M.S. Program in Applied Physics

The program of study leading to the degree of Master of Science, while emphasizing continued work in basic physics, permits many options in several applied physics specialties. The program may be considered simply as additional education in areas beyond the bachelor’s level, or as preparatory to doctoral studies in the applied physics fields of plasma physics, laser physics, or solid-state physics.

All degree requirements must be completed within five years. A candidate is required to maintain at least a 2.5 grade point average.

Specific course requirements for the master’s degree are determined in consultation with the program adviser, but must include four of the six core courses listed below.

Core Courses:


The core courses provide a student with a solid foundation in the fundamentals of applied physics, but with the approval of the faculty adviser, other graduate-level courses (4000, 6000, 8000, or 9000-level) with APPH designators not listed below may also count as core courses.

Other Possible Core Courses


M.S. students with an interest in Plasma Physics should take the following courses:

M.S. students with an interest in Solid State Physics should take the following courses:

  • APPH E4018: Applied physics laboratory (2 pts)
     
  • APPH E4112: Laser physics (3 pts)
     
  • ELEN E4301: Introduction to semiconductor devices (3 pts)
     
  • ELEN E6331-2: Principles of semiconductor physics I and II (3 pts)
     
  • MSAE E4206: Electronic and magnetic properties of solids (3 pts)
     
  • or their equivalent for solid state


M.S. students with an interest in Optical Physics should take the following courses:

  • APPH E4018: Applied physics laboratory (2 pts)
     
  • APPH E4100: Quantum physics of matter (3 pts)
     
  • APPH E4110: Modern optics (3 pts)
     
  • APPH E4112: Laser physics (3 pts)
     
  • APPH E6110: Laser interactions with matter (3 pts)
     
  • ELEN E9402: Seminar in quantum electronics (3 pts)
     
  • or their equivalent for optical physics
     

Elective Courses: 

In addition to core courses, M.S. students must select elective courses from those listed above or below. These courses can be chosen from other Applied Physics classes or from related academic fields such as Applied Mathematics, Materials Science and Engineering, and Electrical Engineering, subject to the approval of the faculty advisor. Some suggested elective courses include: 


 

Applied Mathematics Elective Courses 



  • APMA E4001: Principles of applied mathematics 

(3 pts)
     
  • APMA E4101: Introduction to nonlinear dynamical systems 



(3 pts)
     
  • APMA E4200: Partial differential equations 

(3 pts)  


     
  • APMA E4204: Functions of a complex variable 

(3 pts)
     
  • APMA E4300: Intro to numerical methods 

(3 pts) 

   
  • APMA E6302: Numerical analysis of partial differential equations (3 pts)


Electrical Engineering Elective Courses

  • ELEN E4301: Introduction to semiconductor devices 

(3 pts)
     
  • ELEN E4312: Analog electronic circuits (3 pots)
     
  • ELEN E4321: Digital VLSI circuits 

(3 pts)
     
  • ELEN E4401: Wave transmission and fiber optics 

(3 pts)
     
  • ELEN E4815: Random signals and noise (3 pts)
     
  • ELEN E6318: Microwave circuit design 

(3 pts)
     
  • ELEN E6412: Lightwave devices 

(3 pts)
     
  • ELEN E6488: Optical interconnects and interconnection networks (3 pts)
     
  • ELEN E4944: Principles of device microfabrication 

(3 pts)


Other Elective Courses (Mechanical Engineering, & Materials Science)

  • MSAE E4090: Nanotechnology (3 pts)
     
  • MSAE E4202: Thermodynamics and reactions in solids (3 pts)
     
  • MSAE E4206: Electronic and magnetic properties of solids 

(3 pts)
     
  • MSAE E4215: Mechanical behavior of structural materials 

(3 pts)
     
  • MSAE E4250: Ceramics and composites (3 pts)
     
  • EEME E4601: Digital control systems 

(3 pts)
     
  • MECE E6100: Advanced mechanics of fluids 

(3 pts)
     
  • MECE E6700: Carbon nanotube science and technology (3 pts)
     

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Ph.D. and Eng.Sc.D. Programs

After completing the M.S. program in applied physics, doctoral students specialize in one applied physics field. Some specializations have specific course requirements for the doctorate; elective courses are determined in consultation with the program adviser. Successful completion of an approved 30-point program of study is required in addition to successful completion of a written qualifying examination taken after two semesters of graduate study. An oral examination, taken within one year after the written qualifying examination, and a thesis proposal examination, taken within two years after the written qualifying examination, are required of all doctoral candidates.

