'Zero Bias Resonant Tunnelling Diode for Use in THz Rectenna'

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WoDiM 2014: 18th Workshop on Dielectrics in Microelectronics 9-11 June 2014, Kinsale, Ireland

Zero Bias Resonant

Tunnelling Diode for

Use in THz Rectenna

Naser Sedghi*, I. Z. Mitrovic, J. F. Ralph, and S. Hall

Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool L69 3GJ, UK

*nsed@liv.ac.uk

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Outline

• Motivation: Harvesting THz energy by rectennas

• Rectifiers needs:

• Small signal rectification with zero bias

• High degree of non-linearity around zero volt

• Small dynamic resistance

• A design model for resonant tunneling at zero bias MIIM

diodes

• Theory

• Results

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WoDiM 2014, 9-11 June 2014, Kinsale, Ireland

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Rectenna (

Rec

tifying An

tenna

)

• Capture the EM waves in broad-band antennas.

• Can be used for solar energy harvesting (feasible range: IR). • For solar energy harvesting the technology far less expensive than

photovoltaics.

• Very high efficiencies with full wave rectification (> 80%). • Absorption at all frequencies.

• Omnidirectional.

LOAD Antenna

LPF & Impedance matching

Rectifier

DC pass filter

Rectifiers: the Biggest Challenge

• p-n junction diodes:

• Switching speed is limited by minority carrier charge storage. • Maximum frequency: 0.2 THz.

• Schottky diodes:

• Are faster since minority carrier storage is negligible. • Switching speed is limited by parasitic capacitance. • Maximum frequency: 5 THz.

• MIM and MIIM diodes:

• Transport is limited by tunneling rate. • Transit time ~ 1/tunneling probability (circa fs).

• Maximum frequency: 100 THz (MIM), > 100 THz (MIIM).

• Geometric diode:

• Small diode capacitance. • Graphene a promising candidate

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5

Small Signal Rectification

• In large signal rectification the high forward (on) current usually starts after a turn-on voltage (usually a fraction of a volt in typical diodes).

• Large signal rectification ~ on/off (forward/reverse) current ratio. • In rectenna signal amplitude captured by antenna: mV and even µV.

• Large signal rectification out of scope.

• Small signal rectification is realized by nonlinearity of device.

• (Square law rectification using the first two terms in Taylor’s expansion.)

• Responsivity defined as the ratio of rectified dc current to input ac power:

• A good measure of non-linearity in small signal rectification.

• The highest degree of non-linearity is around turn-on voltage. • Poor rectification at zero volts

• Minimum degree of non-linearity.

• Not efficient for THz signal in rectennas without external bias. p V d

dI

dV

r

=

d

d V

in dc

r

dV

dr

I

P

I

Resp

p

2

1

2

1 ₌

′

′′

=

6

Resonant Tunneling IN MIIM Diodes

Metal 1 Metal 2

Dielectrics 1 2

• Tunneling probability is increased by bound states in the potential well at positive bias to Metal 2.

• Resonant tunneling through bound

states enhances the current and transit speed.

• No resonant tunneling in reverse bias: Improves large signal rectification. • Largest responsivity at onset of

resonant tunneling. However:

• The onset of resonant tunneling is at voltages larger than barrier height of Metal 1 to dielectric (typically > 0.25 V).

• Not efficient for signal in rectennas without external bias.

Symmetric MIIM in flat band condition

MIIM positive bias at Metal 2

Metal 1

Metal 2 Dielectrics

1 2 Potential Well Bound States

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7

Calculation of

Bound States

• Hamiltonian matrix is made using a set of localized base states in the stack.

• Eigenstates /energy levels are found by diagonalization or solving time independent Schrödinger equation.

• Only states localized in the potential well (lower than Elmaxand Ermax) are considered. • For each bound state in the 1D well, there are also a set of transverse excitations

which generate a band of closely spaced states.

EF2 EF1

qVox1

∆ECB

Ermax Potential Well Oxide layer 1 Oxide

Layer 2 Metal 2

Elmax Left Barrier Right Barrier Metal 1 qVox2

∆E1

∆E2

-2 -1 0 1 2 3 4 5 6 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 E n e rg y , E [ e V ]

Distance from First Oxide Surface, x [nm] Conduction Band Energy

Eigenstates State 0 State 1 State 2 State 3

Oxide Voltage = - 0.7 V tox1 = 3 nm

tox2 = 1 nm

Bound States = 1

Current Density Calculation

• A modified multi-barrier Tsu-Esaki method*is used.

• Dielectric stack: multiple slices of oxide with different barrier heights.

• J depends on DoS (E) and average occupancy of each state (uses F-D).

• Transmission probability T_coeffcalculated by transfer matrix (TM) model for tunneling through multiple barriers, containing resonant states.

