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A comparison between Piecewise constant Potential Barrier Tool and Periodic Potential lab

A comparison between Piecewise constant Potential Barrier Tool and Periodic Potential lab. By Samarth Agarwal, Abhijeet Paul, Junzhe Geng & Gerhard Klimeck NCN @ Purdue University. Motivation : Repeated wells and band formation. 10 barriers.

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A comparison between Piecewise constant Potential Barrier Tool and Periodic Potential lab

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  1. A comparison betweenPiecewise constant Potential Barrier Tool and Periodic Potential lab By Samarth Agarwal, Abhijeet Paul, Junzhe Geng & Gerhard Klimeck NCN @ Purdue University

  2. Motivation : Repeated wells and band formation 10 barriers As the number of barriers are increased more and more energy resonances begin to appear and energy bands are formed. 2 barriers =>1 resonance 20 barriers 30 barriers 3 barriers =>2 resonance n barriers =>n-1 resonance

  3. Comparison with Periodic structure Repeated indefinitely e ∞ -∞ e Finite barriers 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). Electrons above the barrier however feel the difference between the actual finite barrier structure and a periodic structure.

  4. Comparison between tools Here we compare two tools with different approaches. • 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.

  5. Input Parameters for PCPBT Lab PCPBT-Piecewise constant Potential Barrier Tool Energy Inputs: • 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 Well Parameters: Well Geometry:

  6. Input Parameters for PPL PPL-Periodic Potential Lab • Well Type: • 80 ang total well-width and 20 • ang barriers • Material Types: • GaAs (m* = 0.067) • InAs (m* = 0.023) Energy Details: Well Geometry: Potential Type:

  7. 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.

  8. 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.

  9. GaAs Well Comparison – 80 Barriers Results from both the tools match very well for GaAs for 80 barrier case in PCBPT with PPL result.

  10. 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.

  11. InAs Well Comparison – 30 Barriers Results from both the tools match very well for InAs for 30 barrier case in PCBPT with PPL result.

  12. 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.

  13. 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.

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