Design, Modeling and Simulation of Optoelectronic Devices

1
Design, Modeling and Simulation of Optoelectronic
Devices

• A course on
• Device Physics Processes
• Governing Equations
• Solution Techniques
• Result Interpretations

2
Course Outline

• Introduction
• Optical equations
• Material model I single electron band structure
• Material model II optical gain and refractive
  index
• Carrier transport and thermal diffusion equations
• Solution techniques
• Design, modeling and simulation examples
• Semiconductor lasers
• Electro-absorption modulators
• Semiconductor optical amplifiers
• Super-luminescent light emitting diodes
• Integrated optoelectronic devices

3
Introduction - Motivation

• Increased complexity in component design to meet
  the enhanced performance on demand
• Monolithic integration for cost effectiveness -
  similarity to the development of electronic
  integrated circuits
• Maturity of fabrication technologies
• Better understanding on device physics
• Maturity of numerical techniques
• which leads to the recent rapid progress on the
  computer-aided design, modeling and simulation of
  optoelectronic devices

4
Introduction - Motivation
Conventional Approach
New idea
New idea
Computer-aided design and modeling
Back of envelop design
Simulation
Experiment (costly)
Works?
No (very likely)
Yes
Works?
No (very likely)
Experiment (costly)
Yes
End
Works?
No (less likely)
Effective Approach
Yes
End
5
Introduction - Physics Processes in
Optoelectronic Device
6
Introduction - Description of Physics Processes

• From external bias to electron and hole
  generation carrier transport model (Maxwells
  equations in its quasi-static electric field form
  for bulk, or Heisenberg equation for
  low-dimension materials such as QW and QD)
• From electron and hole recombination to optical
  gain generation semiconductor material model
  (SchrÖdinger equation)
• From optical gain to photon generation and
  propagation Maxwells equations (in its full
  dynamic form)
• Unwanted accompanying thermal process thermal
  diffusion model

7
Introduction - Course Organization

• Optical equations 8 hours
• Material model I 8 hours
• Material model II 6 hours
• Carrier transport and thermal diffusion 2 hours
• Solution techniques 4 hours
• Design, modeling and simulation examples 8 hours
• Total 36 hours over 12 weeks
• Assessment
• Minor project on modeling (governing equation
  extraction for given components) 40
• Major project on simulation (problem solving on
  the extracted governing equation) 60
• Open-book, take-home (open-discussion), and
  team-working

8
Optical Equations 1 Maxwells equations A
historical review for better understanding
9
Electrostatic Field

• Coulombs law
• Feature 1 why inversely proportional to the
  distance square?
• Implication flux conservation in the 3D space
• Hence we have Gauss law (electric)

10
Electrostatic Field

• Feature 2 centered force
• Implication zero-curled field (swirl free)
• Hence we can introduce the scalar potential to
  obtain Poissons equation
• Advantages of using scalar potential instead of
  vectorial field 1. only single variable is
  involved 2. with both two features in the
  electrostatic field embedded
• Disadvantage PDE order is raised

11
Electrostatic Field

• Summary the electrostatic field is divergence
  driven, curl free, and fully described by
  Poissons equation.

12
Home Work 1

• How would Coulombs law look like if our space
  world was 2D, or 1D?
• Is it possible to generate swirls in a
  centered-force field? If yes, how?

13
What happens for the dielectric media in the
electrostatic field?

• Methodology to treat the dielectric media
• Dipole forms inside the dielectric media if we
  move this media into an electrostatic field
  generated by a single charge
• Dipole generates a new (extra) electrostatic
  field which can be calculated by Poissons
  equation
• Equivalent this extra electrostatic field to a
  field generated by another (equivalent) single
  charge
• Sum up the electrostatic fields generated by the
  two charges
• Using the linear superposition theory, we can
  treat the dielectric media (with many dipoles) in
  any electrostatic field (formed by an arbitrary
  charge distribution).

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What happens for the conductive media in the
electrostatic field?

