**4.2.1 Background of sub-micrometer scale tunnel junctions**

Sub-micrometer scale tunnel junctions have attracted much interest due to their potential application in magnetic random access memories (MRAMs), fast detectors of terahertz (THz) and IR radiation and superconducting quantum interference devices (SQUIDs). Magnetic tunnel junctions (MTJs), which consist of two ferromagnetic metals separated by thin insulators, can be expected as ultrahigh-density MRAM devices because of the giant TMR effect at room temperature (Miyazaki et al., 1995; Moodera et al., 1995; Yuasa et al., 2004; Parkin et al., 2004). CoFeB/MgO/CoFeB MTJs with a small junction area of 0.02 m2 exhibit a large TMR ratio of 98 %, where a clear current-induced magnetization switching (CIMS) with a low switching current density of 3.6 MA/cm2 have been observed (Hayakawa et al., 2008). Antenna-coupled tunnel junction devices, which consist of metal/insulator/metal tunnel junctions coupled to a thin-film metal antenna, can also be expected as fast detectors of THz and IR radiation (Sanchez et al., 1978; Kale, 1985; Hobbs et al., 2005). Ni/NiO/Ni tunnel junctions with a junction area of 0.16m2 coupled to thin-film metal antennas can serve as IR detectors and frequency mixers in the 10 m band (Wilke et al., 1994; Fumeaux et al., 1996). Moreover, much effort has been devoted to the development of sub-micrometer scale SQUIDs, which are very promising devices with a high magnetic flux sensitivity (Rugar et al., 2004; Troeman et al., 2007; Huber et al., 2008; Kirtley et al., 2009). Aluminum SQUIDs with an effective area of 0.034m2 display a high flux sensitivity

Lithography-Free Nanostructure Fabrication Techniques Utilizing Thin-Film Edges 581

22 2 { ( ) }, <sup>2</sup>

*<sup>n</sup> k k m l*

*z*

(5)

(6)

*mE* (8)

2

2

(11)

2

*z z x*

*mE m l*

 *mE m l*

(10)

2

*mE m l*

(9)

(7)

*x y*

where *Ex*, *Ey* and *Ez* are the *x*, *y* and *z* components of the total energy of electrons, respectively, *m* is the electron mass, *ky* is the *y*-direction wave number and *n* is the positive integer. *T*(*kx*) is the transmission probability of electrons through the barrier. *T*(*kx*) is calculated by the well-known Wentzel-Kramers-Brillouin (WKB) approximation. The

> 2 0 0 <sup>1</sup> ( ) () , <sup>2</sup> *n kx <sup>y</sup> <sup>z</sup> f E dk dk*

where *f* (*E*) is the Fermi-Dirac distribution function. Substituting Eqs. (5) and (6) in Eq. (4)

2 3 0 0 0

Since the density of states in the *ky* direction for the top metal is equal to the solution of one-

. <sup>2</sup> *y y y*

2 2

*n y z*

(x) is the unit step function. The number of electrons per unit area and unit time

2 2

*n z y*

2 2

*x y y n y z*

( ) ( ( )) ] . <sup>2</sup> <sup>2</sup>

*m n f E eV <sup>E</sup> dE dE mE m l*

2

<sup>1</sup> | ( )| [ ( ) ( ( ) ) ] . 4 2 <sup>2</sup>

*S x z z x*


*<sup>e</sup> m n Tk fE <sup>E</sup> dE*

*m n <sup>N</sup> T k f E eV <sup>E</sup> dE dE*

<sup>1</sup> | ( )| [ ( ) ( ( ) ) ] , 4 2 <sup>2</sup>

*S x y y x*

from the bottom to top metal is also derived in a similar manner. When the positive bias *V* is applied to the bottom metal, the Fermi-Dirac distribution function is written by *f* (*E*+*eV*).

*m n <sup>N</sup> Tk fE <sup>E</sup> dE dE*

*<sup>m</sup> dk dE*

<sup>1</sup> | ( )| [ ( ) ] . <sup>4</sup> *<sup>T</sup> N T S x <sup>y</sup> z x k f E dk dk dE*

2

potential profile is illustrated in Fig. 11(b). Here, the electron density is given by

3 0 0

Thus, the number of electrons from the bottom to top metal is

<sup>3</sup> 0 0 <sup>1</sup>

<sup>0</sup> <sup>1</sup>

( )

*J eN N*

*T B S S*

3 0 0

Substituting Eqs. (5) and (8) in Eq. (7) gives

*T*

*B*

dimensional density of states, the relation between *ky* and *Ey* is given by

1

 

1

Consequently, we obtain for the net current density *J* through the barrier

*n z y*

yields

where  *EE E E*

*xyz*

of 1.8×10-6 0/Hz1/2, where 0=*h*/2*e* is the flux quantum, and operates in fields as high as 0.6 T (Finkler et al., 2010). Thus, sub-micrometer scale tunnel junctions can find a wide range application in various functional electronic devices.

