WO2014030490A1

WO2014030490A1 - Circuit design assistance device, method, and program

Info

Publication number: WO2014030490A1
Application number: PCT/JP2013/070259
Authority: WO
Inventors: 崎村　昇; 杉林　直彦; 洋紀小池; 哲郎遠藤; 貴弘羽生; 大野　英男
Original assignee: 日本電気株式会社; 国立大学法人東北大学
Priority date: 2012-08-23
Filing date: 2013-07-19
Publication date: 2014-02-27
Also published as: JPWO2014030490A1; JP6256951B2

Abstract

A circuit design assistance device (30) is provided with: an MTJ element identification unit (33) for identifying an MTJ element from circuit information indicative of the configuration of a spintronics integrated circuit; a magnetization reversal determination unit (35) for determining whether to cause a magnetization reversal, on the basis of MTJ element property information indicative of properties of an MTJ element and on the basis of an electrical current value supplied to the identified MTJ element; an approximation formula storage unit (37) for storing a first and second formula with which the relationship between the electrical current values supplied to the MTJ element and a time constant pertaining to magnetization is approximated on the basis of different theoretical models; and an operational information output unit (36) for outputting the resistance value of the MTJ element. The magnetization reversal determination unit has a first computing means for computing the time constant needed for the magnetization reversal on the basis of the first and second formulae, and a second computing means for computing a magnetization reversal probability from the computed time constant. The magnetization reversal determination unit determines whether to cause a magnetization reversal on the basis of the magnetization reversal probability. This makes it possible to swiftly and precisely simulate the operation of an integrated circuit that includes an MTJ element.

Description

Circuit design support apparatus, method and program

The present invention relates to a circuit design support apparatus, method and program, and more particularly to a circuit design support apparatus and a simulator program used for designing a spintronics integrated circuit.

Today's information communication technology has been developed separately for semiconductor device technology using electron charge and magnetic device technology using electron spin. In recent years, each technology has increased in maturity, and is hitting the walls of the limit of information processing performance of semiconductor devices and the limit of information storage capability of magnetic devices. Therefore, spintronics technology that attempts to break these limits by a synergistic effect utilizing both the degree of freedom of charge of electrons and the degree of freedom of spin has attracted attention.
A typical example of a spintronic device is a magnetoresistive device (MTJ (Magnetic Tunnel Junction) device). A typical MTJ element has a pinned magnetic layer whose magnetization is fixed in one direction (also referred to as a magnetization fixed layer) and a free magnetic layer whose magnetization direction can be arbitrarily changed to one of two directions (also referred to as a magnetization free layer). And a tunnel barrier layer formed between these magnetic layers. One bit of information (“0” or “1”) is assigned to the magnetization (direction) of the free magnetic layer. When a voltage is applied between the fixed magnetic layer and the free magnetic layer, the current flowing through the MTJ element changes depending on the magnetization of the free magnetic layer. That is, when the magnetizations of the two magnetic layers are parallel to each other (in the same direction), the tunnel current passing through the tunnel barrier layer increases (low resistance state). Conversely, when the magnetizations of the two magnetic layers are antiparallel (opposite directions), the tunnel current decreases (high resistance state). Using this property, information written in the MTJ element can be taken out. One-bit information is rewritten by inverting the magnetization direction of the free magnetic layer by applying a magnetic field of a certain level or higher to the MTJ element or by passing a spin-polarized current.
FIG. 1 is a diagram showing state transitions (states (a) to (d)) of a typical MTJ element.
The illustrated MTJ element has a pinned magnetic layer 11, a free magnetic layer 12, and a tunnel barrier layer 13 provided therebetween. An upper electrode n1 is connected to the pinned magnetic layer 11, and a lower electrode n2 is connected to the free magnetic layer 12. Here, a direction from the upper electrode n1 to the lower electrode n2 is defined as a positive direction, and a current flowing in this direction is defined as a positive current. Conversely, a direction from the lower electrode n2 toward the upper electrode n1 is defined as a negative direction, and a current flowing in this direction is defined as a negative current.
The directions of magnetization of the pinned magnetic layer 11 and the free magnetic layer 12 in the states (a) and (c) are indicated by arrows, respectively. In the state (a), the magnetization of the pinned magnetic layer 11 and the magnetization of the free magnetic layer 12 are in a parallel state (low resistance state). An MTJ element in state (a) can transition to state (c) via state (b). In the state (b), a negative current Iw1 is passed between the upper electrode n1 and the lower electrode n2 of the MTJ element. In state (b), the magnetization direction of free magnetic layer 12 is reversed, and the MTJ element transitions to state (c). In the state (c), the magnetization of the pinned magnetic layer 11 and the magnetization of the free magnetic layer 12 are in an antiparallel state (high resistance state). Further, the MTJ element in the state (c) can transition to the state (a) through the state (d). In the state (d), a positive current Iw0 is passed between the upper electrode n1 and the lower electrode n2 of the MTJ element. In the state (d), the magnetization of the free magnetic layer 12 is reversed, and the MTJ element transitions to the parallel state (low resistance state) of the state (a).
In this field of spintronics, MTJ elements are applied to semiconductor devices, and magnetic random access memories (MRAM) that can realize unprecedented performance with high capacity, high speed, and non-volatility to replace DRAM are put into practical use. Is in the process of becoming MRAM is an attempt to make a conventional semiconductor memory non-volatile, but an attempt to simultaneously realize an arithmetic function and a non-volatile memory function by incorporating an MTJ element in a logic circuit is also active. For example, Non-Patent Document 1 discloses a spintronics element logic circuit that performs a logical operation on bit information of an MTJ element and bit information input by voltage. Such various spintronic element logic circuits are complicatedly connected to realize a logic circuit capable of executing a larger and more complicated operation with a smaller area and power saving than a conventional CMOS circuit. it can. Furthermore, since the logic information inside the logic circuit is non-volatile, the calculation result before power off is not lost. Therefore, it is not necessary to store the calculation result in the nonvolatile storage device before turning off the power. Therefore, it is possible to realize high performance and power saving of the logic circuit by reducing the amount of information transferred on the data bus. In addition, the power supply can be cut off frequently, and the leakage current during non-operation, which has been increasing in recent years, can be reduced or zero. Thus, the spintronics element logic circuit is also expected as a technology that enables low power design, which has been difficult to realize in the past.

