full quantum simulation, design, and analysis of si tunnel diodes, mos leakage and capacitance,...
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Full Quantum Simulation, Design, and Analysis of Si Tunnel Diodes, MOS Leakage and Capacitance,
HEMTs, and RTDs
Roger Lake and Cristian Rivas
Department of Electrical Engineering, University of California, Riverside, California 92521-0204
Eric Jonsson School of Engineering, University of Texas at Dallas, Richardson, TX 75083-0688
UCR
OUTLINE
• Nanoelectronic Engineering Modeling Software (NEMO) status
• Examples of NEMO supporting experimental programs: QMOS, HEMTs, and RTDs.– Versatility
• Full Band modeling of Si tunnel diodes– Theoretical extension– Comparison with experimental measurements– Verification
• Conclude
NEMO Status
• Developed during the years 1993 to 1997 and delivered to the U. S. Government.
• Raytheon owns the software and is not currently distributing it.• CFDRC is negotiating with Raytheon to commercialize NEMO.• NASA JPL has extended NEMO to 3D QDots.• For URLs and references see Proceedings.
OUTLINE
• Nanoelectronic Engineering Modeling Software (NEMO) status
• Examples of NEMO supporting experimental programs: QMOS, HEMTs, and RTDs.– Versatility
• Full Band modeling of Si tunnel diodes– Theoretical extension– Comparison with experimental measurements– Verification
• Conclude
NEMO Design / Analysis Examples
• NEMO was used extensively at TI and Raytheon to support experimental device programs: – Quantum MOS (QMOS)– HEMT / RTD circuits for ADCs and TSRAM – RTDs for THz sources and detectors.
Design / Analysis Example
• QMOS Si / SiO2
– Extraction of m* of SiO2
-4
-3
-2
-1
0
1
2
3
25 30 35 40
En
erg
y (e
V)
Position (nm)
SiSiO
2
EF
EC
EV
V=3V
Al
Brar, Wilk, and Seabaugh, APL, 69, 2728 (1996).
Band Diagramn-Si / SiO2 / Al
20
40
60
80
100
120
28 29 30 31 32 33
Den
sity
(1
018 c
m-3
)
Position (nm)
V = 3V
SiO2 edge
Quantum Charge
Single Band Calculations
Design / Analysis Example
• QMOS Si / SiO2
– n-Si / SiO2 / Al
– C-V
Brar, Wilk, and Seabaugh, APL, 69, 2728 (1996).
Experimental Data
300400500600700800
90010001100
-3 -2 -1 0 1 2 3
Cap
aci
tan
ce (
nF
/cm
2 )
Voltage (V)
NEMOData
3.1 nm oxide
(a)
C-V
Single Band Calculations
Design / Analysis Example
• QMOS Si / SiO2
– n-Si / SiO2 / Al
• I-Vs – tox = 1.65 nm - 3.51
nm– I = 10-13 - 102 A/cm2
– mox = 0.3 m0
Experimental Data
Brar, Wilk and Seabaugh, APL, 69, 2728 (1996).
