JP3297934B2 - Quantum box coupling device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION This invention related <br/> the quantum boxes binding element.

[0002]

2. Description of the Related Art In recent years, in quantum wave electronics, a micro-box structure having a cross-sectional dimension comparable to the de Broglie wavelength of electrons, that is, a so-called quantum box, has been attracting attention. There is great interest in the quantum effects exhibited by two-dimensional electrons.

A quantum box coupling element is a combination of a plurality of such quantum boxes, and for example, the one shown in FIG. 9 can be considered. As shown in FIG. 9, the quantum box coupling device has a plurality of cylindrical quantum boxes arranged therein, and causes quantum mechanical tunneling of electrons (e ⁻ ) between the quantum boxes to reduce the electron distribution. It is intended to perform information processing by changing.

[0004]

The quantum box coupling device shown in FIG. 9 described above has the same symmetry (360 ° rotational symmetry) because all the quantum boxes have a cylindrical shape, and therefore have the same symmetry. The only way to control the transition probability of electrons between quantum boxes is to change the relative distance between quantum boxes. However, when the average quantum box density of the quantum box coupling element is determined, the average value of the relative distance between the quantum boxes is also determined, and therefore, only the fluctuation from the average value can be actually changed. . For this reason, the degree of freedom in designing the quantum box coupling device shown in FIG. 9 is small.

It is therefore an object of the present invention is to provide a degree of freedom is large quantum boxes binding element design.

[0006]

In order to achieve the above object, a quantum box coupling device according to a first aspect of the present invention comprises a plurality of quantum boxes including at least two types of quantum boxes having different symmetries from each other. And at least one quantum box
Is at least one pair of quantum
It includes a box .

[0007] A quantum box coupling device according to a second aspect of the present invention comprises a plurality of quantum boxes including at least a cylindrical quantum box and a polygonal quantum box.

A quantum box coupling device according to a third aspect of the present invention is constituted by a plurality of quantum boxes including at least a quantum box having a cylindrical shape and a quantum box having a quadrangular prism shape.

A quantum box coupling device according to a fourth invention of the present invention is the quantum box coupling device according to the first invention, the second invention or the third invention, wherein a plurality of quantum boxes are periodically arranged. Things.

[0010]

[0011]

According to the present invention, only the relative distance between quantum boxes is determined.
Alternatively, the transition probability of electrons between quantum boxes can be controlled by changing the relative angle between the quantum boxes. As a result, the degree of freedom in design is increased as compared with a quantum box coupling device composed of only a cylindrical quantum box .

[0012]

[0013]

[0014]

Embodiments of the present invention will be described below with reference to the drawings.

In the following, a quantum box capable of accommodating only one electron among a quantum box capable of accommodating one or more electrons is particularly called a quantum dot, and is constituted by combining a plurality of such quantum dots. The device is called a quantum dot coupling device.

The quantum dot is formed by three-dimensionally surrounding a dot-shaped well with a barrier layer. The wave function of the potential well of a single quantum dot and the ground state of electrons in the potential well are conceptually defined. This is represented as shown in FIG.

Now, consider a quantum dot coupling system composed of two quantum dots as shown in FIG. Then, the dynamics of electrons in this quantum dot coupled system is calculated from the exact solution of the electronic state of an isolated hydrogen atom to a hydrogen molecule ion (H ₂
⁺ ) LCAO (Linear Combination of Atomic Orb) known as an effective approximation method when considering the electronic state of
itals).

Considering this LCAO approximation, when the initially isolated quantum dots 1 and 2 approach each other, the ground state | 1> of the electrons of the quantum dot 1 and the ground state | of the electrons of the quantum dot 2 | In the energy level E ₀ of 2>, a split of width 2ΔE occurs, and two states of a coupled state and an anti-coupled state are obtained. The energies and wave functions of these coupled and anti-coupled states are expressed as follows.

[0019]

(Equation 1)

(Equation 2) Here, ΔE is called transfer energy,
As will be described later, it is a measure of the tunnel time τ of electrons between quantum dots.