In order to design an integrated circuit incorporating an MTJ element, it is necessary to confirm whether the designed circuit operates according to specifications by simulating with a circuit simulator. However, commercial circuit simulators that are currently distributed (generally called SPICE: Simulation Program with Integrated Circuit Emphasis) are compatible with the models of transistors, resistors, capacitors, and inductors. not exist. Therefore, an equivalent circuit that realizes the magnetization reversal process and resistance characteristics of the MTJ element can be created using an ideal power supply, an ideal transistor (or an ideal switch), and the like, and used as a sub-circuit. However, in this method, several tens of elements are required to reproduce one MTJ element, and the number of terminals reaches several tens. For this reason, the calculation amount increases remarkably, and the simulation time increases explosively. Therefore, it is difficult to apply SPICE to the design of a large-scale logic operation circuit including MTJ elements.
Further, in the above-described simple MTJ element subcircuit model, it is impossible to completely simulate the behavior in which various characteristics on an actual device change in an analog manner by various parameters. For example, there is a correlation peculiar to the MTJ element as indicated by dots (measured values) in FIG. 2 between the critical current (Ic) required for magnetization reversal and time (τ _P ). If this correlation is not modeled accurately with respect to the actual measurement values, it is difficult to design to guarantee an operation margin or to prevent malfunction. However, since the relationship between the current value and time required for magnetization reversal is determined by different physical actions depending on the magnitude of the current value or the length of the magnetization reversal time, it is complicated and difficult to model with high accuracy. For example, in FIG. 2, when the rewrite current supplied to the MTJ element is sufficiently larger than Ic0 (region 2), this is a mode in which magnetization reversal is mainly caused by spin torque of current electrons, and τ _P is about 10 ns or less. It becomes. On the other hand, when the rewrite current is smaller than Ic0 (region 1), this is a mode in which magnetization reversal is mainly caused by the thermal activation effect, and τ _P is about 100 ns or more. A relational expression between the magnetization reversal critical current value and time in each of the spin torque effect and the thermal activation effect is known from Non-Patent Document 1 and the like (these relational expressions will be described later). However, these relational expressions have a limited time region that matches the actual measurement value, and there are regions that do not match the actual measurement value. For example, when τ _P is in the range of about 10 ns to 100 ns, the actual measurement value does not fit either the relational expression for the spin torque effect or the relational expression for the thermal activation effect. Since this time domain is the area that needs the most optimization in designing the circuit of the spintronics integrated circuit, a fatal circuit design error may occur unless the fitting accuracy in this time domain is improved.
The present invention focuses on the correlation between the magnetization reversal critical current value and time of an actual element, and a circuit that can simulate the correlation in a wide range and with high accuracy regardless of a specific time region (or current value region). A design support apparatus and a circuit simulator are provided.

ADVANTAGE OF THE INVENTION According to this invention, the apparatus which supports the design of the spintronics integrated circuit containing an MTJ element can be provided, and the shortening of the design time and the improvement of reliability can be expected.
Specifically, the circuit design support apparatus includes an MTJ element identification unit that identifies an MTJ element from circuit information (netlist) that represents the configuration of the spintronics integrated circuit, and MTJ element characteristic information (model) that represents the characteristics of the MTJ element. Parameter) and a current value supplied to the identified MTJ element, a magnetization reversal determination unit for determining whether to cause magnetization reversal in the MTJ element, and a supply for the MTJ element An approximate expression storage unit for storing a first expression and a second expression obtained by approximating a relationship between a current value and a time constant related to magnetization based on different theoretical models, and an operation information output for outputting a resistance value of the MTJ element The magnetization reversal determination unit includes: a first computing unit that computes a time constant required for magnetization reversal based on the first expression and the second expression; And a second calculating means for calculating a magnetization reversal probability several, characterized by determining whether cause the magnetization reversal on the basis of the magnetization reversal probability.
Further, each of the first expression and the second expression includes a current value supplied to the MTJ element as a variable, and the first arithmetic unit may arbitrarily set a current value supplied to the MTJ element. The first expression and the second expression contribute to the calculation of the time constant so that the first expression is dominant when the threshold value is greater than or equal to the threshold value, and the second expression is dominant when the threshold is small. And the magnetization reversal determining unit determines that the magnetization reversal is caused when the magnetization reversal probability exceeds an arbitrary threshold value. To do.
The approximate expression storage unit further stores a third expression that determines a ratio of the first expression and the second expression contributing to the calculation of the time constant, and a coefficient included in the third expression Is based on the MTJ element characteristic information.
Further, the third expression is represented by a Butterworth filter function expression.
The second computing means increases the magnetization reversal probability when the current value supplied to the MTJ element is equal to or greater than the threshold current set by the MTJ element characteristic information, and the magnetization reversal when the current value is small. The calculation is performed so that the probability decreases.
A circuit design method for supporting the design of a spintronics integrated circuit including an MTJ element, the first step of identifying the MTJ element from circuit information (net list) representing a configuration of the spintronics integrated circuit, and the MTJ A second step of determining whether to cause the magnetization reversal based on MTJ element characteristic information (model parameter) representing the characteristic of the element and a current value supplied to the identified MTJ element; A third step of outputting a resistance value of the MTJ element, and in the second step, a time constant required for the magnetization reversal is calculated based on the current value, and a magnetization reversal probability is calculated based on the time constant And determining whether to cause the magnetization reversal based on the magnetization reversal probability.
The second step is an equation that approximates a relationship between a current value supplied to the MTJ element and a time constant related to magnetization based on different theoretical models, and is supplied to the MTJ element, respectively. Using the first and second formulas including the current value as a variable, the first formula is mainly used when the current value supplied to the MTJ element is equal to or larger than an arbitrary threshold value, and when the current value is small, the first formula is used. The time constant is changed by changing the ratio of the first expression and the second expression contributing to the calculation of the time constant according to the current value supplied to the MTJ element so that the second expression becomes main. And when it is determined that the magnetization reversal occurs when the magnetization reversal probability exceeds an arbitrary threshold value.

