Method for simulating electromigration failure process of heavy metal structure of spin-orbit moment magnetic memory and acquiring key parameters

Abstract

The invention discloses a method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and acquiring key parameters. The method comprises the following steps: step 1, simulating the electromigration failure process of the heavy metal structure of the spin-orbit moment magnetic memory based on a Korhonen equation and predicting the electromigration failure time; and 2, based on the electromigration failure time predicted in the step 1, carrying out electromigration failure test on the heavy metal structure to obtain key parameters, including diffusion activation energy, a diffusion coefficient and a difference value between threshold stress and residual stress of the test structure. According to the invention, resistance change characteristics of a cavity nucleation stage and a cavity growth stage can be combined, a resistance-time change chart obtained by an actual electromigration test is compared, and a specific position of a cavity generated in a test structure is predicted; and perfecting the simulation method of the electromigration failure process by using the obtained parameter values, and predicting the electromigration failure time of the heavy metal structure of the magnetic memory with different spin-orbit moments by using the method.

Description

Technical Field

[0001] The invention belongs to the technical field of semiconductor integrated circuit manufacturing, and in particular relates to a method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters. Background Art

[0002] With the rise of mobile Internet, traditional storage technology faces increasingly severe problems of static power consumption and extra energy consumption. Researchers have proposed the use of new non-volatile storage technology to replace traditional storage technology. Among all non-volatile storage technologies, magnetic RAM (MRAM) has become one of the most popular next-generation storage technologies with its high density and large capacity, low read latency, low power consumption, and almost unlimited read and write cycles. The new third-generation MRAM, spin-orbit torque magnetic RAM (SOT-MRAM), has an ultra-high data write speed of less than 1ns and data write energy consumption of fJ level, so it can be used in handheld computing devices and even supercomputers.

[0003] However, in the actual application of SOT-MRAM, there is a major reliability problem - the electromigration (EM) failure of the bottom heavy metal layer (Heavy Metal, HM) and the through hole. The essence of electromigration is that the metal ions migrate from the cathode end to the anode end due to the external electric field, which eventually manifests as a void at the cathode end of the metal or a hillock at the anode end, causing the metal resistance to increase and fail, seriously affecting the life of the integrated circuit. Compared with traditional aluminum and copper interconnects, the main material of the heavy metal layer and through hole of SOT-MRAM is heavy metal tungsten (Tungsten, W), which has a large resistivity and diffusion coefficient. When powered on, it will produce greater current concentration, Joule heat and other problems, resulting in a greatly increased probability of electromigration failure.

[0004] Most of the existing electromigration failure prediction methods use the semi-empirical formula Black's equation. However, due to the fitting parameters in the Black equation, the parameter values ​​obtained in the experiment may not be suitable for predicting the device life under working conditions. On the other hand, the Black equation is designed for linear interconnect structures and does not include the transition between different materials and structural ends. Therefore, it is not suitable for predicting the life of heavy metal layers and through holes of SOT-MRAM. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for simulating the electromigration failure process of the heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters in view of the deficiencies of the above-mentioned prior art, so as to realize the simulation and key parameter acquisition for predicting the electromigration failure process of the heavy metal structure of the spin-orbit moment magnetic memory.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0007] A method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters, comprising:

[0008] Step 1: Simulate the electromigration failure process of the heavy metal structure of the spin-orbit moment magnetic memory based on the Korhonen equation and predict the electromigration failure time;

[0009] Step 2: Based on the electromigration failure time predicted in step 1, perform electromigration failure test on the heavy metal structure to obtain key parameters, including the diffusion activation energy, diffusion coefficient, and the difference between the threshold stress and the residual stress of the test structure.

[0010] To optimize the above technical solutions, the specific measures taken also include:

[0011] The Korhonen equation described in step 1 above is as follows:

[0012]

[0013] Among them, D a is the diffusion coefficient, B is the effective bulk elastic modulus, Ω is the atomic lattice volume, k B is the Boltzmann constant, e is the effective charge per unit electron, Z is the effective number of migrating atoms, ρ is the resistivity; t is time, σ is the electromigration stress, T is the test temperature, j is the DC current density, and x is the horizontal coordinate in the length direction of the test structure.

