1. nanoMOS 4.0: A Tool to Explore Ultimate Si Transistors and Beyond
Xufeng Wang
School of Electrical and Computer Engineering
Purdue University
West Lafayette, IN 47906

2. Outline Why nanoMOS simulator? Device geometries in nanoMOS.
nanoMOS development history and my involvement
Overview of nanoMOS code structure
Overview of nanoMOS software development
Conclusion
Acknowledgement

3. Introduction

4. Si/III-V double gate MOSFET
Featured devices
Si/III-V double gate MOSFET
SOI MOSFET
spinFET
HEMT
Flexible and efficient modeling is needed to explore these device proposals.

5. Why nanoMOS?
It studies a very general structure: double gate, thin body, n-MOSFET with fully depleted channel.
It features several transport models: drift-diffusion, semiclassical ballistic, quantum ballistic, and quantum dissipative.
It is computationally efficient, easily modified, written in MATLAB, and freely available on nanohub.org with Rappture interface
Well documented on various thesis and papers.

6. Development history Quantum transport for III-V material Creation
Kurtis Cantley
Zhibin Ren
S. Clark, S. Ahmed
Quantum transport for III-V material
Creation
Rappture interface
2008
nanoMOS 1.0
nanoMOS 2.0
nanoMOS 3.0
Asymmetrical gate configuration
Code restructure: modulation, testing suite
Code restructure: modulation, testing suite
2000
Himadri Pal
X. Wang, D. Nikonov
nanoMOS HEMT
Xufeng Wang
Yang Liu
Unification of branches
Unification of branches
nanoMOS phonon scattering
Himadri Pal
Xufeng Wang
Xufeng Wang
Drift-diffusion transport for III-V material
Drift-diffusion transport for III-V material
Parallel support, Rappture interface
Parallel support, Rappture interface
nanoMOS 3.5
nanoMOS spinFET
nanoMOS 4.0
Yunfei Gao
Today

7. Inside thesis
Unification of branches
Code restructure: modulation, testing suite
Drift-diffusion transport for III-V material
Parallel support, Rappture interface
Code restructure: modulation, testing suite
Models and techniques
Software development
Various transport models
Non-linear damping
Boundary conditions
Recursive Green’s function
Scharfetter and Gummel method
nanoMOS applications ……
Rappture interface
nanoMOS parallelization
Benchmark and testing suite
Unification of branches
Drift-diffusion transport for III-V material
Parallel support, Rappture interface
GOAL: Deliver a comprehensive documentation and understanding of nanoMOS, physics and software wise.

8. Gummel’s Method Numerical Approach No Yes Converge!
Solve Poisson’s Equation
Solve Transport Equations
Initial Guess for carrier density No
Converge!
Yes
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
Regardless how we start, all equations must be self-consistently satisfied at the same time

9. “Straight-forward” Method of Solving Transport Equations
Solving the Transport Equations
“Straight-forward” Method of Solving Transport Equations
In order to solve this equation, we first need to find a linear approximation to turn the differential equation into a discretized linear equation.
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
First step is to use the mesh point variables to interpolate the midpoint variables

10. “Straight-forward” Method of Solving Transport Equations
Solving the Transport Equations
“Straight-forward” Method of Solving Transport Equations
 Substitute the approximated variables back to transport equations
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
 Continuity Equation tells us:
Ji-1/2
Ji+1/2

11. Then, at least 1 carrier density is forced to be negative
Solving the Transport Equations
Stability Problem of “Straight-forward” Method
Observe the equation:
If both > 2
Then, at least 1 carrier density is forced to be negative
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
This means if electric potential difference between any two neighboring nodes is greater than 2kT/q, the “straight-forward” method might get negative non-physical carrier density solutions.
Therefore, a finer grid is required at regions that the rate of change of electric potential is high. This may lead to a huge number of grid nodes, thus increasing the computational cost dramatically.

12. Scharfetter and Gummel Method
Solving the Transport Equations
Scharfetter and Gummel Method
We will attempt a direct integration by introducing the following factor:
Carrier density
Exponential of electric potential
An unknown function of x
 Find the derivative of carrier density (n)
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
 Substitute the introduced factor into transport equation

13. Scharfetter and Gummel Method
Solving the Transport Equations
Scharfetter and Gummel Method
 Recast the equation
 Attempt a direct integration on both sides of the equation
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
Now, let’s look at this equation’s left and right hand side separately.

14. is the Bernoulli Function
Solving the Transport Equations
Scharfetter and Gummel Method
 Join the left and right hand side together
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
is the Bernoulli Function

15. Scharfetter and Gummel Method
Solving the Transport Equations
Scharfetter and Gummel Method
at node xi-1/2
This is the 1-D electron Transport Equation via finite difference with Scharfetter and Gummel Method at node xi-1/2
Similarly, one can write down the transport equation at node xi+1/2
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
at node xi+1/2
Now, just as what we did in “straight forward” method, we can use the relationship establish by Continuity Equations to solve the problem

16. Scharfetter and Gummel Method
Solving the Transport Equations
Scharfetter and Gummel Method
How can the stability of transport equation be guaranteed by Scharfetter and Gummerl Method?
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
Notice that the Bernoulli Function is ALWAYS positive.
One coefficient is always negative, so the carrier densities are no longer forced to be negative.

17. Gummel’s Method Numerical Approach No Yes Converge!
Solve Poisson’s Equation
Solve Transport Equations
Initial Guess for carrier density No
Converge!
Yes
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
Regardless how we start, all equations must be self-consistently satisfied at the same time

18. Boundary Conditions for Poisson Equation
Solving the Poisson Equation
Boundary Conditions for Poisson Equation
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
Although source and drain bias are given as inputs, we still use Neumann boundary for source and drain ends to avoid convergence problem.
Source and drain bias are used to calculate electron density, thus indirectly influence the potential at ends.

19. Between 2D Poisson solver and 1D transport
Effective mass and subband
Effective mass Schrodinger equation is solved in confinement direction

20. Complete Scheme of Drift-Diffusion Modeling
Solving the Transport Equations
Complete Scheme of Drift-Diffusion Modeling
Solve Poisson’s Equation
Solve Transport Equations
Initial Guess for carrier density No
Converge!
Yes
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide. No
Newton Iteration Converge?
Yes
Schrodinger Equation Solver

21. Other available transport models
Drift-diffusion
computationally efficient
mobility difficult to determine
Semiclassical ballistic
evaluates device ballistic limit
may be too optimistic
Quantum ballistic
RGF based; quantum effects
no scattering; longer run time
Quantum dissipative with phonon scattering
Phonon scattering
longest run time

22. Software development: Overview
test & benchmark
SVN
Developer
User
Rappture on nanoHUB
parallel job submitter

23. Software development: Rappture interface

24. Conclusion Overviewed nanoMOS development history
Demonstrated Scharfetter and Gummel method as numerical sample
Demonstrated Rappture interface as software sample
GOAL: Deliver a comprehensive documentation and understanding of nanoMOS, physics and software wise.

25. Acknowledgement
Committee members: Professor Klimeck, Professor Lundstrom, and Professor Strachan.
Funding and support from my advisors.
Encouragement and help when needed from my colleagues.
Mrs. Cheryl Haines and Mrs. Vicki Johnson for scheduling the examination and being the most helpful secretaries.
As always, thank and love to my entire family.

26. Now, welcome the questions……

28. Device geometry #1: Si/III-V double gate MOSFETs
Sample double gate MOSFET geometry
3D electron density
Conduction band profile
Si/III-V as channel material
Thin body (< 10nm). Single channel conduction if thin enough.
Double gates can be biased separately
Source/drain can be metallic and turn into Schottky barrier FET

29. Device geometry #2: SOI MOSFET
3D conduction band
near front gate
Sample SOI geometry
Conduction band in
transverse direction
Si/III-V as channel material.
Similar to previous structure, except the bottom oxide layer is thick.
Back gate can be biased to push channel electron toward front gate.

30. Device geometry #3: HEMT
Charge and conduction band
profile from Yang Liu *
Sample HEMT geometry
Intrinsic III-V material as channel = high mobility.
Delta-doped layer controls threshold voltage.
* Y. Liu, M. Lundstrom, “Simulation-Based Study of III-V HEMTs Device Physics for High-Speed Low-Power Logic Applications”, ECS meeting, 2009

31. Device geometry #4: spinFET
Sample spinFET geometry
Device structure suggested by Sugahara & Tanaka
Controls current by manipulating electron spin

