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Multi-Dielectric Energy Band Diagram Program

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About the Program

The Nanoscale Materials and Device Group has developed an easy-to-use, interactive simulation tool for complex, multi-layer dielectric, MOS and MIM devices. This program is useful for visualizing approximations of energy band diagrams, and performing back-of-the-envelope calculations of their important parameters.


Feature Overview

  • Draw band diagrams for MOS devices in static mode
  • Draw band diagrams for MOS and MIM gate stacks with various dielectrics, including high-κ dielectrics
  • Show band diagram movement for MOS and MIM devices as gate voltage is swept through a range
  • Calculate these parameters for applied voltages both in inversion and accumulation regimes:
    • energy
    • electric field
    • charge
    • potential as a function of distance
  • Calculate the following device parameters (and more):
    • threshold voltage
    • flat band voltage
    • equivalent oxide thickness (EOT)
    • stack capacitance
    • layer capacitance
    • tunneling distance
    • electric field
    • voltage drop
  • Plot and export device parameters as a function of gate voltage
  • Approximate changes in parameters due to temperature (down to 100 K)
  • Insert fixed charge into dielectrics

Example Applications

Band Bending With Gate Voltage Shifts

Energy bands can be modeled at varying gate voltages in the program. The following graphs depict a high-κ nMOSFET with the gate bias being swept from -1V to 2V. The program can play a continuous animation of the sweep.

TiN-HfO2-SiO2-pSi Stack Band Bending

Fixed Charge Insertion

Fixed sheet charges can be placed in any dielectric layer at a user specified distance into the dielectric. Resulting shifts in device parameters and energy levels are easy to observe. Here, a novel dielectric stack for application in nonvolatile memory (NVM) is charged after a ‘write’ operation, and the resulting change in stack capacitance is observed.

TiN-SiO2-Si3N4-SiO2-pSi stack after charge inserted (red). CV shifts to the right (light blue) as a result.

Temperature Dependence of Device Parameters

The program can simulate temperature effects on dielectric stacks from 100K to ~600K. A 3.2nm SiO2 nMOSFET was modeled in the program and the threshold and stack capacitance monitored during a temperature sweep.

polySi-SiO2-pSi stack. Red arrows show increasing temperature for CV curve (left). Vth shift is shown (right).

Comparison of Stack Parameters

By modeling different dielectric stacks, device parameters can be calculated. Demonstrated here is a comparison of three different stacks for possible application to NVM. We compare energy band diagrams (left) and critical stack parameters (right).

Comparison of NVM stacks. Smaller EOT and larger Cox are desired.


Assumptions Used in the Program

In order to draw the diagram and calculate the parameter, many simplifying assumptions have been made and incorporated into the program:

  • Ionized dopant temperatures
  • Fermi-Dirac approximated with Maxwell-Boltzmann statistics
  • Semiconductor doping >> intrinsic carrier concentration
  • Complete ionization of dopant atoms
  • Non-degeneracy in the semiconductor
  • Charge sheet approximation
  • Uniformly doped silicon
  • Intrinsic Fermi level equals half the bandgap in the semiconductor
  • Oxides act as perfect capacitors in series
  • Metal gate

Note: Please understand that this program is to be used to gain familiarity of energy band diagrams under bias and is not to meant to replace more accurate models and calculations. Be advised that there are bugs in the program. Relative to both these statements, you should use the program with caution.


Program Download & Tutorial Video

 


Changelog
Version 3.1.6 – Now compatible with all non-English versions of Windows
Version 3.1.5 – Added the ability to import materials libraries
Version 3.1.4 – Fixes some issues with graph export
Version 3.1.3 – Java based release

Microsoft Windows Installer
File: band3.1.6.exe 3.4Mb

Mac OS X
File: band3.1.6-Mac.zip 3.9Mb
“For those with newer Macs, one can obtain Java 6 for OS X Yosemite here.”

Linux Generic
file: band3.1.6-Generic.zip 3.2Mb

Tutorial Video: Energy Band Diagram


Team


References

Primary References

Richard G. Southwick III*, and William B. Knowlton, Stacked Dual Oxide
MOS Energy Band Diagram Visual Representation Program, Invited Paper,
IEEE Transactions on Device and Materials Reliability, 6(2) (2006) p.
136-145.

Southwick III*, R.G., A. Sup, A. Jain, and W.B. Knowlton, An
Interactive Simulation Tool For Complex Multilayer Dielectric Devices,
in print in IEEE Transactions on Device and Materials Reliability
(Feb. 2011).

Additional References

[1] Richard Southwick III, Michael Ogas and William B. Knowlton, Interactive dual oxide MOS energy band diagram program, poster presentation at the 2005 IEEE International Integrated Reliability Workshop, (October 2005).

[2] Aaron Sup, Richard G. Southwick III, Amit Jain, and William B. Knowlton, Arbitrary Oxide Multi-Layer MIM Energy Band Diagram Program, poster presentation at the 2007 IEEE International Integrated Reliability Workshop, (October 15-18, 2007).

[3] Richard Southwick III, Aaron Sup, Amit Jain, and W.B. Knowlton, Multi-Layer Metal-Insulator-Semiconductor (MIS) Energy Band Diagram Program, poster presentation at the 2008 IEEE International Integrated Reliability Workshop, (October 2008).