[0014] The above electromigration failure process is divided into two stages: void nucleation stage and void growth stage. The void nucleation stage refers to the electromigration stress at the cathode end of the heavy metal structure reaching the critical stress σ at which the void begins to grow. crit The time during which the resistance of the test structure remains unchanged; the void growth stage refers to the voids inside the heavy metal structure that begin to grow after nucleation is completed, causing the resistance of the heavy metal structure to begin to increase. When the resistance increases to a set ratio, the heavy metal structure is deemed to have failed;

[0015] The electromigration failure process is simulated with the following assumptions:

[0016] First, the metal and dielectric barriers are absolutely rigid, and the atomic diffusion rates do not depend on stress;

[0017] Second, at any location inside the grain, the vacancy concentration and stress are in equilibrium at any time;

[0018] Third, the stress evolution is caused only by the atomic flux divergence;

[0019] Fourth, if there is no dielectric barrier wrapped around the heavy metal, the electromigration failure time is the void nucleation time t nuc , otherwise the electromigration failure time is the void nucleation time t nuc and the cavity growth time t grow The sum.

[0020] The above-mentioned void nucleation time t nuc The simulation prediction process is:

[0021] In the void nucleation stage, for a finite line with a length of L, the diffusion blocking ends are located at x = 0 and x = L of the finite line respectively. The test temperature T and the DC current density j are fixed, and the Korhonen equation is solved by the separation of variables method to obtain formula (2):

[0022]

[0023] Among them, the residual stress σ res It refers to the residual thermal stress generated inside the metal due to temperature changes and the mismatch of thermal expansion coefficients of adjacent materials. κ represents the formula

[0024] When the stress σ at the cathode end of the finite line, that is, x = 0, reaches σ crit When σ(0,t)=σ crit , and the void nucleation time t is obtained nuc The predicted value of is as follows:

[0025]

[0026] The above-mentioned cavity growth time t grow The simulation prediction process is:

[0027] During the void growth stage, as the cross-sectional area of ​​the metal line at the location where the void is formed continues to decrease, the resistance of the test structure increases; when the hole cuts off the entire cross-sectional area of ​​the metal line, it forces the test current to flow through the high-resistance dielectric barrier; when the resistance growth exceeds 20% of the initial resistance, the test structure fails, and the time taken is the void growth time t grow , the formula is as follows:

[0028]

[0029] Among them, R 0 is the initial resistance of the test structure, and R_incr_rate is the resistance growth rate, which is given by the following formula:

[0030]

[0031] Among them, ρ b , A bare the resistivity and cross-sectional area of ​​the outer barrier layer of the metal interconnect or via, respectively, W , A W are the resistivity and cross-sectional area of ​​the metal interconnect or via, respectively. It represents the drift velocity of metal ions, and its formula is as follows:

[0032]

[0033] The electromigration failure test of the heavy metal structure described in step 2 above uses a test structure based on a combination of aluminum metallized metal lines, vias and heavy metal layers as the test structure for the electromigration experiment according to JEDEC JESD87; the test structure is subjected to wafer-level electromigration testing.

[0034] The above diffusion activation energy E a The acquisition process is:

[0035] Provide electromigration test samples, each of which has a probe card; place the samples in a constant temperature box, and set the test temperature in the constant temperature box to T 1 , a test current j is passed through the sample to be tested 1 ; Use EDA tools to record the resistance growth process and failure time of the samples to be tested; Under the same test conditions, complete 12 groups of effective electromigration failure tests to ensure the median failure time t 50％ can be accurately estimated; under the same test conditions, the time taken for 50% of the test structures in the same group of 12 test structure samples to fail due to electromigration is the median failure time t of the test structure under the test conditions. 50％ ;

[0036] Maintain the test current j 1 Change the test temperature in the thermostat to T 2 、T 3 , repeat the above electromigration failure test experiment, where T 1 <T 2 <T 3 ; get j respectively 1 / T 1 、j 1 / T 2 and j 1 / T 3 Median failure time t of the test structure under test conditions 50％ ;

[0037] The median failure time t is calculated using the Black equation 50％ Perform curve fitting and calculate the diffusion activation energy E of the test structure a .

