Graduate Programs in Materials Science and Engineering

Master of Science Degree

Candidates for the Master of Science degree in Materials Science and Engineering will follow a program of study formulated in consultation with and approved by a faculty adviser. Thirty points of credit are required at a minimum.

The following five courses (15 points) are required for the degree:

18 points:
   MSAE E4100: Crystallagraphy
   MSAE E4200: Theory of crystalline materials
   MSAE E4201: Materials thermodynamics and phase diagrams
   MSAE E4202: Kinetics of transformations in materials
   MSAE E4206: Electronic and magnetic properties of solids
   MSAE E4215: Mechanical behavior of structural materials

If a candidate has already taken one or more of these courses at Columbia University, substitutions from the Type I Elective list may be approved.

The remaining 12 points will be chosen from elective courses, 6 points of which must be Type I and 6 points of which may be Type I or Type II:

Type I Electives:
   MSAE E4090: Nanotechnology
   MSAE E4101: Structural analysis of materials
   MSAE E4102: Synthesis and processing of materials
   MSAE E4132: Fundamentals of polymers and ceramics
   MSAE E4250: Ceramics and composites
   MSAE E4260: Electrochemical materials and devices: from structure to performance
   MSAE E4301: Materials science laboratory
   MSAE E4990: Special topics in materials science and engineering
   MSAE E6085: Computing the electronic structure of complex materials
   MSAE E6091: Magnetism and magnetic materials
   MSAE E6225: Techniques in X-ray and neutron diffraction
   MSAE E6229: Energy and particle beam processing of materials
   MSAE E6230: Kinetics of phase transformations
   MSAE E6251: Thin films and layers
   MSAE E6273: Materials science reports
   MSAE E8235: Selected topics in materials science
   MSAE E4000-, 6000- or 8000-level courses not listed here

Type II Electives:
   BMEN E4300: Solid biomechanics
   BMEN E4301: Structure, mechanics, and adaptation of bone
   BMEN E4501: Tissue engineering, I
   APPH E4100: Quantum physics of matter
   APPH E4110: Modern optics
   APPH E4130: Physics of solar energy
   APPH E6081: Solid state physics, I
   APPH E6082: Solid state physics, II
   ELEN E4301: Intro to semiconductor devices
   ELEN E4411: Fundamentals of photonics
   ELEN E4944: Principles of device microfabrication
   EAEE E4001: Industrial ecology of earth resources
   EAEE E4160: Solid and hazardous waste management
   ENME E4113: Advanced mechanics of solids
   ENME E4114: Mechanics of fracture and fatigue
   ENME E4608: Manufacturing processes
   CHEE E4252: Intro to surface and colloid chemistry
   CHEE E4530: Corrosion of metals
   CHEN E4620: Intro to polymers and soft materials
   CHEN E4640: Polymer surfaces and interfaces
   CHEM GU41680: Materials chemistry
   MECE E4211: Energy sources and conversion
   APMA E4101: Intro to dynamical systems
   APMA E4200: Partial differential equations
   APMA E4300: Intro to numerical methods
   APMA E4400: Intro to biophysical modeling

Columbia Video Network (CVN) students may have their programs approved by faculty. Special reports (3 points) are required of CVN students.

All degree requirements must be completed within five years. A candidate is required to maintain at least a 2.5 GPA. Applicants for admission are required to take the Graduate Record Examinations.

Doctoral Program

At the end of the first year of graduate study in the doctoral program, candidates are required to take a comprehensive written qualifying examination, which is designed to test the ability of the candidate to apply course work in problem solving and creative thinking. The standard is first-year graduate level. There are two four-hour examinations over a two-day period.

Candidates in the program must take an oral examination within one year of taking the qualifying examination. Within two years of taking the qualifying examination, candidates must submit a written proposal and defend it orally before a Thesis Proposal Defense Committee consisting of three members of the faculty, including the adviser. Doctoral candidates must submit a thesis to be defended before a Dissertation Defense Committee consisting of five faculty members, including two professors from outside the doctoral program. Requirements for the Eng.Sc.D. (administered by the School of Engineering and Applied Science) and the Ph.D. (administered by the Graduate School of Arts and Sciences) are listed elsewhere in this bulletin.

Areas of Research

Materials science and engineering is concerned with synthesis, processing, structure, and properties of metals, ceramics, polymers, and other materials, with emphasis on understanding and exploiting relationships among structure, properties, and applications requirements. Our graduate research programs encompass projects in areas as diverse as polycrystalline silicon, electronic ceramics grain boundaries and interfaces, microstructure and stresses in microelectronics thin films, oxide thin films for novel sensors and fuel cells, optical diagnostics of thin-film processing, ceramic nanocomposites, electrodeposition and corrosion processes, structure, properties, and transmission electron microscopy and crystal orientation mapping, magnetic thin films for giant and colossal magnetoresistance, chemical synthesis of nanoscale materials, nanocrystals, carbon nanotubes, nanostructure analysis using X-ray and neutron diffraction techniques, and electronic structure calculation of materials using density functional and dynamical mean-field theories. Application targets for polycrystalline silicon are thin film transistors for active matrix displays and silicon-on-insulator structures for ULSI devices. Novel applications are being developed for oxide thin films, including uncooled IR focal plane arrays and integrated fuel cells for portable equipment. Long-range applications of high-temperature superconductors include efficient power transmission and highly sensitive magnetic field sensors.

