JP5546160B2 - Model parameter determination device, model parameter determination method and program - Google Patents

Description

  The present invention relates to a model parameter determination device, a model parameter determination method, and a program, and more particularly to a model parameter determination device, a model parameter determination method, and a program for determining model parameters for a device model for circuit simulation.

  In designing a semiconductor integrated circuit, a circuit simulation is performed using a device model obtained by compactizing the characteristics of a semiconductor element (device). The specifications of device models such as BSIM4 are standardized as industry standard device models. By using a device model with standardized specifications, compatibility of device characteristic simulation can be ensured even between different designers or different simulation tools.

  The device model includes a plurality of parameters whose values can be adjusted. By appropriately setting the values of these parameters, the electrical characteristics of the actual device can be accurately reproduced by the device model. Here, these parameters included in the device model are referred to as model parameters.

  The device model is generally based on a physical model (that is, a physical phenomenon expressed as a mathematical expression), and many model parameters correspond to physical quantities that characterize the device. When the device is a MOSFET, the physical quantity includes the thickness of the gate insulating film, the dielectric constant, the impurity concentration, the depth of the impurity distribution, and the like. Here, the physical quantity that characterizes the device is called a physical parameter.

  However, the model parameters include ambiguous physical meanings such as fitting parameters introduced for the purpose of improving numerical accuracy. Further, even if a model parameter originally corresponds to a physical quantity, when the value is extracted by fitting, it may be a value far from the original physical quantity.

  When a new device with different characteristics from the existing device is developed by changing the process for manufacturing the semiconductor device from the existing process, the value of the model parameter corresponding to the device manufactured by the changed process Need to be newly set. As a model parameter setting method in such a case, for example, the following method is known.

  In the model parameter extraction method described in Patent Document 1, fitting is not performed directly to the measured IV (current vs. voltage) characteristic data, but Vth-Lg (Sh Generate intermediate data such as threshold voltage vs. gate length) characteristics or Vth-Wg (threshold voltage vs. gate width) characteristics, fit corresponding model parameters to these intermediate data, and set the model parameter values Extract.

  In addition, according to the characteristic simulation method described in Patent Document 2, in the newly developed characteristic simulation of a device, the current model in the device model is obtained from the current model created by polynomial fitting based on the measured current data of the device. By performing the replacement, a highly accurate characteristic simulation is performed.

JP 2000-322456 A JP 2007-328688 A

  In either of the model parameter extraction method or the characteristic simulation method described in Patent Document 1 or Patent Document 2, model parameters are set based on the fitting. However, since the model parameter is extracted by the fitting process that reduces the error between the measurement data and the simulation data, the physical meaning of the model parameter is ambiguous. If the correspondence between the change in manufacturing process conditions and the amount of change in model parameters and the mutual relationship between multiple model parameters are clear, even before the transistor after the change in manufacturing process conditions is actually created, Device characteristics can be predicted with high accuracy. However, it is difficult to predict device characteristics of model parameters based on fitting because the above correspondence is unclear. Furthermore, the work of extracting a large number of model parameters by fitting requires labor, and there is a risk of falling into a local solution during the fitting.

  As a method for dealing with such a problem, it is conceivable to change the device model itself. However, if you modify the standardized device model, compatibility will be lost. Therefore, it is desirable to deal with it by changing the model parameters while keeping the device model itself.

  Therefore, when a process for manufacturing a semiconductor integrated circuit is changed, a model parameter included in the device model can be easily determined in order to represent a semiconductor element manufactured by the changed process by the device model. It becomes a problem. An object of the present invention is to provide a model parameter determination device, a model parameter determination method, and a program for solving such a problem.

