Transcript 2D electron Gas-MBE and QHE

Fabrication of 2D electron System by MBE
and QHE
Aseem Talukdar
Department of Physics
University of Cincinnati
Cincinnati-OH
02-June-2003
Outlines:
2 D electron System
MBE technique
QHE
2D electron System
 2
 
H  (P  eA) / 2m * m  B
En=(n+1/2) ħwc+ gmBB+ez
wc=eB/m*
nk(r)~n(y+cpx/eB) ei(kxx+kzz)
Density of States ::
d d 2 pd 2r
m
g (e )  2 
n(e ) ~
de
h2
h 2

A  ( yB,0,0)
Potential well of width d
e~ 2 ħ2/(2md2)
for 2D behavior
kBT<De
d ~ 10 nm
T~130 K
E~100 meV
d~ 2 nm
Examples::
 MOS structure
(MOSFET)
 GaAs/Ga1-xAlxAs
heterostructure
Molecular Beam Epitaxy::
 Technique for growing
semiconductor layered
structure
 Allows Controlled growth of
semiconductor layers with
monolayer precision.
MBE::
Schematic of MBE
 Effusion Cells
 CAR assembly
 Cryopanels
 RHEED Gun
Classical Hall Effect(1879)
Lorentz Force Law ::
Rh=Ey/(Jx B)=Vy d/(BIx)
Rh – Hall Coefficient
d - thickness (along Z-axis)
Drude Picture ::
Rh=-1/(ne)
=>Hall Resistance
Rxy=-Ey/Jx=RhB a B
QHE-Klaus von Klitzing (1980)
Transverse resistance a B
Conclusions::
MBE provides a convenient way to prepare
2D electron system
Ability to control band gap and grow one layer
of semiconductor material at a time results in
the possibility of development of electronic
and optoelectronic devices