• Inside the conductive media, the electrostatic
  field is zero (due to the motion of free
  electrons, which must distribute in such a way
  that makes the field generated by the
  redistribution cancelled out with the original
  field applied to this conductive media).
• Consequently, inside the conductive media, the
  scalar potential is identical everywhere.

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Home Work 1 (continued)

• Prove that the solution to Poissons equation is
  unique once the domain boundary condition is
  fully given.
• Prove that, by introducing an electric
  displacement vector
• governing equations for the electrostatic
  field inside an dielectric media are given as
• What is the electrostatic field inside an empty
  (charge-free) closed conductive media cavity that
  is placed in an given electrostatic field? What
  is the charge distribution in the inner surface
  of this cavity? Name an application for such
  cavity.
• The point charge source generates the
  electrostatic field inversely proportional to the
  square of the distance, how to generate the
  electrostatic field which is an inverse-linear
  function of the distance? an inverse-sub-linear
  function of the distance? and an
  inverse-super-quadratic function of the distance?
  

or
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What happens if the charge moves?

• Current forms as
• The total number of charges must be conserved,
  hence the current flow through the surface of a
  closed region equals to the reduction of the
  charge density rate inside the closed region,
  i.e., (carrier continuity equation)
• The current is driven by the Coulomb force, hence
  Ohms law holds

17
Static Motion (DC Current)

• Inside the current flow region, the carrier
  continuity leads to a continuous current flow
• Outside the current flow region, the field is
  still electrostatic as it is formed by the
  constant charge distribution inside the DC
  current flow region.
• Therefore, the electric field originated from a
  DC current is still swirl free, i.e.,
• It can be mapped to the electrostatic field
  inside a dielectric media if we view J as D, s as
  e0er, and E the same. Known as the electrostatic
  imitation, this mapping is widely used for
  electrostatic field measurement.
• What is the new effect of the charge motion then?

18
Static Motion (DC Current)

• Outside of the current flow region, if there is
  another charge stream in a static motion (i.e., a
  DC current), this charge stream feels a new
  force that is described by Biot-Saverts law in a
  form analogous to Coulombs law, except for the
  two involved scalar charges must be replaced by
  the two involved vectorial DC currents
• A swirl is generated, we name it the magnetic
  flux, since this swirl acts on the moving charge
  only without any effect to the stay still charge,
  hence it differs from the electric field.

19
Static Motion (DC Current)

• Therefore, the magnetic interaction between two
  moving charges is a reflection of a purely
  derivative effect
• Whereas the electric interaction between two
  charges, regardless of their status, in motion or
  at rest, is a reflection of a static effect.

20
Magneto-static Field

• Feature 1 the flux is a closed vectorial flow
• Implication the flux is continuous in the 3D
  space, known as zero-diverged (source/drain free)
  
• Hence we can introduce the vector potential and
  Gauss law (magneto) holds

21
Magneto-static Field

• Feature 2 non-centered force, otherwise, the
  magneto-static flux has neither divergence nor
  curl, which makes it zero everywhere according to
  the Helmholtzs theorem the flux is, again,
  inversely proportional to the distance square
• Implication flux conservation in the 3D space
• Hence we have (the derivative form of) Amperes
  law

22
Magneto-static Field

• Summary the magneto-static flux is divergence
  free, curl driven, and fully described by the
  vectorial Poissons equation
• However, unlike the scalar potential introduced
  in the electrostatic field, the vectorial
  potential introduced in the magneto-static field
  is not so popular as it has little advantage
  compared to the flux description.

23
Summary on the Electro- and Magneto- Static
Fields

24
Summary on the Electro- and Magneto- Static
Fields

25
Home Work 1 (continued)

• We all understand that power can be delivered
  through the electromagnetic wave (e.g., AC power
  transmission through line/waveguide or wave
  radiation through antenna). Explain why we manage
  to deliver power through the static
  electromagnetic field without wave involved. What
  is the speed of the power transmission?
• An information transmission system is designed in
  the following sketch
• Can this system send signals at a speed
  surpasses the speed of the light in vacuum?