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.