Ion implanted shallow energy donor centres in diamond the effect of negative electron affinity
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Ion-implanted, shallow-energy, donor centres in diamond: the effect of negative electron affinity. Johan F. Prins Department of Physics, University of Pretoria, Pretoria 0002 Gauteng, South Africa. 4 th International Conference on:

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Ion-implanted, shallow-energy, donor centres in diamond: the effect of negative electron affinity.

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Ion-implanted, shallow-energy, donor centres in diamond: the effect of negative electron affinity.

Johan F. Prins

Department of Physics, University of Pretoria, Pretoria 0002

Gauteng, South Africa.

4th International Conference on:

Radiation Effects on Semiconductor Materials Detectors and Devices

July 10-12, 2002

Florence, Italy


Questions of faith:


Questions of faith:

  • Do you believe that the Second Law of Thermodynamics

  • can be negated? Energy generation from nothing? Perpetual motion?


Questions of faith:

  • Do you believe that the Second Law of Thermodynamics

  • can be negated? Energy generation from nothing? Perpetual motion?

  • Do you believe that Heisenberg’s Uncertainty Relationship

  • is a fundamental law of Physics? Does God play dice?


Questions of faith:

  • Do you believe that the Second Law of Thermodynamics

  • can be negated? Energy generation from nothing? Perpetual motion?

  • Do you believe that Heisenberg’s Uncertainty Relationship

  • is a fundamental law of Physics? Does God play dice?

3. Do you believe that the Pauli Exclusion Principle is a

fundamental law of Physics? Can the periodic table be explained without Pauli?


Questions of faith:

  • Do you believe that the Second Law of Thermodynamics

  • can be negated? Energy generation from nothing? Perpetual motion?

  • Do you believe that Heisenberg’s Uncertainty Relationship

  • is a fundamental law of Physics? Does God play dice?

3. Do you believe that the Pauli Exclusion Principle is a

fundamental law of Physics? Can the periodic table be explained without Pauli?

I believe in all three wholeheartedly!!


A simple circuit diagram

I  0

V1  V2


A simple circuit diagram

I  0

V1  V2

Current flows through S without a field in S


A simple circuit diagram

I  0

V1  V2

Current flows through S without a field in S

Resistance of S is zero


A simple circuit diagram

I  0

V1  V2

Current flows through S without a field in S

Resistance of S is zero

S is superconducting!


Outline of talk:

  • 1. Introduction:

  • n-Type doping and cold cathode action from such diamond?

  • 2. Formation of shallow donor levels in diamond:

  • Ion implantation of O+- or N+-ions to form metastable flaws.

  • 3. Donor levels above the vacuum level:

  • (a) Conditions at interface to vacuum

  • (b) Extraction of electrons at the interface

  • 4. Electron tunnelling into vacuum.

  • 5. An experimental result.

  • 6. Superconduction is required for steady-state current flow.

  • 7. Electron pair formation without phonon interaction.

  • 8. Formation of a Bose-Einstein Condensate.

  • 9. Conclusion


Negative Electron Affinity (NEA) of (111) p-type diamond surface terminated with hydrogen atoms

Himpsel et al. Phys. Rev. B 20, 624-627 (1979)


Expected behaviour of n-type diamond with negative electron affinity


The quest for n-type diamond

Substitutional nitrogen donor at 1.7 eV below conduction band:

Too deep for room temperature conduction

Phosphorus-doped diamond now being generated by CVD-growth

or ion implantation:  0.6 eV below conduction band:

Better, but electron extraction could not be obtained to date.


The quest for n-type diamond

Substitutional nitrogen donor at 1.7 eV below conduction band:

Too deep for room temperature conduction

Phosphorus-doped diamond now being generated by CVD-growth

or ion implantation:  0.6 eV below conduction band:

Better, but electron extraction could not be obtained to date.

Is diamond inherently a negative electron affinity material?


Mechanism of electron affinity change

Ristein, Maier, Riedel, Cui and Ley, Phys. Stat. Sol. (a) 181, 65-76 (2000)


What if diamond is inherently a negative electron affinity material?


What if diamond is inherently a negative electron affinity material?

Shallow donor levels imply that they should be at

energies higher than the vacuum level!


What if diamond is inherently a negative electron affinity material?

Shallow donor levels imply that they should be at

energies higher than the vacuum level!