The present invention can provide a design support apparatus and a program capable of performing an operation simulation of an electronic circuit including an MTJ element at high speed and with high accuracy.

FIG. 1 is a diagram for explaining a state transition of a typical MTJ element.
FIG. 2 is a graph showing the relationship between the magnetization reversal critical current Ic and the magnetization relaxation time τ _P.
FIG. 3 is a block diagram showing a schematic configuration of the electronic circuit design support apparatus according to the embodiment of the present invention.
FIG. 4 is a block diagram showing a schematic configuration of a computer system used for realizing the electronic circuit design support apparatus of FIG.
FIG. 5 is a flowchart for explaining the operation of the magnetization reversal determination unit included in the electronic circuit design support apparatus of FIG.
FIG. 6 is an operation (or state) waveform diagram of each unit obtained by the operation (calculation) of the magnetization reversal determination unit of FIG.
FIG. 7 is a graph showing a fitting curve applied to the electronic circuit design support apparatus of FIG.
Figure 8 is a graph showing the dependence of the magnetization relaxation time tau _P for the parameter α used in the realization of the fitting curve in Fig.
FIG. 9 shows that the approximate expression is Taylor-expanded near the discontinuous points in the approximate expression so that the solution does not diverge when the time constant is obtained from the approximate expression, and the number of terms kmax when the number of terms is kmax It is a graph which shows the relationship with the error (epsilon).
Figure 10 is a graph for explaining the method of obtaining the rewriting current value Iw from the magnetization relaxation time tau _P by Newton's method.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 3 is a diagram showing the configuration of the electronic circuit design support apparatus 30 according to the embodiment of the present invention. The circuit design support device 30 shown in FIG. 3 is a support device for designing a circuit including an MTJ element. With respect to arbitrary circuit information, various active element and passive element models including the MTJ element that is a component of the circuit. It is possible to perform a simulated operation based on the parameters. The support device 30 includes a circuit information input unit 31, an element information input unit 32, an MTJ element identification unit 33, a voltage / current calculation unit 34, a magnetization reversal determination unit 35, an operation information output unit 36, and an approximate expression storage unit 37. Prepare.
The circuit information input unit 31 receives circuit information representing the configuration of the spintronics integrated circuit to be designed and signal waveform information input to the circuit. The element information input unit 32 is linked to the approximate expression storage unit 37. In addition to model parameters of active elements such as CMOS transistors and passive elements such as resistors and capacitors, model parameters representing the characteristics of MTJ elements are input to the element information input unit 32. These model parameters correspond to the coefficient values in the approximate expression registered in the approximate expression storage unit 37.
The MTJ element identification unit 33 identifies the MTJ element included in the circuit from the input circuit information (net list). This identification function is realized by referring to the MTJ element model parameter input from the element information input unit 32 and checking whether the netlist includes a model name that matches the MTJ element model name described therein. The
The voltage / current calculation unit 34 uses the input waveform information input to the circuit information input unit 31 and the element information input unit 32 as the current flowing through each element included in the netlist and the voltage generated at the terminal connecting the elements. Calculated from the model parameters input to. The calculator 34 has a function of calculating a rewrite current supplied to each MTJ element and a bias voltage at both ends thereof.
The magnetization reversal determination unit 35 calculates a time constant related to magnetization reversal from the rewrite current value supplied to each MTJ element (first calculation means), and calculates a magnetization reversal probability from the time constant (second calculation). In addition, it is determined whether to cause magnetization reversal in the MTJ element based on the calculated magnetization reversal probability. The time constant and the magnetization reversal probability are calculated from the approximate expression stored in the approximate expression storage unit 37 and the value of the MTJ element model parameter.
The operation information output unit 36 operates in accordance with an instruction preliminarily described in the net list, in addition to the voltage at an arbitrary terminal and the current flowing through the element, as well as the operation waveform such as the magnetization state of the MTJ element, the resistance value, the rewrite current, and the current during sensing. The result is output by display or printing.
The electronic circuit design support device 30 can be realized by a computer system shown in FIG. A computer system 40 shown in FIG. 4 includes a storage medium 41 that stores various data necessary for calculation for calculating a magnetization reversal time such as a net list and model parameters, and a computer main body 42.
