryo-SEM, freezing samples in or for fracture and under vacuum. Volatile or wet samples demand to avoid chamber contamination, with magnetic samples fixed to prevent movement. Imaging modes include secondary electron detection for surface topography, revealing features like fractures or textures; backscattered electron for atomic number contrast, distinguishing elements without elemental analysis; and (EDS) integration for chemical mapping via characteristic X-rays. detects light emission for or studies, while electron channeling patterns assess orientation. Magnifications span 10x to over 1,000,000x, with field widths from millimeters to nanometers. Applications span for fracture analysis and characterization, for cellular ultrastructure, for mineral textures, and forensics for like . In , SEM inspects circuit features at nanometer scales, supporting standards. Recent extensions include via serial sectioning or milling combined with SEM (FIB-SEM) for volumetric imaging. Advantages include deep (100–1000 times optical), versatile signal detection, and compatibility with , but limitations involve vacuum constraints excluding live specimens without specialized setups, potential beam damage to organics, and artifacts from preparation like coating obscuring fine details. remains inferior to for internal structures, though SEM excels in surface detail.

Mathematics and Statistics

Structural Equation Modeling

Structural equation modeling (SEM) is a multivariate statistical technique that combines elements of and path analysis to specify, estimate, and test hypothesized relationships among observed and latent variables. It allows researchers to model complex causal structures by accounting for measurement error and interdependencies, representing theories as systems of linear equations where latent constructs—unobserved variables inferred from multiple indicators—drive relationships. SEM is particularly suited for testing theoretical models in fields like and , where direct observation of constructs such as or attitudes is infeasible. The methodology's foundations trace to Charles Spearman's in 1904, which decomposed observed correlations into underlying factors, and Sewall Wright's path analysis introduced in 1918 to quantify causal pathways in . Modern SEM emerged in the 1970s through Karl G. Jöreskog's development of the LISREL framework, enabling of covariance structures and of latent variables with recursive and non-recursive models. Subsequent advancements by researchers like Peter M. Bentler (EQS software, 1980s) and Bengt Muthén (multilevel extensions, 1990s) expanded its scope to handle hierarchical data and longitudinal processes, such as latent growth curves. SEM decomposes into a , which links observed indicators to latent variables via factor loadings (e.g., y = \Lambda_y \eta + \epsilon for endogenous latents and x = \Lambda_x \xi + \delta for exogenous), and a structural model, which defines regressions among latents (e.g., \eta = B \eta + \Gamma \xi + \zeta). Model specification requires theoretical justification for parameters, ensuring where the number of free parameters does not exceed available information from the . Estimation primarily uses maximum likelihood () assuming multivariate normality for efficient, consistent results, with alternatives like (GLS) or asymptotically distribution-free () methods for non-normal data, though the latter demands samples exceeding 1,000 for stability. Fit assessment involves chi-squared tests for exact fit, supplemented by indices like RMSEA (values ≤0.06 indicate close fit) and CFI (≥0.95 for good fit), but these can be inflated in large samples or misspecified models. Key assumptions include multivariate of residuals, large sample sizes (typically N > 200, ideally >400 for complex models), , no omitted variables biasing paths, and proper model identification to avoid under- or over-specification. Violations, such as non- or , inflate Type I errors and bias standard errors; robust estimators like Satorra-Bentler corrections mitigate this but reduce power. Popular software as of 2023 includes proprietary packages like LISREL (for covariance-based SEM), Mplus (flexible for mixtures and growth models), and (integrated with ), alongside open-source options such as lavaan in and SmartPLS for partial variants suited to smaller samples or formative constructs. Applications encompass mediation analysis (e.g., testing intervening latent effects), moderation via interactions, and multi-group comparisons for invariance across populations, with empirical use surging in the following accessible software. Limitations include the problem, where mathematically identical models yield identical fit but differ substantively, necessitating theory-driven selection; to specification errors, which propagate biases; and challenges in causal claims from , as correlations do not imply directionality without temporal or experimental controls. Critics note overuse in non-experimental contexts leads to overreliance on fit indices masking omitted variables or lower-order effects, urging integration with analyses and replication.