A shallow donor level, most probably, needs to be an

anti-bonding electron orbital!


What if diamond is inherently a negative electron affinity material?

Shallow donor levels imply that they should be at

energies higher than the vacuum level!

A shallow donor level, most probably, needs to be an

anti-bonding electron orbital!

Flaws in the lattice, at which such levels form, will thus, most probably, have to be metastable defects.


What if diamond is inherently a negative electron affinity material?

Shallow donor levels imply that they should be at

energies higher than the vacuum level!

A shallow donor level, most probably, needs to be an

anti-bonding electron orbital!

Flaws in the lattice, at which such levels form, will thus, most probably, have to be metastable defects.

This could be the reason why it has been difficult to

dope diamond n-type with shallow donors.


“Quenching” in shallow donor levels:

Ion implantation at liquid nitrogen temperature, followed by rapid heating to a relatively low temperature (500 oC), was used to ”quench” in suitable, shallow donor levels, which are believed to be metastable:

O+-ions give an activation energy of  0.32 eV

J F Prins Phys. Rev. B 61 (2000) 7191.

N+-ions give an activation energy of  0.28 eV

J F Prins Semicond. Sci. Technol. 16 (2001) L50.


“Quenching” in shallow donor levels:

Ion implantation at liquid nitrogen temperature, followed by rapid heating to a relatively low temperature (500 oC), was used to ”quench” in suitable, shallow donor levels, which are believed to be metastable:

O+-ions give an activation energy of  0.32 eV

J F Prins Phys. Rev. B 61 (2000) 7191.

N+-ions give an activation energy of  0.28 eV

J F Prins Semicond. Sci. Technol. 16 (2001) L50.

The lattice flaws responsible for these levels are believed to be

the implanted atoms trapped next to vacancies and “chemically

bonded” to them.


Well, then go ahead and extract electrons!!


Well, then go ahead and extract electrons!!

However, this diagram is not physically possible! A dipole has to form at the interface to the vacuum to establish Thermodynamic equilibrium.


Equilibrium dipole at the surface of an n-type semiconductor with negative electron affinity


Attempting to extract electrons from an n-type semiconductor with negative electron affinity


Conditions required to keep on extracting electrons from the n-type semiconductor, with NEA, into the electron-charge layer:


Conditions required to keep on extracting electrons from the n-type semiconductor, with NEA, into the electron-charge layer:

It is essential to over-dope the near-surface region with shallow energy donors in order to facilitate tunnelling of the electrons from the conduction band through the surface


When does current flow between the semiconductor and anode initiate?


When does current flow between the semiconductor and anode initiate?

When, at a critical applied potential C, the extracted electrons fill the whole gap between them:

Electrical contact is then established between the

semiconductor and the anode.


When does current flow between the semiconductor and anode initiate?

When, at a critical applied potential C, the electron-charge layer fills the whole gap between them:

Electrical contact is then established between the

semiconductor and the anode.

The applied potential now manifests itself as an offset

between the Fermi levels of the

semiconductor and the anode


Critical potential C at which current flow into anode initiates:


Acceleration of classical electrons from cathode to anode:

z

cathode

anode


Schematic of equipment used to extract electrons from oxygen-ion doped diamond


An experimental result: electron extraction from oxygen-doped diamond:


Did we miss something?


The field in the gap does more than only accelerate electrons!


The field in the gap does more than only accelerate electrons!

As long as there is a field within the gap, at

the diamond’s surface, the depletion layer

below the surface will increase in width, and thus

CONTINUE TO INJECT ELECTRONS INTO THE GAP!


The field in the gap does more than only accelerate electrons!

As long as there is a field within the gap, at

the diamond’s surface, the depletion layer

below the surface will increase in width, and thus

CONTINUE TO INJECT ELECTRONS INTO THE GAP!