The storage medium 41 stores computer-readable information non-temporarily. The storage medium 41 stores programs for identifying MTJ elements, calculating voltages and currents, and determining the timing of magnetization reversal of MTJ elements. As will be described in detail later, this program determines whether to invert the magnetization from the first step of identifying the MTJ element from the designed circuit information, and the MTJ element characteristic information and the rewrite current value supplied to the MTJ element. Is a program that realizes at least the second step of judging the above and the third step of outputting the resistance value of the MTJ element. This program calculates the time constant required for magnetization reversal from the current value supplied to the MTJ element in the second step, calculates the magnetization reversal probability from the time constant, and generates magnetization reversal based on the magnetization reversal probability. It is characterized by making it judge whether it is made to do.
The computer main body 42 also includes an input / output device 43 for inputting / outputting data, a storage device 44 for storing a program or data read from the storage medium 41, an arithmetic device 45 for performing overall control and calculation, and a calculation result. And a display device 46 for displaying the images, and these are connected to each other by a bus 47.
In the computer system 40 configured as described above, the circuit information input unit 31 and the element information input unit 32 are realized by the input / output device 43. Further, the MTJ element identification unit 33, the voltage / current calculation unit 34, and the magnetization reversal determination unit 35 are realized by the calculation device 45. The approximate expression storage unit 37 is realized by the storage device 44 in a state incorporated in the program. The operation information output unit 36 is realized by the display device 46.
For example, the arithmetic device 45 executes a program read from the storage medium 41 and developed in the storage device 44, and calculates the timing of magnetization reversal of the MTJ element from the current value supplied to the MTJ element. At that time, the arithmetic unit 45 stores the circuit information including the MTJ elements and the element information input from the input / output device 43 via the bus 47 and the approximate expression storage unit 37 realized by the storage medium 41. An approximate expression including a stored constant (coefficient) is used. Further, the arithmetic device 45 causes the display device 46 to display operation information including a resistance value resulting from the magnetization state of the MTJ element.
Next, the operation of the electronic circuit design support apparatus 30 according to this embodiment will be described.
First, when the electronic circuit design support device 30 is activated, the arithmetic device 45 shown in FIG. 4 reads and executes a program stored in advance in the storage medium 41 and the storage device 44. Thereby, each functional block of FIG. 3 is realized by the arithmetic unit 45 as described below. That is, the arithmetic unit 45 identifies the MTJ element with reference to the circuit information (net list) and the element information (model parameter). Next, the arithmetic unit 45 calculates the initial state (voltage, current, etc.) at each element and terminal. At this time, the magnetization state and resistance value of the MTJ element are set in advance in a state designated by a netlist or model parameter. Subsequently, the arithmetic unit 45 calculates the state at each time while advancing the simulation time in increments of Δt using input signal information, model parameters, and approximate expressions. At this time, whether or not the magnetization state of the MTJ element is reversed is determined by monitoring the rewrite current flowing through the MTJ element. The time is advanced by Δt until the simulation end time described in the netlist, and the above calculation is performed each time. This calculation result is output to the storage device 44 and the storage medium 41 in FIG. 4, and the user can observe the calculation result as operation waveform data via the display device 46.
FIG. 5 shows a calculation flow of the magnetization reversal determination unit 35 in the present embodiment. Here, it is assumed that the simulation time has changed from t0 to t1 = t0 + Δt (step A0). The rewrite current value Iw has a positive or negative sign depending on the write data, but the calculation flow is basically the same in both cases of parallelization and antiparallelization. Therefore, the absolute value of the rewrite current value Iw is shown in FIG. Will be handled.
At time t1, it is compared whether or not the rewrite current value | Iw (t1) | flowing through the MTJ element is greater than or equal to an arbitrary threshold current | Ic_min | set in the model parameter file (step A1).
If the comparison result is | Iw (t1) | ≧ | Ic_min | (yes in step A1), the magnetization relaxation time constant τ is determined according to the approximate expression described later._PIs calculated (step A2). Otherwise (no in step A1), τ_PIs the intrinsic time constant τ that does not cause magnetization reversal_NOSW(Step B2). This time constant τ_NOSWIs a value previously described in the model parameter file.