• Uses WKB for wave-function at each ‘slice’ through a potential barrier by constructing a piecewise constant TM for each ‘slice’.

• Tcoeff, hence J depend on barrier height, energy,

and distance, or the area under CB.

*R. Tsu and L. Esaki, Appl. Phys. Lett. 22, 562 (1973).

( )

_[

₍

[

(

)

₎

]

_]

x

app FR x FL x x coeff L R R L dE kT qV E E kT E E E T qkT m J J

J → →

∫

∞

        − − + − + = − = 0 3 2 * exp 1 exp 1 ln 2π h

(

)

[

]

{

Bj xj j

}

Tj

m

q

E

d

P

=

exp

−

2

*

φ

−

12 Metal 1

Metal 2

Dielectrics 1 2

Potential Well Bound States

JL-R

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9

MIIM Current

-6 -4 -2 0 2 4 6

0 5 10 15

C

u

rr

e

n

t,

I

[

µµµµ

A

]

Applied Voltage, V [V]

10-10 10-8 10-6 10-4 10-2

C

u

rr

e

n

t,

I

[

A

]

Step tunneling: limited only by the wide band gap oxide.

FN

Direct tunneling through the right oxide and FN tunneling in the left oxide.

Oxide Voltage = - 2.5 V

Oxide Voltage = - 1 V

Oxide Voltage = 1.5 V Bound States = 3

Sharp rise in current due to resonant tunneling into bound states in potential well.

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Previous MIIM Results

*

Dielectric Layers Thickness

Al/Ta2O5/Al2O3 (1 nm)/Al

• Most effect of resonant tunneling on device with first oxide thickness of 3 nm (no bound states at 1 nm).

*N. Sedghi et al., ESSDERC (2013).

-3 -2 -1 0 1 2 3

10-16 10-13 10-10 10-7 10-4

C

u

rr

e

n

t,

I

[

A

]

Applied Voltage, V [V]

Thickness of first oxide

1 nm 2 nm 3 nm 4 nm

-3 -2 -1 0 1 2 3

102 105 108 1011 1014 D y n a m ic R e s is ta n c e , rd [ ΩΩΩΩ ]

Applied Voltage, V [V]

Thickness of first oxide 1 nm

2 nm

3 nm

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Previous MIIM Results

*

Various Structures

• All devices have the total thickness of 4 nm.

• Device with no resonant tunneling has no advantage over asymmetrical MIM.

• Nb₂O₅/Al₂O₃has the highest band offset between oxide layers and lowest barrier to the left metal, hence the largest effect of RT.

*N. Sedghi et al., ESSDERC (2013).

Metal 1

Metal 2

Dielectrics 1 2

Potential Well Bound States

-3 -2 -1 0 1 2 3

10-18 10-15 10-12 10-9 10-6 10-3

Asymmetric MIM Ta2O5/Al2O3 no RT

Ta2O5/Al2O3

Nb2O5/Al2O3

Nb2O5/Ta2O5

C

u

rr

e

n

t,

I

[

A

]

-3 -2 -1 0 1 2 3

101

104

107

1010

1013

1016

D

y

n

a

m

ic

R

e

s

is

ta

n

c

e

,

rd

[

ΩΩΩΩ

]

Applied Voltage, V [V] Asymmetric MIM

Ta2O5/Al2O3 no RT

Ta

2O5/Al2O3

Nb2O5/Al2O3

Nb2O5/Ta2O5

Proposed Structure

Flat band Zero Bias

• Work function of Metal 2 slightly lower than Metal 1.

• Bound states exist at zero bias when the band offset between two dielectrics is high enough.

• Even at very small positive voltage at Metal 2 the current is by resonant tunneling. • At negative voltage to Metal 2 the bound states leak to the left: no resonant

tunneling.

Metal 1 Metal 2

Dielectrics 1 2

Metal 1

Metal 2

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Design Considerations

• Large band offset between two dielectrics increases the number of bound states in the potential well.

• A good choice: Nb2O5/Al2O3.

• Small barrier height at left:

• Resonant tunneling at very small positive voltage,

• Bound states leak to the left at very small negative voltage.

• A good choice: Al/Nb₂O₅.

Metal 1

Metal 2

Dielectrics 1 2 Potential Well Bound State

• Wide choice of metals with close values of work function to fine tune the device:Al, Ti, V, Cr, Fe, Cu, Zn, Mo, Nb, Ag, W, and Ta.

• For more precise work function tuning: alloy of above metals, TaN, or TiN. • Thickness of dielectric layers can also shift the onset of resonant tunneling.

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Simulation Results

• The work function of left contact is kept at 4.5 eV and the work function of right contact is varied.

• The onset of resonant tunneling on symmetric device is at 0.25 V.

• For right metal contact work function of 4.26 eV the onset of resonant tunneling is at zero volts.