10-4
10-3
10-2
10-1
100
101
102
103
0 0.5 1 1.5 2
2165 1.65 nmThomas FermiHartree
Cu
rren
t (A
/cm2 )
Voltage (V)
10-6
10-5
10-4
10-3
10-2
10-1
100
101
0 0.5 1 1.5 2
2169 2.15 nmThomas_FermiHartree
Cu
rren
t (A
/cm2 )
Voltage (V)
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 0.5 1 1.5 2
2163 2.25 nmThomas FermiHartree
Cu
rren
t (A
/cm2 )
Voltage (V)
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
0 0.5 1 1.5 2
2171 2.86 nmThomas-FermiHartree
Cu
rren
t (A
/cm2 )
Voltage (V)
Single Band Calculations
-0.5
0.0
0.5
1.0
-1.0
Ene
rgy
(eV
)
-1.5
Sb d-doped
B d-doped
|HH1>
|LH>|Xz>
|Xxy>
HH
LH
Xz
Xxy
V = 0.325 VT = 300K
16 18 20 22 24 26 28 30Position (nm)
|HH2>
(b)
4 nmSi0.5Ge0.5
intrinsic
Design 4/2/98
Multiple SingleBand Calculation
NDR 5/98
0
4
8
12
0 0.2 0.4 0.6 0.8
ud18700.pVOLTAGE (V)
CU
RR
EN
T (
mA
)
Si/SiGe 6 different devices
T = 300 K
Data
Design / Analysis Example• QMOS Si / SiGe
– MBE grown Tunnel Diode
LH and HH states
Xxy and Xz statesXxy
Xz
V=0.2 V
d-doped 1021 p
d-doped 1021 n
(a)
8nmSi0.5Ge0.5
n+ / p+
Experimental Device 4/1/98
No reproducible NDR
Rommel et al., APL, 73, 2191 (10/98)
Design / Analysis Example• HEMT In0.48Al0.52As / In0.47Ga0.53As on InP
– Gate tunnel current
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 20 40 60 80 100
Ene
rgy
(eV
)
Position (nm)
In0.53
Ga0.47
As
channel
In0.52
Al0.48
As
barrier
Ef
Si d-doped
In0.52
Al0.48
As
(b)
10-7
10-5
10-3
10-1
101
103
105
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
-70 C-20 C
50 CC
urre
nt (
A/c
m2 )
Voltage (V)
NEW DATA
10-7
10-5
10-3
10-1
101
103
105
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
-73 C-23 C27 C77 C
Cur
ren
t (A
/cm
2 )
Voltage (V)
Coupled 2-Band Calculation
Gate recess etch process had gone South
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
C1.TXT
C1.0C1.1C1.2C1.3C1.4C1.5
I [
A ]
V [ V ]
3054-02 250Å InAlAs barrier (25 ¥25 µm, 80 to -20 in 20°C)
OLD DATA
Design / Analysis Example• HEMT In0.48Al0.52As / In0.47Ga0.53As on InP
– Gate tunnel current– Temperature Dependence
0.2
0.4
0.6
0.8
1
1.2
10-15 10-13 10-11 10-9 10-7 10-5 0.001 0.1
J(E) at 200KJ(E) at 300 KTransmission coefficient
En
ergy
(eV
)
Transmission (unitless)and J(E) (arb.units)
Design / Analysis Example• HEMT In0.48Al0.52As / In0.47Ga0.53As on InP
– Non-alloyed ohmic contacts
-1.5
-1
-0.5
0
0.5
1
0 20 40 60 80 100 120
Ene
rgy
(eV
)
Position (nm)
In0.53
Ga0.47
As
channel
In0.52
Al0.48
As
barrier
1e19 Si doped
In0.53
Ga0.47
As
Digitally graded alloy
In0.52
Al0.48
As6e19 InPI II
III
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 20 40 60 80 100
Ene
rgy
(eV
)
Position (nm)
In0.53
Ga0.47
As
channel
In0.52
Al0.48
As
barrier
Ef
3 nm 1019 Si doped
In0.52
Al0.48
As
25 nm
Design / Analysis Example• HEMT In0.48Al0.52As / In0.47Ga0.53As on InP
– Non-alloyed ohmic contacts
-1.5
-1
-0.5
0
0.5
1
0 20 40 60 80 100 120
Ene
rgy
(eV
)
Position (nm)
In0.53
Ga0.47
As
channel
In0.52
Al0.48
As
barrier
1e19 Si doped
In0.53
Ga0.47
As
Digitally graded alloy
In0.52
Al0.48
As6e19 InPI II
III
• Goal: Simplify epi– 1. Remove the superlattice
– 2. Remove the doped In0.52Al0.48As.