The electron density in the gap keeps on increasing


Current flow through diamond and gap into the anode

gap:

electron density ngap

anode

diamond

diam

gap

Janode

Jdiam

Applied potential:  = diam + gap

Through diamond: Jdiam = (diam/ddiam)

Into anode: Janode = engap(2e gap/m)1/2

Current: I = AdiamJdiam = AanodeJanode


Current flow through diamond and gap into the anode

gap:

electron density ngap

anode

diamond

diam

gap

Janode

Jdiam

Applied potential:  = diam + gap

Through diamond: Jdiam = (diam/ddiam)

Into anode: Janode = engap(2e gap/m)1/2

Current: I = AdiamJdiam = AanodeJanode

The current I keeps on increasing while Egap = gap/dgap keeps on decreasing, for as long as Egap  0


An unequivocal conclusion:


An unequivocal conclusion:

Steady-state current flow, as required by the Second law of Thermodynamics, can only be achieved when

Egap = 0


An unequivocal conclusion:

Steady-state current flow, as required by the Second law of Thermodynamics, can only be achieved when

Egap = 0

For Egap to become zero, the electrons within the gapHAVE TO FORM A SUPERCONDUCTING PHASE!


An unequivocal conclusion:

Steady-state current flow, as required by the Second law of Thermodynamics, can only be achieved when

Egap = 0

For Egap to become zero, the electrons within the gapHAVE TO FORM A SUPERCONDUCTING PHASE!

If this has to happen,

Mother Nature will find a way!!!


The conditions which (we now know) are required to form a superconducting phase:


The conditions which (we now know) are required to form a superconducting phase:

  • The charge carriers must have integral spin: i.e.

  • they must act like bosons.


The conditions which (we now know) are required to form a superconducting phase:

  • The charge carriers must have integral spin: i.e.

  • they must act like bosons.

  • The charge carriers must form a single, collective

  • and coherent wave function similar to a:

  • Bose-Einstein Condensate.


Increasing electron density and the Heisenberg Uncertainty Relationship


What happens at the Heisenberg limit?


What happens at the Heisenberg limit?

The electrons become confined within adjacent volumes

as pairs with zero spin.


What happens at the Heisenberg limit?

The electrons become confined within adjacent volumes

as pairs with zero spin.

The movement of an individual electron out of such a

volume into an adjacent one is forbidden by the Pauli

Exclusion Principle.


What happens at the Heisenberg limit?

The electrons become confined within adjacent volumes

as pairs with zero spin.

The movement of an individual electron out of such a

volume into an adjacent one is forbidden by the Pauli

Exclusion Principle.

Electrons can only move as pairs: The volumes within

which they are confined by the Heisenberg Uncertainty

Relationship, act as charge carriers with zero spin:

Bosons have formed!!


Einstein’s prediction 1925:Bose-Einstein Condensationof particles with mass.

“When a given number of particles approach each other sufficiently closely, and move sufficiently slowly, they will together convert to the lowest energy state possible.”


Einstein’s prediction 1925:Bose-Einstein Condensationof particles with mass.

“When a given number of particles approach each other sufficiently closely, and move sufficiently slowly, they will together convert to the lowest energy state possible.”

We now know that the particles must be bosons

or fermions, which have paired to form bosons


Automatic formation of a Bose-Einstein-like Condensate


Automatic formation of a Bose-Einstein-like Condensate

In the present experiment the electron density increases

(the electrons approach each other ever closer) and the field within the gap decreases (they are accelerated less and their speeds approach zero)


Automatic formation of a Bose-Einstein-like Condensate

In the present experiment the electron density increases

(the electrons approach each other ever closer) and the field within the gap decreases (they are accelerated less and their speeds approach zero)

At the Heisenberg limit, a close-packed arrangement of

boson-like charge carriers ensue: A Bose-Einstein-like

Condensate automatically forms.


Automatic formation of a Bose-Einstein-like Condensate

In the present experiment the electron density increases

(the electrons approach each other ever closer) and the field within the gap decreases (they are accelerated less and their speeds approach zero)

At the Heisenberg limit, a close-packed arrangement of

boson-like charge carriers ensue: A Bose-Einstein-like

Condensate automatically forms.

A superconducting phase forms!!!!


Band structure and fields after superconducting phase has formed


Schematic representation of a pure electron Bose-Einstein Condensate in vacuum:


Conclusions:

1. Diamond can be doped with shallow-energy donors.

2. Diamond is an inherent negative electron affinity material.

3. Electrons can be extracted from n-type diamond,

provided the surface is highly-doped such that these

electrons can tunnel from the conduction band into

the vacuum.

4. Once current flow into an anode is achieved, the

extracted electrons form a superconducting phase

between the diamond surface and the anode.

5. Superconduction is possible at room temperature!


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