CN104051022A - Method for measuring state density of resistive random access memory - Google Patents

Abstract

The invention discloses a method for measuring the state density of a resistive random access memory. The method comprises the steps of testing a relaxation effect for measuring current of the resistive random access memory so as to obtain a current value measured by the experiment on the resistive random access memory, wherein the width of the state density of the resistive random access memory is selected according to the current value measured by the experiment; calculating the state density of the resistive random access memory according to the selected state density width of the resistive random access memory. According to the method disclosed by the invention, a measurement process is simple, and the state densities of the resistive random access memories which are prepared from various materials and have different structures can be obtained.

Description

A kind of method of measuring resistance-variable storing device state density

Technical field

The present invention relates to semiconductor memory technologies field, especially a kind of method of measuring resistance-variable storing device state density.

Background technology

Storer is the important semiconductor devices of a class, along with the especially development of portable electric appts of continuous progress of electronic technology, nonvolatile memory shared share in whole storage market is increasing, and wherein more than 90% share is occupied by flash memory (Flash).But along with device size constantly dwindles, the development of Flash is restricted, its program voltage can not reduce in proportion on the one hand, and on the other hand along with device size reduces, tunnel oxidation layer attenuate, charge holding performance declines.This is paid close attention to the Nonvolatile resistance variation memory (Resistive Random Access Memory, RRAM) that carries out data storage based on resistance variations widely.

Resistance-variable storing device (RRAM), as a kind of new nonvolatile memory, has the advantages such as simple in structure, operating rate is fast, low in energy consumption, Information preservation is stable, is one of strong rival of nonvolatile memory of future generation.But unintelligible due to RRAM microphysics mechanism, has seriously hindered its development.From the microphysics mechanism of the most basic microcosmic point research RRAM, there is important directive function for the storage characteristics of control and raising device.

In semiconductor applications, the electric charge transmission in semiconductor material is to determine one of key factor of performance of semiconductor device, and determines that the key factor of charge transmission is power spectrum, is also referred to as state density (Density of states, DOS).In statistical mechanics and Condensed Matter Physics, state density or the density of states be near a certain energy between per unit energy range in the number of microstate.For the material with regular crystal structure, mainly to calculate and obtain its state density by first principle, but for the material of disordered structure, unique method is to carry out matching by the state density method of comparative experiments use experience to obtain its state density at present.

For resistance-variable storing device, the resistive phenomenon showing due to its I-E characteristic mainly ascribes conductive filament to, therefore, the structure of device itself and material behavior have material impact for the formation of conductive filament, in addition, composition and the structure of conductive filament have uncertainty, therefore, the state density of calculating to obtain resistance-variable storing device by first principle cannot realize, and then how to obtain resistance-variable storing device state density be the large technical barrier existing at present.

Summary of the invention

(1) technical matters that will solve

In view of this, fundamental purpose of the present invention is to provide a kind of method of measuring resistance-variable storing device state density, to obtain the state density of the various materials resistance-variable storing device different with structure.

(2) technical scheme

For achieving the above object, the invention provides a kind of method of measuring resistance-variable storing device state density, the method comprises:

The relaxation effect of experiment measuring resistance-variable storing device electric current, obtains the current value of this resistance-variable storing device experiment measuring;

Choose the state density width of this resistance-variable storing device according to the current value of this experiment measuring;

Calculate this resistance-variable storing device state density according to the state density width of this resistance-variable storing device of choosing.

In such scheme, the relaxation effect of described experiment measuring resistance-variable storing device electric current, obtain the current value of this resistance-variable storing device experiment measuring, comprise: adopt characteristic of semiconductor analytic system to measure the relaxation effect of resistance-variable storing device electric current, obtain the current value of this resistance-variable storing device experiment measuring, the current value of this experiment measuring is time dependent.

In such scheme, the described current value according to this experiment measuring is chosen the state density width of this resistance-variable storing device, comprising: the number of states N that first determines unit volume _t, grating constant α ^-1and the frequency v of phonon vibration ₀these three parameters, then choose different state density width cs substitution formula (1) to the theoretical time dependent current value of this resistance-variable storing device that calculates of formula (10), in the time that the error of the time dependent current value of this resistance-variable storing device of theory calculating and the current value of described experiment measuring is less than 5%, choose the state density width cs that state density width cs is now this resistance-variable storing device.