The Hamiltonian of this coupled quantum dot system is

(Equation 3) And write

(Equation 4) Is the eigenstate of this Hamiltonian as shown by the following equation.

(Equation 5)

Now, for example, if electrons are localized in the quantum dot 1, this state is as follows.

(Equation 6) Can be written. When this state is evolved over time by the Schrodinger equation, the state at time t is

(Equation 7) Becomes

From this,

(Equation 8) At time t that satisfies, it is understood that the electrons localized in the quantum dot 1 have reached the quantum dot 2. Therefore, within the range of the LCAO approximation, the tunnel time τ of the electron from the quantum dot 1 to the quantum dot 2 is set as follows.

(Equation 9) Can be considered.

This tunnel time τ is more generally

(Equation 10) You should think like .

As described above, if the dynamics of the electrons in the quantum dot coupled system is most simplified, the electrons move by tunneling depending on the magnitude of the transfer energy ΔE between the quantum dots.

Next, the expression of the transfer energy ΔE in the range of the LCAO approximation is obtained.

Now, considering a single square quantum dot having a side length of 2d, its potential energy is

[Equation 11] It is. Therefore, if we write the kinetic energy as K, the Hamiltonian of this system is

(Equation 12) It is. The ground state of this Hamiltonian is

(Equation 13) And if its energy is E ₀ ,

[Equation 14] Holds.

On the other hand, the Hamiltonian of a quantum dot coupled system composed of two square quantum dots (see FIG. 2) can be written as the following equation.

[0028]

(Equation 15) However, if the center coordinates of one quantum dot and the center coordinates of the other quantum dot are written as shown in FIG.

(Equation 16) It is.

On the other hand, the wave function of the ground state of the Hamiltonian of a single square quantum dot represented by the equation (10) is

[Equation 17] In Although,

(Equation 18) Respectively

[Equation 19] Meets.

When the above preparations are completed, the energy eigenvalue of the Hamiltonian of the quantum dot coupled system represented by the equation (12) is calculated on the two-dimensional subspace spanned by the eigenstate of the single square quantum dot represented by the equation (15). Ask for. Since the two eigenstates represented by the equation (15) are not orthogonal, if an orthogonal basis is first constructed, this is as follows, for example.

[0031]

(Equation 20)

When the Hamiltonian matrix element is calculated on the orthogonal basis,

(Equation 21)

(Equation 22)

(Equation 23)

(Equation 24) Becomes However, in calculating these matrix elements,
Equation (16) and the following equation were used.

[0033]

(Equation 25)

As can be seen from Equations (20) and (21), the off-diagonal elements of the Hamiltonian matrix are 0, and thus this Hamiltonian matrix is actually diagonalized. Therefore, the energy eigenvalue is

(Equation 26) And their eigenvectors are

[Equation 27] It has become.

In the equations (18) and (19), from the localization of the wave function,

[Equation 28] Can be said, as energy

(Equation 29) Can be thought of as

FIG. 4 shows the result of precise calculation of the transfer energy ΔE for the two-dimensional square quantum dot coupled system as shown in FIG. 3 based on the theory described above. However, in this calculation, GaSb (barrier)
/ InAs (well) Assuming a quantum dot having a heterostructure, the length of one side of the quantum dot is 2d = 10 nm, and the effective mass of electrons inside the quantum dot, that is, the well portion of _InAs is m _InAs = 0.027 m _e. ( _Me : mass of electron in vacuum), and the effective mass of electron outside the quantum dot, ie, the barrier portion made of GaSb, is expressed as m _GaSb = 0.049.
m _e , the height of the potential barrier at the GaSb / InAs hetero interface was set to V ₀ = 0.8 eV.

FIG. 4 shows that even when the distance 2r between the quantum dots is fixed, ΔE changes greatly due to a change in the relative angle θ. For example, when 2r = 17.5 nm, as θ changes in the range of 0 to π / 4, Δ
E has changed by more than eight digits. Thus, the tunnel time τ of electrons between quantum dots can be changed by eight digits or more.