Next, magnetization relaxation time constant τ_PMagnetization reversal probability P_PRBCalculate If it is determined in step A1 that | Iw (t1) | ≧ | Ic_min |, the magnetization reversal probability P when the time t has elapsed from the current application time_PRBIs P_PRB= 1−exp (−t / τ_P). In this case, the magnetization reversal probability increases with time (step A3). On the other hand, if it is determined in step A1 that | Iw (t1) | <| Ic_min | (this corresponds to the case where time t has elapsed since the supply of the rewrite current is stopped), the magnetization reversal probability P_PRBIs P_PRB= Exp (-t / τ_P). In this case, the magnetization reversal probability decreases with time (step B3).
In step A3, the magnetization reversal probability P_PRBIn step A4, the obtained magnetization reversal probability P is obtained._PRBIs compared with an arbitrary threshold value | Pth |. Magnetization reversal probability at time t1 | P_PRBIf | is greater than or equal to | Pth |, magnetization inversion occurs in the MTJ element, and the resistance value of the MTJ element changes accordingly (step A5). If not exceeded, magnetization reversal is not caused in the MTJ element, and the MTJ element maintains its state (step B5). In step B3, the magnetization reversal probability P_PRBEven when the value is obtained, the MTJ element maintains that state.
FIG. 6 is a waveform diagram showing the operation or state in each part when a transient response is simulated based on the flowchart of FIG. In order to parallelize the magnetization of the MTJ element, the rewrite current pulse Iw0 is applied in the positive direction during the period from time T0 to T1. Furthermore, in order to make the magnetization of the MTJ element antiparallel, the rewrite current pulse Iw1 is applied in the negative direction during the period from time T2 to T3.
Since Iw0 ≧ Ic_min0 at time T0, τ_PIs calculated with Iw0 as a variable, and P_PRBIs calculated. P_PRBAt a time when Pth0 exceeds Pth0 (time TR0), the magnetization of the MTJ element changes from antiparallel to parallel state, and its resistance value Rmtj is reduced in resistance (R_AP→ R_P) That is, the time from time T0 to TR0 is the magnetization reversal time (magnetization reversal delay tW0).
When the time T1 is reached, the supply of the rewrite current Iw is stopped (Iw0 <Ic_min0), τ_PIs constant (= time constant τ_NOSW) Time constant τ_NOSWIs the magnetization reversal probability P_PRBAnd finally to 0%.
Since | Iw1 | ≧ | Ic_min1 | at time T2, τ_PIs calculated with Iw1 as a variable, and P_PRBIs calculated. Here, P in the case of anti-parallelization_PRBThe sign of is defined as negative. ｜ P_PRBAt a timing when | exceeds | Pth1 | (time TR1), the magnetization of the MTJ element transitions from a parallel state to an antiparallel state, and its resistance value Rmtj is increased in resistance (R_P→ R_AP) That is, the time from time T2 to TR1 is the magnetization reversal time (magnetization reversal delay tW1).
When the time T3 is reached, the supply of the rewrite current is stopped (| Iw1 | <| Ic_min0 |), τ_PIs constant (= time constant τ_NOSW) And the magnetization reversal probability P_PRBApproaches 0.
Magnetization relaxation time constant τ in the embodiment of the present invention_PBefore describing the details of the calculation method (step A2), the relationship between the magnetization reversal current and time in a typical MTJ element will be described in detail with reference to FIG. 2 again (this relationship is described in Non-Patent Document 1). Disclosed). In the following description, the rewrite current Iw supplied to the MTJ element and the magnetization reversal critical current Ic are clearly distinguished and described. However, when incorporated in the present design support apparatus and program, τ_PIn the process of calculating Ic = Iw, it can be handled synonymously.
In FIG. 2, the upper part shows the magnetization reversal current Ic and the time ln (τ) when the magnetization of the MTJ element is parallelized._P/ T0), the lower part shows the magnetization reversal current Ic and the time ln (τ) when the magnetization of the MTJ element is made non-parallel_P/ T0). In each of the upper part and the lower part of FIG. 2, dots indicate actual measurement values, and solid lines (1) and (2) indicate approximate lines thereof.
Approximate line (1) in FIG. 2 shows the critical current Ic by the thermal activation model, and is represented by the following equation according to Non-Patent Document 1.
Ic = Ic0 {1-f_T(Τ_P}} (1)
f_T(Τ_P) = (K_BT / E) ln (τ_P/ Τ₀) ... (1 ')
Where k_BIs the Boltzmann constant, T is the absolute temperature, E is the energy barrier, τ₀Is generally 1 ns in trial time in thermal reversal. In addition, the term represented by the formula (1 ′) is referred to as a thermal activation term. In this approximation, τ_P>> τ₀(Τ_PIs about 100 ns or more), and is known to match the measured value well.
Approximate line (2) in FIG. 2 shows the critical current Ic based on the spin torque effect model, and is represented by the following equation according to Non-Patent Document 1.
Ic = Ic0 {1 + f_S(Τ_P)}} (2)
f_S(Τ_P) = (Τ_relax/ Τ_P) · Ln {π / (2√ (k_BT / E))) ... (2 ')
Where τ_relaxIs the relaxation time of the magnetic moment. In addition, the term represented by the expression (2 ′) is called a precession term. In this approximation, τ_PIs τ_relaxIt is known that in the region close to (approximately 10 ns or less), the measured value matches well.
