Download - A comparison between Piecewise constant Potential Barrier Tool and Periodic Potential lab
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Network for Computational Nanotechnology (NCN)UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP
A comparison betweenPiecewise constant Potential
Barrier Tool and Periodic Potential lab
BySamarth Agarwal, Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
NCN @ Purdue University
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Motivation : Repeated wells and band formation
2 barriers =>1 resonance
3 barriers =>2 resonance
n barriers =>n-1 resonance
As the number of barriers are increased more and more energy resonances begin to appear and energy bands are formed.
As the number of barriers are increased more and more energy resonances begin to appear and energy bands are formed.
20 barriers
30 barriers
10 barriers
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Comparison with Periodic structure
ee
Repeated indefinitely
As the number of barriers is increased the electrons below the barrier see no difference between the actual structure and a structure that is simply modeled as being repeated indefinitely (Periodic).
As the number of barriers is increased the electrons below the barrier see no difference between the actual structure and a structure that is simply modeled as being repeated indefinitely (Periodic).
ee
-∞ ∞
Finite barriers
Electrons above the barrier however feel the difference between the actual finite barrier structure and a periodic structure.
Electrons above the barrier however feel the difference between the actual finite barrier structure and a periodic structure.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Comparison between tools
•PCPBT: Piecewise Constant Potential Barrier Tool.•Models structures with a finite number of barriers•Gives discrete states that resemble bands
•PPL: Periodic Potential Lab.•Models structures that are periodic.•Gives continuous bands.
Here we compare two tools with different approaches.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Input Parameters for PCPBT Lab
•Geometry: 6nm wells and 2nm barriers •Well Material : GaAs (m* = 0.067) InAs (m* = 0.023)•Methods for solution : TM-Transfer matrices TB-Tight Binding
•Geometry: 6nm wells and 2nm barriers •Well Material : GaAs (m* = 0.067) InAs (m* = 0.023)•Methods for solution : TM-Transfer matrices TB-Tight Binding
Energy Inputs:
Well Geometry:
Well Parameters:
PCPBT- Piecewise constant
Potential Barrier Tool
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
•Well Type: 80 ang total well-width and 20 ang barriers •Material Types: GaAs (m* = 0.067) InAs (m* = 0.023)
•Well Type: 80 ang total well-width and 20 ang barriers •Material Types: GaAs (m* = 0.067) InAs (m* = 0.023)
Input Parameters for PPL
PPL-Periodic Potential Lab
Well Geometry:
Energy Details:
Potential Type:
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
GaAs Well Comparison – 30 Barriers
30 barriers in PCPBT tool.
Results from both the tools match very well for GaAs for 30 barrier case in PCBPT with PPL result.
Results from both the tools match very well for GaAs for 30 barrier case in PCBPT with PPL result.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Difference in PPL and PCPBT : 30 Barrier GaAs
•Results from both the tools match very well.•Error in the energy bands is less than 5% from both tools.•Error is higher for the upper band showing that higher energy electrons feel the difference between a finite and infinite well- barrier structure.
•Results from both the tools match very well.•Error in the energy bands is less than 5% from both tools.•Error is higher for the upper band showing that higher energy electrons feel the difference between a finite and infinite well- barrier structure.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
GaAs Well Comparison – 80 Barriers
Results from both the tools match very well for GaAs for 80 barrier case in PCBPT with PPL result.
Results from both the tools match very well for GaAs for 80 barrier case in PCBPT with PPL result.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Difference in PPL and PCPBT : 80 Barrier GaAs
•Results from both the tools match very well.•Error in the energy bands is less than 5% from both tools.•Error is higher for the upper band showing that higher energy electrons feel the difference between a finite and infinite well- barrier structure.
•Results from both the tools match very well.•Error in the energy bands is less than 5% from both tools.•Error is higher for the upper band showing that higher energy electrons feel the difference between a finite and infinite well- barrier structure.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
InAs Well Comparison – 30 Barriers
Results from both the tools match very well for InAs for 30 barrier case in PCBPT with PPL result.
Results from both the tools match very well for InAs for 30 barrier case in PCBPT with PPL result.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Difference in PPL and PCPBT : 30 Barrier InAs
•Results from both the tools match very well.•Error in the energy bands is less than 5% from both tools.•Error is higher for the upper band showing that higher energy electrons feel the difference between a finite and infinite well- barrier structure.
•Results from both the tools match very well.•Error in the energy bands is less than 5% from both tools.•Error is higher for the upper band showing that higher energy electrons feel the difference between a finite and infinite well- barrier structure.
Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
Conclusions
• Results from PCPBT and PPL match pretty well.
• Results have been verified for »Different material types .»Different number of barriers.
• Results from two different codes and three different theoretical formulations have been benchmarked.