A model parameter determining apparatus according to a first aspect of the present invention includes a plurality of models included in a first physical parameter characterizing a semiconductor element manufactured by a first manufacturing method and a device model for representing characteristics of the semiconductor element. A plurality of first model parameters for representing a semiconductor device manufactured by the first manufacturing method and a second physical parameter characterizing the semiconductor device manufactured by the second manufacturing method; A plurality of second model parameters for expressing the characteristics of the semiconductor element manufactured by the manufacturing method 2 by the device model, at least one of the plurality of first model parameters, the first physical parameter, and the second Determine based on physical parameters. Here, each of the plurality of second model parameters is a function including at least one of the plurality of first model parameters, the first physical parameter, and the second physical parameter as arguments, It is determined using a function based on the physical model to be specified. In addition, the function for determining one second model parameter among the plurality of second model parameters further includes another second model parameter among the plurality of second model parameters as an argument.

The model parameter determining method according to the second aspect of the present invention is included in a device model in which a computer represents a first physical parameter that characterizes a semiconductor element manufactured by the first manufacturing method and characteristics of the semiconductor element. A plurality of first model parameters for representing a semiconductor element manufactured by the first manufacturing method, and a second physical parameter characterizing the semiconductor element manufactured by the second manufacturing method. A step of reading from the storage device, and a plurality of second model parameters for representing characteristics of the semiconductor element manufactured by the second manufacturing method by the device model, and at least one of the plurality of first model parameters Determining based on the first physical parameter and the second physical parameter. Here, the computer is a function including, as arguments, a plurality of second model parameters, respectively, at least one of the plurality of first model parameters, the first physical parameter, and the second physical parameter. A device model is determined using a function based on a physical model. In addition, the function for determining one second model parameter among the plurality of second model parameters further includes another second model parameter among the plurality of second model parameters as an argument.

The program according to the third aspect of the present invention includes a first physical parameter characterizing a semiconductor element manufactured by the first manufacturing method and a plurality of model parameters included in a device model for representing characteristics of the semiconductor element. A process of reading a plurality of first model parameters for representing a semiconductor element manufactured by the first manufacturing method and a second physical parameter characterizing the semiconductor element manufactured by the second manufacturing method from the storage device; A plurality of second model parameters for representing the characteristics of the semiconductor element manufactured by the second manufacturing method by the device model are at least one of the plurality of first model parameters, the first physical parameter, and the second And processing to determine based on the physical parameters of the computer. Here, the program is a function including a plurality of second model parameters, each of which includes at least one of the plurality of first model parameters, the first physical parameter, and the second physical parameter as arguments. A computer executes a process of determining using a function based on a physical model that defines a device model. In addition, the function for determining one second model parameter among the plurality of second model parameters further includes another second model parameter among the plurality of second model parameters as an argument.

  According to the model parameter determination apparatus, the model parameter determination method, and the program according to the present invention, when a process for manufacturing a semiconductor integrated circuit is changed, a device is used to represent a semiconductor element manufactured by the process after the change by the device model. Model parameters included in the model can be easily determined.

It is a block diagram which shows the structure of the model parameter determination apparatus which concerns on the 1st Embodiment of this invention. It is a flowchart which shows operation | movement of the model parameter determination apparatus which concerns on the 1st Embodiment of this invention. It is a figure which shows typically a mode that a some model parameter interlock | cooperates in the model parameter determination apparatus which concerns on the 1st Embodiment of this invention. It is a block diagram which shows the structure of the model parameter determination apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows operation | movement of the model parameter determination apparatus which concerns on the 2nd Embodiment of this invention. It is a figure which shows the P-type high concentration area | region in the area | region of the source-drain vicinity of an N channel transistor. It is the figure which simplified the impurity distribution inside a transistor. It is the figure which simplified the impurity distribution inside a transistor. It is a figure which shows the gate length dependence of Vth in Example 2 of this invention. It is a figure which shows the gate length dependence of DIBL in Example 2 of this invention. It is a block diagram which shows the structure of the model parameter determination apparatus which concerns on Example 3 of this invention. It is a block diagram which shows the structure of the conventional model parameter determination apparatus. It is a flowchart which shows operation | movement of the conventional model parameter determination apparatus.

  The model parameter determination device according to the first development form is preferably a model parameter determination device according to the first viewpoint.