Using either equation (1) or equation (2), τ_POr a method of switching according to the rewrite current value supplied to the MTJ element. However, since there are no tangent lines in the expressions (1) and (2), it is difficult to determine a current value to be switched.
Therefore, in the embodiment according to the present invention, new coefficients α and β that combine the expressions (1) and (2) are introduced. That is, the magnetization reversal critical current Ic is
Ic = Ic0 {1 + αf_S(Τ_P) -Βf_T(Τ_P)} ... (3)
It shall be expressed by the following formula. Where the coefficients α and β are τ_PAlternatively, a coefficient whose value varies depending on Ic takes a range of 0 to 1. For example, τ_PIs τ₀In the region of the thermal activity model that is sufficiently larger than, α approaches 0 (the precession term approaches zero), and β approaches 1. On the other hand, in the region of the spin torque model, α approaches 1 and β approaches 0 (the thermal activity term approaches zero). Such α and β may be introduced as fitting function equations.
(3) Critical current Ic and magnetization relaxation time constant τ_PThis relationship is indicated by a thick line in FIG. As shown in FIG. 7, by the introduction of α and β, the measurement is performed in the region between the thermally active region and the spin torque region, that is, in the region where neither of the equations (1) and (2) can be fitted. An approximate expression that can be fitted to a value can be realized.
As an example of the functions of α and β, a Butterworth low-pass filter function equation can be given. This function is expressed by the following equation.
α = 1 / (1 + a (τ_P/ Τ₀)^2m) (4)
β = 1−1 / (1 + b (τ_P/ Τ₀)²ⁿ) ... (4 ')
Here, each coefficient (a, b, m, n) of the equations (4) and (4 ′) is modeled to fit the measured values in the region between the spin torque region and the thermally active region. It becomes possible. Here, the parameters may be reduced by setting a = b and m = n (in this case, β = 1−α). It is also possible to change only α while β = 1 is fixed.
Fig. 8 shows the value of α when the parameter a in equation (4) is fixed at 1 (a = 1) and the value of m is changed from 1 to 5._PIs illustrated as a variable. α is τ_PIs a function that decreases monotonously as the value of increases, and the steepness of the change can be changed by the value of m. This feature is optimal in that it can be used as a fitting equation in the region between the thermally active region and the spin torque region.
(1) to (4) described above are τ_PThis is an expression for obtaining Ic from, and is convenient when deriving a model parameter for an actual measurement value. However, in step A2 of FIG. 5 in the electronic circuit design support apparatus and the simulation program according to the present invention, τ from the rewrite current Iw (= Ic) supplied to the MTJ element._PNeed to be calculated. That is, it is necessary to incorporate inverse functions of these equations into the simulation program. Although the inverse functions of Equation (1) and Equation (2) can be easily derived, it is not easy to obtain the inverse function of Equation (3) that combines them.
Therefore, in this embodiment, the time constant τ calculated from the inverse function of equation (1)_P ^TAAnd the time constant τ calculated from the inverse function of equation (2)_P ^PRBy performing the same combination as in equation (3), the final τ_PIs calculated.
Describing in detail, from the inverse function of equation (1) shown below, τ_P ^TAIs calculated.
τ_P ^TA= Τ₀Exp [(E / k_BT) {1- (Ic / Ic0)}] (5)
Also, from the inverse function of equation (2) shown below, τ_P ^PRIs calculated.
τ_P ^PR= Τ_relaxLn {π / (2√ (k_BT / E))} / {(Ic / Ic0) -1} (6)
Furthermore, based on the same idea as the derivation of equation (3), the final τ_PIs calculated.
τ_P= Γτ_P ^PR+ Δτ_P ^TA... (7)
Here, γ and δ are expressed by the following equations.
γ = 1−1 / (1 + a (Ic / Ic0)^2m) ... (8)
δ = 1 / (1 + b (Ic / Ic0)²ⁿ) ... (8 ')
Here, a, b, m, and n are model parameters. According to the equations (5) to (8), τ that can ensure fitting accuracy over a wide range based on both the thermal activation model and the spin torque model._PCan be calculated. For example, when the rewriting current Ic (= Iw) is sufficiently larger than Ic0, γ approaches 1 and δ approaches 0. Therefore, τ_PIs obtained from the spin torque effect τ_PPRBecomes dominant. On the other hand, when Ic is smaller than Ic0, γ approaches 0 and δ approaches 1. Therefore, τ_PThe value of τ is obtained from the thermal activation effect_PTABecomes dominant. When Ic is in the vicinity of Ic0, the ratio varies depending on the value of Iw in a region where both effects are mixed.
Here, since there is a {(Ic / Ic0) -1} term in the denominator in equation (6), if Ic = Ic0, τ_P ^PRIt should be noted that diverges. In order to prevent this divergence, τ at Ic ≦ Ic0_P ^PRIt is good to parameterize the value of.
Alternatively, as another method for preventing divergence, there is a method of replacing g (Ic) with a continuous function that takes a value close to g (Ic) represented by the following formula and does not diverge when Ic = Ic0.
g (Ic) ≡1 / {(Ic / Ic0) -1} (9)
As an example of such a continuous function, there is a function obtained by Taylor expansion of the right side of the equation (9). Since the equation (6) is an expression in the spin torque region, it can be considered that Ic> Ic0 (ie, 1> Ic0 / Ic). When the equation (9) is Taylor-expanded by the term (Ic0 / Ic), the following equation is obtained. .

