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Lecture 15: Resonant Tunneling Diode

2011-02-28 1Lecture 15, High Speed Devices 2011

• Operation

• Bi-stable switch

• Oscillator

• Fundamental Physics

• Application Example

Resonant Tunneling Diode


E1

E2

An RTD consists of two large bandgap material forming a quantum well with quasi-bound states (in z-direction):

V

I

V

I

V

I

Energy and k conserved during tunneling – negative differential resistance

z

E

Resonant Tunneling Diode


I

80

60

40

20

0

Cu

rren

t (k

A/c

m2)

1.61.20.80.40.0

Collector Voltage (V)

Experimental Data (T=300K)

Ideal device, T=0K

•Important DC figure of merits:•Peak current density (Jp)•Peak Voltage (Vp)•Valley current density (Jv)•Valley Voltage (Vv)• Peak-to-valley ratio: Jp/Jv

Jp

Jv

Vp Vv

Valley current is larger than 0 in a real device:

Thermionic emmision

Field-assisted tunneling

Transport through 2nd subband

Elastic/inelastic scattering

V

Plateau is an artifact from oscillations in the bias network

Application: Bistable Switch


80

60

40

20

0

Cu

rren

t (k

A/c

m2)

1.61.20.80.40.0


The two stable bias-points:Associated with the double barrier is a capacitance:

tb tw tb

wb

s

ttC

2

Vp,Ip

Vf,If

Vs

RL V1

IRTD(V1)

IRL(V1)

Assume RTD biased at V1=Vp – small increase in Vs forces new biasing point Vf

Charge stored over C will increase:

pf VVCQ

Speed Index


80

60

40

20

0

Cu

rren

t (k

A/c

m2)

1.61.20.80.40.0


Vp,Ip

Vf,If

Vs

RL V1

IRTD(V1)IRL

(V1)

pf VVCQ

1

11 )()(dV

VJVJ

Cf

p L

V

V RTDR

This charge has to be supplied through RL – delay in V1

Switching time:

IRL

Area inbetween curves gives current to charge C with Q

pv

pf

pvp

pf

V

V vp JJ

VV

J

C

JJ

VVCdV

JJ

Cf

p/1

1

Speed Index 1/PVR

Fast switching requires a large Jp!

AlSb/InAs/AlSb Switch Transition


E. Özbay, EDL 1993

1.7 pS switching of ~ 0.7V

Slew-rate of 300mV/pS

1.7 pS

tb=1.8nmtw=7.5 nm10 nm drift region after RTD

~ 1.5 pS

Application: Negative resistance oscillator


V

I The RTD has negative differential resistance (NDR):

0 NDRVVdv

dir

Rs

-gd

L

C

t

LCjt

C

gd

eiti

1

0

If Rs (series resistance in diode) ~0, the equivivalent circuit is a simple RLC:

VNDR

i(t)

If gd is negative, the oscillations amplitude grows instead of decaysAn RTD biased in the NDR region will oscillate between Ip and Iv

80

60

40

20

0

Cu

rren

t (k

A/c

m2)

1.61.20.80.40.0


Some inductance in the biasing circuit.DC measurment averages over oscillations

High Frequency Oscillators


Rs

-gdjwC

LCfosc

2

1

Zin

The oscillation frequency is essentially set by the effectiv LC-networkCan oscillate as long as Re(Zin)<0

gd=di/dv

2

max,2

1d

s

dosc g

R

g

Cf

vp

vp

dVV

IIg

For a high fmax, we want small Rs, small C and large gd

Highest RTD fmax ~ 850 GHz, which is the highest fundamental mode oscillator made as of today

2

1

woutP Low output power limits applications

Calculation of current


dkkTkvkEEfq

kTkEEfkvqvqnIxk

sFsF

0

,, ,,2

Assume fully coherent transport:

1D-0D-1D-system

Ef,l Ef,l-qVsd

T(Ez,Vsd)

Transmission probability

Where T(Ez,Vsd) is the transmission probability of the quantum system

0, 0

,3, exp1ln)(2

,2zyx kkk

zzlfzsFz dEEEETqmkT

kTkEEfkvqvqnJ

3D-2D-3D

T(Ez)

z

E

m

kE z

z2

22

qVds

Transmission Probability


Assuming plane waves

I II III IV V

V

III

II

I

Ie

FeEe

DeCe

BeAe

z

ikz

ikzikz

zz

ikzikz

......

EVm

Emk

0

*

*

2

2

E=0

E=V0

Match wavefunction and its derivative at all interfaces:

az

II

IIaz

I

I

III

z

z

mz

z

m

aa

**

11

z=a

2

2

A

IET

Solve for A ... I (e.g. Using the transfer matrix

method)

real kimag K

E

Should use complex bandstructure..

EC

Ev

Transmission Probability II


10-5

10-4

10-3

10-2

10-1

100

Transmission Probability

0.6

0.4

0.2

En

erg

y (

eV

)

At resonance for a symmetric systemT=1Finite lifetime in well gives rise to a broadening of the state

Gt=FWHM

22 4/

2/

nzn

nz

EEET

G

G

Around the transmission peak, T(Ez) is essentially Lorenzian.

G

1

2*

2

1

22

Rbm

TEnn

b

T1 is the transmission probability through a single barrier

0

,3exp1ln)(

2zzlfz dEEEET

qmkTJ

If we want J+ to be large – T(Ez) should be ’wide’ in energy!

Build RTD with thin barriers and a thin well!

Design example: AlGaAs/GaAs/InGaAs RTD


80

60

40

20

0

Cu

rren

t (k

A/c

m2)

1.61.20.80.40.0


102

103

104

105

Cu

rren

t D

ensi

ty (

kA

/cm

2)

4.03.53.02.52.01.51.0

Barrier Thickness (nm)

Calculated

Exponential Fit

J=4.6910610

(-1.194x)

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Qu

antu

m w

ell

ener

gy

(eV

)

3020100

In (%) in notch

50

40

30

20

10

0Pea

k C

urr

ent

Den

sity

(kA

/cm

2)

3020100

In (%) in notch

E

z InxGa1-xAs

Al0.8Ga0.2As

b

GaAs

4nm

An indium-rich notch lowers 1st subband, and increases 2nd – higher peak to valley ratio

Strong dependency on barrier thickness

T=300K

Startup Decay

Application Example: Ultra Wideband Source


Very quick turn on/off due to the high slew-rate

Application Example: Ultra Wideband Source


Gated Resonant Tunnel diode

Inductor

2 Gpulses/s On-Off Keying at 60 GHz


Potential applications:UWB communication systems (Gbit/s over short ranges)Pulse-based radar systems THz spectroscopy (short pulse – large bandwidth)

RTD Conclusions


Large research effort at universities and industry during 1990-2000At that time: ft,fmax of HEMT/HBTs were ~ 100 GHz, RTD had fmax ~ 700 GHz!

RTD – unipolar two-terminal component, with added functionality due to the NDRSimple design gives small capacitance fast switching, high oscillation frequency

Today – ft, fmax of transistors are approaching THz, limited usage for RTDs

Unique IV – can lead to simpler circuit solutions, e.g. oscillators as compared with traditional transistor technology.

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