As shown in the previous section, our nanostructure fabrication method using thin-film edges offers a way to overcome the feature size limit of conventional lithography. This method can be extended to fabricating nanoscale tunnel junctions. The realization of nanoscale tunnel junctions leads to the enhancement of the performance in MRAMs, fast detectors of THz and IR radiation and SQUIDs. From this motivation, it is of great importance to fabricate QC devices with tunnel barriers and very meaningful to investigate their *J-V* characteristics.

**4.2.2 Derivation of a formula for J-V characteristics of QC devices with tunnel barriers**  We derive a formula for *J-V* characteristics in QC devices with tunnel barriers, which consist of thin insulating barriers sandwiched between two thin metal films whose edges are crossed, shown in Fig. 11. The thicknesses of the top and bottom metal films are *lz* and *ly*, respectively. The barrier height and the barrier thickness are and *d*, respectively. The number of electrons per unit area and unit time from the top to bottom metal is given by

$$\begin{split} N\_S^T &= \int\_0^\infty v\_\mathbf{x} n(v\_\mathbf{x}) \|\, T(v\_\mathbf{x})\|^2 \, dv\_\mathbf{x} \\ &= \frac{1}{2\pi} \int\_0^\infty \frac{1}{\hbar} \frac{\partial E}{\partial k\_\mathbf{x}} n(k\_\mathbf{x}) \|\, T(k\_\mathbf{x})\|^2 \, dk\_\mathbf{x} \, \end{split} \tag{4}$$

Fig. 11. (a) QC devices with tunnel barriers and (b) the potential profile of the barrier, which is used for the calculation of the transmission probability.

where *vx* is the *x*-direction velocity, *n*(*vx*) is the number of electrons per unit volume and unit velocity, *kx* is the *x*-direction wave number, *n*(*kx*) is the electron density, is Planck's constant divided by 2 and *E* is the total energy of electrons, which is expressed by

$$\begin{aligned} E &= E\_x + E\_y + E\_z\\ &= \frac{\hbar^2}{2m} \{k\_x\:^2 + k\_y\:^2 + (\frac{n\pi}{l\_z})^2\}, \end{aligned} \tag{5}$$

where *Ex*, *Ey* and *Ez* are the *x*, *y* and *z* components of the total energy of electrons, respectively, *m* is the electron mass, *ky* is the *y*-direction wave number and *n* is the positive integer. *T*(*kx*) is the transmission probability of electrons through the barrier. *T*(*kx*) is calculated by the well-known Wentzel-Kramers-Brillouin (WKB) approximation. The potential profile is illustrated in Fig. 11(b). Here, the electron density is given by

$$m(k\_x) = \frac{1}{2\pi^2} \int\_0^\infty \int\_0^\infty f(E) dk\_y dk\_{z\_{\bar{z}}} \,\,\,\,\,\tag{6}$$

where *f* (*E*) is the Fermi-Dirac distribution function. Substituting Eqs. (5) and (6) in Eq. (4) yields

$$N\_S^T = \frac{1}{4\pi^3\hbar} \int\_0^\infty |T(k\_x)|^2 \left[\int\_0^\infty \int\_0^\infty f(E)dk\_y dk\_z\right] dE\_x. \tag{7}$$

Since the density of states in the *ky* direction for the top metal is equal to the solution of onedimensional density of states, the relation between *ky* and *Ey* is given by

$$dk\_y = \frac{m}{\hbar \sqrt{2mE\_y}} dE\_y. \tag{8}$$

Substituting Eqs. (5) and (8) in Eq. (7) gives

580 Recent Advances in Nanofabrication Techniques and Applications

of 1.8×10-6 0/Hz1/2, where 0=*h*/2*e* is the flux quantum, and operates in fields as high as 0.6 T (Finkler et al., 2010). Thus, sub-micrometer scale tunnel junctions can find a wide range

As shown in the previous section, our nanostructure fabrication method using thin-film edges offers a way to overcome the feature size limit of conventional lithography. This method can be extended to fabricating nanoscale tunnel junctions. The realization of nanoscale tunnel junctions leads to the enhancement of the performance in MRAMs, fast detectors of THz and IR radiation and SQUIDs. From this motivation, it is of great importance to fabricate QC devices with tunnel barriers and very meaningful to investigate

**4.2.2 Derivation of a formula for J-V characteristics of QC devices with tunnel barriers**  We derive a formula for *J-V* characteristics in QC devices with tunnel barriers, which consist of thin insulating barriers sandwiched between two thin metal films whose edges are crossed, shown in Fig. 11. The thicknesses of the top and bottom metal films are *lz*

The number of electrons per unit area and unit time from the top to bottom metal is

( )| ( )|

*S xx x x*

*N v n v T v dv*

*x*

Fig. 11. (a) QC devices with tunnel barriers and (b) the potential profile of the barrier, which

where *vx* is the *x*-direction velocity, *n*(*vx*) is the number of electrons per unit volume and unit velocity, *kx* is the *x*-direction wave number, *n*(*kx*) is the electron density, is Planck's

constant divided by 2 and *E* is the total energy of electrons, which is expressed by

1 1 ( )| ( )| , <sup>2</sup>

2

*<sup>E</sup> n k T k dk*

2

*xxx*

and *d*, respectively.

