A comparison between Piecewise constant Potential Barrier Tool and by ylo13183

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									Network for Computational Nanotechnology (NCN)
    UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP



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

   Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
                 Motivation : Repeated wells and band formation
                                                     10 barriers


                                                                      As the number
                                                                      of barriers are
2 barriers =>1 resonance                                              increased
                                                     20 barriers      more and more
                                                                      energy
                                                                      resonances
                                                                      begin to
                                                                      appear and
                                                                      energy bands
                                                     30 barriers      are formed.
3 barriers =>2 resonance

n barriers =>n-1 resonance
       Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
                                           Comparison with Periodic structure


    e                                                                  Repeated indefinitely
            -∞                                                              ∞


    e


                                                                         Finite barriers
As the number of barriers is
increased the electrons below the                            Electrons above the barrier
barrier see no difference between                            however feel the difference
the actual structure and a structure                         between the actual finite barrier
that is simply modeled as being                              structure  and    a      periodic
repeated indefinitely (Periodic).                            structure.
        Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
                                                           Comparison between tools

       Here we compare two tools with different approaches.



•PCPBT: Piecewise Constant
                                                        •PPL: Periodic Potential Lab.
 Potential Barrier Tool.
                                                        •Models structures that are
•Models structures with a finite
                                                         periodic.
 number of barriers
                                                        •Gives continuous bands.
•Gives discrete states that
 resemble bands




     Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
                                               Input Parameters for PCPBT Lab
PCPBT- Piecewise constant                                   Energy Inputs:
Potential Barrier Tool

•Geometry:
 6nm wells and 2nm barriers
•Well Material :
 GaAs (m* = 0.067)
 InAs (m* = 0.023)
•Methods for solution :                               Well
 TM-Transfer matrices                              Parameters:
 TB-Tight Binding

                          Well Geometry:




     Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck
                                                             Input Parameters for PPL
                             PPL-Periodic Potential Lab
•Well Type:                                                         Well Geometry:
  80 ang total well-width and 20
  ang barriers
•Material Types:
 GaAs (m* = 0.067)
 InAs (m* = 0.023)


                                                                      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.




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.


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.




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.


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.




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.


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.




     Samarth Agarwal,Abhijeet Paul, Junzhe Geng & Gerhard Klimeck

								
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