In the embodiment of the present invention, the control of the tunnel time τ of electrons between quantum dots by the control of ΔE and the control of the transition probability are used.

FIG. 5 shows a quantum dot coupling device according to a first embodiment of the present invention.

As shown in FIG. 5, in the quantum dot coupling device according to the first embodiment, a cylindrical quantum dot having 360 ° rotational symmetry and a regular square prism having 90 ° rotational symmetry are provided. A plurality of quantum dots composed of two types of quantum dots having different symmetry from the quantum dots are periodically arranged at regular intervals. In this case, the cylindrical quantum dots include at least two types of quantum dots having different diameters.

In the quantum dot coupling device according to the first embodiment, the shape of the quantum dot (cylindrical or square prism), the relative angle between the quantum dots of the square prism, the size of the cylindrical quantum dot, and the like are determined. The tunneling of electrons between quantum dots is controlled by changing the quantum dot coupling element according to the purpose of use, thereby performing information processing by changing the electron distribution.

According to the first embodiment, even if the relative distance between the quantum dots, and hence the quantum dot density, is fixed, the shape of the quantum dots, the relative angle between the quantum dots in the shape of a square prism, the quantum dots in the shape of a cylinder, By changing the size of the
Since the strength of the coupling between the quantum dots, that is, the transition probability of electrons between the quantum dots, can be controlled, a quantum dot coupling device having a desired information processing function can be realized.

FIG. 6 shows a quantum dot coupling device according to a second embodiment of the present invention.

As shown in FIG. 6, the quantum dot coupling device according to the second embodiment is composed of a plurality of two types of quantum dots having different symmetries, that is, a quantum dot having a cylindrical shape and a quantum dot having a square prism shape. Is constituted by the quantum dot coupling element according to the first embodiment, but the plurality of quantum dots are arranged non-periodically, and the interval between the quantum dots is not constant. This is different from the first embodiment.

According to the second embodiment, the relative distance between the quantum dots can be changed in addition to the shape of the quantum dots, the relative angle between the square-shaped quantum dots, the size of the cylindrical-shaped quantum dots, and the like. Also, since the transition probability of electrons between quantum dots can be controlled, there is an advantage that the degree of freedom in designing the quantum dot coupling device is large.

FIG. 7 shows a quantum dot coupling device according to a third embodiment of the present invention.

As shown in FIG. 7, in the quantum dot coupling device according to the third embodiment, a cylindrical quantum dot having a rotational symmetry of 360 ° and a regular quadrangular prism having a rotational symmetry of 90 ° are provided. A plurality of quantum dots composed of three types of quantum dots having different symmetry, that is, a quantum dot and a regular triangular prism-shaped quantum dot having a rotational symmetry of 120 °, are periodically arranged at regular intervals. As in the first embodiment, quantum dots having a columnar shape include at least two types of quantum dots having different diameters.

According to the third embodiment, as in the first embodiment, even when the relative distance between the quantum dots, that is, the quantum dot density is fixed, the shape of the quantum dot (a cylindrical shape, a square prism shape, or a positive The transition probability of electrons between quantum dots can be controlled by changing the relative angle between the quantum dots in the shape of a triangular prism, the square in the shape of a square prism, and the size of the quantum dots in a cylindrical shape. Can be realized.

In the quantum dot coupling device according to the second embodiment, three types of quantum dots, ie, a cylindrical quantum dot, a square quadrangular prism quantum dot, and a regular triangular prism quantum dot, are used. The degree of freedom of design of the quantum dot coupling device according to the second embodiment is different from that of the quantum dot coupling device according to the first embodiment using two types of quantum dots, namely, a cylindrical quantum dot and a square quadrangular quantum dot. It becomes bigger.

As described above, the transfer energy ΔE can be largely changed by changing the relative angle between the quantum dots. However, by changing the relative distance 2r between the quantum dots, ΔE can be naturally changed. It can vary greatly. However, the fact that the latter has a limited degree of freedom will be described below.