(4)

and *ly*, respectively. The barrier height and the barrier thickness are

0

*k*

*T*

is used for the calculation of the transmission probability.

0

application in various functional electronic devices.

their *J-V* characteristics.

given by

$$N\_S^T = \frac{1}{4\pi^3\hbar} \int\_0^\infty |T(k\_\mathbf{x})|^2 \mathbf{I} \sum\_{n=1}^\infty \int\_0^\infty f(E) \frac{m}{\hbar \sqrt{2mE\_y}} \theta(E\_y - \frac{\hbar^2}{2m}(\frac{n\pi}{l\_z})^2) dE\_y] dE\_{\mathbf{x}'} \tag{9}$$

where (x) is the unit step function. The number of electrons per unit area and unit time from the bottom to top metal is also derived in a similar manner. When the positive bias *V* is applied to the bottom metal, the Fermi-Dirac distribution function is written by *f* (*E*+*eV*). Thus, the number of electrons from the bottom to top metal is

$$N\_S^B = \frac{1}{4\pi^3\hbar} \int\_0^\alpha |T(k\_x)|^2 \left[\sum\_{n=1}^\phi \int\_0^\alpha f(E+eV)\frac{m}{\hbar\sqrt{2mE\_z}}\theta(E\_z - \frac{\hbar^2}{2m}(\frac{n\pi}{l\_y})^2)dE\_z\right]dE\_x. \tag{10}$$

Consequently, we obtain for the net current density *J* through the barrier

$$\begin{split} J &= e(N\_S^T - N\_S^B) \\ &= \frac{e}{4\pi^3 \hbar} \int\_0^\infty |T(k\_x)|^2 \Big[ \sum\_{n=1}^\infty \int\_0^\infty f(E) \frac{m}{\hbar \sqrt{2mE\_y}} \theta(E\_y - \frac{\hbar^2}{2m}(\frac{n\pi}{I\_z})^2) dE\_y \\ &- \sum\_{n=1}^\infty \int\_0^\infty f(E + eV) \frac{m}{\hbar \sqrt{2mE\_z}} \theta(E\_z - \frac{\hbar^2}{2m}(\frac{n\pi}{I\_y})^2) dE\_z \Big] dE\_x \Big] .\end{split} \tag{11}$$

Lithography-Free Nanostructure Fabrication Techniques Utilizing Thin-Film Edges 583

to these experiments, the energy gap is 4.0-4.3 eV, which agrees with recent calculation results performed using the full-potential linearized augmented plane wave (FLAPW) method within the LSDA(GGA)+U (LSDA, local-spin-density approximation; GGA, generalized gradient approximation; U, on-site Coulomb interation) (Cai et al., 2009). Since the Fermi energy of NiO is located in the level of 1.0 eV higher than the top of the valence band (Sawatzky et al., 1984), the barrier height in metal/NiO/metal tunnel junctions is estimated to be 3.0-3.3 eV. However, several researchers have reported that the barrier height in metal/NiO/metal tunnel junctions tends to become smaller than the estimated value of 3.0-3.3 eV (Doudin et al., 1997; Ono et al., 1997; Hobbs et al., 2005). For example, the barrier height of Ni/NiO/Ni tunnel junctions with a junction area of 0.3 m2 is as low as 0.18-0.22 eV with a barrier thickness of 2.5 nm (Hobbs et al., 2005). Electrodeposited Ni/NiO/Co tunnel junctions with a cross section of 0.01 m2 exhibit a low barrier height of 0.2-0.4 eV with a barrier thickness of 2-3 nm (Doudin et al., 1997). Thus, the barrier height of NiO thin films is reported to be smaller than that of NiO bulk materials. In our experiments, the barrier height in Ni/NiO/Ni QC devices is also estimated to be as low as 0.8 eV. This means that the derived formula is useful for the evaluation of the barrier height and the barrier thickness in QC devices with tunnel barriers. This fact also indicates that highquality NiO thin films were formed and Ni/NiO/Ni QC devices worked well as nanoscale tunnel devices. Therefore, our method to fabricate nanoscale junctions utilizing thin-film edges can be expected to work as a new technique for the creation of nanoscale tunnel

In this section, we present *I-V* characteristics in Ni/P3HT:PCBM/Ni QC devices, which consist of P3HT:PCBM organic molecules sandwiched between two Ni thin films whose edges are crossed. First, we introduce the background of molecular electronic devices and the motivation for fabricating QC devices with organic molecules. Then, we show the theoretical calculation for *I-V* characteristics of QC devices with organic molecules and compare them with experimental results. Finally, we discuss their possibility for switching