Standard Error of the Mean

The of the (SEM) quantifies the variability of sample means drawn from the same , representing the standard deviation of the of the sample . It provides a measure of the precision with which the sample estimates the population , decreasing as sample size increases due to the averaging effect that reduces random error. The formula for the population SEM is \sigma / \sqrt{n}, where \sigma is the population deviation and n is the sample . When \sigma is unknown, it is estimated using the sample standard deviation s, yielding s / \sqrt{n}. This expression derives from the variance of the sample under the assumption of and identically distributed (IID) observations with finite variance. The variance of the sample mean \bar{X} is \mathrm{Var}(\bar{X}) = \mathrm{Var}\left( \frac{1}{n} \sum_{i=1}^n X_i \right) = \frac{1}{n^2} \sum_{i=1}^n \mathrm{Var}(X_i) = \frac{1}{n^2} \cdot n \sigma^2 = \frac{\sigma^2}{n}, assuming and \mathrm{Var}(X_i) = \sigma^2 for all i. Taking the yields the SEM as \sigma / \sqrt{n}. SEM differs from the sample standard deviation, which measures data dispersion around the sample , whereas SEM assesses how closely repeated sample means cluster around the true . In applications, SEM underpins confidence intervals for the (e.g., \bar{x} \pm t \cdot \mathrm{SEM} for small samples) and t-tests, enabling inference about parameters from sample . Violations of IID assumptions, such as dependence or non-constant variance, inflate the true SEM beyond the formula's estimate, potentially leading to overly narrow intervals and invalid inferences.

Standard Error of Measurement

The standard error of measurement (SEM) quantifies the precision of individual scores by estimating the standard deviation of measurement errors around a person's true score in (CTT). In CTT, an observed score X decomposes into a true score T and random error E, such that X = T + E, where E has a of zero and is uncorrelated with T. The SEM represents the standard deviation of this error term, \sigma_E, which arises from factors like construction, administration conditions, and respondent variability, rather than systematic biases. The formula for SEM derives from the reliability coefficient \rho_{XX}, defined as the proportion of observed score variance attributable to true score variance: \rho_{XX} = \sigma_T^2 / \sigma_X^2, where \sigma_X is the standard deviation of observed scores. Thus, error variance is \sigma_E^2 = \sigma_X^2 (1 - \rho_{XX}), and SEM = \sigma_X \sqrt{1 - \rho_{XX}}. Reliability \rho_{XX} is typically estimated via methods like test-retest, parallel forms, or (e.g., ), with values ranging from 0 (no reliability) to 1 (perfect reliability); SEM decreases as \rho_{XX} increases, equaling zero only for flawless and \sigma_X for complete unreliability. SEM enables construction of confidence intervals around an observed score to infer the likely true score range, assuming errors are normally distributed. For instance, approximately 68% of repeated measurements fall within \pm 1 SEM of the true score, and 95% within \pm 1.96 SEM. Consider a test with \sigma_X = 15 and \rho_{XX} = 0.81: SEM = $15 \sqrt{1 - 0.81} = 15 \times 0.45 = 6.75; for an observed score of 100, the 95% for the true score is roughly 100 ± (1.96 × 6.75), or 86.8 to 113.2. This interval reflects measurement imprecision, distinct from captured by the of the mean. In psychometrics, SEM informs decisions like score banding in (e.g., educational assessments) and evaluating change scores, where the minimal detectable change is often 1.96 × √2 × SEM for reliable pre-post differences. Basic CTT assumes constant SEM across score levels, but extensions like conditional SEM adjust for varying reliability by ability, using or stratified estimates for more accurate inference at extremes. Empirical studies emphasize SEM's superiority over raw reliability for assessing score , as it directly scales error magnitude to the test's standard deviation.

