Epitaxial superconducting devices and method of forming same

1. A method forming a superconducting region comprising the steps of:

a. providing monolayers of a crystal;

b. cleaning the surface of said crystal;

c. introducing a plurality of molecules containing acceptor atoms to an uppermost monolayer of the crystal, thereby allowing said acceptor atoms to bind with said crystal;

d. allowing said acceptor atoms to incorporate into said crystal to provide a doped region of said crystal;

e. growing at least one monolayer of crystal over said doped region to form a new uppermost layer;

f. repeating steps c-e until a density of said acceptor atoms in said doped region is sufficient to allow the doped region to function as a superconductor at a desired critical temperature; and

g. encapsulating said superconducting region by growing a monolayer of crystal over said superconducting region.

2. The method of claim 1 , wherein said acceptor atoms are selected from Group III.

3. The method of claim 1 , wherein the density of acceptors n h is determined by: n h =(rDN1/b^2)/[(a/4)(N1−1)k+dB], where

r D represents the rate of doping;

N 1 represents the number of monolayers which have been doped;

b represents the distance between neighboring crystal sites;

a represents the lattice constant of the crystal;

k represents the frequency with which monolayers are doped; and

d B represents the diameter of the effective electron density region.

4. The method of claim 1 , further including the step of:

repeating steps c-g to form an additional superconductor within the crystal.

5. The method of claim 1 , further comprising the steps of:

determining the width and length of a superconducting device to be formed utilizing said superconducting regions; and

etching said monolayers of said crystal to form the superconducting device.

6. A method forming a superconducting region comprising the steps of:

a. providing monolayers of a crystal;

b. cleaning the surface of said crystal;

c. depositing a passivation layer on an uppermost monolayer;

d. selectively removing a portion of said passivation layer to expose a portion of said uppermost monolayer;

e. introducing a plurality of molecules containing acceptor atoms to said uppermost monolayer of the crystal, thereby allowing said acceptor atoms to bind with said crystal;

f. allowing said acceptor atoms to incorporate into said crystal to provide a doped region of said crystal;

g. desorbing the passivation layer;

h. growing at least one monolayer of crystal over said doped region to form a new uppermost layer;

i. repeating steps c-h until a density of said acceptor atoms in said doped region is sufficient to allow the doped region to function as a superconductor at a desired critical temperature; and

j. encapsulating said superconducting region by growing a monolayer of crystal over said superconducting region.

7. The method of claim 6 , wherein said acceptor atoms are selected from Group III.

8. The method of claim 6 , wherein the density of acceptors n h is determined by: n h =(rDN1/b^2)/[(a/4)(N1−1)k+dB], where

r D represents the rate of doping;

N 1 represents the number of monolayers which have been doped;

b represents the distance between neighboring crystal sites;

a represents the lattice constant of the crystal;

k represents the frequency with which monolayers are doped; and

d B represents the diameter of the effective electron density region.

9. The method of claim 6 , wherein said passivation layer is provided by hydrogen.

10. The method of claim 6 , wherein said step of selectively removing is provided by lithography.

11. The method of claim 6 , wherein said step of selectively removing is provided by an STM.

12. The method of claim 6 , further comprising the steps of:

determining the width, length and depth of the superconducting region to be formed,

determining the portion of said passivation layer to be removed based upon said determined width and length of said superconducting region; and

wherein the number of times said steps of growing to form a new uppermost layer and introducing acceptors is determined by said determined depth of said superconducting region.

13. The method of claim 6 , further including the step of:

repeating steps c-i to form an additional superconductor within the crystal.

14. The method of claim 13 , wherein a tunneling Josephson Junction is formed: wherein a charging-energy Ee of said Josephson junction is approximated by Ec=((2e) ^2 /2)(d/εrε0 A), where e represents electron charge, d represents the distance between superconducting regions of the Josephson Junction, εr represents the permittivity of said crystal, ε0 represents the permittivity of a vacuum, and A represents the area of an overlapping portion of said superconducting region; wherein a junction energy E1 of said Josephson junction is approximated by Ej=[hπΔ(0)]/[(2e)^2Rn], where h represents Planck's constant, and Δ represents the superconducting energy gap; and wherein the normal resistance Rn of said Josephson junction is defined by Rn=10^4e^5.6d/A.

15. The method of claim 6 , wherein a Josephson junction is formed.

16. The method of claim 15 , wherein a tunneling Josephson junction is formed:

Wherein a charging energy Ec of said Josephson junction is approximated by Ec=((2e)^2/2)(d/εrε0 A), where e represents electron charge, d represents the distance between superconducting regions of the Josephson Junction, ε r represents the permittivity of said crystal, ε 0 represents the permittivity of vacuum, and A represents the area of an overlapping portion of said superconducting region; wherein a junction energy Ej of said Josephson Junction is approximated by Ej=[hπΔ(0)]/[(2e)^2Rn], where h represents Planck's constant divided by 2π and Δ represents the superconducting energy gap; and wherein the normal resistance Rn of said Josephson Junction is defined by Rn=10^4e^5.6d/A.

17. The method of claim 15 , wherein a weak link Josephson Junction is formed including a weak link region: wherein a charging energy E c of said Josephson Junction is approximated by E c =((2e)^2/2)(d/εrε0 A), where e represents electron charge, d represents the distance between superconducting regions of the Josephson Junction, ε r represents the permittivity of said crystal, ε 0 represents the permittivity of vacuum, and A represents the area of an overlapping portion of said superconducting region; wherein a junction energy Ej of said Josephson Junction is approximated by Ej=[hπΔ(0)]/[(2e)^2Rn], where h represents Planck's constant divided by 2π and Δ represents the superconducting energy gap; and wherein the normal resistance Rn of said Josephson Junction is defined by R n =ρ n d/A wl , where ρ n is the resistivity of the weak link region and A wl is the area of the weak link region.

18. The method of claim 6 , wherein a qubit is formed.