[0038] The above curve fitting is performed using the Black equation to calculate the diffusion activation energy E of the test structure. a , as follows:

[0039] By transforming the Black equation shown in formula (7), we get the following formula (8):

[0040]

[0041] Among them, A is a constant; k is the Boltzmann constant; E a is the diffusion activation energy; n is the current density index; MTTF is the median failure time t of the sample under various test conditions 50％ ; lnA-nlnj is a constant;

[0042] Let parameter C = lnA-nlnj, and we get the following formula (9):

[0043]

[0044] From formula (9), we know that when the test current density j is constant, the logarithm of the median failure time lnMTTF and the inverse of the test temperature There is a linear relationship;

[0045] According to j 1 / T 1 、j 1 / T 2 and j 1 / T 3 Median failure time t of the test structure under test conditions 50％ , curve fitting is performed on the Black equation to obtain the logarithm of the median failure time lnMTTF and the inverse of the test temperature The corresponding straight line fitting graph;

[0046] According to the straight line slope in the straight line fitting diagram The diffusion activation energy E is obtained a .

[0047] The diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ) is obtained as follows:

[0048] Provide electromigration test samples, each of which has a probe card; place the samples in a constant temperature box, and set the test temperature in the constant temperature box to T 2 , a test current j is passed through the sample to be tested 1; Use EDA tools to record the resistance growth process and failure time of the sample to be tested; Under the same test conditions, complete 12 groups of effective electromigration failure tests to ensure that the median failure time t 50％ can be accurately estimated; under the same test conditions, the time taken for 50% of the test structures in the same group of 12 test structure samples to fail due to electromigration is the median failure time t of the test structure under the test conditions. 50％ ;

[0049] Maintain the test temperature T in the thermostat 2 The test current is changed to j 2 、j 3 、j 4 , repeat the above electromigration failure test experiment, where j 1 <j 2 <j 3 <j 4 ; get j respectively 1 / T 2 、j 2 / T 2 、j 3 / T 2 and j 4 / T 2 Median failure time t of the test structure under test conditions 50％ ; Using the void nucleation time Centering failure time t 50％ Fit and calculate the diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ) size.

[0050] The above-mentioned use of void nucleation time Centering failure time t 50％ Fit and calculate the diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ), comprising the following steps:

[0051] right After simplification, we get the following formula (10):

[0052]

[0053] Among them, the parameters is the diffusion coefficient D a Related formulas; parameters is the difference between the threshold stress and the residual stress (σ crit -σ res ) related formulas;

[0054] By transforming formula (10), we get the following formula (11):

[0055]

[0056] in, And the parameters a′ and b′ have the following relationship with the parameters a and b respectively:

[0057] a=c·a′(12)

[0058] b=d·b′(13)

[0059] Among them, parameter c and parameter d are constants, indicating that the parameters a and b are transformed by multiples;

[0060] By formula It is known that when the test temperature T is constant, the void nucleation time t of the test structure nuc There is a certain functional relationship with the test current density j;

[0061] According to j 1 / T 2 、j 2 / T 2 、j 3 / T 2 and j 4 / T 2 Median failure time t of the test structure under test conditions 50％ , for the formula Perform curve fitting to obtain the curve fitting diagram corresponding to the median failure time MTTF and current density j and the values ​​of parameters a′ and b′;

[0062] The parameter diffusion coefficient D is determined by the values ​​of parameters a′ and b′. a and the difference between the threshold stress and the residual stress (σ crit -σ res ) size.

[0063] The present invention has the following beneficial effects:

[0064] The present invention proposes a method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory, which method includes two parts: a simulation method for the void nucleation stage and a simulation method for the void nucleation stage. The electromigration failure process of the heavy metal layer of the spin-orbit moment magnetic memory includes the void nucleation stage; and the electromigration failure process of the through hole includes the void nucleation stage and the void growth stage. Therefore, by combining the resistance change characteristics of the void nucleation stage and the void growth stage and comparing the resistance-time change diagram obtained by the actual electromigration test, it is possible to predict the specific position where the void is generated in the test structure.