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Columbia, one of the leading university centers for training in plasma physics, offers a graduate program leading to the Master of Science (MS), Master of Philosophy (MPhil), Doctor of Philosophy (PhD) and Doctor of Engineering Science (Eng.Sc.D. or DES) degrees.  The program builds a foundation in the science and application of plasma physics and features a specialty in the high-temperature plasma physics needed for controlled fusion energy. Besides a sound basic training in relevant areas of applied physics, students develop expertise in experimental, theoretical, and computational plasma physics. This instruction provides the background needed to conduct research in Columbia University’s Plasma Research Laboratory and in other national plasma research facilities.  Since its inception in 1960, the program at Columbia has granted more than 110 doctoral degrees with many of our graduates playing leading roles in all phases of plasma physics, including, in particular, the worldwide program to develop controlled fusion energy.

Degree Requirements for Master of Science (M.S.) in Applied Physics

  • 30 points (usually 10 courses) of courses taken for a letter grade with a 2.5 Minimum GPA
     
  • There are no specific course requirements for this degree, it is tailored to the student’s interests, but will usually include at least 5 core courses with an APPH designator and additional courses with PHYS/ELEN designators or advisor-approved courses from other departments.
     
  • Students with an interest in Plasma Physics should take the following courses:


Degree Requirements for Doctor of Philosophy (Ph.D.) in Applied Physics: Plasma Physics

  • Complete requirements for the M.S. with a 3.0 Minimum GPA 
    (unless a Master’s Degree from another institution has already been earned, in which case students receive 30 points and 2 Residence Units of advanced standing)
     
  • Complete requirements for the Master of Philosophy (M.Phil.) Degree:
    • Written Qualifying Examination
      Courses suggested for preparation at the level of the general and plasma physics parts of the written qualifying examination are listed in the qualifying examination memorandum.

    • 30 points of courses and/or research (beyond M.S.) taken for a letter grade with minimum 3.0 GPA
      Can be fulfilled with core and related courses of specialization not used for the MS degree as well as research points, but no more than 15 points of research can be applied to this 30 point requirement.
       
    • 6 Residence Units
      One per semester not including summer, takes 3 years without M.S. or 2 years with M.S.

    • Oral Exam (usually Spring of 2nd year)
       
    • Thesis proposal (usually Spring of 3rd year)

    • Ethics requirements
      Online ethics course during Fall of 1st, year, attend departmental ethics seminar during Spring of 1st and 2nd years
       
    • Master of Philosophy Degree awarded
       
  • Complete Dissertation
     
  • Successful Defense

Degree Requirements for Doctor of Engineering Science (Eng.Sc.D. or DES) in Applied Physics: Plasma Physics

  • Complete requirements for the M.S. with a 3.0 Minimum GPA
    (unless a Master’s Degree from another institution has already been earned, in which case student receives 30 points and 2 Residence Units of advanced standing)
     
  • Written Qualifying Examination
    Courses suggested for preparation at the level of the general and plasma physics parts of the written qualifying examination are listed in the qualifying examination memorandum.

  • Ethics requirement
    Online ethics course during Fall of 1st year, attend departmental ethics seminar during Spring of 1st and 2nd years

  • Oral Exam (usually Spring of 2nd year)
     
  • 30 points of courses and/or research (beyond M.S. taken for a letter grade with 3.0 GPA
    Can be fulfilled with core and related courses of specialization not used for the M.S. degree as well as research points, but no more than 15 points of research can be applied toward this 30 point requirement
  • 12 points of APAM E9800: Doctoral Research Instruction
     
  • Thesis proposal  (usually Spring of 3rd year) 
     
  • Complete Dissertation
     
  • Successful Defense

 


Core Courses

  • CHEM G4230: Statistical thermodynamics (4.5 pts)


Related Courses of Specialization

  • APPH E6110: Laser interactions with matter (3 pts)
  • APPH E4010: Introduction to nuclear science (3 pts)
  • APMA E4204: Functions of a complex variable (3 pts)
  • APMA E6901: Special topics in applied math (3 pts)
  • APMA E8308: Asymptotic methods in applied math (3 pts)
  • ELEN E4501: Electromagnetic devices and energy conversion (3 pts)
  • PHYS G4019: Mathematical methods in physics (3 pts)


Plasma Physics Faculty

Allen H. Boozer
Andrew J. Cole
Michael E. Mauel - Applied Physics Program Committee Chair
Gerald A. Navratil - Plasma Physics Doctoral Committee Chair
Francesco A. Volpe

Research Scientists and External Advisors

Admitted students may work with scientific advisors external to the applied physics faculty, as long as student secures funding from said faculty.  Examples of other researchers or faculty external to the department include:

James Bialek, Research Scientist/PPPL
Darren Garnier, MIT
Steven Sabbagh, Adjunct Professor & Research Scientist/PPPL

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Solid State Physics Graduate Specialty

This graduate specialty encompasses the study of the electrical, optical, magnetic, thermal, high-pressure, and ultrafast dynamical properties of solids, with an aim to understanding them in terms of the atomic and electronic structure. The field emphasizes the formation, processing, and properties of thin films, low-dimensional structures—such as one- and two-dimensional electron gases, nanocrystals, surfaces of electronic and optoelectronic interest, and molecules.  Facilities include a microelectronics laboratory, high-pressure diamond anvil cells, a molecular beam epitaxy machine, ultrahigh vacuum systems, lasers, equipment for the study of optical properties and transport on the nanoscale, and the instruments in the shared facilities overseen by the Columbia Nano Initiative. There are also significant resources for electrical and optical experimentation at low temperatures and high magnetic fields. Specific course requirements for the solid-state physics doctoral specialization are set with the academic adviser, in consultation with the Committee on Materials Science and Engineering/Solid-State Science and Engineering.

Optical Physics Graduate Specialty

This graduate specialty involves a basic training in relevant areas of applied physics with emphasis in quantum mechanics, quantum electronics, and related areas of specialization. Some active areas of research in which the student may concentrate are laser modification of surfaces, optical diagnostics of film processing, inelastic light scattering in nanomaterials, nonlinear optics, ultrafast optoelectronics photonic switching, optical physics of surfaces, and photon integrated circuits. Specific course requirements for the optical and laser physics doctoral specialization are set with the academic adviser.

Degree Requirements for Master of Science (M.S.) in Applied Physics

  • 30 points (usually 10 courses) of courses taken for a letter grade with a 2.5 Minimum GPA
     
  • There are no specific course requirements for this degree, it is tailored to the student’s interests, but will usually include at least 5 core courses with an APPH designator and additional courses with PHYS/ELEN designators or advisor-approved courses from other departments. 
     
  • Students with an interest in Solid State Physics should take the following courses:
    • APPH E4018: Applied physics laboratory (2 pts)
       
    • APPH E4112: Laser physics (3 pts)
       
    • ELEN E4301: Introduction to semiconductor devices (3 pts)
       
    • ELEN E6331-2: Principles of semiconductor physics I and II (3 pts)
       
    • MSAE E4206: Electronic and magnetic properties of solids (3 pts)
       
    • or their equivalent for solid state
       
  • Students with an interest in Optical Physics should take the following courses:
    • APPH E4018: Applied physics laboratory (2 pts)
       
    • APPH E4100: Quantum physics of matter (3 pts)
       
    • APPH E4110:  Modern optics (3 pts)
       
    • APPH E4112: Laser physics (3 pts)
       
    • APPH E6110: Laser interactions with matter (3 pts)
       