Molecular electronics have stimulated considerable interest as a technology that offers the prospect of scaling down device dimensions to a few nanometers and that also promotes a practical introduction to high-density memory applications (Chen et al., 1999; Reed et al., 2001; Chen et al., 2003; Lau et al., 2004; Wu et al., 2005; Mendes et al., 2005; Green et al., 2007). Especially, in the ITRS 2009 edition, molecular memory devices have been expected as candidates for beyond-CMOS devices since they offer the possibility of nanometerscale components. For examples, Au/2'-amino-4-ethynylphenyl-4'-ethynylphenyl-5' nitro-1-benzenethiolate/Au molecular devices with a junction area of 30×30-50×50 nm2 have been fabricated using nanopore methods, and have exhibited a negative differential resistance and a large on-off peak-to-valley ratio (Chen et al., 1999). Molecular devices, which comprise a monolayer of bistable [2]rotaxanes sandwiched between two Ti/Pt metal electrodes with a linewidth of 40 nm, have also been fabricated using nanoimprint lithography, and have shown bistable *I-V* characteristics with high on-off ratios and reversible switching properties (Chen et al., 2003). Moreover, cross-bar molecular devices

junctions.

devices with high on-off ratios.

**4.3 I-V characteristics of Ni/P3HT:PCBM/Ni QC devices** 

**4.3.1 Background of molecular electronic devices** 

We can calculate *J-V* characteristics as a function of the metal thickness, the barrier height and the barrier thickness using Eq. (11).

#### **4.2.3 J-V characteristics of Ni/NiO/Ni QC devices**

Fig. 12 shows the *J-V* characteristics for Ni/NiO/Ni QC devices at room temperature. Since the Ni thickness is 24 nm, the junction area is 24×24 nm2. In Fig. 12(a), solid circles are experimental data and dashed, solid and dotted lines are calculation results for barrier heights of 0.6, 0.8 and 1.0 eV, respectively, with a constant barrier thickness of 0.63 nm. In Fig. 12(b), solid circles are experimental data and dashed, solid and dotted lines are calculation results for barrier thicknesses of 0.42, 0.63 and 0.84 nm, respectively, with a barrier height of 0.8 eV. As seen from Fig. 12, experimental results are in good agreement with calculation results for a barrier height of 0.8 eV and a barrier thickness of 0.63 nm. Since the crystal structure of NiO is a NaCl-type structure with a lattice constant a = 0.42 nm, 2 monolayer of NiO is formed as shown in the inset of Fig. 12. Here, we discuss the barrier height of NiO insulating layers. The bulk NiO is a charge-transfer insulator, which has been approved by X-ray absorption (Kuiper et al., 1989) and X-ray photoemission and bremsstrahlung isochromat spectroscopy (Sawatzky et al., 1984; Elp et al., 1992). According

Fig. 12. (a) Barrier height dependence and (b) barrier thickness dependence of *J-V* characteristics for Ni/NiO/Ni QC devices with a junction area of 24×24 nm2 at room temperature.

We can calculate *J-V* characteristics as a function of the metal thickness, the barrier height

Fig. 12 shows the *J-V* characteristics for Ni/NiO/Ni QC devices at room temperature. Since the Ni thickness is 24 nm, the junction area is 24×24 nm2. In Fig. 12(a), solid circles are experimental data and dashed, solid and dotted lines are calculation results for barrier heights of 0.6, 0.8 and 1.0 eV, respectively, with a constant barrier thickness of 0.63 nm. In Fig. 12(b), solid circles are experimental data and dashed, solid and dotted lines are calculation results for barrier thicknesses of 0.42, 0.63 and 0.84 nm, respectively, with a barrier height of 0.8 eV. As seen from Fig. 12, experimental results are in good agreement with calculation results for a barrier height of 0.8 eV and a barrier thickness of 0.63 nm. Since the crystal structure of NiO is a NaCl-type structure with a lattice constant a = 0.42 nm, 2 monolayer of NiO is formed as shown in the inset of Fig. 12. Here, we discuss the barrier height of NiO insulating layers. The bulk NiO is a charge-transfer insulator, which has been approved by X-ray absorption (Kuiper et al., 1989) and X-ray photoemission and bremsstrahlung isochromat spectroscopy (Sawatzky et al., 1984; Elp et al., 1992). According

Fig. 12. (a) Barrier height dependence and (b) barrier thickness dependence of *J-V* characteristics

0 1 2 3

Voltage (V)

0 1 2 3

Voltage (V)

0

0

0.2

0.4

Current denstiy (

×104A/m2

)

0.6

0.8

1

(b)

 Exp. 

> *d* = 0.42 nm (Cal.) 0.63 0.84

0.2

0.4

Current denstiy (

×104A/m2

)

0.6

0.8

1

(a)

 Exp. 

 = 0.6 eV (Cal.) 0.8 1.0

for Ni/NiO/Ni QC devices with a junction area of 24×24 nm2 at room temperature.

and the barrier thickness using Eq. (11).