[0065] In addition, the present invention also proposes a method for obtaining electromigration test parameters to improve the simulation method of the electromigration failure process, including the steps of: providing a wafer with a complete set of electromigration test structures, wherein the wafer includes a plurality of samples to be tested, and each sample to be tested has a probe card; using a resistance sensor to measure the resistance of the sample to be tested at fixed intervals; placing the sample to be tested in a constant temperature box, and passing a small current of μA level through the sample to be tested, at which time only negligible Joule heat is generated inside the sample to be tested, so the resistance recorded by the resistance sensor is the initial resistance R 0 ; Then, a constant direct current is passed through the sample to be tested, the resistance of the sample to be tested is monitored in real time using a resistance sensor, and the failure time of the sample to be tested is recorded using an EDA tool; based on the actual test conditions (including temperature, current density) of each sample to be tested and the failure time under this test condition, the diffusion activation energy E of the test structure is obtained. a , diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ) and other parameter values. The parameter values ​​are used to improve the simulation method of the electromigration failure process of the heavy metal structure of the spin-orbit moment magnetic memory, and the simulation method can be used to predict the electromigration failure time of different heavy metal structures of the spin-orbit moment magnetic memory in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 It is a flow chart of the implementation of the present invention;

[0067] Figure 2 It is a straight line fitting diagram corresponding to the failure probability (Prof.) and logarithmic failure time (lnTTF) of a group of test structures under the same test conditions of the present invention;

[0068] Figure 3 is the logarithm of the median failure time lnMTTF and the reciprocal of the operating temperature provided in the embodiment of the present invention The corresponding straight line fitting graph;

[0069] Figure 4It is a curve fitting diagram corresponding to the median failure time MTTF and the current density j provided in the embodiment of the present invention. DETAILED DESCRIPTION

[0070] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0071] The present invention proposes a method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters, comprising:

[0072] In the first aspect, the present invention proposes to use a method for simulating electromigration failure process based on the Korhonen equation to predict the electromigration failure time of a heavy metal structure of a spin-orbit moment magnetic memory, referring to Figure 1 , including the steps of:

[0073] A simulation method of electromigration failure process based on Korhonen equation is proposed to predict the electromigration failure time of heavy metal structure of spin-orbit moment magnetic memory.

[0074] The Korhonen equation is shown in equation (1):

[0075]

[0076] Among them, D a is the diffusion coefficient, B is the effective bulk elastic modulus, Ω is the atomic lattice volume, k B is the Boltzmann constant, e is the effective charge per unit electron, Z is the effective number of migrating atoms, and ρ is the resistivity.

[0077] The electromigration failure process is mainly divided into two stages: the void nucleation stage and the void growth stage.

[0078] The void nucleation stage refers to the critical stress σ at the cathode end of the test structure when the void begins to grow. crit The resistance of the test structure remains almost unchanged during this process.

[0079] The void growth stage refers to the voids inside the test structure that begin to grow after nucleation is completed, causing the resistance of the test structure to begin to increase. When the resistance increases by a certain proportion (for example, 10% or 20% of the initial resistance), the test structure is considered to have failed.

[0080] Depending on whether there is a barrier layer, the failure process of the heavy metal structure of the spin-orbit moment magnetic memory can be divided into two types:

[0081] There is a barrier layer outside the tungsten via, so the electromigration failure time of the via is the sum of the void nucleation time and the void growth time;

[0082] There is no barrier layer outside the heavy metal layer, so the electromigration failure time of the heavy metal is the void nucleation time.

[0083] Specifically, the electromigration failure process simulation method proposed in the present invention includes the following assumptions:

[0084] First, it is assumed that the constraints (metal and dielectric barriers) are absolutely rigid and the atomic diffusion rates do not depend on stress;

[0085] Second, at any location inside the grain, the vacancy concentration and stress are in equilibrium at any time;

[0086] Third, the stress evolution is caused only by the atomic flux divergence;

[0087] Fourth, assuming that there is no dielectric barrier wrapped around the heavy metal, the electromigration failure time is the void nucleation time t nuc .

[0088] Specifically, calculating the electromigration failure time of the test structure mainly includes two steps:

[0089] (1) Based on the simplified assumptions, solve the void nucleation time t nuc .

[0090] For a finite line with a length of L, the diffusion blocking ends are located at x = 0 and x = L of the finite line. By fixing the test temperature T and the DC current density j, the Korhonen equation is solved by the separation of variables method to obtain formula (2):

[0091]

[0092] Among them, the residual stress σ res It refers to the residual thermal stress generated inside the metal due to temperature changes and the mismatch of thermal expansion coefficients of adjacent materials; κ represents the formula

[0093] When the stress σ at the cathode end (x = 0) of the finite line reaches σ crit When σ(0,t)=σ crit , and the void nucleation time t is obtained nuc The approximate value of is as follows:

[0094]

[0095] (2) After the void nucleation stage, the void growth time t is calculated. grow .

[0096] During the void growth phase, the resistance of the test structure increases as the cross-sectional area of ​​the metal line at the location where the void is formed continues to decrease.

[0097] In extreme cases, when the hole cuts off the entire cross-section of the metal line, the test current is forced to flow through the high-resistance dielectric barrier.

[0098] When the resistance growth exceeds 20% of the initial resistance, the test structure is specified to fail, and the time taken is the void growth time t grow .

[0099] t grow The calculation formula is as follows:

[0100]

[0101] Among them, R 0 is the initial resistance of the test structure, and R_incr_rate is the resistance growth rate under a certain test condition, and its formula is as follows:

[0102]

[0103] Among them, ρ b , A b are the resistivity and cross-sectional area of ​​the outer barrier layer of the metal interconnect or via, respectively, W , A W are the resistivity and cross-sectional area of ​​the metal interconnect or via, respectively. It represents the drift velocity of metal ions, and its formula is as follows:

[0104]

[0105] In a second aspect, the present invention provides a method for obtaining electromigration test parameters, comprising the following steps:

[0106] Complete electromigration failure experiments on the test structure.

[0107] First, according to JEDEC JESD87, a test structure based on a combination of metal lines, vias, and heavy metal layers with aluminum metallization is used as the test structure for electromigration experiments.

[0108] In the present invention, the spin-orbit moment magnetic memory (SOT-MRAM) heavy metal structure refers to the heavy metal layer and heavy metal through hole in the SOT-MRAM; the sample to be tested refers to the wafer used in the experiment; and the test structure refers to the heavy metal structure of the SOT-MRAM inside the sample to be tested.

[0109] Second, the test structure is subjected to electromigration testing at the wafer level.

[0110] Third, the sample size of the test structure under each test condition is 12 valid data points to ensure the median failure time (MTF) 50％) can be accurately estimated using the following method: Figure 2 shown.

[0111] Providing a wafer with a complete set of electromigration test structures, wherein the wafer includes a plurality of samples to be tested, and each sample to be tested has a probe card;

[0112] Using a resistance sensor to measure the resistance of the sample to be tested at fixed intervals;

[0113] The sample to be tested is placed in a constant temperature box and a small current of μA level is passed through the sample to be tested. At this time, only negligible Joule heat is generated inside the sample to be tested. At this time, the resistance recorded by the resistance sensor is the initial resistance R 0 ;

[0114] A constant DC current is passed through the sample to be tested, the resistance of the sample to be tested is monitored in real time using a resistance sensor, and the failure time of the sample to be tested is recorded using an EDA tool;

[0115] Based on the actual test conditions (including temperature and current density) of each sample to be tested and the failure time under these test conditions, the diffusion activation energy E of the test structure is obtained. a , diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ) and other parameter values.

[0116] Specifically, (1) the diffusion activation energy E of the test structure a The method to obtain is:

[0117] Determine the diffusion activation energy E a When the test current density j is fixed 1 Three different test temperatures (T 1 <T 2 <T 3 ), and the failure time (TTF) of each test structure is obtained. Under the same test conditions, the time taken for 50% of the 12 test structure samples in the same group to fail due to electromigration is the median failure time t of the test structure under the test conditions. 50％ . We get j 1 / T 1 、j 1 / T 2 and j 1 / T 3 Median failure time t of the test structure under test conditions 50％ , the Black equation is used for curve fitting to obtain the diffusion activation energy E of the electromigration test structure. a The specific steps are as follows:

[0118] Providing electromigration test samples, each sample to be tested has a probe card;

[0119] Place the sample to be tested in a constant temperature box and set the test temperature in the constant temperature box to T 1 , a test current j is passed through the sample to be tested 1 ;

[0120] Use EDA tools to record the resistance growth process and failure time TTF of the sample to be tested;

[0121] Under the same test conditions, 12 groups of effective electromigration failure tests were completed to ensure the median failure time t 50％ can be accurately estimated;

[0122] Under the same test conditions, the time taken for 50% of the 12 test structure samples in the same group to fail due to electromigration is the median failure time t of the test structure under the test conditions. 50％ ;

[0123] Maintain the test current j 1 Keep the test temperature in the thermostat unchanged (T 1 <T 2 <T 3 ), repeat the above electromigration failure test experiment;

[0124] Get j 1 / T 1 、j 1 / T 2 and j 1 / T 3 Median failure time t of the test structure under test conditions 50％ ;

[0125] The Black equation was used to fit the curve and calculate the diffusion activation energy E of the test structure. a .

[0126] The Black equation can be expressed as follows:

[0127]

[0128] Among them, A is a constant, which is only related to the material and structure; k is the Boltzmann constant, and k = 8.616 × 10 -5 eV / K; E a is the diffusion activation energy; n is the current density index; MTTF is the median failure time t of the sample under various test conditions 50％ .

[0129] The process of curve fitting using Black's equation includes the following steps:

[0130] By transforming the Black equation (the above formula (7)), we get the following formula (8):

[0131]

[0132] Where, lnA-nlnj is a constant, then let C = lnA-nlnj, and we get the following formula (9):

[0133]

[0134] From formula (9), we can see that when the test current density j is constant, the logarithm of the median failure time lnMTTF and the inverse of the test temperature T 1 is a linear relationship;

[0135] According to j 1 / T 1 、j 1 / T 2 and j 1 / T 3 Median failure time t of the test structure under test conditions 50％ By fitting the Black equation, we can get the logarithm of the median failure time, lnMTTF, and the inverse of the test temperature. The corresponding straight line fitting graph is as follows: Figure 3 As shown;

[0136] The logarithm of the median failure time, lnMTTF, and the inverse of the test temperature are determined by formula (9): The corresponding straight line slope shown in the straight line fitting diagram The diffusion activation energy E can be obtained a .

[0137] (2) Diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ) is obtained as follows:

[0138] When determining the diffusion coefficient, four different test current densities (j 1 <j 2 <j 3 <j 4 ), and obtain the failure time of each test structure. 1 / T 2 、j 2 / T 2 、j 3 / T 2 and j 4 / T 2Median failure time t of the test structure under test conditions 50％ The Korhonen equation was used for curve fitting to obtain the diffusion coefficients D a and the difference between the threshold stress and the residual stress (σ crit -σ res ). The specific steps are as follows:

[0139] Providing electromigration test samples, each sample to be tested has a probe card;

[0140] Place the sample to be tested in a constant temperature box and set the test temperature in the constant temperature box to T 2 , a test current j is passed through the sample to be tested 1 ;

[0141] Use EDA tools to record the resistance growth process and failure time TTF of the sample to be tested;

[0142] Under the same test conditions, 12 groups of effective electromigration failure tests were completed to ensure the median failure time t 50％ can be accurately estimated;

[0143] Under the same test conditions, the time taken for 50% of the 12 test structure samples in the same group to fail due to electromigration is the median failure time t of the test structure under the test conditions. 50％ ;

[0144] Maintain the test temperature T in the thermostat 2 The test current (j 1 <j 2 <j 3 <j 4 ), repeat the above electromigration failure test experiment;

[0145] Get j 1 / T 2 、j 2 / T 2 、j 3 / T 2 and j 4 / T 2 Median failure time t of the test structure under test conditions 50％ ;

[0146] Formula (3) obtained by solving the Korhonen equation: Fit and calculate the diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ) size.

[0147] The process of curve fitting the formula (3) obtained by solving the Korhonen equation includes the following steps:

[0148] Simplifying the above formula (3), we get the following formula (10):

[0149]

[0150] Among them, the parameters is the diffusion coefficient D a Related formulas; parameters is the difference between the threshold stress and the residual stress (σ crit -σ res ) related formulas.

[0151] By transforming formula (10), we get the following formula (11):

[0152]

[0153] in, And the parameters a′ and b′ have the following relationship with the parameters a and b respectively:

[0154] a=c·a′ (12)

[0155] b=d·b′(13)

[0156] Among them, parameter c and parameter d are constants, indicating that parameter a and parameter b are transformed by multiples.

[0157] By formula It can be seen that when the test temperature T is constant, the void nucleation time t of the test structure is nuc There is a certain functional relationship with the test current density j;

[0158] According to j 1 / T 2 、j 2 / T 2 、j 3 / T 2 and j 4 / T 2 Median failure time t of the test structure under test conditions 50％ , for the formula By performing curve fitting, we can obtain the curve fitting diagram corresponding to the median failure time MTTF and current density j ( Figure 4 ) and the values ​​of parameters a′, b′;

[0159] The diffusion coefficient D is determined by the values ​​of the curve fitting parameters a′ and b′. a and the difference between the threshold stress and the residual stress (σcrit -σ res ) size. The curve fitting function of MATLAB is used for curve fitting.

[0160] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters, characterized in that: include: Step 1: Simulate the electromigration failure process of the heavy metal structure of the spin-orbit moment magnetic memory based on the Korhonen equation and predict the electromigration failure time; Step 2: Based on the electromigration failure time predicted in step 1, perform electromigration failure test on the heavy metal structure to obtain key parameters, including the diffusion activation energy, diffusion coefficient, and the difference between the threshold stress and the residual stress of the test structure.

2. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 1, characterized in that: The Korhonen equation described in step 1 is as follows: Among them, D a is the diffusion coefficient, B is the effective bulk elastic modulus, Ω is the atomic lattice volume, k B is the Boltzmann constant, e is the effective charge per unit electron, Z is the effective number of migrating atoms, ρ is the resistivity; t is time, σ is the electromigration stress, T is the test temperature, j is the DC current density, and x is the horizontal coordinate in the length direction of the test structure.

3. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 2, characterized in that: The electromigration failure process is divided into two stages: the void nucleation stage and the void growth stage. The void nucleation stage refers to the electromigration stress at the cathode end of the heavy metal structure reaching the critical stress σ at which the void begins to grow. crit The time during which the resistance of the test structure remains unchanged; the void growth stage refers to the voids inside the heavy metal structure that begin to grow after nucleation is completed, causing the resistance of the heavy metal structure to begin to increase. When the resistance increases to a set ratio, the heavy metal structure is deemed to have failed; The electromigration failure process is simulated with the following assumptions: First, the metal and dielectric barriers are absolutely rigid, and the atomic diffusion rates do not depend on stress; Second, at any location inside the grain, the vacancy concentration and stress are in equilibrium at any time; Third, the stress evolution is caused only by the atomic flux divergence; Fourth, if there is no dielectric barrier wrapped around the heavy metal, the electromigration failure time is the void nucleation time t nuc , otherwise the electromigration failure time is the void nucleation time t nuc and the cavity growth time t grow The sum.

4. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 3, characterized in that: The void nucleation time t nuc The simulation prediction process is: In the void nucleation stage, for a finite line with a length of L, the diffusion blocking ends are located at x = 0 and x = L of the finite line respectively. The test temperature T and the DC current density j are fixed, and the separation of variables method is used to solve the Korhonen equation to obtain formula (2): Among them, the residual stress σ res It refers to the residual thermal stress generated inside the metal due to temperature changes and the mismatch of thermal expansion coefficients of adjacent materials; κ represents the formula When the stress σ at the cathode end of the finite line, that is, x = 0, reaches σ crit When σ(0,t)=σ crit , and the void nucleation time t is obtained nuc The predicted value of is as follows:

5. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 3, characterized in that: The cavity growth time t grow The simulation prediction process is: During the void growth stage, as the cross-sectional area of ​​the metal line at the location where the void is formed continues to decrease, the resistance of the test structure increases; when the hole cuts off the entire cross-sectional area of ​​the metal line, it forces the test current to flow through the high-resistance dielectric barrier; when the resistance growth exceeds 20% of the initial resistance, the test structure fails, and the time taken is the void growth time t grow , the formula is as follows: Where R0 is the initial resistance of the test structure and R_incr_rate is the resistance growth rate, which is given by the following formula: Among them, ρ b , A b are the resistivity and cross-sectional area of ​​the outer barrier layer of the metal interconnect or via, respectively, W , A W are the resistivity and cross-sectional area of ​​the metal interconnect or via, respectively, d It represents the drift velocity of metal ions, and its formula is as follows:

6. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 1, characterized in that: The electromigration failure test of the heavy metal structure described in step 2 uses a test structure based on a combination of metal lines, through-holes and heavy metal layers with aluminum metallization as the test structure for the electromigration experiment according to JEDEC JESD87; the test structure is subjected to wafer-level electromigration testing.

7. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 1, characterized in that: Diffusion activation energy E a The acquisition process is: Providing electromigration test samples, each of which has a probe card; placing the samples in a constant temperature box, setting the test temperature in the constant temperature box to T1, and passing a test current j1 through the samples; using an EDA tool to record the resistance growth process and failure time of the samples; Under the same test conditions, 12 groups of effective electromigration failure tests were completed to ensure the median failure time t 50％ can be accurately estimated; under the same test conditions, the time taken for 50% of the test structures in the same group of 12 test structure samples to fail due to electromigration is the median failure time t of the test structure under the test conditions. 50％ ; Keep the passed test current j1 unchanged, change the test temperature in the thermostat to T2 and T3, and repeat the above electromigration failure test experiment, where T1 < T2 < T3; respectively obtain the median failure time t of the test structure under the test conditions of j1 / T1, j1 / T2, and j1 / T3 50％ ; The median failure time t is calculated using the Black equation 50％ Perform curve fitting and calculate the diffusion activation energy E of the test structure a .

8. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 7, characterized in that: The Black equation is used to perform curve fitting to calculate the diffusion activation energy E of the test structure. a , as follows: By transforming the Black equation shown in formula (7), we get the following formula (8): Among them, A is a constant; k is the Boltzmann constant; E a is the diffusion activation energy; n is the current density index; MTTF is the median failure time t of the sample under various test conditions 50％ ; lnA-nlnj is a constant; Let parameter C = lnA-nlnj, and we get the following formula (9): From formula (9), we know that when the test current density j is constant, the logarithm of the median failure time lnMTTF and the inverse of the test temperature There is a linear relationship; According to the median failure time t of the test structure under j1 / T1, j1 / T2 and j1 / T3 test conditions 50％ , curve fitting is performed on the Black equation to obtain the logarithm of the median failure time lnMTTF and the inverse of the test temperature The corresponding straight line fitting graph; According to the straight line slope in the straight line fitting diagram The diffusion activation energy E is obtained a .

9. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 1, characterized in that: Diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ) is obtained as follows: Providing electromigration test samples, each of which has a probe card; placing the samples in a constant temperature box, setting the test temperature in the constant temperature box to T2, and passing a test current j1 through the samples; using an EDA tool to record the resistance growth process and failure time of the samples; Under the same test conditions, 12 groups of effective electromigration failure tests were completed to ensure the median failure time t 50％ can be accurately estimated; under the same test conditions, the time taken for 50% of the test structures in the same group of 12 test structure samples to fail due to electromigration is the median failure time t of the test structure under the test conditions. 50％ ; Keep the test temperature T2 in the incubator constant, change the passing test currents to j2, j3, and j4, and repeat the above electromigration failure test experiment, where j1 < j2 < j3 < j4; respectively obtain the median failure times t of the test structure under the test conditions of j1 / T2, j2 / T2, j3 / T2, and j4 / T2 50％ ; Use the void nucleation time to fit the median failure time t 50％ and calculate the diffusion coefficient D a and the magnitude of the difference between the threshold stress and the residual stress (σ crit - σ res ).

10. The method for simulating the electromigration failure process of a heavy metal structure of a spin-orbit moment magnetic memory and obtaining key parameters according to claim 9, characterized in that: Using the void nucleation time Centering failure time t 50％ Fit and calculate the diffusion coefficient D a and the difference between the threshold stress and the residual stress (σ crit -σ res ), comprising the following steps: right After simplification, we get the following formula (10): Among them, the parameters is the diffusion coefficient D a Related formulas; parameters is the difference between the threshold stress and the residual stress (σ crit -σ res ) related formulas; By transforming formula (10), we get the following formula (11): in, And the parameters a′ and b′ have the following relationship with the parameters a and b respectively: a=c·a′ (12) b=d·b′ (13) Among them, parameter c and parameter d are constants, indicating that the parameters a and b are transformed by multiples; By formula It is known that when the test temperature T is constant, the void nucleation time t of the test structure nuc There is a certain functional relationship with the test current density j; According to the median failure time t of the test structure under the test conditions of j1 / T2, j2 / T2, j3 / T2 and j4 / T2 50％ , for the formula Perform curve fitting to obtain the curve fitting diagram corresponding to the median failure time MTTF and current density j and the values ​​of parameters a′ and b′; The parameter diffusion coefficient D is determined by the values ​​of parameters a′ and b′. a and the difference between the threshold stress and the residual stress (σ crit -σ res ) size.

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