In such scheme, the number of states N of described definite unit volume _t, grating constant α ^-1and the frequency v of phonon vibration ₀these three parameters, N _tscope be 1 × 10 ²²to 1 × 10 ²⁹m ³, grating constant α ^-1scope be 0.5nm to 5nm, the frequency v of phonon vibration ₀scope is 1 × 10 ¹⁰s ^-1to 1 × 10 ¹³s ^-1.

In such scheme, described in choose different state density width cs substitution formula (1) to the theoretical process of calculating the time dependent current value of this resistance-variable storing device of formula (10), state density width cs is from 1k _bt starts, and step-length is 0.1k _bt, at 1k _bt to 6k _bwithin the scope of T, choose.

In such scheme, describedly choose different state density width cs substitution formula (1) to the theoretical process of calculating the time dependent current value of this resistance-variable storing device of formula (10), formula (1) is as follows respectively to formula (10):

Based on Miller-Abrahams theory, according to the speed of charge carrier probability calculation carrier transition of transition in energy space,

$v=v_0\exp (-\left\{\begin{array}{cc}2\mathrm{\&alpha;}{R}_{\mathrm{ij}}(1+\mathrm{\&beta;}\cos \mathrm{\&theta;})+E_j-E_i.& E_j\&GreaterEqual;E_i-\mathrm{\&beta;}\cos \mathrm{\&theta;}\\ 2\mathrm{\&alpha;}{R}_{\mathrm{ij},}& E_j<E_i-\mathrm{\&beta;}\cos \mathrm{\&theta;}\end{array}\right.),---\left(1\right)$

V in formula ₀the frequency that represents phonon vibration, α represents the inverse of grating constant, R _ijrepresent the space length of position i and position j, β=Fe/ (2 α k _bt), wherein F represents the added electric field in device two ends, k _brepresent Boltzmann constant, T represents temperature, and θ represents the angle of transition direction and direction of an electric field, and scope is 0 to π;

Based on the feature of randomness system, will select gauss' condition density to represent the distribution situation of charge carrier, gauss' condition density is:

$g\left(E\right)=\frac{N_t}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp (-\frac{E^2}{2{\mathrm{\&sigma;}}^2\mathrm{}}),---\left(2\right)$

N in formula _tthe number of states of representation unit volume, E represents the energy after normalization, σ=σ ^*.k _bt represents the width of state density;

Based on Miller-Abrahams theory, in energy space, be not expressed as by the empty position of carriers occupying:

$N(T,\mathrm{\&beta;},E_i,R)=\frac{1}{{8\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{0}{\overset{R}{\&Integral;}}\mathrm{dr}2\mathrm{\&pi;r}2\underset{-\&infin;}{\overset{R+E_i-r(1+\mathrm{\&beta;}\cos \mathrm{\&theta;})}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F)),---\left(3\right)$

F (E in formula _j, E _f)=1/ (1+exp (E _j-E _f)) represent that Fermi-Di Lake distributes, 1-f (E _j, E _f) represent the rearmost position probability that is empty position;

By changing integration variable, formula (3) will become following form:

$\begin{array}{c}N(T,\mathrm{\&beta;},E_i,R)=\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F))\\ +\frac{2\mathrm{\&pi;}}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\overset{E_i+R}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F)){\left(\frac{E_i-E_j+R}{1+\mathrm{\&beta;}\cos \mathrm{\&theta;}}\right)}^3\end{array},---\left(4\right)$

The right Section 1 represents that charge carrier is to the number in deep level motion with empty position in formula (4), and Section 2 represents the number of shallow energy level; For the Relaxation Phenomena in randomness system, charge carrier moves downward leads accounting for, and therefore, the charge carrier moving upward will not consider, formula (4) will be expressed as:

$N(T,\mathrm{\&beta;},E_i,R)\&ap;\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)[1-f(E_j,E_F)],---\left(5\right)$

According to range transition theory, under the condition of a given electric field and temperature, carrier transition to new position, this position must meet minimum energy, and therefore, the scope of carrier transition can be passed through N (T, β, E _i, R)=1 to try to achieve, formula (5) will become:

$\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)[1-f(E_j,E_F)]=1,---\left(6\right)$

By simultaneous equations (1) and equation (6), can obtain following equation:

$\frac{2\mathrm{\&pi;}{\left[\ln \left(v_{0}t\right)\right]}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_d\left(t\right)-\ln \left(v_{0}t\right)\mathrm{\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F))=1,---\left(7\right)$

In addition, consider that charge carrier all moves downward after entering system before Relaxation Phenomena occurs, therefore, the probability that can suppose to have in system before Relaxation Phenomena occurs acupuncture point is 100%, that is, and and 1-f (E _j, E _f)=1;

The electric current of last characterizing device, in system, the diffusion constant of charge carrier can be expressed as:

$D\left(E\right)=\frac{{\stackrel{\&OverBar;}{R\left(E\right)}}^2}{6{\left(2\mathrm{\&alpha;}\right)}^2}{v}_0\exp (-\stackrel{\&OverBar;}{R\left(E\right)}),---\left(8\right)$

Electricity in system is led and is expressed as:

${\mathrm{\&sigma;}}_c=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}d{\mathrm{Ee}}^{2}D\left(E\right)f(E,E_d\left(t\right))g\left(E\right),---\left(9\right)$

Reometer is shown:

I _n＝σ _c×F×S， (10)

In formula, S represents the area of device.

In such scheme, the state density width of this resistance-variable storing device that described basis is chosen calculates this resistance-variable storing device state density, comprising:

By the state density width cs substitution formula (2) of this selected resistance-variable storing device, calculate g (E) and be the state density of resistance-variable storing device, wherein formula (2) is as follows:

Gauss' condition density $g\left(E\right)=\frac{N_t}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp (-\frac{E^2}{2{\mathrm{\&sigma;}}^2})---\left(2\right)$

N in formula _tthe number of states of representation unit volume, E represents the energy after normalization, σ=σ ^*/ k _bt represents the width of state density.

(3) beneficial effect

Can find out from technique scheme, the present invention has following beneficial effect:

1, the method of this measurement resistance-variable storing device state density provided by the invention, according to the analysis to Related Research Domain present situation, transition theory based on charge carrier and the relaxation characteristic of charge carrier, first the relaxation effect of experiment measuring resistance-variable storing device electric current obtains the current value of this resistance-variable storing device experiment measuring, then choose the state density width of this resistance-variable storing device according to the current value of this experiment measuring, the last state density width according to this resistance-variable storing device of choosing calculates this resistance-variable storing device state density, the method measuring process is simple, can obtain the state density of the various materials resistance-variable storing device different with structure.

2, the method for this measurement resistance-variable storing device state density provided by the invention, mainly adopts experiment measuring and the theoretical method combining of calculating, by the control to error, and the state density of acquisition resistance-variable storing device that can be more accurate; In addition, compared with the existing method of calculating acquisition state density by first principle, the present invention has shortened the required time of measurement and calculation greatly; Finally, haveing nothing to do of method provided by the invention and material structure, therefore, can be applied to the various devices with different materials structure in principle.

Brief description of the drawings

Fig. 1 is the method flow diagram of measurement resistance-variable storing device state density provided by the invention.

Fig. 2 be according to the embodiment of the present invention by experiment and models fitting obtain Cu/WO ₃the result of/Pt resistance-variable storing device Relaxation Phenomena and the size of state density width cs.

Fig. 3 is the Cu/WO according to the acquisition of the embodiment of the present invention ₃the state density result of/Pt resistance-variable storing device.

Fig. 4 be according to the embodiment of the present invention by experiment and models fitting obtain SnO ₂: F/Fe ₂o ₃the result of/Au resistance-variable storing device Relaxation Phenomena and the size of state density width cs.

Fig. 5 is the SnO according to the acquisition of the embodiment of the present invention ₂: F/Fe ₂o ₃the state density result of/Au resistance-variable storing device.

Embodiment

For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.

As shown in Figure 1, the invention provides the method for measuring resistance-variable storing device state density, comprise the following steps:

Step 1: the relaxation effect of experiment measuring resistance-variable storing device electric current, obtains the current value of this resistance-variable storing device experiment measuring;

Step 2: the state density width of choosing this resistance-variable storing device according to the current value of this experiment measuring;

Step 3: calculate this resistance-variable storing device state density according to the state density width of this resistance-variable storing device of choosing.

The relaxation effect of the resistance-variable storing device of experiment measuring described in step 1 electric current, obtain the current value of this resistance-variable storing device experiment measuring, comprise: adopt characteristic of semiconductor analytic system to measure the relaxation effect of resistance-variable storing device electric current, obtain the current value of this resistance-variable storing device experiment measuring, the current value of this experiment measuring is time dependent.

In step 2, the described current value according to this experiment measuring is chosen the state density width of this resistance-variable storing device, comprising: the number of states N that first determines unit volume _t, grating constant α ^-1and the frequency v of phonon vibration ₀these three parameters, then choose different state density width cs substitution formula (1) to the theoretical time dependent current value of this resistance-variable storing device that calculates of formula (10), in the time that the error of the time dependent current value of this resistance-variable storing device of theory calculating and the current value of described experiment measuring is less than 5%, choose the state density width cs that state density width cs is now this resistance-variable storing device.

Wherein, the number of states N of described definite unit volume _t, grating constant α ^-1and the frequency v of phonon vibration ₀these three parameters, N _tscope be 1 × 10 ²²to 1 × 10 ²⁹m ³, grating constant α ^-1scope be 0.5nm to 5nm, the frequency v of phonon vibration ₀scope is 1 × 10 ¹⁰s ^-1to 1 × 10 ¹³s ^-1.Describedly choose different state density width cs substitution formula (1) to the theoretical process of calculating the time dependent current value of this resistance-variable storing device of formula (10), state density width cs is from 1k _bt starts, and step-length is 0.1k _bt, at 1k _bt to 6k _bwithin the scope of T, choose.

Describedly choose different state density width cs substitution formula (1) to the theoretical process of calculating the time dependent current value of this resistance-variable storing device of formula (10), formula (1) is as follows respectively to formula (10):

Based on Miller-Abrahams theory, according to the speed of charge carrier probability calculation carrier transition of transition in energy space,

$v=v_0\exp (-\left\{\begin{array}{cc}2\mathrm{\&alpha;}{R}_{\mathrm{ij}}(1+\mathrm{\&beta;}\cos \mathrm{\&theta;})+E_j-E_i.& E_j\&GreaterEqual;E_i-\mathrm{\&beta;}\cos \mathrm{\&theta;}\\ 2\mathrm{\&alpha;}{R}_{\mathrm{ij},}& E_j<E_i-\mathrm{\&beta;}\cos \mathrm{\&theta;}\end{array}\right.),---\left(1\right)$

V in formula ₀the frequency that represents phonon vibration, α represents the inverse of grating constant, R _ijrepresent the space length of position i and position j, β=Fe/ (2 α k _bt), wherein F represents the added electric field in device two ends, k _brepresent Boltzmann constant, T represents temperature, and θ represents the angle of transition direction and direction of an electric field, and scope is 0 to π;

Based on the feature of randomness system, will select gauss' condition density to represent the distribution situation of charge carrier, gauss' condition density is:

$g\left(E\right)=\frac{N_t}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp (-\frac{E^2}{2{\mathrm{\&sigma;}}^2\mathrm{}}),---\left(2\right)$

N in formula _tthe number of states of representation unit volume, E represents the energy after normalization, σ=σ ^*/ k _bt represents the width of state density;

Based on Miller-Abrahams theory, in energy space, be not expressed as by the empty position of carriers occupying:

$N(T,\mathrm{\&beta;},E_i,R)=\frac{1}{{8\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{0}{\overset{R}{\&Integral;}}\mathrm{dr}2\mathrm{\&pi;r}2\underset{-\&infin;}{\overset{R+E_i-r(1+\mathrm{\&beta;}\cos \mathrm{\&theta;})}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F)),---\left(3\right)$

F (E in formula _j, E _f)=1/ (1+exp (E _j-E _f)) represent that Fermi-Di Lake distributes, 1-f (E _j, E _f) represent the rearmost position probability that is empty position;

By changing integration variable, formula (3) will become following form:

$\begin{array}{c}N(T,\mathrm{\&beta;},E_i,R)=\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F))\\ +\frac{2\mathrm{\&pi;}}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\overset{E_i+R}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F)){\left(\frac{E_i-E_j+R}{1+\mathrm{\&beta;}\cos \mathrm{\&theta;}}\right)}^3\end{array},---\left(4\right)$

The right Section 1 represents that charge carrier is to the number in deep level motion with empty position in formula (4), and Section 2 represents the number of shallow energy level; For the Relaxation Phenomena in randomness system, charge carrier moves downward leads accounting for, and therefore, the charge carrier moving upward will not consider, formula (4) will be expressed as:

$N(T,\mathrm{\&beta;},E_i,R)\&ap;\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)[1-f(E_j,E_F)],---\left(5\right)$

According to range transition theory, under the condition of a given electric field and temperature, carrier transition to new position, this position must meet minimum energy, and therefore, the scope of carrier transition can be passed through N (T, β, E _i, R)=1 to try to achieve, formula (5) will become:

$\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)[1-f(E_j,E_F)]=1,---\left(6\right)$

By simultaneous equations (1) and equation (6), can obtain following equation:

$\frac{2\mathrm{\&pi;}{\left[\ln \left(v_{0}t\right)\right]}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_d\left(t\right)-\ln \left(v_{0}t\right)\mathrm{\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F))=1,---\left(7\right)$

In addition, consider that charge carrier all moves downward after entering system before Relaxation Phenomena occurs, therefore, the probability that can suppose to have in system before Relaxation Phenomena occurs acupuncture point is 100%, that is, and and 1-f (E _j, E _f)=1;

The electric current of last characterizing device, in system, the diffusion constant of charge carrier can be expressed as:

$D\left(E\right)=\frac{{\stackrel{\&OverBar;}{R\left(E\right)}}^2}{6{\left(2\mathrm{\&alpha;}\right)}^2}{v}_0\exp (-\stackrel{\&OverBar;}{R\left(E\right)}),---\left(8\right)$

Electricity in system is led and is expressed as:

${\mathrm{\&sigma;}}_c=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}d{\mathrm{Ee}}^{2}D\left(E\right)f(E,E_d\left(t\right))g\left(E\right),---\left(9\right)$

Reometer is shown:

I _n＝σ _c×F×S， (10)

In formula, S represents the area of device.

Described in step 3, calculate this resistance-variable storing device state density according to the state density width of this resistance-variable storing device of choosing, comprising:

By the state density width cs substitution formula (2) of this selected resistance-variable storing device, calculate g (E) and be the state density of resistance-variable storing device, wherein formula (2) is as follows:

Gauss' condition density $g\left(E\right)=\frac{N_t}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp (-\frac{E^2}{2{\mathrm{\&sigma;}}^2})---\left(2\right)$

N in formula _tthe number of states of representation unit volume, E represents the energy after normalization, σ=σ ^*/ k _bt represents the width of state density.

Embodiment 1

The present embodiment is with Cu/WO ₃/ Pt resistance-variable storing device device is implemented as an exemplary, and first Cu/WO is measured in experiment ₃the time dependent current value of/Pt resistance-variable storing device device, result is as shown in Figure 2; Then the theoretical Cu/WO that calculates ₃the time dependent current value of/Pt resistance-variable storing device device, and then the acquisition simulation curve consistent with experimental result, in the time calculating, select following parameter: N according to relevant bibliographical information _t=1 × 10 ²⁸m ^-3, α ^-1=2.7nm, v ₀=1 × 10 ¹²s ^-1, then repeatedly choose different state density width cs substitution formula (1) to formula (10) and calculate Cu/WO ₃the time dependent current value of/Pt resistance-variable storing device device, in the present embodiment, as σ=3.2K _bwhen T, the theoretical result of calculating is consistent with experimental results, and result as shown in Figure 2.Finally σ=3.2K _bt substitution formula (2) obtains Cu/WO ₃the state density of/Pt resistance-variable storing device device, result as shown in Figure 3.

Embodiment 2

The present embodiment is with SnO ₂: F/Fe ₂o ₃/ Au resistance-variable storing device device is implemented as an exemplary, and first SnO is measured in experiment ₂: F/Fe ₂o ₃the time dependent current value of/Au resistance-variable storing device device, result is as shown in Figure 4; Then the theoretical SnO that calculates ₂: F/Fe ₂o ₃the time dependent current value of/Au resistance-variable storing device device, carries out and obtains the simulation curve consistent with experimental result, in the time calculating, according to relevant bibliographical information, selects following parameter: N _t=1 × 10 ²⁴m ^-3, α ^-1=2.7nm, v ₀=1 × 10 ¹²s ^-1, then repeatedly choose different state density width cs substitution formula (1) to formula (10) and calculate SnO ₂: F/Fe ₂o ₃the time dependent current value of/Au resistance-variable storing device device, in the present embodiment, σ=2K _bwhen T, theoretical result and the experimental results calculating causes, and result as shown in Figure 4.σ=2K _bt substitution formula (2) obtains SnO ₂: F/Fe ₂o ₃the state density of/Au resistance-variable storing device device, result as shown in Figure 5.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (7)

1. a method of measuring resistance-variable storing device state density, is characterized in that, the method comprises:

The relaxation effect of experiment measuring resistance-variable storing device electric current, obtains the current value of this resistance-variable storing device experiment measuring;

Choose the state density width of this resistance-variable storing device according to the current value of this experiment measuring;

Calculate this resistance-variable storing device state density according to the state density width of this resistance-variable storing device of choosing.

2. the method for measurement resistance-variable storing device state density according to claim 1, is characterized in that, the relaxation effect of described experiment measuring resistance-variable storing device electric current obtains the current value of this resistance-variable storing device experiment measuring, comprising:

Adopt characteristic of semiconductor analytic system to measure the relaxation effect of resistance-variable storing device electric current, obtain the current value of this resistance-variable storing device experiment measuring, the current value of this experiment measuring is time dependent.

3. the method for measurement resistance-variable storing device state density according to claim 1, is characterized in that, the described current value according to this experiment measuring is chosen the state density width of this resistance-variable storing device, comprising:

First determine the number of states N of unit volume _t, character constant alpha ^-1and the frequency v of phonon vibration ₀these three parameters, then choose different state density width cs substitution formula (1) to the theoretical time dependent current value of this resistance-variable storing device that calculates of formula (10), in the time that the error of the time dependent current value of this resistance-variable storing device of theory calculating and the current value of described experiment measuring is less than 5%, choose the state density width cs that state density width cs is now this resistance-variable storing device.

4. the method for measurement resistance-variable storing device state density according to claim 3, is characterized in that, the number of states N of described definite unit volume _t, grating constant α ^-1and the frequency v of phonon vibration ₀these three parameters, N _tscope be 1 × 10 ²²to 1 × 10 ²⁹m ³, grating constant α ^-1scope be 0.5nm to 5nm, the frequency v of phonon vibration ₀scope is 1 × 10 ¹⁰s ^-1to 1 × 10 ¹³s ^-1.

5. the method for measurement resistance-variable storing device state density according to claim 3, it is characterized in that, describedly choose different state density width cs substitution formula (1) to the theoretical process of calculating the time dependent current value of this resistance-variable storing device of formula (10), state density width cs is from 1k _bt starts, and step-length is 0.1k _bt, at 1k _bt to 6k _bwithin the scope of T, choose.

6. the method for measurement resistance-variable storing device state density according to claim 3, it is characterized in that, describedly choose different state density width cs substitution formula (1) to the theoretical process of calculating the time dependent current value of this resistance-variable storing device of formula (10), formula (1) is as follows respectively to formula (10):

Based on Moller-Abrahams theory, according to the speed of charge carrier probability calculation carrier transition of transition in energy space,

$v=v_0\exp (-\left\{\begin{array}{cc}2\mathrm{\&alpha;}{R}_{\mathrm{ij}}(1+\mathrm{\&beta;}\cos \mathrm{\&theta;})+E_j-E_i.& E_j\&GreaterEqual;E_i-\mathrm{\&beta;}\cos \mathrm{\&theta;}\\ 2\mathrm{\&alpha;}{R}_{\mathrm{ij},}& E_j<E_i-\mathrm{\&beta;}\cos \mathrm{\&theta;}\end{array}\right.),---\left(1\right)$

V in formula ₀the frequency that represents phonon vibration, α represents the inverse of grating constant, R _ijrepresent the space length of position i and position j, β=Fe/ (2 α k _bt), wherein F represents the added electric field in device two ends, k _brepresent Boltzmann constant, T represents temperature, and θ represents the angle of transition direction and direction of an electric field, and scope is 0 to π;

Based on the feature of randomness system, will select gauss' condition density to represent the distribution situation of charge carrier, gauss' condition density is:

$g\left(E\right)=\frac{N_t}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp (-\frac{E^2}{2{\mathrm{\&sigma;}}^2\mathrm{}}),---\left(2\right)$

N in formula _tthe number of states of representation unit volume, E represents the energy after normalization, σ=σ ^*/ k _bt represents the width of state density;

Based on Miller-Abrahams theory, in energy space, be not expressed as by the empty position of carriers occupying:

$N(T,\mathrm{\&beta;},E_i,R)=\frac{1}{{8\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{0}{\overset{R}{\&Integral;}}\mathrm{dr}2\mathrm{\&pi;r}2\underset{-\&infin;}{\overset{R+E_i-r(1+\mathrm{\&beta;}\cos \mathrm{\&theta;})}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F)),---\left(3\right)$

F (E in formula _j, E _f)=1/ (1+exp (E _j-E _f)) represent that Fermi-Di Lake distributes, 1-f (E _j, E _f) represent the rearmost position probability that is empty position;

By changing integration variable, formula (3) will become following form:

$\begin{array}{c}N(T,\mathrm{\&beta;},E_i,R)=\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F))\\ +\frac{2\mathrm{\&pi;}}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\overset{E_i+R}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F)){\left(\frac{E_i-E_j+R}{1+\mathrm{\&beta;}\cos \mathrm{\&theta;}}\right)}^3\end{array},---\left(4\right)$

The right Section 1 represents that charge carrier is to the number in deep level motion with empty position in formula (4), and Section 2 represents the number of shallow energy level; For the Relaxation Phenomena in randomness system, charge carrier moves downward leads accounting for, and therefore, the charge carrier moving upward will not consider, formula (4) will be expressed as:

$N(T,\mathrm{\&beta;},E_i,R)\&ap;\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)[1-f(E_j,E_F)],---\left(5\right)$

According to range transition theory, under the condition of a given electric field and temperature, carrier transition to new position, this position must meet minimum energy, and therefore, the scope of carrier transition can be passed through N (T, β, E _i, R)=1 to try to achieve, formula (5) will become:

$\frac{2\mathrm{\&pi;}{R}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_i-\mathrm{R\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)[1-f(E_j,E_F)]=1,---\left(6\right)$

By simultaneous equations (1) and equation (6), can obtain following equation:

$\frac{2\mathrm{\&pi;}{\left[\ln \left(v_{0}t\right)\right]}^3}{24{\mathrm{\&alpha;}}^3}\underset{0}{\overset{\mathrm{\&pi;}}{\&Integral;}}\mathrm{d\&theta;}\sin \mathrm{\&theta;}\underset{-\&infin;}{\overset{E_d\left(t\right)-\ln \left(v_{0}t\right)\mathrm{\&beta;}\cos \mathrm{\&theta;}}{\&Integral;}}d{E}_{j}g\left(E_j\right)(1-f(E_j,E_F))=1,---\left(7\right)$

In addition, consider that charge carrier all moves downward after entering system before Relaxation Phenomena occurs, therefore, the probability that can suppose to have in system before Relaxation Phenomena occurs acupuncture point is 100%, that is, and and 1-f (E _j, E _f)=1;

The electric current of last characterizing device, in system, the diffusion constant of charge carrier can be expressed as:

$D\left(E\right)=\frac{{\stackrel{\&OverBar;}{R\left(E\right)}}^2}{6{\left(2\mathrm{\&alpha;}\right)}^2}{v}_0\exp (-\stackrel{\&OverBar;}{R\left(E\right)}),---\left(8\right)$

Electricity in system is led and is expressed as:

${\mathrm{\&sigma;}}_c=\underset{-\&infin;}{\overset{+\&infin;}{\&Integral;}}d{\mathrm{Ee}}^{2}D\left(E\right)f(E,E_d\left(t\right))g\left(E\right),---\left(9\right)$

Reometer is shown:

I _n＝σ _c×F×S， (10)

In formula, S represents the area of device.

7. the method for measurement resistance-variable storing device state density according to claim 1, is characterized in that, the state density width of this resistance-variable storing device that described basis is chosen calculates this resistance-variable storing device state density, comprising:

By the state density width cs substitution formula (2) of this selected resistance-variable storing device, calculate g (E) and be the state density of resistance-variable storing device, wherein formula (2) is as follows:

$g\left(E\right)=\frac{N_t}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\exp (-\frac{E^2}{2{\mathrm{\&sigma;}}^2})---\left(2\right)$

N in formula _tthe number of states of representation unit volume, E represents the energy after normalization, σ=σ ^*/ k _bt represents the width of state density.