    • ELEN E9402: Seminar in quantum electronics (3 pts)
       
    • or their equivalent for optical physics

 

Degree Requirements for Doctor of Philosophy (Ph.D.) in Applied Physics: Solid State or Optical Physics

  • Complete requirements for the M.S. with a 3.0 Minimum GPA
    (unless a Master’s Degree from another institution has already been earned, in which case students receive 30 points and 2 Residence Units of advanced standing)
     
  • Complete requirements for the Master of Philosophy (M.Phil.) Degree

    • Written Qualifying Examination
      Courses suggested for preparation at the level of the general, and solid state and optical physics parts of the written qualifying examination are listed in the qualifying examination memorandum.

    • 30 points of courses and/or research (beyond M.S.) taken for a letter grade with minimum 3.0 GPA
      Can be fulfilled with core and related courses of specialization not used for the M.S. degree as well as research points, but no more than 15 points of research can be applied to this 30 point requirement

    • 6 Residence Units
      Students who have earned the MS register for 1 Residence Unit per semester not including summer   
       
    • Oral Exam (usually Spring of 2nd year)

    • Thesis proposal (usually Spring of 3rd year)
       
    • Ethics requirements
      Online ethics course during Fall of 1st, year, attend departmental ethics seminar during Spring of 1st and 2nd years
       
    • Master of Philosophy Degree awarded
       
  • Complete Dissertation

  • Successful Defense

Degree Requirements for Doctor of Engineering Science (Eng.Sc.D. or DES) in Applied Physics: Solid State or Optical Physics

  • Complete requirements for the MSwith a 3.0 Minimum GPA
    (unless a Master’s Degree from another institution has already been earned, in which case student receives 30 points of advanced standing)

  • Written Qualifying Examination
    Courses suggested for preparation at the level of the general, and solid state and optical physics parts of the written qualifying examination are listed in the qualifying examination memorandum.
     
  • Ethics requirement
    Online ethics course during Fall of 1st year, attend departmental ethics seminar during Spring of 1st and 2nd years
     
  • Oral Exam (usually Spring of 2nd year)

  • 30 points of courses and/or research (beyond M.S. taken for a letter grade with 3.0 GPA
    Can be fulfilled with core and related courses of specialization not used for the M.S. degree as well as research points, but no more than 15 points of research can be applied toward this 30 point requirement
     
  • 12 points of APAM E9800: Doctoral Research Instruction
     
  • Thesis proposal (usually Spring of 3rd year)

  • Complete Dissertation

  • Successful Defense

 




Core Courses

  • ELEN E4301: Introduction to semiconductor devices


Related Courses of Specialization

  • ELEN E4944: Principles of device microfabrication
  • ELEN E6140: Gallium arsenide materials processing
  • ELEN E6151: Surface physics and analysis of electronic materials
  • MSAE E6225: Techniques in x-ray and neutron diffraction
  • MSAE E6229: Energy and particle beam processing of materials
  • MSAE E6240: Impurities and defects in semiconductor materials
  • MSAE E8235: Selected topics in materials science
  • PHYS G8050: Advanced mathematical methods in physics


Solid-State Physics and Optical & Laser Physics Faculty

William E. Bailey
Katayun Barmak
Simon Billinge
Siu-Wai Chan
Alexander Gaeta
Irving P. Herman
James S. Im
Chris A. Marianetti
I.C. Noyan
Aron Pinczuk, Physics & APAM - Solid State and Optical Physics Doctoral Committee Chair
Latha Venkataraman
Wen I. Wang, EE & APAM
Nanfang Yu

Multidisciplinary and External Advisors

Admitted students may work with scientific advisors external to the applied physics faculty, as long as student secures funding from said faculty.  Examples of other faculty in areas closely related to applied physics include:

Louis Brus, Chemical Engineering and Chemistry
Kenneth Eisenthal, Chemistry
Richard Friesner, Chemistry
Yasutomo Uemura, Physics
Shalom Wind, APAM

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For information, please see the Medical Physics program pages.

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