slide1
Download
Skip this Video
Download Presentation
Raghuraj Hathwar Advisor : Dr. Dragica Vasileska

Loading in 2 Seconds...

play fullscreen
1 / 29

Raghuraj Hathwar Advisor : Dr. Dragica Vasileska - PowerPoint PPT Presentation


  • 170 Views
  • Uploaded on

Generalized Monte Carlo Tool for Investigating Low-Field and High Field Properties of Materials Using Non-parabolic Band Structure Model. Raghuraj Hathwar Advisor : Dr. Dragica Vasileska. Outline. Motivation of modeling different materials - Strained Silicon

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Raghuraj Hathwar Advisor : Dr. Dragica Vasileska' - yazid


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Generalized Monte Carlo Tool for Investigating Low-Field and High Field Properties of Materials Using Non-parabolic Band Structure Model

Raghuraj Hathwar

Advisor : Dr. Dragica Vasileska

outline
Outline
  • Motivation of modeling different materials

- Strained Silicon

- III-V and II-VI materials

- Silicon Carbide

  • The generalized Monte Carlo code

- Free-Flight and drift velocity calculation

  • Rappture interfacing
  • Results
  • Conclusions and future work.
slide4

Strained Silicon

  • The four minima of the conduction band in directions parallel to the plane of strain are raised. This results in higher electron mobility.
  • There is also a splitting of the light and heavy hole bands leading to increased hole mobility.
slide5

III-V and II-VI Materials

  • High electron mobility of compared to silicon.
  • AlGaAs/GaAs are lattice matched.
  • AlGaN/GaN interfaces have spontaneous polarization.
slide6

Silicon Carbide (SiC)

  • Very useful in high voltage devices because of its thermal conductivity, high band gap and high breakdown field.
  • In fact the thermal conductivity of 4H-SiC is greater than that of copper at room temperature.
slide7

The Monte Carlo Method

  • The Boltzmann Transport Equation
  • The Chamber-Rees Path Integral
types of scattering
Types of Scattering
  • Acoustic Phonon Scattering
  • Zeroth order Intervalley Scattering
  • First order Intervalley Scattering
  • Piezoelectric Scattering
  • Polar Optical Phonon Scattering
  • Ionized Impurity Scattering
slide10

Fermi’s Golden Rule and Scattering Rates Calculation

  • Calculate the Matrix Element
  • Use Fermi’s Golden Rule
  • Sum over all k’ states
slide11

Band Structure Model

e.g. GaAs

3 Valley Approximation

Full Band Structure

(equilibrium)

slide12

E-k relation for a General Valley

Here k1 , k2and k3are the wave vectors along the three mutually perpendicular directions that define the valley and m1 , m2and m3 are the effective masses of the electrons along those directions

slide13

Conversion from Anisotropic Bands to Isotropic Bands

In order to make the conversion between energy and momentum easy all anisotropic bands are converted to isotropic bands using

Which gives the following E-k relation

where

slide14

Carrier Free-Flight

From Newton’s 2nd law and Q.M.

slide15

For simplicity the wave vectors of all electrons are only stored in the x,y and z coordinate system.

  • Therefore before drifting, the wave vectors are transformed from the x,y,z coordinate system to the 1,2,3 coordinate system using,

where [a1b1c1], [a2b2c2] and [a3b3c3] are the three mutually perpendicular directions that define the valley.

slide16

The electric fields must also be transformed to the directions along the wave vectors

  • The electrons are then drifted and transformed back into the x,y,z coordinate system.
slide18

The drift velocities must then be transformed to the x,y,z coordinate system so that an average can be taken over all electrons.

rappture integration
Rappture Integration
  • The Rappture toolkit provides the basic infrastructure for a large class of scientific applications, letting scientists focus on their core algorithm when developing new simulators.
  • Instead of inventing your own input/output, you declare the parameters associated with your tool by describing Rappture objects in the Extensible Markup Language (XML).
  • Create an xml file describing the input structure.
  • Integrate the source code with Rappture to read input values and to output results to the Rappture GUI.
slide23

Silicon

Electron Energy vs Electric Field

Drift Velocity vs Electric Field

slide24

Gallium Arsenide (GaAs)

Electron Energy vs Electric Field

Drift Velocity vs Electric Field

slide26

Germanium (Ge)

Drift Velocity vs Electric Field

Electron Energy vs Electric Field

conclusions and future work
Conclusions and Future Work
  • Uses non-parabolic band structure making it as accurate as possible for an analytic representation of the band structure.
  • Interfacing the tool with Rappture enables easy handling of the parameters and reduces the complexity of using the tool.
  • Existing materials band structures can be easily modified to improve existing results.
  • New materials can easily be added to the code.
  • The tool can be extended to include impact ionization scattering to better model high field properties.
  • Full band simulation for holes.
ad