-1.0 -0.5 0.0 0.5 1.0

10-12 10-10 10-8 10-6 10-4 10-2 100

Highest nonlinearity for larger small signal rectification.

C

u

rr

e

n

t,

I

[

A

]

Right Metal WF 4.5 eV 4.3 eV 4.26 eV 4.1 eV

The onset shifts to zero by changing metal WF.

-1.0 -0.5 0.0 0.5 1.0

100 102 104 106 108

Right Metal WF 4.5 eV 4.3 eV 4.26 eV 4.1 eV

D

y

n

a

m

ic

R

e

s

is

ta

n

c

e

,

rd

[ΩΩΩΩ

]

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15

Simulation Results

Low Voltage

• Simulation at very low voltages (up to 10 mV) with step size of 10 µV. • Percentile and adjacent average algorithms used to smooth the

resonant peaks.

• Sharp rise in current after start of resonant tunneling.

-0.010 -0.005 0.000 0.005 0.010

10-12

10-10

10-8

Right Metal WF 4.269 eV (RT at 0 V) 4.274 eV (RT at 0.005 V)

C

u

rr

e

n

t,

I

[

A

]

Applied Voltage, V [V] Start of Resonant Tunneling

-0.010 -0.005 0.000 0.005 0.010 105

106 107 108

Right Metal WF 4.269 eV (RT at 0 V) 4.274 eV (RT at 0.005 V)

D

y

n

a

m

ic

R

e

s

is

ta

n

c

e

,

rd

[

ΩΩΩΩ

]

Device Nonlinearity (Responsivity)

• Rectification depends on device nonlinearity. • Highest degree of

nonlinearity (largest responsivity) at start of resonant tunneling. • The start of resonant

tunneling can be brought to zero volts.

• Large rectification for very small amplitude signals (µV) without bias.

-0.010 -0.005 0.000 0.005 0.010

-200 0 200 400 600 800 1000

Right Metal WF

4.269 eV 4.274 eV

R

e

s

p

o

n

s

iv

it

y

[

A

/W

]

Applied Voltage, V [V]

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Practical Considerations

• Selection of right metals and fine tuning the work

functions.

• This is not always straightforward.

• Stored charge at the interface of two dielectrics gives

shift to the IV characteristics.

• The right barrier heights might not be achieved due to

Fermi pinning.

• Native oxide on the bottom metal electrode is a big

issue.

• Its thickness is close to that of main dielectrics.

• …

Solutions?

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Practical Considerations

Possible Solutions

• The onset of resonant tunneling can be fine tuned

practically on trial samples.

• Metal work functions, oxide layers thicknesses, dielectric type, nitrogen or forming gas annealing.

• The IV characteristics shift due to stored charge is

insignificant for low voltage applications.

• Native oxide on metal electrodes can be removed by

dry etching prior to oxide deposition.

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Fabrication Process

Shadow Mask Photolithography

• Cross over structure by shadow mask, overlap structure by lithography. • Device dimensions: 5-100 µm.

• Single or double dielectric layers deposition by ALD or rf sputtering.

Preliminary Experimental Results

*

• MIIM device with Ta₂O₅as the main dielectric and native oxide as the second dielectric.

• Device with Cr contacts has larger current than one with Al contacts

• Smaller barrier to Cr2O3than Al2O3.

• Responsivity of 8 A/W on sample with Al contacts (close to state-of-the-art values for MIIM with resonant tunneling).

*Don Weerakkody, Electrical Engineering and Rob Treharne, Stephenson's Institute, University of Liverpool are acknowledged for device fabrication.

-1.0 -0.5 0.0 0.5 1.0

-300 -200 -100 0 100 200 300 400

C

u

rr

e

n

t

D

e

n

s

it

y

,

J

[

A

/c

m

2]

Al Contact Cr Contact

-1.0 -0.5 0.0 0.5 1.0

10-4

10-3

10-2

10-1

100

101

102

103

C

u

rr

e

n

t

D

e

n

s

it

y

,

J

[

A

/c

m

2]

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Conclusions

• Rectenna has the potential of harvesting THz energy.

• MIIM diodes benefit from resonant tunneling within bound states, increasing the operating frequency to a few 100 THz, in the range of light spectrum.

• Signals captured by antenna have very small amplitude and large signal rectification concept is not applicable.

• IN MIIM diodes the highest degree of nonlinearity is at the onset of resonant tunneling (a fraction of volt in conventional symmetric MIIM diodes).

• Poor rectification around 0 V for small signals.

• An MIIM device configuration is proposed which can bring the onset of resonant tunneling to 0 V.

• Large degree of nonlinearity for rectification of very small amplitude signals.

• Responsivity values of a few hundreds A/W around 0 V.

• Typical values without resonant tunneling few tens of A/W.

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Acknowledgement

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