Silicon-germanium heterostructures with quantum wells having oscillatory germanium concentration profiles for increased valley splitting
Semiconductor heterostructures, methods of making the heterostructures, and quantum dots and quantum computation devices based on the heterostructures are provided. The heterostructures include a quantum well of strained silicon seeded with a relatively low concentration of germanium impurities disposed between two quantum barriers of germanium or a silicon-germanium alloy. The quantum wells are characterized in that the germanium concentration in the wells has an oscillating profile that increases the valley splitting in the conduction band of the silicon quantum well.
1. A semiconductor heterostructure comprising:
a first quantum barrier comprising a layer of silicon-germanium alloy or a layer of germanium;
a second quantum barrier comprising a layer of silicon-germanium alloy or a layer of germanium; and
a quantum well comprising strained, germanium-seeded silicon disposed between the first quantum barrier and the second quantum barrier, wherein the germanium concentration in the germanium-seeded silicon has an oscillating profile across the quantum well and the conduction band of the quantum well has a valley splitting of at least 20 μeV.
2. The heterostructure of claim 1 , wherein the first quantum barrier and the second quantum barrier comprise the layer of silicon-germanium alloy.
3. The heterostructure of claim 2 , wherein the oscillating profile is a sinusoidally varying profile.
4. The heterostructure of claim 2 , wherein the oscillating profile has a wavelength of 1.8 nm.
5. The heterostructure of claim 2 , wherein the oscillating profile has a wavelength of 0.32 nm.
6. The heterostructure of claim 2 , wherein the maximum concentration of germanium along the germanium concentration profile is no greater than 30 at. %.
7. The heterostructure of claim 2 , wherein the maximum concentration of germanium along the germanium concentration profile is no greater than 20 at. %.
8. The heterostructure of claim 1 , wherein the quantum well has a valley splitting in the range from 20 μeV to 100 μeV.
9. A gate-controlled quantum dot comprising:
a semiconductor heterostructure comprising:
a first quantum barrier comprising a layer of silicon-germanium alloy or a layer of germanium;
a second quantum barrier comprising a layer of silicon-germanium alloy or a layer of germanium; and
a quantum well comprising strained, germanium-seeded silicon disposed between the first quantum barrier and the second quantum barrier, wherein the germanium concentration in the germanium-seeded silicon has an oscillating profile across the quantum well; and
one or more electrostatic gates in electrical communication with the semiconductor heterostructure, wherein the one or more electrostatic gates are configured to apply a controllable potential to the quantum well that confines electrons in the quantum well in three dimensions.
10. The quantum dot of claim 9 , wherein the first quantum barrier and the second quantum barrier comprise the layer of silicon-germanium alloy.
11. The quantum dot of claim 9 , wherein the oscillating profile is a sinusoidally varying profile.
12. The quantum dot of claim 9 , wherein the oscillating profile has a wavelength of 1.8 nm.
13. The quantum dot of claim 9 , wherein the oscillating profile has a wavelength of 0.32 nm.
14. The quantum dot of claim 9 , wherein the maximum concentration of germanium along the germanium concentration profile is no greater than 30 at. %.
15. The quantum dot of claim 9 , wherein the maximum concentration of germanium along the germanium concentration profile is no greater than 20 at. %.
16. A quantum computing system for performing quantum computation, the system comprising:
a semiconductor heterostructure comprising:
first quantum barrier comprising a layer of silicon-germanium alloy or a layer of germanium;
a second quantum barrier comprising a layer of silicon-germanium alloy or a layer of germanium; and
a quantum well comprising strained, germanium-seeded silicon disposed between the first quantum barrier and the second quantum barrier, wherein the germanium concentration in the germanium-seeded silicon has an oscillating profile across the quantum well; and
one or more electrostatic gates in electrical communication with the semiconductor heterostructure, the one or more electrostatic gates being configured to apply controllable potentials to the quantum well, wherein the controllable potentials define one or more gate-controlled qubits in the heterostructure;
a controller for controlling the potentials applied by the one or more electrostatic gates; and
a sensor for reading out a state of the one or more qubits.
17. The quantum computing system of claim 16 , wherein the first quantum barrier and the second quantum barrier comprise the layer of silicon-germanium alloy.
18. The quantum computing system of claim 17 , wherein the oscillating profile is a sinusoidally varying profile.
19. The quantum computing system of claim 17 , wherein the oscillating profile has a wavelength of 1.8 nm.
20. The quantum computing system of claim 17 , wherein the oscillating profile has a wavelength of 0.32 nm.
21. The quantum computing system of claim 17 , wherein the maximum concentration of germanium along the germanium concentration profile is no greater than 30 at. %.
22. The quantum computing system of claim 17 , wherein the maximum concentration of germanium along the germanium concentration profile is no greater than 20 at. %.
23. A method of forming a quantum-confined semiconductor heterostructure, the method comprising:
growing a quantum well layer of strained, germanium-seeded silicon on a first quantum barrier layer comprising germanium or a germanium-silicon alloy via pulsed chemical vapor deposition using a pulse sequence comprising:
a first pulse having a germanium concentration that corresponds to a peak germanium concentration; and
a germanium-free pulse, wherein the pulse sequence is repeated at least twice; and
growing a second quantum barrier layer comprising germanium or a germanium-silicon alloy over the quantum well layer.
24. The method of claim 23 , wherein the pulse sequence further comprises:
one or more intermediate pulses between the first pulse and the germanium-free pulse, the one or more intermediate pulses having germanium concentrations between zero and the peak germanium concentration; and
one or more additional intermediate pulses after the germanium-free pulse, the one or more additional intermediate pulses having germanium concentrations between zero and the peak germanium concentration.