32. What are we trying to solve?
Problem Statement and the Semiconductor Equations
What are we trying to solve?
Source
Drain
Top Gate
Buttom Gate
NEMO can provide the modeling essential for accelerating the development of nanoelectronics.
The physical model begins at the atomic level with the atomic orbitals. Efficient numerical algorithms allow NEMO to model practical semiconductor devices of several thousand atomic layers. NEMO includes the effect of open contacts, lattice vibration, alloy disorder and interface roughness to calculate macroscopic quantities such as the electron and hole density and the current.
The computational algorithms are accessed by a flexible graphical user interface (GUI) for rapid design prototyping and analysis. The figure at the right consists of screen dumps from the GUI chosen to illustrate its versatility.
The 3 figures in the upper right show
the band profile of of an ultra-scaled MOS device with
the electron charge calculated both semi-classically and quantum mechanically and
the calculated and experimental tunnel current for different SiO2 barrier thicknesses.
The two figures in the lower right display
the band profile of an optoelectronic switch and
the calculated quantum states of the device. The comparison of the experimental and calculated current for this device is shown in the lower right quadrant of the following slide.
Given device geometry and material parameters (such as gate length, dielectric constant, mobility)
Look for solution for:
carrier density
electric potential
Both carrier density and electric potential solutions must satisfy all the equations.
Regardless how we start, all equations must be self-consistently satisfied at the same time

33. Transport model #1: drift-diffusion
Computationally efficient
Account scattering via mobility, thus suitable for long channel devices
Do not consider quantum effects such as tunneling and interference.

34. Scharfetter and Gummel Method
If apply finite difference method directly:
If both > 2
Then, at least 1 carrier density is forced to be negative
Introduce Scharfetter and Gummel method
Scharfetter and gummel
Carrier density
Exponential of electric potential
An unknown function of x
SG method ensures stability of carrier density solutions.

35. Transport model #2: Semiclassical ballistic
Injection velocity
Simple model exploring device behavior at ballistic limit
Do not consider quantum effects such as tunneling and interferences.

36. Transport model #3 & #4 : Quantum ballistic & dissipative

37. Transport model #3 & #4 : Quantum ballistic & dissipative
For dissipative transport, nanoMOS can treat phonon scattering, or general scattering via Buttiker probe approach (now obsolete).

38. Development history nanoMOS 1.0 (Published in 2000)
Developer: Zhibin Ren
Original nanoMOS code for silicon MOSFETs is written in MATLAB.
nanoMOS 2.0 (Published in 2005)
Developer: Steve Clark, Shaikh S. Ahmed
Rappture interface is added to nanoMOS, and the code becomes avaliable on nanoHUB.org.
nanoMOS 3.0 (Published in 2007)
Developer: Kurtis Cantley
Support for III-V materials in semi-classical ballistic and quantum ballistic transport models is added. Rappture interface is updated to reflect the III-V implementation.
Developer: Himadri Pal
Top and bottom gate can now have asymmetric configurations with different gate dielectrics and capping layers.
nanoMOS 3.5 (Published in 2008)
Developer: Xufeng Wang
Support for III-V materials in drift-diffusion transport is added. Additional mobilities models are added.
nanoMOS 3.5 (Published in 2009)
Developer: Xufeng Wang, Dmitri Nikonov
nanoMOS source code is restructured and modularized. Material parameters are separated out as a mini-library. Debugging functions are planted within source code to assist code developments. Benchmark and testing suite is created based on a script from Dmitri Nikonov.
nanoMOS 4.0 (Developed in 2009)
Developer: Himadri Pal
Support for Schottky FET is added. NanoMOS now has the ability to simulate a double gate MOSFETs structure with metallic source/drain via NEGF\ formalism.
Developer: Yang Liu
Support for HEMT is added. NanoMOS now has the ability to simulate a III-V HEMT structure via NEGF formalism.
Developer: Xufeng Wang
Parallel Jobs Submitter (PJS) is added. PJS allows nanoMOS to sweep gate/source bias and run each bias on a cluster node. It supports only clusters with Portable Batch System (PBS) installed such at steele (steele.rcac.purdue.edu) or coates (coates.rcac.purdue.edu).
Developer: Yunfei Gao
Support for SpinFET is added. NanoMOS now has the ability to simulate a SpinFET structure via NEGF formalism.
nanoMOS 4.0 (To be published in 2010)
Merge working branches of Schottky FET, HEMT, and SpinFET modules. Code is restructrued. Rappture interface is updated to accommodate the newly published features.