  The model parameter determining apparatus according to the second development form includes a model parameter included in the second model parameter group, a physical parameter included in the first physical parameter group, a physical parameter included in the second physical parameter group, and a second parameter. Preferably, it is determined by a function based on a physical model that includes model parameters included in one model parameter group as arguments.

  In the model parameter determining apparatus according to the third development form, it is preferable that the function is derived based on a function that defines a device model.

  The model parameter determining apparatus according to the fourth development form preferably further includes a fitting unit that fits the second model parameter group with respect to the characteristics measured for the semiconductor element manufactured by the second manufacturing method. .

  In the model parameter determining apparatus according to the fifth development mode, the function further includes a model parameter other than the model parameter determined by the function, which is a model parameter included in the second model parameter group, as an argument. Also good.

A model parameter determining apparatus according to a sixth development mode includes a model parameter for determining the strength of the inverse short channel effect, a characteristic length for determining the strength of the short channel effect or a model parameter for correcting the characteristic length, and DIBL The function that determines the characteristic length that determines the gate length dependency or the model parameter that corrects the characteristic length is a physical model in which the increase in the average impurity concentration in the short gate length region is proportional to the reciprocal of the effective channel length. Represented on the basis of
The model parameter for determining the strength of the reverse short channel effect is determined by a function including a parameter corresponding to the channel impurity concentration as an argument so that the strength of the reverse short channel effect is proportional to the inverse of the channel impurity concentration,
At least one of a characteristic length that determines the strength of the short channel effect or a model parameter that corrects the characteristic length, and a characteristic length that determines the gate length dependency of DIBL or a model parameter that corrects the characteristic length is Alternatively, the characteristic length may be determined by a function including a model parameter as an argument for determining the strength of the inverse short channel effect so that the characteristic length is proportional to the -1/4 power of the average impurity concentration.

  A model parameter determining apparatus according to a seventh development form includes a characteristic length for determining the short channel effect or a model parameter for correcting the characteristic length, and a characteristic length for determining the gate length dependency of the DIBL or the characteristic thereof. A function that determines at least one of the model parameters for correcting the length may be expressed based on a model that considers the influence of the impurity distribution in a region near the substrate surface and in a deeper region.

  It is preferable that the model parameter determination apparatus according to the eighth development mode further includes a function input unit that uses a function designated by the user as the above function.

  The model parameter determination method according to the ninth development form is preferably the model parameter determination method according to the second viewpoint.

  In the model parameter determination method of the tenth development mode, in the parameter determination step, the model parameters included in the second model parameter group are converted into physical parameters included in the first physical parameter group and second physical parameter group. It is preferable to determine by a function based on the physical model including the physical parameter included and the model parameter included in the first model parameter group as arguments.

  In the model parameter determination method of the eleventh development mode, it is preferable that the function is derived based on a function that defines a device model.

  It is preferable that the model parameter determination method according to the twelfth development mode further includes a step of fitting the second model parameter group with respect to the characteristics measured for the semiconductor element manufactured by the second manufacturing method.

  The program in the thirteenth development form is preferably a program according to the third viewpoint.

  In the parameter development process, the program in the fourteenth development mode uses the model parameters included in the second model parameter group as the physical parameters included in the first physical parameter group and the physical parameters included in the second physical parameter group. It is preferable to cause the computer to execute a process of determining a parameter and a function based on a physical model including a model parameter included in the first model parameter group as an argument.

  In the program of the fifteenth development form, the function is preferably derived based on a function that defines a device model.

  It is preferable that the program in the sixteenth development mode further causes the computer to execute a process of fitting the second model parameter group to the characteristics measured for the semiconductor element manufactured by the second manufacturing method.

(Embodiment 1)
A model parameter determination device according to a first embodiment of the present invention will be described with reference to the drawings.

  First, the configuration of a conventional model parameter determination device will be described. FIG. 12 is a block diagram showing a configuration of a conventional model parameter determination device 501. As shown in FIG.