**4.2.3 J-V characteristics of Ni/NiO/Ni QC devices** 

to these experiments, the energy gap is 4.0-4.3 eV, which agrees with recent calculation results performed using the full-potential linearized augmented plane wave (FLAPW) method within the LSDA(GGA)+U (LSDA, local-spin-density approximation; GGA, generalized gradient approximation; U, on-site Coulomb interation) (Cai et al., 2009). Since the Fermi energy of NiO is located in the level of 1.0 eV higher than the top of the valence band (Sawatzky et al., 1984), the barrier height in metal/NiO/metal tunnel junctions is estimated to be 3.0-3.3 eV. However, several researchers have reported that the barrier height in metal/NiO/metal tunnel junctions tends to become smaller than the estimated value of 3.0-3.3 eV (Doudin et al., 1997; Ono et al., 1997; Hobbs et al., 2005). For example, the barrier height of Ni/NiO/Ni tunnel junctions with a junction area of 0.3 m2 is as low as 0.18-0.22 eV with a barrier thickness of 2.5 nm (Hobbs et al., 2005). Electrodeposited Ni/NiO/Co tunnel junctions with a cross section of 0.01 m2 exhibit a low barrier height of 0.2-0.4 eV with a barrier thickness of 2-3 nm (Doudin et al., 1997). Thus, the barrier height of NiO thin films is reported to be smaller than that of NiO bulk materials. In our experiments, the barrier height in Ni/NiO/Ni QC devices is also estimated to be as low as 0.8 eV. This means that the derived formula is useful for the evaluation of the barrier height and the barrier thickness in QC devices with tunnel barriers. This fact also indicates that highquality NiO thin films were formed and Ni/NiO/Ni QC devices worked well as nanoscale tunnel devices. Therefore, our method to fabricate nanoscale junctions utilizing thin-film edges can be expected to work as a new technique for the creation of nanoscale tunnel junctions.

#### **4.3 I-V characteristics of Ni/P3HT:PCBM/Ni QC devices**

In this section, we present *I-V* characteristics in Ni/P3HT:PCBM/Ni QC devices, which consist of P3HT:PCBM organic molecules sandwiched between two Ni thin films whose edges are crossed. First, we introduce the background of molecular electronic devices and the motivation for fabricating QC devices with organic molecules. Then, we show the theoretical calculation for *I-V* characteristics of QC devices with organic molecules and compare them with experimental results. Finally, we discuss their possibility for switching devices with high on-off ratios.

### **4.3.1 Background of molecular electronic devices**

Molecular electronics have stimulated considerable interest as a technology that offers the prospect of scaling down device dimensions to a few nanometers and that also promotes a practical introduction to high-density memory applications (Chen et al., 1999; Reed et al., 2001; Chen et al., 2003; Lau et al., 2004; Wu et al., 2005; Mendes et al., 2005; Green et al., 2007). Especially, in the ITRS 2009 edition, molecular memory devices have been expected as candidates for beyond-CMOS devices since they offer the possibility of nanometerscale components. For examples, Au/2'-amino-4-ethynylphenyl-4'-ethynylphenyl-5' nitro-1-benzenethiolate/Au molecular devices with a junction area of 30×30-50×50 nm2 have been fabricated using nanopore methods, and have exhibited a negative differential resistance and a large on-off peak-to-valley ratio (Chen et al., 1999). Molecular devices, which comprise a monolayer of bistable [2]rotaxanes sandwiched between two Ti/Pt metal electrodes with a linewidth of 40 nm, have also been fabricated using nanoimprint lithography, and have shown bistable *I-V* characteristics with high on-off ratios and reversible switching properties (Chen et al., 2003). Moreover, cross-bar molecular devices

Lithography-Free Nanostructure Fabrication Techniques Utilizing Thin-Film Edges 585

Here, *H*electrodes is the Hamiltonian of both of the metal electrodes, *H*molecules is the Hamiltonian of the molecule sandwiched between the metal electrodes and *H*t is the transfer Hamiltonian between the sandwiched molecule and each electrode. *H*electrodes, *H*molecules and

> electrodes , , ,

*k*

 

( . .).

and *k* is a two-dimensional wavenumber.

*V c a hc*

*k i*

is the free electron energy of 2 2 *k m* / 2 , where *m* is the free electron mass, is

indicates the top or bottom metal electrode. 0(*i*) represents the *i*th energy level

*i i*

 

*ia a*

 

,

*kkk*

*c c*

 

,

(13)

 ,*kc*

 in 

 ,*k*

F F

T(B)() is

are creation and annihilation operators for

0(2)=1.95 eV, which are estimated from Fermi levels

electrode. In this calculation, we assume the molecule has

) is the Fermi-Dirac distribution function.