Device Contact R ( cm2)1. Standard HEMT 0.622. 1e19 InP 1.354. 1e19 InP, no SL (II) 1.55. 1e19 InP, no SL (II), no doped InAlAs (III), 2e19InGaAs (I)
5.0
• Coupled 2-Band coherent tunneling calculations:– Metal to channel
– Digital superlattice to channel
– Gate Barrier to channel
Design / Analysis Example• Design InAs / AlAs RTD LOs
for THz recivers
-1
-0.5
0
0.5
1
1.5
2
2.5
50 100 150
Ene
rgy
(eV
)
Position (nm)
(a)
1.2
1.4
1.6
1.8
2
2.2
2.4
0.6 0.8 1 1.2 1.4
Cap
ac
ita
nc
e (
fF /
m 2
)
Voltage (V)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.5 1 1.5 2
Cu
rre
nt
(10 5
A/c
m2 )
Voltage (V)
• Approach– Coupled 2-band DC calculations of I-V
and C-V
Design / Analysis Example• Design InAs / AlAs RTD LOs for THz recivers• Approach
– Coupled 2-band DC calculations of I-V and C-V
– Calculate small signal R = (dI/dV)-1
-600
-500
-400
-300
-200
-100
1.4
1.6
1.8
2
2.2
2.4
0.9 1 1.1 1.2 1.3
Res
ista
nc
e (
m2 )
Cap
ac
itan
ce
(fF / m
2 )
Voltage (V)
– Use R & C in circuit model RCL Model
Z
Rs
C-RLs
RTD
-Lqu = -R qu
– Calculate max frequency
0.5
1
1.5
2
0.9 1 1.1 1.2 1.3
Fre
qu
ency
(T
Hz)
Voltage (V)
Self-resonant frequencyResistive Cutoff frequency
Ls = 4 pH
Rs = 10
Ls = 20 pH
Ls = 10 pH
Rs = 20
Rs = 50
OUTLINE
• Nanoelectronic Engineering Modeling Software (NEMO) status
• Examples of NEMO supporting experimental programs: QMOS, HEMTs, and RTDs.– Versatility
• Full Band modeling of Si tunnel diodes– Theoretical extension– Comparison with experimental measurements– Verification
• Conclude
LT-MBE Grown Si Tunnel Diode
• Delta-doped Sb and B on either side of the tunnel junction
• SIMS data for as-grown and after 1 min. RTA.
• Indirect, Interband, Phonon Assisted Tunneling– Main current from 4 X4 valleys.
2.5 x 1020 B2 x 1020 Sb
Questions:
What is the effect of confinement in the contacts?
Can we model this device using modern quantum device modeling techniques?
-Peak current?-Excess current?
Atomic scale physics
Practicaldevices
Full quantum calculation of current, voltage, and capacitance.
STMMicrograph
AtomicLayers
• Non-equilibrium Green function formalism• Fermi’s Golden Rule in Green function form.• 2nd neighbor sp3s* • 1st neighbor sp3s*d5.• Read in SIMS doping profile.• Perform a semiclassical calculation of the charge and potential profile.
• Calculate direct and phonon-assisted tunnel current.
• TA and TO phonons.• The phonon wavevector is fixed at the -X valley minimum wavevector of 0.82 2/a <100>
• Approximate the overlap of the Bloch states with a constant deformation potential.
• Numerically calculate the overlap of the wavefunction envelopes between the X-conduction-band and -valence band states.
• Include a finite lifetime in the calculation of the spectral function of the contacts ==> bandtails.
Theoretical Approach
Transport Equation• Phonon assisted tunneling current
11,tr
1,tr
1,tr
11,tr
,,,tr2442 1
,11,11,2
2
2
22
BLj
BLj
BLj
BLj
N
jL
RjL
LL
Aj
Ltp
nEfEfEA
nEfEfEA
nEfEfEA
nEfEfEA
EGEEGdEdd
a
KDeJ
k
k
k
k
kkkkk
EGEEGEA AjNNN
RNjj ,,,, ,,,
kkkk Is the component of the spectral function injected from the right contact.
meV) 6.57 phonon, (TO eV/cm 106.5
meV) 4.18 phonon,(TA eV/cm 1045.28
8
KDT
Interband (100) phonons:
layer. atomican in orbitalsplanar *ssp 20 over the tracetr 3
Imaginary potential used for calculating the surface Green funcitons contained in and L
Partitioning of Device into “Contacts” & “Tunnel Region”
• Exact bulk surface Green function is calculated in the flat band region to left and then “moved in” using the recursive Green function algorithm.
• Finite lifetime included in left and right contacts.
-1
-0.5
0
0.5
1
1.5
2
90 100 110 120
Ene
rgy
(eV
)
Position (nm)
Right Contact
Left Contact
EFL
EFR
Non-equilibriumTunnel Region
g00(E, k)
site 0gs(E, k)
rgf
X
Effect of Confinement in Contacts
• 3 Current calculations: TA phonon-assisted, TO phonon-assisted, and direct tunneling (X2 - ).
• Direct tunneling current ~ 5 orders of magnitude < phonon-assisted tunneling current.
• Structure most notable in NDR region.
-1
-0.5
0
0.5
1
1.5
2
90 100 110 120
Ene
rgy
(eV
)
Position (nm)
Right Contact
Left Contact
EFL
EFR
Non-equilibriumTunnel Region
= 165 fs
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25 0.3
ritd
esaki
Voltage ( V )
Cur
rent
( A
/cm
2 )Effect of Confinement in Contacts• Comparison of bulk contacts vs. quasi-2D contacts.
-1
-0.5
0
0.5
1
1.5
2
90 100 110 120
Ene
rgy
(eV
)
Position (nm)
Right Contact
Left Contact
EFL
EFR
Non-equilibriumTunnel Region
= 165 fs
Band Tails and the Excess Current• Effect of band tails in the contacts on the tunnel current
-1.5
-1
-0.5
0
0.5
1
100 102 104 106 108 110
Ene
rgy
(eV
)
Position (nm)
AC
BV
Excess current mechanism
0
100
200
300
400
500
600
700
800
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
10 meV5 meV2 meV
Cur
rent
(A
/cm
2 )
Voltage (V)
PVCR Energy Broadening (meV) /Lifetime (fs)
7.7 2 meV / 165 fs
3.4 5 meV / 66 fs
1.9 10 meV / 33 fs
• ALL of the current above is tunnel current.• NONE is p-n diode current
-0.1
0
0.1
0.2
0.3
85 90 95 100 105 110
Ener
gy (e
V)
Position (nm)
0
10
20
30
0 0.1 0.2 0.3 0.4
Cur
rent
(mA
)
Voltage (V)
As Grown
RTA 700o C
Comparison with the Data
5 1019
1 1020
1.5 1020
2 1020
2.5 1020
3 1020
3.5 1020
4 1020
80 85 90 95 100 105 110 115 120
B as grown
Sb as grownB RTA
Sb RTA
Con
cent
rati
on (
cm-3
)
Position (nm)
80729.4
SIMS Data
0.1
1
10
100
0 0.2 0.4 0.6 0.8 1
as grown
650 C600 C
700 C
10 meV5 meV
Cur
rent
(m
A)
Voltage (V)
8729.4
The features around 0.5 - 0.6V from gap states.
Gap States?
Calculations
• Hump current observed in experiments ==> midgap states in tunnel region.
Verification
• Doping profile• Activation• Deformation potentials• Gap states.
Determine Tunneling
(From old parameter set)
ElectronLight Hole
• Band parameters– Imaginary wavevectors in
gap?
Conclusion
• NEMO status• NEMO in Design / Analysis role - versatility• First modern full-band treatment of phonon-assisted, indirect,
interband tunneling.• Qualitative agreement with I-V - peak and excess current.• Experimental unknowns - verification
– Doping profile and activation ==> tunnel barrier thickness– Gap states– Complex wavevectors in gap