  Referring to FIG. 12, the model parameter determination apparatus 501 reads a device model 502, an initial model parameter group 503, and device measurement data 504 as input values, and outputs a model parameter group 505.

  The device model 502 is a device model such as BSIM4, for example. The initial model parameter group 503 is a set of model parameters corresponding to the device model 502. For example, the device measurement data 504 is data obtained by measuring the drain current while changing the bias conditions for the gate voltage, the drain voltage, and the substrate voltage.

  Referring to FIG. 12, the model parameter determination device 501 includes a parameter storage unit 511, a characteristic calculation unit 512, an error determination unit 513, and a parameter change unit 514.

  FIG. 13 is a flowchart showing the operation of the model parameter determination device 501.

  Referring to FIG. 13, the model parameter determination apparatus 501 reads the device model 502, the initial model parameter group 503, and the device measurement data 504, and stores the initial model parameter group 503 in the parameter storage unit 511 (steps S500 to S502).

  The characteristic calculation unit 512 performs characteristic calculation based on the model parameters stored in the device model 502 and the parameter storage unit 511 (step S503).

  The error determination unit 513 compares the device measurement data with the calculated characteristic data (step S504).

  When the error determining unit 513 determines that the error is equal to or greater than the predetermined threshold ε (No in step S504), the parameter changing unit 514 changes the model parameter (step S505), and uses the changed model parameter as a parameter. Record in the storage unit 511. Thereafter, the loop of steps S503 to S505 is repeated in the same manner. In this loop, the values of many model parameters are changed.

  On the other hand, when the error determination unit 513 determines that the error is smaller than the predetermined threshold ε (Yes in step S504), the model parameter determination device 501 uses the model parameter stored in the parameter storage unit 511 as a model. The parameter group 505 is output (step S506), and the model parameter determination operation is terminated.

  As described above, the model parameter determination device 501 determines the model parameter by numerical fitting to the measurement data.

  The model parameter determination apparatus according to the present embodiment determines a model parameter group for reproducing the characteristics of a device manufactured by changing a manufacturing process from an existing one using a device model. Here, it is assumed that a model parameter group for a device manufactured by an existing manufacturing process is determined in advance, or a model parameter group corresponding to an existing manufacturing process can be determined by some method.

  FIG. 1 is a block diagram showing a configuration of a model parameter determination device 1 according to the present embodiment. Referring to FIG. 1, a model parameter determination apparatus 1 includes a model parameter group 2 for a device manufactured by a manufacturing process before change, a physical parameter group 3 of a device manufactured by a manufacturing process before change, and a post-change The physical parameter group 4 of the device manufactured by the manufacturing process is read as an input value, and the model parameter group 5 corresponding to the device manufactured by the manufacturing process after the change is output. The device model 6 is a device model such as BSIM4.

  The model parameter determination device 1 includes at least one model parameter included in the model parameter group 2 as a model parameter group 2 for a manufacturing process before change, a physical parameter group 3 for a manufacturing process before change, and a change. While calculating as a function of the physical parameter group 4 of the subsequent manufacturing process, the value of the model parameter is replaced with the calculated value, and the model parameter group 5 corresponding to the device manufactured in the manufacturing process after the change is output.

  The above function is described by a mathematical formula based on a physical model. The model parameter groups 2 and 5 are model parameter groups corresponding to the device model 6, and the above-described mathematical expressions of the model parameter determination apparatus 1 are based on the device model 6. However, the device model 6 itself is not changed when determining the model parameters.

  The physical parameter is a parameter that characterizes each device manufactured by the manufacturing process before and after the change. The physical parameters include, for example, parameters related to the device structure such as the thickness and dielectric constant of the gate insulating film, and the impurity concentration and the depth of the impurity distribution. These device structure parameters may be estimated by process simulation based on manufacturing process conditions such as impurity implantation dose, implantation energy, heat treatment time, etc., and may include electrical characteristics such as threshold voltage and mobility. It may be estimated based on this. As physical parameters, process conditions (temperature, time, implantation dose, etc.) and electrical characteristics may be used.

