Quantum Capacitance Quantum Capacitance in Scaled-Down III-V FETs - - PowerPoint PPT Presentation

SLIDE 1

Quantum Capacitance Quantum Capacitance in Scaled-Down III-V FETs

Donghyun Jin, Daehyun Kim*, Taewoo Kim and g y , y , Jesús A. del Alamo Microsystems Technology Laboratories y gy Massachusetts Institute of Technology

* Presently with Teledyne Scientific Acknowledgement: FCRP-MSD Center, Intel

1

SLIDE 2

Overview Overview

1 Motivation

• 1. Motivation
• 2. Gate Capacitance Model for III-V FETs

3 M t f C I G A HEMT

• 3. Measurements of CG on InGaAs HEMTs
• 4. Comparison of Model and Experiments
• 5. Projection for 10 nm III-V MOSFETs

6 Conclusions

• 6. Conclusions

2

SLIDE 3

1 Motivation : III-V CMOS

• 1. Motivation : III V CMOS

Gate

III-V MOSFET

III‐V Channel

Source Drain

• III-V CMOS: III-V semiconductor in channel
• High electron velocity Low effective mass (m*)

3

SLIDE 4

1 Motivation : III-V CMOS

• 1. Motivation : III V CMOS

Gate

III-V MOSFET

III‐V Channel

Source Drain

• III-V CMOS: III-V semiconductor in channel
• High electron velocity Low effective mass (m*)
• Low m* small Density of States (DOS)

Low m small Density of States (DOS)

low sheet carrier concentration (NS) in channel

Will III V CMOS attain required N

• Will III-V CMOS attain required NS

at the 10 nm node?

4

SLIDE 5

Gate Capacitance Gate Capacitance in III-V MOSFET

III V MOS

Ccent V Gate

III-V MOS

ins

C

S

ψ

ins

C

EC

VG VG Insulator

III‐V Channel

inv

C

S

ψ

S

ψ

cent

C

Q

C

Metal III-V Channel EF

CQ

• Inversion-layer capacitance (Cinv) is series of

Quantum capacitance (C ):

Insulator

• Quantum capacitance (CQ):

EF penetration in CB, proportional to DOS

• Centroid capacitance (Ccent):

Finite distance of electrons away from interface Finite distance of electrons away from interface

5

SLIDE 6

Gate Capacitance Gate Capacitance in III-V MOSFET

III V MOS

Ccent V Gate

III-V MOS

ins

C

S

ψ

ins

C

EC

VG VG Insulator

III‐V Channel

inv

C

S

ψ

S

ψ

cent

C

Q

C

Metal III-V Channel EF

CQ

• Inversion-layer capacitance (Cinv) is series of

Quantum capacitance (C ):

Insulator

• Quantum capacitance (CQ):

EF penetration in CB, proportional to DOS

• Centroid capacitance (Ccent):

Finite distance of electrons away from interface Finite distance of electrons away from interface

6

m*↓ DOS↓ CQ↓ Problem in III-V MOSFET?

SLIDE 7

Gate Capacitance in III-V HEMTs Gate Capacitance in III V HEMTs

Goal: Experimental and theoretical study of CG in III-V HEMTs

L

III-V High Electron Mobility Transistor

tins LG

Source Drain Barrier Si δ doping

tch

Channel Buffer tins = Barrier thickness tch = Channel thickness

• Experimentally extract CG for HEMTs with different tins and tch
• Build CG model including DOS effect
• Project CG and NS of scaled down III-V FETs

7

SLIDE 8

Experimental HEMT Cross Section Experimental HEMT Cross Section

PR

Metal Gate

PR

Barrier = In0.52Al0.48As (4 or 10 nm)

S D

Etch stopper Oxide

Gate

Cap

Channel = In0.53Ga0.47As (2 nm) Channel= In Ga As (8 nm)

tch = 10 nm

Buffer = In0.52Al0.48As (~400 nm) Channel = In0.53Ga0.47As (3 nm)

Etch stopper

Barrier Channel Buffer tins tch

Channel = In0.7Ga0.3As (8 nm) Core

• r InAs (5 nm)

L 30

• Three different heterostructures explored :

Substrate = InP (~300 nm)

LG = 30 nm Type B HEMT

tins (nm) tch (nm) Channel Core Reference LG range (nm) Type A 10 10 InAs (5 nm) Kim, unpublished 40 ~ 100 ( ) i 2008 30 200 Type B 4 10 InAs (5 nm) Kim, IEDM 2008 30 ~ 200 Type C 4 13 In0.7Ga0.3As (8 nm) Kim, IEDM 2006 40 ~ 100

8

SLIDE 9

• 2. Gate Capacitance Model

p

C

S

ψ

ins

C

S

ψ

ins

C

ins

C

inv

C

S

ψ

1 inv

C

…

2 inv

C

…

1 cent

C

1 Q

C

2 cent

C

2 Q

C

( ) 1

S

Q C ∂ −

∑

1st Subband 2nd Subband 2nd Subband 1st Subband

1 cent

_ _

( ) 1 1

S inv i S Q i cent i

Q C C C ψ = = ∂ +

∑

9

SLIDE 10

• 2. Gate Capacitance Model

p

C

S

ψ

ins

C

S

ψ

ins

C

ins

C

inv

C

S

ψ

1 inv

C

…

2 inv

C

…

1 cent

C

1 Q

C

2 cent

C

2 Q

C

1st Subband 2nd Subband 2nd Subband 1st Subband

1 cent

( ) 1

S

Q C ∂ −

∑

_ _

( ) 1 1

S inv i S Q i cent i

Q C C C ψ = = ∂ +

∑

( )

F i

E E C C ∂ − =

Quantum capacitance

• f subband i

Centroid capacitance

• f subband i

2D DOS

* 2 || 2

m q C π

_ _

( )

cent i Q i i C

C C E E = ⋅ ∂ −

_

1 exp( )

Q i i F

C E E kT π = − +

10

SLIDE 11

Verification of Physical Model Verification of Physical Model

12

I G A (t 13 t 4 )

• Solid line :

Type A 8 10 m2]

InAs (tch= 10 nm, tins= 4 nm) InGaAs (tch= 13 nm, tins= 4nm)

Numerical simulation results from 1D Poisson-Schrodinger solver (Nextnano)

Type B 4 6 CG [fF/μm

InAs (tch= 10 nm, tins= 10 nm)

Type C

(- )

S G G

d Q C dV =

0 4 0 2 0 2 0 4 2

• Symbols :

Physical model results (using Nextnano to extract Ei )

• 0.4
• 0.2

0.2 0.4 VG [V]

(using Nextnano to extract Ei )

Good agreement g between model and numerical simulations

11

SLIDE 12

• 3. Experimental CG in a HEMT

f S

• btained from S – parameter measurements

½ Cgext ½ Cgext Gate LG

Small VDS 2500 3000 [fF/mm]

VGS = 0.4 V 0.35 0 3 VDS = 10 mV

Type B

Barrier Channel

Cgi

1000 1500 2000

G(VGS = -0.3 V)

0.3 0.25

CG (in fF/μm) = Cgi (in fF/μm2) x LG + Cgext

Intrinsic Gate Capacitance Parasitic Gate Capacitance

50 100 150 200 250 500 L [nm] CG - CG

0.2

Slope = Cgi

LG [nm]

Cgi = Slope of CG - CG(VG = -0.3V) with LG

12

gi G G( G

)

G

SLIDE 13

Experimental Intrinsic Gate Capacitance Experimental Intrinsic Gate Capacitance

15

Type B

10

μm2]

Type B Type C

5

Cgi [fF/μ

Type A

• 0.3
• 0.2
• 0.1

0.1 0.2 0.3

V [V] VG [V]

Comparison with physical model:

13

y Cins , CQ , Ccent contribution to Cgi

SLIDE 14

• 4. Comparison of measurements and model :

T A (I A h l t 10 t 10 ) Type A (InAs channel, tch = 10 nm, tins = 10 nm)

0 8

50

0 4 0.6 0.8

V]

E2

30 40 F/μm2] Experiment (CG)

Ccent1

0.2 0.4

Ei - EF [eV

E1 EF

20 30 apacitance [fF

Cins (tins = 10 nm) CQ1 Cinv1

• 0.4
• 0.2

0.2 0.4

• 0.2

EF

• 0.4
• 0.2

0.2 0.4 10 V [V] Ca

CG Cinv2

• Good agreement between measurements and model

C bl t C C 62% f C

VG [V]

VG [V]

• Cins comparable to Cinv CG ~ 62% of Cins
• Only 1st subband populated

14

SLIDE 15

Comparison of measurements and model :

T B (I A h l t 10 t 4 )

0.8

Type B (InAs channel, tch = 10 nm, tins = 4 nm)

50 Experiment (C )

0.4 0.6 [eV]

E2

30 40 [fF/μm2] Experiment (CG)

Cins (tins = 4 nm)

0.2 Ei - EF [

E1 EF

10 20 Capacitance

Ccent1 CQ1 Cinv1

• 0.4
• 0.2

0.2 0.4

• 0.2

VG [V]

• 0.4
• 0.2

0.2 0.4 10 VG [V]

CG Cinv2

• Moderate agreement
• CQ1 < Cins CG limited by CQ1: CG ~ 47% of Cins

G

Q1 ins G

y

Q1 G ins

• Only 1st subband populated

15

SLIDE 16

Comparison of measurements and model :

T C (I G A h l t 13 t 4 )

0.8

Type C (In0.7Ga0.3As channel, tch = 13 nm, tins = 4 nm)

50 Experiment (C )

0.4 0.6 [eV]

E2

30 40 [fF/μm2] Experiment (CG)

Cins (tins = 4 nm)

0.2 Ei - EF [

E1 EF

10 20 Capacitance

Ccent1 CQ1 Cinv1 CG

• 0.4
• 0.2

0.2 0.4

• 0.2

VG [V]

• 0.4
• 0.2

0.2 0.4 VG [V]

Cinv2

• Good agreement
• Thicker channel: Ccent1 comparable to Cins

G

CG ~ 35% of Cins

• 1st subband dominant, 2nd subband minor

16

SLIDE 17

Summary of Key Findings

Type A (InAs , tch = 10 nm, tins = 10 nm)

50 Experiment (CG) 50 Experiment (CG) 50 Experiment (CG)

Type B (InAs , tch = 10 nm, tins = 4 nm) Type C (In0.7Ga0.3As, tch = 13 nm, tins = 4 nm)

20 30 40 itance [fF/μm2]

Ccent1 CQ1

20 30 40 itance [fF/μm2]

Cins ( tins = 4 nm) C

20 30 40 tance [fF/μm2]

Cins ( tins = 4 nm) CQ1

• 0.4
• 0.2

0.2 0.4 10 20 Capaci

Cins ( tins = 10 nm) Cinv1 CG Cinv2

• 0.4
• 0.2

0.2 0.4 10 20 V [V] Capac

Ccent1 CQ1 Cinv1 CG Cinv2

• 0.4
• 0.2

0.2 0.4 10 20 Capaci

Ccent1 Cinv1 CG Cinv2

• Finite Cinv severely reduces CG below Cins
• CQ1 smallest in lower m* channel

VG [V] VG [V] VG [V]

Q1

• 1st subband dominates
• Ccent1 relevant: tch ↓ Ccent1 ↑

17

SLIDE 18

Summary of Key Findings

Type A (InAs , tch = 10 nm, tins = 10 nm)

50 Experiment (CG) 50 Experiment (CG) 50 Experiment (CG)

Type B (InAs , tch = 10 nm, tins = 4 nm) Type C (In0.7Ga0.3As, tch = 13 nm, tins = 4 nm)

20 30 40 itance [fF/μm2]

Ccent1 CQ1

20 30 40 itance [fF/μm2]

Cins ( tins = 4 nm) C

20 30 40 tance [fF/μm2]

Cins ( tins = 4 nm) CQ1

• 0.4
• 0.2

0.2 0.4 10 20 Capaci

Cins ( tins = 10 nm) Cinv1 CG Cinv2

• 0.4
• 0.2

0.2 0.4 10 20 V [V] Capac

Ccent1 CQ1 Cinv1 CG Cinv2

• 0.4
• 0.2

0.2 0.4 10 20 Capaci

Ccent1 Cinv1 CG Cinv2

• Finite Cinv severely reduces CG below Cins
• CQ1 smallest in lower m* channel

VG [V] VG [V] VG [V]

Q1

• 1st subband dominates
• Ccent1 relevant: tch ↓ Ccent1 ↑

C ( ) C ( d l) i T B Wh ?

18

CG (exp) > CG (model) in Type B, Why? CQ1 most relevant in Type B

SLIDE 19

Source of Discrepancy for CG in Type B p y

G

yp

1.Uncertainty in tins

• ±0.5 nm error margin from TEM

g

• 2. Increase of in-plane effective mass (m||

*)

• Biaxial channel strain + Non-parabolicity + Quantization

[Theory : Nag APL 1993; Experiment : Wiesner APL 1994] [Theory : Nag APL 1993; Experiment : Wiesner APL 1994]

19

SLIDE 20

Source of Discrepancy for CG in Type B p y

G

yp

1.Uncertainty in tins

• ±0.5 nm error margin from TEM

g

• 2. Increase of in-plane effective mass (m||

*)

• Biaxial channel strain + Non-parabolicity + Quantization

[Theory : Nag APL 1993; Experiment : Wiesner APL 1994]

20 Bulk InAs m||*= 0.026 me m||*= 0.045 me

[Theory : Nag APL 1993; Experiment : Wiesner APL 1994]

10 15 [fF/μm2] m||*= 0.05 me m||*= 0.055 me

5 nm InAs thin channel → m * ≈ 0 05 m

5 CG [ Type A (InAs, tins = 10 nm) Type B

→ m|| ≈ 0.05 me

suggested by N. Kharche at Purdue

• 0.4
• 0.2

0.2 0.4 VG [V] (InAs, tins = 4 nm)

20

SLIDE 21

Source of Discrepancy for CG in Type B p y

G

yp

1.Uncertainty in tins

• ±0.5 nm error margin from TEM

g

• 2. Increase of in-plane effective mass (m||

*)

• Biaxial channel strain + Non-parabolicity + Quantization

[Theory : Nag APL 1993; Experiment : Wiesner APL 1994]

20 Bulk InAs m||*= 0.026 me m||*= 0.045 me

[Theory : Nag APL 1993; Experiment : Wiesner APL 1994]

10 15 [fF/μm2] m||*= 0.05 me m||*= 0.055 me

5 nm InAs thin channel → m * ≈ 0 05 m

5 CG [ Type A (InAs, tins = 10 nm) Type B

Error Bar : C variation by → m|| ≈ 0.05 me

suggested by N. Kharche at Purdue

• 0.4
• 0.2

0.2 0.4 VG [V] (InAs, tins = 4 nm)

Error Bar : CG variation by ±0.5 nm uncertainty in tins

21

SLIDE 22

Source of Discrepancy for CG in Type B p y

G

yp

1.Uncertainty in tins

• ±0.5 nm error margin from TEM

g

• 2. Increase of in-plane effective mass (m||

*)

• Biaxial channel strain + Non-parabolicity + Quantization

[Theory : Nag APL 1993; Experiment : Wiesner APL 1994]

20 Bulk InAs m||*= 0.026 me m||*= 0.045 me

[Theory : Nag APL 1993; Experiment : Wiesner APL 1994]

Residual discrepancy: Band filling effect? [Wiesner APL 1994] V ↑ N ↑ m *↑ (not accounted for)

10 15 [fF/μm2] m||*= 0.05 me m||*= 0.055 me

5 nm InAs thin channel → m * ≈ 0 05 m VGS↑ → NS↑ → m|| ↑ (not accounted for)

5 CG [ Type A (InAs, tins = 10 nm) Type B

Error Bar : C variation by → m|| ≈ 0.05 me

suggested by N. Kharche at Purdue

• 0.4
• 0.2

0.2 0.4 VG [V] (InAs, tins = 4 nm)

Error Bar : CG variation by ±0.5 nm uncertainty in tins

22

SLIDE 23

• 5. What does this mean for 10 nm III-V MOSFETs ?

25 30

Assume : 10 nm III-V MOSFETs

0.06, 4.6 x 1012 0 05 4 1 1012 0.055, 4.4 x 1012 m||

*/me NS [cm-2 ]

15 20 [fF/μm2]

Gate S D

tch = 3 nm

tins = 2.6 nm (ε = 25εo) LG = 10 nm

0.045, 3.9 x 1012 B lk I A

*

0 026 0.05, 4.1 x 1012

m||

*↑

5 10 CG

S D

ch

Low m||

* III-V channel

Bulk InAs m||

*= 0.026 me

NS = 2.9 x 1012 cm-2 @ VG - VT = 0.33 V

• 0.4
• 0.2

0.2 0.4 VG [V]

VDD = 0.5 V

• CQ1 << Cins, Ccent1 CQ1 dominates in CG

23

SLIDE 24

• 5. What does this mean for 10 nm III-V MOSFETs ?

25 30

Assume : 10 nm III-V MOSFETs

0.06, 4.6 x 1012 0 05 4 1 1012 0.055, 4.4 x 1012 m||

*/me NS [cm-2 ]

15 20 [fF/μm2]

Gate S D

tch = 3 nm

tins = 2.6 nm (ε = 25εo) LG = 10 nm

0.045, 3.9 x 1012 B lk I A

*

0 026 0.05, 4.1 x 1012

m||

*↑

5 10 CG

S D

ch

Low m||

* III-V channel

Bulk InAs m||

*= 0.026 me

NS = 2.9 x 1012 cm-2 @ VG - VT = 0.33 V

• 0.4
• 0.2

0.2 0.4 VG [V]

VDD = 0.5 V

• CQ1 << Cins, Ccent1 CQ1 dominates in CG
• Non-parabolicity + Quantization + In-grown biaxial strain
• pa abo c ty

Qua t at o g o b a a st a

m||

* CQ1↑ NS ≈ mid 1012 cm-2 @ VDD = 0.5 V

24

SLIDE 25

Conclusions Conclusions

• Developed a simple quantitative model

p p q for CG in III-V FETs

• Key findings :

Key findings :

• Small CQ in low m||* channel limits CG
• Quantization + non-parabolicity + biaxial strain

p y contribute to increase m||*

• Ccent increased by using thin channel
• To improve CG scaling
• Thin channel designs increase CQ and Ccent

N id 1012

2

ibl f 10 FET @ 0 5 V NS ~ mid 1012 cm-2 possible for 10 nm FET @ 0.5 V

25