Thin film synthesis and processing in this program include evaporation, sputtering, electrodeposition, and plasma and laser processing. For analyzing materials structures and properties, faculty and students employ electron microscopy, scanning probe microscopy, cathodoluminescence and electron beam–induced current imaging, photoluminescence, dielectric and anelastic relaxation techniques, ultrasonic methods, magnetotransport measurements, and X-ray diffraction techniques. Faculty members have research collaborations with Lucent, Exxon, IBM, and other New York area research and manufacturing centers, as well as major international research centers. Scientists and engineers from these institutions also serve as adjunct faculty members at Columbia. The National Synchrotron Light Source at Brookhaven National Laboratory is used for high-resolution X-ray diffraction and absorption measurements.

Entering students typically have undergraduate degrees in materials science, metallurgy, physics, chemistry, or other science and engineering disciplines. First-year graduate courses provide a common base of knowledge and technical skills for more advanced courses and for research. In addition to coursework, students usually begin an association with a research group, individual laboratory work, and participation in graduate seminars during their first year.


Solid-state science and engineering is an interdepartmental graduate specialty that provides coverage of an important area of modern technology that no single department can provide. It encompasses the study of the full range of properties of solid materials, with special emphasis on electrical, magnetic, optical, and thermal properties. The science of solids is concerned with understanding these properties in terms of the atomic and electronic structure of the materials in question. Insulators (dielectrics), semiconductors, ceramics, and metallic materials are all studied from this viewpoint. Quantum and statistical mechanics are key background subjects. The engineering aspects deal with the design of materials to achieve desired properties and the assembling of materials into systems to produce devices of interest to modern technology, e.g., for computers and for energy production and utilization.

Areas of Research

The graduate specialty in solid-state science and engineering includes research programs in semiconductor nanocrystals (Professor Brus, Chemistry/Chemical Engineering); optics of semiconductors and nanomaterials (Professor Herman, Applied Physics and Applied Mathematics); chemical physics of surfaces and photoemission (Professor Osgood, Electrical Engineering/ Applied Physics and Applied Mathematics); molecular beam epitaxy leading to semi-conductor devices (Professor Wang, Electrical Engineering/Applied Physics and Applied Mathematics); metamaterials and infrared optoelectronic devices (Professor Yu, Applied Physics and Applied Mathematics); and inelastic light scattering in low-dimensional electron gases within semiconductors (Professor Pinczuk, Applied Physics and Applied Mathematics/Physics); large-area electronics and thin-film transistors (Professor Im, Henry Krumb School of Mines/Applied Physics and Applied Mathematics); structural analysis and high Tc superconductors (Professor Chan, Henry Krumb School of Mines/Applied Physics and Applied Mathematics); X-ray microdiffraction and stresses (Professor Noyan, Henry Krumb School of Mines/Applied Physics and Applied Mathematics); electronic and magnetic metal thin films (Professor Barmak, Applied Physics and Applied Mathematics); magnetic properties of thin films (Professor Bailey, Applied Physics and Applied Mathematics); the structure of nanomaterials (Professor Billinge, Applied Physics and Applied Mathematics); and electronic structure calculations of materials (Professor Marianetti, Applied Physics and Applied Mathematics).

Program of Study

The applicant for the graduate specialty must be admitted to one of the participating programs: applied physics and applied mathematics, or electrical engineering. A strong undergraduate background in physics or chemistry and in mathematics is important.

The doctoral student must meet the formal requirements for the Eng.Sc.D. or Ph.D. degree set by the department in which he or she is registered. However, the bulk of the program for the specialty will be arranged in consultation with a member of the interdepartmental Committee on Materials Science and Engineering/ Solid-State Science and Engineering. At the end of the first year of graduate study, doctoral candidates are required to take a comprehensive written examination concentrating on solid-state science and engineering.

The following are regarded as core courses of the specialty:

   APPH E4100: Quantum physics of matter
   APPH E4110: Modern Optics
   APPH E4112: Laser physics
   APPH-MSAE E6081-E6082: Solid state physics, I and II
   CHEM GU4230: Statistical thermodynamics

   CHAP E4120: Statistical mechanics
   ELEN E4301: Introduction to semiconductor devices
   ELEN E4944: Principles of device microfabrication
   ELEN E6331-E6332: Principles of semiconductor physics
   ELEN E6403: Classical electromagnetic theory

   PHYS GR6092: Electromagnetic theory, I
   MSAE E4100: Crystallography
   MSAE E4206: Electronic and magnetic properties of solids
   MSAE E6240: Impurities and defects in semiconductor materials
   PHYS GR6018: Physics of the solid state
   PHYS GR6037: Quantum mechanics