  FIG. 2 is a flowchart showing the operation of the model parameter determination apparatus 1 according to the present embodiment. Referring to FIG. 2, the model parameter determination apparatus 1 includes a model parameter group 2 corresponding to a device manufactured in a manufacturing process before change, a physical parameter group 3 in a manufacturing process before change, and a physical parameter in a manufacturing process after change. Group 4 is read sequentially (steps S1 to S3). Note that the reading order of the parameter group in steps S1 to S3 is arbitrary.

  Next, the model parameter determination apparatus 1 calculates the value of the model parameter corresponding to the device manufactured in the manufacturing process after the change by using a function (step S4). The model parameter determination device 1 calculates a model parameter using a function based on a physical model including a model parameter of a process before the change, a physical parameter of the process before the change, and a physical parameter of the process after the change, The value of the model parameter included in the model parameter group 5 manufactured in the manufacturing process before the change is replaced with the calculated value.

  The model parameter determination device 1 outputs the model parameter after replacement as a model parameter group 4 corresponding to the manufacturing process after change (step S5). The existing and changed model parameter group is a parameter group corresponding to some device model such as BSIM4, and the function used in step S4 is a function based on the device model.

  Also in the conventional model parameter determination device 501, the model parameter corresponding to the manufacturing process before the change can be adopted as the initial model parameter. However, the relationship between the set model parameter and the model parameter of the manufacturing process before the change may be lost in the process of numerical fitting.

  According to the model parameter determining apparatus 1 of the present embodiment, since the model parameter is uniquely determined by the mathematical formula, the model parameter corresponding to the manufacturing process after the change is the model parameter corresponding to the manufacturing process before the change, and Related to changes in manufacturing process conditions. Therefore, the characteristics of the device can be predicted even before the device is manufactured or before the device measurement data is acquired. In addition, since parameters are automatically determined by a function rather than fitting by trial and error, labor for determining parameters can be saved.

  When the manufacturing process conditions are changed, there are a plurality of model parameters whose values are to be changed, and these model parameters may change in conjunction with each other. FIG. 3 is a diagram schematically illustrating how a plurality of model parameters are linked.

  In FIG. 3, it is assumed that the value of the physical parameter X changes to X ′ due to a change in the manufacturing process. The model parameter group includes model parameters P1 and P2, and each of the model parameters P1 and P2 is a model parameter whose value needs to be changed according to a change in the physical parameter X. At this time, the function f2 for calculating the model parameter P2 ′ after the change of the model parameter P2 is not only the model parameter P2 and the physical parameters X and X ′ but also the model parameter P1 or the model parameter P1 ′ after the change of the model parameter P1. Including at least one of the following. At this time, the model parameter P2 changes in conjunction with the model parameter P1.

  In the device model, even if it is a model parameter that originally has a relationship in electrical characteristics, the relationship is not modeled, and each model parameter may be expressed as an independent model parameter. When the values of these model parameters are individually set by fitting or the like, there is a possibility that the relevance inherent in the model parameters is lost. However, in the model parameter determination apparatus 1, the relationship between the model parameters can be maintained by describing the variation of one model parameter by a function including the other model parameter.

  When expressed in terms of physical parameters, for example, the effects expressed by a plurality of physical parameters such as the peak position, concentration, and spread of the impurity distribution are simple on the device model from the viewpoint of influence on electrical characteristics. It may be expressed by one model parameter. In such a case, the number of physical parameters included in the function argument can be reduced by using the model parameter as an input variable of the function. As an example, only physical parameters that have been changed due to changes in the manufacturing process can be used as function arguments.