When kmax is finite, under the condition of Ic0 / Ic <1, the larger the number of additions (kmax) on the right side of equation (10), the more the error ε of equation (10) with respect to the original equation (9) becomes: Get smaller. The error ε is expressed by the following equation.
[epsilon] = {right side of equation (10)}-(9) right side} / {right side of equation (9)} × 100 (11)
In numerical calculation, with reference to the relationship between kmax and ε shown in FIG. 9, kmax is determined so that ε falls within a desired range.
From rewrite current Iw (= Ic) to τ_PAs another embodiment of the present invention for calculating τ, for example, τ represented by the expressions (1) to (4) of the present invention_PThere is a method in which an expression for obtaining Iw is first obtained, and then an inverse function is obtained by numerical calculation. An algorithm such as Newton's method is effective as a numerical calculation method. An example of the inverse function calculation method using the Newton method is shown below. In FIG. 10, for the purpose of explaining this example, τ_PThe method of calculating | requiring by the Newton method is shown graphically.
Iw (τ_P) = Iwc (constant) (12)
Obviously, the formula Iw = Iw (τ_P) And the intersection of the straight line Iw = Iwc is the solution of equation (12).
First, a suitable initial solution τ_P0Set. Iw = Iw (τ_P), Τ = τ_P0Tangent line (tangent line 1) is drawn and the x coordinate of the intersection with Iw = Iwc is τ_P1And Next, this time Iw = Iw (τ_P), Τ = τ_P1Tangent line (tangent line 2) is drawn, and the x coordinate of the intersection with Iw = Iwc is τ_P2And This operation is repeated until the (n-1) th Iw (τ_Pn-1) And n-th Iw (τ_Pn) Is a preset error value ε_nΤ when smaller than_PnIs the solution of equation (12). This τ_PnI.e., τ for a given Iw = Iwc_PIs the value of
According to the embodiment of the present invention, it is possible to provide a design support apparatus and program capable of performing operation verification of an electronic circuit including an MTJ element with high accuracy in a short time. In particular, the rewriting characteristics in the region between the spin torque model region and the thermal activation model region can be calculated by using an approximate expression that is very suitable for the actually measured value. This is practically impossible to achieve in the conventional subcircuit model because the circuit becomes too complex and the computation time is enormous.
The present invention has been described with reference to specific embodiments. It is obvious that the present invention is not limited to the above-described embodiment, and can be appropriately changed within the scope of the technical idea of the present invention. For example, the expression of the coefficients α, β, γ, and δ is not limited to the Butterworth function, and other filter function expressions can be used. In the above embodiment, the spin injection MTJ element has been described as an example. However, the present invention is also applied to an MTJ element that rewrites using a current magnetic field and an MTJ element that uses the phenomenon of domain wall motion. Is possible. In addition to MTJ elements, other resistance variable elements (ReRAM (Resistance Random Access Memory) elements, PRAM (Phase change RAM) elements, atomic switch elements, etc.) whose resistance value changes by supplying current or voltage are also included. Obviously, application to the included circuit is also within the scope of the present invention.
Some or all of the above embodiments can be described as in the following supplementary notes, but are not limited thereto.
(Supplementary note 1) As described above, as described above, the thermal activation term (1 ′) and the spin torque term (2 ′) are used as coefficients representing the magnetization reversal critical current Ic using the coefficients α and β. Including expression (3).
(Appendix 2) Another feature of the present invention is that the time constant τ_PA method for determining the magnetization reversal critical current Ic from As one method, Ic and τ in the thermally active region_PAnd Ic and τ in the spin torque region_PInverse relational expression (2) is obtained (Equations (5) and (6), respectively), and is expressed as Expression (7) using coefficients γ and δ.
(Appendix 3) Also, time constant τ_PAs another method for obtaining the magnetization reversal critical current Ic from the_PBased on the relational expression for obtaining Ic from the equation, an inverse function is obtained by numerical calculation, that is, given Ic to τ_PIncluding a method of calculating
(Additional remark 4) Moreover, in order to prevent the divergence in Ic = Ic0 of Formula (6) as another characteristic of this invention, it replaces Formula (6) with the continuous function which does not diverge by Ic = Ic0.
(Additional remark 5) The approximate expression memory | storage part which memorize | stores the 1st and 2nd approximate expression which approximated the relationship between the electric current value supplied to an MTJ element, and the time constant regarding magnetization reversal based on a mutually different theoretical model,
A calculation unit for obtaining a current value supplied to the MTJ element at time t based on circuit information representing a configuration of an integrated circuit including the MTJ element and element characteristic information on the MTJ element;
A magnetization reversal determination unit for determining whether to cause magnetization reversal in the MTJ element based on the obtained current value and the first and second approximate expressions;
A circuit design support apparatus comprising:
(Additional remark 6) The said magnetization reversal judgment part calculated | required the 1st calculation result obtained based on the 1st approximation, and the 2nd calculation result obtained based on the said 2nd approximation Weighted addition is performed using a parameter that changes so that one of the first calculation result and the second calculation result becomes dominant according to the magnitude of the current value, and the magnetization reversal is caused based on the addition result. 6. The circuit design support device according to appendix 5, wherein the circuit design support device determines whether or not.
(Additional remark 7) The said magnetization reversal judgment part determines whether the said magnetic reversal is caused when the calculated | required electric current value is more than a 1st threshold value. The circuit design support apparatus described.
(Appendix 8) The magnetization reversal determination unit is configured to respond to the calculated current value based on the first and second approximate expressions when the calculated current value is equal to or greater than a first threshold value. A constant is obtained, and a magnetization reversal probability is further obtained using the obtained time constant, and it is determined that the magnetization reversal is caused when the obtained magnetization reversal probability is equal to or higher than a second threshold value. The circuit design support device according to appendix 7.
(Supplementary Note 9) When the obtained current value is smaller than the first threshold value, the magnetization reversal determination unit adopts a predetermined constant as a time constant corresponding to the obtained current value. 9. The circuit design support device according to appendix 8, wherein a magnetization reversal probability is further obtained using a time constant.
(Supplementary note 10) The circuit design support device according to any one of supplementary notes 5 to 9, wherein the calculation unit and the magnetization reversal determination unit repeat operations every time Δt time elapses.
(Additional remark 11) Based on the circuit information showing the structure of the integrated circuit containing an MTJ element and the element characteristic information regarding the said MTJ element, the electric current value supplied to the said MTJ element in the time t is calculated | required,
Based on the first and second approximate expressions that approximate the relationship between the current value supplied to the MTJ element and the time constant related to magnetization reversal based on different theoretical models, and the MTJ, Determine whether to cause magnetization reversal in the element,
A circuit design support method characterized by this.
(Additional remark 12) The step which calculates | requires the electric current value supplied to the said MTJ element in the time t based on the circuit information showing the structure of the integrated circuit containing an MTJ element, and the element characteristic information regarding the said MTJ element;
Based on the first and second approximate expressions that approximate the relationship between the current value supplied to the MTJ element and the time constant related to magnetization reversal based on different theoretical models, and the MTJ, Determining whether to cause magnetization reversal in the element;
A program characterized by causing a computer to execute.