That is, consider a quantum dot coupling system as shown in FIG.
Assume that there are quantum dots. Then, since the average value of the relative distance between the quantum dots in this case, that is, the average distance is determined as <r> = (S / N) ^1/2 , the relative distance between the quantum dots is equivalent to the fluctuation from this average distance. It can only be changed to a degree. In other words, for example, the relative distance l ₁₂ between the quantum dots 1 and 2 in FIG.
If it is to be larger than r>, the relative distance d _1j between the quantum dot 1 and another quantum dot adjacent thereto, for example, the quantum dot j, and the quantum dot 2 and another quantum dot adjacent thereto, for example, the quantum dot j relative distance d _2i
Is smaller than <r> on average.

Although the embodiments of the present invention have been specifically described above, the present invention is not limited to the above embodiments, and various modifications based on the technical concept of the present invention are possible.

For example, it is possible to use a quadrangular prism-shaped quantum dot other than a quadrangular prism in place of the quadrangular prism-shaped quantum dot in the first, second and third embodiments described above. Similarly, instead of the regular triangular prism shaped quantum dots in the third embodiment, a triangular prism shaped quantum dot other than a regular triangular prism can be used.

Further, more generally, a quantum dot coupling element can be constituted by a cylindrical quantum dot and one or two or more types of polygonal quantum dots.

For example, a quantum wire coupling device can be formed by extending each quantum dot of the quantum dot coupling device shown in FIG. 5, 6, or 7 in a direction perpendicular to the surface thereof. In the thus configured quantum wire coupling device, by controlling the strength of the coupling between the quantum wires in the same manner as described in the above-described embodiment, the transition probability of electrons between the quantum wires can be controlled. Is possible.

[0056]

As described above, according to the present invention,
Consisting of a plurality of quantum boxes including at least two types of quantum boxes having different symmetries from each other, at least one type of quantum box is composed of at least one pair of non-zero relative angles between quantum boxes.
Since the child box is included , the transition probability of electrons between quantum boxes can be controlled not only by the relative distance between quantum boxes but also by the relative angle between quantum boxes and the like, so that the degree of freedom in design is large.

[Brief description of the drawings]

FIG. 1 is a schematic diagram conceptually showing a potential well of a single quantum dot and a wave function of a ground state of electrons in the potential well.

FIG. 2 is a schematic diagram illustrating a quantum dot coupling system including two quantum dots.

FIG. 3 is a schematic diagram showing a relative distance and a relative angle between quantum dots in a two-dimensional square quantum dot coupling system.

FIG. 4 is a graph showing changes in transfer energy ΔE and tunnel time τ according to the relative angle θ in the square quantum dot coupling system shown in FIG. 3;

FIG. 5 is a perspective view showing the quantum dot coupling device according to the first embodiment of the present invention.

FIG. 6 is a perspective view showing a quantum dot coupling device according to a second embodiment of the present invention.

FIG. 7 is a perspective view showing a quantum dot coupling device according to a third embodiment of the present invention.

FIG. 8 is a schematic diagram for explaining a limit in a case where transfer energy ΔE is changed by changing a relative distance between quantum dots.

FIG. 9 is a perspective view showing a quantum box coupling device configured by combining a plurality of cylindrical quantum boxes.

────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-4-137521 (JP, A) JP-A-2-210332 (JP, A) JP-A-4-354170 (JP, A) (58) Field (Int.Cl. ⁷ , DB name) H01L 29/68 H01L 29/06 H01L 29/66

Claims (4)

(57) [Claims] 1. A plurality of quantum boxes including at least two types of quantum boxes having different symmetries from each other, wherein at least one type of quantum box has a small relative angle between quantum boxes that is not zero.
A quantum box coupling device including at least a pair of quantum boxes . 2. A quantum box coupling device comprising a plurality of quantum boxes including at least a quantum box having a cylindrical shape and a quantum box having a polygonal pillar shape. 3. A quantum box coupling device comprising a plurality of quantum boxes including at least a quantum box having a cylindrical shape and a quantum box having a quadrangular prism shape. 4. The quantum box coupling device according to claim 1, wherein said plurality of quantum boxes are periodically arranged .