Business and Marketing

Search Engine Marketing

Search engine marketing (SEM) encompasses paid advertising strategies designed to promote websites in search engine results pages (SERPs), primarily through (PPC) models where advertisers bid on keywords relevant to user queries. In this system, ads appear above or alongside results, with charges incurred only upon user clicks, enabling targeted exposure to high-intent searchers. Unlike search optimization, SEM relies on auction-based platforms where ad rank is determined by bid amounts, ad quality scores, and relevance factors, fostering competition among advertisers for visibility. The practice originated in the late 1990s with the advent of PPC advertising; IdealGo, later renamed GoTo.com, launched the first PPC model in 1998, charging based on clicks rather than flat fees. introduced AdWords in October 2000, revolutionizing the field by integrating contextually relevant ads into search results and introducing quality-based scoring to reward relevant content over sheer bidding power. This innovation spurred rapid growth, with SEM evolving alongside search engine algorithms and expanding to include display networks, shopping ads, and remarketing by the . Dominant platforms include , which commands approximately 90.4% of global as of September 2025, enabling advertisers to reach billions of daily queries. (formerly Bing Ads), leveraging 's engine, holds about 4.08% worldwide but performs stronger in certain demographics, such as older users in the U.S., where it captures around 7.56% of searches. Other platforms like Yahoo! (1.46% share) integrate with these ecosystems but contribute marginally to overall SEM volume. SEM effectiveness stems from its ability to deliver immediate from users exhibiting purchase , with U.S. search ad spending reaching $137 billion in , representing 40% of total digital ad expenditures. Annual growth in SEM investment averages 8%, driven by measurable outcomes like click-through rates (CTRs) and conversions, though (ROI) varies by industry—often exceeding 200% in but lower in saturated sectors due to escalating cost-per-click () rates. A McKinsey indicates AI-enhanced SEM campaigns yield an average 20% ROI uplift through better keyword targeting and bid optimization. However, challenges include ad fatigue, rising competition inflating CPCs (averaging $1–$2 for broad keywords), and reliance on platform algorithms, which can penalize low-quality ads via reduced visibility. Key SEM tactics involve to identify high-volume, low-competition terms; crafting compelling ad copy with extensions like site links and callouts; and optimizing landing pages for s to improve quality scores and lower costs. Bidding strategies range from manual to automated rules incorporating for real-time adjustments. Performance tracking relies on metrics such as impression share, value, and attribution models, with tools like providing granular data to refine campaigns. Regulatory considerations include compliance with data privacy laws like GDPR and transparency in ad disclosures to mitigate risks, estimated at 10–20% of traffic in some studies. Despite these hurdles, SEM's causal link to —evidenced by controlled A/B tests showing 2–3x higher rates versus display ads—positions it as a core channel for performance-driven .

Other Uses

Places

Sem is a village in Municipality, county, , situated approximately 5 kilometers west of city center. The area features rural landscapes and historical sites, including remnants linked to Viking-era settlements, such as a discovered near a former royal estate dating back to at least 1834. Sem served as the administrative center for a former municipality of the same name, which encompassed villages like Barkåker and covered about 102 square kilometers before its merger. The village's name derives from roots associated with regional place names in during the Iron and Viking Ages.

People

Sem Benelli (August 10, 1877 – December 18, 1949) was an , essayist, and librettist whose works included dramatic tragedies staged internationally in the early . Georges Goursat (July 10, 1863 – 1934), professionally known as Sem, was a prominent caricaturist and who depicted the elite of Parisian society through satirical drawings published in magazines and books from the 1890s onward. The given name Sem, derived from the Hebrew Shem meaning "name" or "renown," has also been used by contemporary athletes such as Dutch footballer Sem Verbeek, but these figures lack the historical prominence of earlier bearers.

Organizations and Societies

The Society for (SEM), founded in 1955, is a professional organization dedicated to the interdisciplinary study of music as a cultural phenomenon, encompassing research, performance, and pedagogy across global traditions. It hosts an annual meeting attracting over 900 participants, featuring scholarly presentations, workshops, and performances, and publishes the journal Ethnomusicology. The Society for Experimental Mechanics (SEM), established in , focuses on advancing experimental methods in mechanics, including dynamic testing, , and validation of engineering designs through techniques like digital image correlation and strain gage applications. Comprising engineers and scientists, it organizes conferences, publishes journals such as Experimental Mechanics, and supports student chapters to foster early-career development in . The Society for Economic Measurement (SEM), formed to promote rigorous in , emphasizes advanced statistical and econometric tools for measuring economic variables, including , , and policy impacts. It facilitates research dissemination via conferences and the journal Journal of Economic Measurement, prioritizing empirical validation over theoretical abstraction alone. The Swedish Evangelical Mission (SEM), originating in the 19th century as a low-church movement within , operates as an independent missionary organization emphasizing , social service, and ecumenical cooperation in regions including , , and . By 2023, it maintained partnerships with over 20 national churches and focused on projects alongside faith-based outreach.