DESCRIPTION OF SYMBOLS 11 Magnetization free layer 12 Magnetization fixed layer 13 Barrier layer 30 Electronic circuit design support apparatus 31 Circuit information input part 32 Element information input part 33 MTJ element identification part 34 Voltage / current calculation part 35 Magnetization inversion judgment part 36 Operation information output part 37 Approximation Expression storage unit 40 Computer system 41 Storage medium 42 Computer main body 43 Input / output device 44 Storage device 45 Computing device 46 Display device This application is based on Japanese Patent Application No. 2012-184142 filed on August 23, 2012. All the disclosures of which are hereby incorporated by reference.

Claims

A circuit design support apparatus for supporting the design of a spintronics integrated circuit including an MTJ element,
An MTJ element identification unit for identifying the MTJ element from circuit information (net list) representing the configuration of the spintronics integrated circuit;
Magnetization for determining whether to cause magnetization reversal in the MTJ element based on MTJ element characteristic information (model parameter) representing the characteristic of the MTJ element and the current value supplied to the identified MTJ element An inversion judgment unit;
An approximate expression storage unit that stores a first expression and a second expression that approximate a relationship between a supplied current value and a time constant related to magnetization of the MTJ element based on different theoretical models;
An operation information output unit that outputs a resistance value of the MTJ element;
The magnetization reversal determination unit includes first computing means for computing a time constant required for magnetization reversal based on the first equation and the second equation;
Second calculating means for calculating a magnetization reversal probability from the calculated time constant;
A circuit design support apparatus for determining whether or not to cause the magnetization reversal based on the magnetization reversal probability.
The circuit design support apparatus according to claim 1,
Each of the first equation and the second equation includes a current value supplied to the MTJ element as a variable,
The first calculation means is configured so that the first expression is mainly used when the current value supplied to the MTJ element is not less than an arbitrary threshold value, and the second expression is mainly used when the current value is small. The ratio of the first expression and the second expression contributing to the calculation of the time constant is changed according to the current value supplied to the MTJ element,
The circuit design support device, wherein the magnetization reversal determination unit determines to cause the magnetization reversal when the magnetization reversal probability exceeds an arbitrary threshold value.
The circuit design support apparatus according to claim 1,
The approximate expression storage unit further stores a third expression that determines a ratio at which the first expression and the second expression contribute to the calculation of the time constant,
The circuit design support apparatus, wherein a coefficient included in the third equation is based on the MTJ element characteristic information.
The circuit design support device according to claim 3,
The circuit design support apparatus, wherein the third expression is represented by a Butterworth filter function expression.
The circuit design support apparatus according to claim 1,
The second calculation means increases the magnetization reversal probability when the current value supplied to the MTJ element is equal to or higher than the threshold current set by the MTJ element characteristic information, and reduces the magnetization reversal probability when the current value is small. A circuit design support device characterized in that the calculation is performed so as to be lowered.
A circuit design support method for supporting the design of a spintronics integrated circuit including an MTJ element,
A first step of identifying the MTJ element from circuit information (net list) representing a configuration of the spintronics integrated circuit;
A second step of determining whether or not to cause the magnetization reversal based on MTJ element characteristic information (model parameter) representing characteristics of the MTJ element and a current value supplied to the identified MTJ element; ,
A third step of outputting a resistance value of the MTJ element,
In the second step, a time constant required for the magnetization reversal is calculated based on the current value, a magnetization reversal probability is calculated based on the time constant, and the magnetization reversal is caused based on the magnetization reversal probability A circuit design support method characterized by determining whether or not.
The circuit design support method according to claim 6,
The second step is an expression obtained by approximating a relationship between a current value supplied to the MTJ element and a time constant related to magnetization based on different theoretical models, and the current value supplied to the MTJ element, respectively. The first equation is mainly used when the current value supplied to the MTJ element is equal to or larger than an arbitrary threshold value, and the second equation is used when the current value is small. The ratio of the first expression and the second expression contributing to the calculation of the time constant is changed according to the current value supplied to the MTJ element so that the expression of And determining that the magnetization reversal is caused when the magnetization reversal probability exceeds an arbitrary threshold value.
A program that causes a computer to operate as a circuit design support device that supports the design of a spintronics integrated circuit including an MTJ element,
In the computer,
A first step of identifying the MTJ element from circuit information (net list) representing a configuration of the spintronics integrated circuit;
A second step of determining whether to cause the magnetization reversal based on MTJ element characteristic information (model parameter) representing the characteristic of the MTJ element and a current value supplied to the identified MTJ element;
A third step of outputting a resistance value of the MTJ element;
Let it run
In the second step, a time constant required for the magnetization reversal is calculated based on the current value, a magnetization reversal probability is calculated based on the time constant, and whether the magnetization reversal is performed based on the magnetization reversal probability A program characterized by judgment.
The program according to claim 8, wherein
The second step is an expression obtained by approximating a relationship between a current value supplied to the MTJ element and a time constant related to magnetization based on different theoretical models, and the current value supplied to the MTJ element, respectively. The first equation is mainly used when the current value supplied to the MTJ element is equal to or larger than an arbitrary threshold value, and the second equation is used when the current value is small. The ratio of the first expression and the second expression contributing to the calculation of the time constant is changed according to the current value supplied to the MTJ element so that the expression of And determining that the magnetization reversal occurs when the magnetization reversal probability exceeds an arbitrary threshold value.
An approximate expression storage unit that stores first and second approximate expressions that approximate a relationship between a current value supplied to the MTJ element and a time constant related to magnetization reversal based on different theoretical models;
An arithmetic unit that obtains a current value supplied to the MTJ element at time t based on circuit information representing a configuration of an integrated circuit including the MTJ element and element characteristic information on the MTJ element;
A magnetization reversal determination unit that determines whether to cause magnetization reversal in the MTJ element based on the obtained current value and the first and second approximate expressions;
A circuit design support apparatus comprising: