Roger Lake and Cristian Rivas

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

[email protected]

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




• 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


• 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



• 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)


-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


– 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)


– 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


– 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




• 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


= 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


= 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

Roger Lake and Cristian Rivas

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