*D V* (15)

2

*c* and

is the transfer matrix

, ( )

*T B*

are creation and annihilation operators for electrons of wavenumber *k* and spin index

in the *i*th energy level of the molecule. *V*

*E*F of the metal electrode, imagining that QC devices consist of the Ni electrodes and the sandwiched molecule of a P3HT:PCBM organic molecule, as shown in Fig. 13(a) (Eastman, 1970; Thompson et al., 2008). *E*F is assumed to be 9.071 eV for Ni electrodes (Wang et al., 1977). Considering *H*t as a perturbation, we can derive a formula for the *I-V* characteristics from the top to the bottom electrode using the many-body perturbation technique. As a result, the current flowing from the top to the bottom electrode can be expressed by

T B

*<sup>e</sup> Γ εΓ ε I d<sup>ε</sup> <sup>f</sup> <sup>ε</sup> eV E - f <sup>ε</sup> <sup>E</sup>*

T B

(14)

2 2

<sup>2</sup> 4 () () [ ( ) ( )], ( ( )) ( ( ) ( ))

the coupling strength between the top (bottom) Ni electrode and the P3HT:PCBM organic

T(B) T(B) T(B) *Γ* ( ) ( )| | ,

the coupling constant between the top (bottom) Ni electrode and the P3HT:PCBM organic molecule. Fig. 13(b) shows the calculated *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices under the strong coupling limit. *V*T(B) is assumed to be 10.0 meV, corresponding to

T(B) of 3927 meV. We have obtained the ohmic *I-V* characteristics with a resistance of 6.7 k. Fig. 14 shows the experimental results of *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices at room temperature. The inset represents the experimental setup. The Ni thickness is 16 nm. Therefore, the junction area is 16×16 nm2. We have obtained ohmic characteristics with a junction resistance of 32 . Here, we compare this experimental value with the

 

) is a density of states of electrons for the top (bottom) Ni electrode and *V*T(B) is

molecules 0 , , , t , , , , ,

*i*

*k i*

 

*T B*

0(1)=0.95 eV and

*H*

*H*

*H*

0

*h ε ε i Γε Γε*

and *<sup>i</sup>*, *<sup>a</sup>*

*H*t can be expressed by

Here, *k*

electrode.

 

electrons of spin index

two energy levels of

Planck's constant divided by 2

of eigenstates of the molecule. *<sup>i</sup>*, *a*

between the molecule and the

F F

where *e* is the elementary charge and *f*(

*E eV <sup>E</sup> <sup>i</sup>*

2

molecule, which is given by

where *D*T(B)(

consisting of a monolayer of bistable [2]rotaxanes sandwiched between top Ti and bottom Si electrodes (16 nm wide at 33 nm pitch) have been fabricated using SNAP methods, and have acted as 160 kbit memories patterned at a density of 100 Gbit/cm2 (Green et al., 2007). Thus, molecular electronic devices can be expected as next-generation high-density memories.

As demonstrated in the previous section, our method using thin-film edges provides the fabrication of nanoscale tunnel junctions. This method can be extended to fabricating nanoscale molecular devices. The realization of nanoscale molecular devices leads to the application in next-generation high-density memories. From this motivation, it is of great significance to fabricate QC devices with organic molecules and very interesting to investigate their *J-V* characteristics.

#### **4.3.2 Theoretical calculation and experimental results of I-V characteristics in Ni/P3HT: PCBM/Ni QC devices**

We calculate the *I-V* characteristics of QC devices with the molecule within the framework of Anderson model (Kondo et al., 2008 & 2009; Kondo, 2010). QC devices with the molecule consist of the molecule sandwiched between two thin metal films whose edges are crossed. The molecule is assumed to have two energy levels. In this calculation model, the Anderson Hamiltonian is given by

$$H = H\_{\text{electrolysis}} + H\_{\text{molecules}} + H\_{\text{t}}.\tag{12}$$

Fig. 13. (a) Energy diagram used in the calculation of *I-V* characteristics for QC devices and (b) the calculated *I-V* characteristics for QC devices under the strong coupling limit.

consisting of a monolayer of bistable [2]rotaxanes sandwiched between top Ti and bottom Si electrodes (16 nm wide at 33 nm pitch) have been fabricated using SNAP methods, and have acted as 160 kbit memories patterned at a density of 100 Gbit/cm2 (Green et al., 2007). Thus, molecular electronic devices can be expected as next-generation high-density

As demonstrated in the previous section, our method using thin-film edges provides the fabrication of nanoscale tunnel junctions. This method can be extended to fabricating nanoscale molecular devices. The realization of nanoscale molecular devices leads to the application in next-generation high-density memories. From this motivation, it is of great significance to fabricate QC devices with organic molecules and very interesting to

We calculate the *I-V* characteristics of QC devices with the molecule within the framework of Anderson model (Kondo et al., 2008 & 2009; Kondo, 2010). QC devices with the molecule consist of the molecule sandwiched between two thin metal films whose edges are crossed. The molecule is assumed to have two energy levels. In this calculation model, the Anderson

electrodes molecules t *HH H H* . (12)

**4.3.2 Theoretical calculation and experimental results of I-V characteristics in** 

Fig. 13. (a) Energy diagram used in the calculation of *I-V* characteristics for QC devices and (b) the calculated *I-V* characteristics for QC devices under the strong coupling limit.

memories.

investigate their *J-V* characteristics.

**Ni/P3HT: PCBM/Ni QC devices** 

Hamiltonian is given by

Here, *H*electrodes is the Hamiltonian of both of the metal electrodes, *H*molecules is the Hamiltonian of the molecule sandwiched between the metal electrodes and *H*t is the transfer Hamiltonian between the sandwiched molecule and each electrode. *H*electrodes, *H*molecules and *H*t can be expressed by

$$\begin{aligned} \boldsymbol{H}\_{\text{electrolysis}} &= \sum\_{\boldsymbol{\alpha}=\boldsymbol{T}\_{\boldsymbol{\sigma}}, \boldsymbol{B}k, \boldsymbol{\sigma}} \sum\_{\boldsymbol{\alpha}, \boldsymbol{\alpha}} \varepsilon\_{k\boldsymbol{\sigma}} c\_{\boldsymbol{\alpha}, k\boldsymbol{\sigma}}^{+} a\_{\boldsymbol{\alpha}, k\boldsymbol{\sigma}} \boldsymbol{\epsilon} \\ \boldsymbol{H}\_{\text{molecules}} &= \sum\_{i, \boldsymbol{\sigma}} \varepsilon\_{0} \begin{pmatrix} \boldsymbol{i} \end{pmatrix} a\_{i, \boldsymbol{\sigma}}^{+} a\_{i, \boldsymbol{\sigma}} \end{aligned} \tag{13}$$
 
$$\boldsymbol{H}\_{\text{t}} = \sum\_{\boldsymbol{\alpha}=\boldsymbol{T}\_{\boldsymbol{\sigma}}, \boldsymbol{B}k} \sum\_{i, \boldsymbol{\sigma}} \sum\_{i, \boldsymbol{\sigma}} (\boldsymbol{V}\_{\boldsymbol{\alpha}} c\_{\boldsymbol{\alpha}, k\boldsymbol{\sigma}}^{+} a\_{i, \boldsymbol{\sigma}} + \text{h.c.}) .$$

Here, *k* is the free electron energy of 2 2 *k m* / 2 , where *m* is the free electron mass, is Planck's constant divided by 2 and *k* is a two-dimensional wavenumber. ,*k c* and ,*k c* are creation and annihilation operators for electrons of wavenumber *k* and spin index in electrode. indicates the top or bottom metal electrode. 0(*i*) represents the *i*th energy level of eigenstates of the molecule. *<sup>i</sup>*, *a* and *<sup>i</sup>*, *<sup>a</sup>* are creation and annihilation operators for electrons of spin index in the *i*th energy level of the molecule. *V* is the transfer matrix between the molecule and the electrode. In this calculation, we assume the molecule has two energy levels of 0(1)=0.95 eV and 0(2)=1.95 eV, which are estimated from Fermi levels *E*F of the metal electrode, imagining that QC devices consist of the Ni electrodes and the sandwiched molecule of a P3HT:PCBM organic molecule, as shown in Fig. 13(a) (Eastman, 1970; Thompson et al., 2008). *E*F is assumed to be 9.071 eV for Ni electrodes (Wang et al., 1977). Considering *H*t as a perturbation, we can derive a formula for the *I-V* characteristics from the top to the bottom electrode using the many-body perturbation technique. As a result, the current flowing from the top to the bottom electrode can be expressed by

$$I\_{\perp} = \frac{2e^2}{h} \int\_{E\_F}^{E\_\Gamma + eV} d\varepsilon \sum\_i \left( \frac{4\Gamma\_\Gamma(\varepsilon)\Gamma\_\mathrm{B}(\varepsilon)}{\left(\varepsilon - \varepsilon\_0(i)\right)^2 + \left(\Gamma\_\mathrm{T}(\varepsilon) + \Gamma\_\mathrm{B}(\varepsilon)\right)^2} \right) \left[f(\varepsilon - eV - E\_\mathrm{F}) - f(\varepsilon - E\_\mathrm{F})\right] \tag{14}$$

where *e* is the elementary charge and *f*() is the Fermi-Dirac distribution function. T(B)() is the coupling strength between the top (bottom) Ni electrode and the P3HT:PCBM organic molecule, which is given by

$$\left|\boldsymbol{F}\_{\mathrm{T(B)}}(\boldsymbol{\varepsilon}) = \pi \,\boldsymbol{D}\_{\mathrm{T(B)}}(\boldsymbol{\varepsilon}) \mid \boldsymbol{V}\_{\mathrm{T(B)}}\right|^{2},\tag{15}$$

where *D*T(B)() is a density of states of electrons for the top (bottom) Ni electrode and *V*T(B) is the coupling constant between the top (bottom) Ni electrode and the P3HT:PCBM organic molecule. Fig. 13(b) shows the calculated *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices under the strong coupling limit. *V*T(B) is assumed to be 10.0 meV, corresponding to T(B) of 3927 meV. We have obtained the ohmic *I-V* characteristics with a resistance of 6.7 k. Fig. 14 shows the experimental results of *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices at room temperature. The inset represents the experimental setup. The Ni thickness is 16 nm. Therefore, the junction area is 16×16 nm2. We have obtained ohmic characteristics with a junction resistance of 32 . Here, we compare this experimental value with the

Lithography-Free Nanostructure Fabrication Techniques Utilizing Thin-Film Edges 587

junction area is as small as nanometer scale, the number of molecule is small, so the energy level can be discrete. This discrete energy level leads to the sharp steps in the *I-V* characteristics, which can produce such a high switching ratio. Thus, Ni/P3HT:PCBM/Ni QC devices utilizing thin-film edges can be expected to have potential application in

Fig. 15. Calculated *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices under the weak

In this chapter, we have introduced structural and electrical properties of Ni/PEN films used as electrodes in QC devices and *I-V* characteristics for three types of QC devices. The three types of QC devices are as follows: (i) Ni/Ni QC devices (17 nm linewidth, 17×17 nm2 junction area), in which two Ni thin films are directly contacted with their edges crossed, (ii) Ni/NiO/Ni QC devices (24 nm linewidth, 24×24 nm2 junction area), in which NiO thin insulators are sandwiched between two Ni thin-film edges and (iii) Ni/P3HT:PCBM/Ni QC devices (16 nm linewidth, 16×16 nm2 junction area), in which P3HT:PCBM organic molecules are sandwiched between two Ni thin-film edges. In our study, we have successfully fabricated various types of QC devices with nano-linewidth and nanojunctions, which have been obtained without the use of electron-beam or optical lithography. Our method will open up new opportunities for the creation of nanoscale patterns and can also be expected as novel technique beyond conventional lithography. Furthermore, we have presented the calculation results of the electronic transport in Ni/organic-molecule/Ni QC devices and discussed their possibility for switching devices. According to our calculation, a high switching ratio in excess of 100000:1 can be obtained under weak coupling condition. These results indicate that QC devices fabricated using thin-film edges can be expected to have potential application in next-generation switching

switching devices with high on-off ratios.

coupling condition.

**5. Conclusions** 

devices with ultrahigh on-off ratios.

calculation result. The calculation result has demonstrated that the resistance is 6.7 k, where the junction area is 1×1 nm2, which is expected as a size of one P3HT:PCBM organic molecule. The number of the conductance channel is four, taking into consideration the spin degeneracy. On the other hand, in experiments, the junction area of P3HT:PCBM organic molecules is 16×16 nm2, which corresponds to 1024 (=4×16×16) conductance channels.

Fig. 14. Experimental results of *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices with a junction area of 16×16 nm2 at room temperature. The inset represents the experimental setup.

Therefore, the junction resistance in a size of 16×16 nm2 is calculated to be 26 (=6.7k/16/16), which is in good agreement with the experimental value of 32 This result indicates that electrons in nanoscale junctions can transport through the molecules in the ballistic regime without any scattering. This also demonstrates that our method to fabricate nanoscale junctions utilizing thin-film edges can be a useful tool for the creation of nanoscale molecular devices.

#### **4.3.3 Possibility of Ni/P3HT:PCBM/Ni QC devices for switching devices**

Finally, we have discussed the possibility of Ni/P3HT:PCBM/Ni QC devices for switching devices with high on-off ratios. Fig. 15 shows the calculated *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices under the weak coupling condition. *V*T(B) is assumed to be 0.2 meV, corresponding to T(B) of 1.57 meV. From Fig. 15, the calculated result shows the sharp steps at the positions of the energy level of the P3HT:PCBM organic molecule. The offstate current *I*0 is 3.8 pA at the voltage *V*0 of 0.03 V, and the on-state current *I*1 is 0.57A at the voltage *V*1 of 1.03 V. As we estimate the switching on-off ratio, the *I*1/*I*0 ratio is found to be in excess of 100000:1. Here, it should be noted that it is essentially important that the junction area is as small as nanometer scale in order to obtain such a high on-off ratio. When the junction area is as large as micrometer scale, the number of molecules sandwiched between the electrodes is large, so the energy level can be broadened. In contrast, when the junction area is as small as nanometer scale, the number of molecule is small, so the energy level can be discrete. This discrete energy level leads to the sharp steps in the *I-V* characteristics, which can produce such a high switching ratio. Thus, Ni/P3HT:PCBM/Ni QC devices utilizing thin-film edges can be expected to have potential application in switching devices with high on-off ratios.

Fig. 15. Calculated *I-V* characteristics for Ni/P3HT:PCBM/Ni QC devices under the weak coupling condition.