  As an example, the model parameter P1 is a model parameter that represents the influence on the electrical characteristics due to complex factors such as the peak position, peak concentration, and spread of the impurity distribution in the local region. On the other hand, the model parameter P2 is a model parameter representing electric characteristics determined from the impurity distribution of the entire device. Further, the physical parameter X is the peak concentration of impurities in the local region. Originally, the model parameter P2 is related to the model parameter P1. Therefore, this relationship can be maintained by describing the model parameter P2 'by a function having the model parameter P1 as an argument. Also, by using the model parameter P1 as a function argument, physical parameters such as peak position and spread can be omitted in the function argument.

  In the function for determining the model parameter P2, the model parameter to be linked is only the model parameter P1. However, the model parameter may be linked with two or more types of model parameters. That is, two or more types of model parameters other than itself may be included in an argument of a function that determines model parameters.

  Further, there may be a model parameter that is further linked to a model parameter that is linked to another model parameter. As an example, in addition to the model parameters P1 and P2, there is a model parameter P3. The value of the model parameter P2 is calculated by a function including the model parameter P1, and the value of the model parameter P3 is calculated by a function including the model parameter P2. You may make it do.

  Further, it is preferable that the user can appropriately set the function for determining the model parameter. This is because the convenience of the model parameter determination device is improved, and the model parameter can be determined even when a more appropriate function is derived by taking in a physical model that has not been considered at first.

  Since the model parameter determination apparatus 1 of the present embodiment sets model parameters using mathematical formulas based on a physical model, the relationship between changes in process conditions and changes in model parameters is clear, and device characteristics can be predicted. It becomes.

  Furthermore, according to the model parameter determination apparatus 1 of the present embodiment, the device model itself is not changed, and only the value of the model parameter is changed. Therefore, the compatibility of the industry standardized device model is not lost.

(Embodiment 2)
A model parameter determination apparatus according to a second embodiment of the present invention will be described with reference to the drawings. FIG. 4 is a block diagram illustrating a configuration of the model parameter determination apparatus 101 according to the present embodiment.

  The model parameter determination apparatus 101 includes an intermediate model parameter setting unit 111 and a fitting unit 121. The model parameter determination apparatus 101 includes a model parameter group 112 corresponding to a device manufactured in the manufacturing process before the change, a physical parameter group 113 that is a physical parameter group of the manufacturing process before the change, and a physical parameter group of the manufacturing process after the change. The physical parameter group 114, the device model 122, and the device measurement data 124 of the changed manufacturing process are read as input values, and the model parameter group 105 corresponding to the device manufactured by the changed manufacturing process is output.

  The intermediate model parameter setting unit 111 is the same as the model parameter determination device 1 (FIG. 1) according to the first embodiment. The intermediate model parameter setting unit 111 reads, as input values, the model parameter group 112 of the manufacturing process before the change, the physical parameter group 113 of the manufacturing process before the change, and the physical parameter group 114 of the manufacturing process after the change. An intermediate model parameter group 123 is generated and output.

  The model parameter group 112 is a parameter group corresponding to the device model 122. The function is a mathematical expression based on the device model 122.

  The intermediate model parameter group 123 output from the intermediate model parameter setting unit 111 is input to the fitting unit 121. In the conventional model parameter determination device 501 (FIG. 12), the fitting unit 121 replaces the input initial model parameter group 503 with the intermediate model parameter group 123 and replaces the device measurement data 504 with the device measurement data 124 of the manufacturing process after the change. This corresponds to the replacement of the device model 502 with the device model 122.

  The fitting unit 121 optimizes the intermediate model parameter group 123 by numerical fitting to the measurement data, calculates a model parameter group corresponding to the changed process, and outputs the model parameter group 105 of the changed manufacturing process.

  FIG. 5 is a flowchart showing the operation of the model parameter determination apparatus according to this embodiment. Referring to FIG. 5, each of steps S101 to S105 corresponds to steps S1 to S4 (FIG. 2) in the first embodiment. However, in the present embodiment, the model parameter group calculated in step S104 is not used as the final model parameter, but is treated as the intermediate model parameter group 123, and the intermediate model parameter group 123 is temporarily stored (step S105). This is different from the first embodiment.

  Steps S106 to S111 correspond to steps S500 and S502 to S506 (FIG. 13) in the operation of the conventional model parameter determination device 501. That is, the fitting unit 121 uses the intermediate model parameter group 123 calculated by the function as an initial model parameter group for fitting, and performs fitting on the device measurement data. The fitting unit 121 outputs the final model parameter group after the change (step S111), and ends the process.

  The model parameter determination device 1 of the present embodiment has the model parameter determination device (1 in FIG. 1) according to the first embodiment as the front stage and the conventional model parameter determination device (501 in FIG. 12) as the rear stage. The model parameters of the manufacturing process after the change are determined by sequentially operating the apparatus.

  There is a possibility that the model parameter corresponding to the manufacturing process before the change is deviated from the physical quantity originally meant. Also, not all related physical phenomena are considered in the function for setting model parameters. Therefore, when the model parameter is determined based only on the function as in the model parameter determination apparatus 1 of the first embodiment, there is a possibility that sufficient accuracy cannot be obtained for the device measurement data. According to the model parameter determination apparatus 1 of the present embodiment, the accuracy of the model can be improved by adding a numerical fitting process.

  In the present embodiment, the intermediate model parameter value is an approximate value of the final model parameter value. At this time, the amount of change in the model parameter in the fitting process is very small, and the calculation time required for fitting can be reduced compared to the conventional determination of the model parameter, and the possibility that the model parameter converges to the local solution is reduced. can do.

  Further, some of the model parameters that need to be fitted in the prior art can be excluded from the fitting target by fixing the values as intermediate model parameters. By narrowing down the number of model parameters that require fitting, the amount of work in fitting can be further reduced.

  As an example, the operation of the above model parameter determination device when the gate insulating film thickness of the MIS field effect transistor is changed will be described.

  It is assumed that a model parameter corresponding to the electrical gate insulating film thickness exists as a model parameter, and Te is a model parameter corresponding to the manufacturing process before the change. The gate insulating film thickness optically measured in the manufacturing process before the change is Tp, and the gate insulating film thickness optically measured in the process after the change is Tp ′.

  The model parameter determination apparatus 1 includes a model parameter group including Te as a model parameter corresponding to a manufacturing process before change, a parameter group including Tp as a physical parameter of the manufacturing process before change, and a physical parameter of the manufacturing process after change. A parameter group including Tp ′ is input.

The model parameter determination device 1 replaces Te included in the model parameter group with a model parameter Te ′ calculated according to the following function, and outputs the model parameter group corresponding to the changed manufacturing process.

  Here, Δ is a constant representing the effects of gate depletion and inversion layer quantization, and the model parameter determination device 1 stores the value of Δ. According to the model parameter determination device 1 according to the present invention, it is possible to automatically change parameters easily.

  When the channel impurity implantation dose is changed in the MIS type field effect transistor, the reverse short channel effect model, DIBL (Drain Induced Barrier Lowering) model, and short channel effect model included in the Vth (threshold voltage) model of the BSIM4 model A method for setting the parameters will be described. The following description will be made using an N-channel transistor in which the channel region is doped P-type and the source / drain regions are doped N-type with high concentration. The parameter setting method is the same for the P-channel transistor.

  The Vth model equation of the BSIM4 model is shown in equation (1-1) in Table 1. The terms extracted by the inverse short channel effect, the short channel effect, and the term contributed by the DIBL model parameter are shown in equations (1-2) to (1-5) in Table 1. Table 2 shows model equations for calculating lt used in these model equations. These model equations are all described in Chapter 2 of “BSIM 4.6.2 MOSFET Model-User's Manual”. Leff is an effective channel length and takes a value obtained by subtracting (or adding) a certain offset amount from the gate length Lg.

  The channel impurity concentration Nch is one of physical parameters that change when the channel impurity implantation dose is changed. The value of Nch for the manufacturing process before and after the change is determined by, for example, simulating each manufacturing process condition with a process simulator and analyzing the impurities in the substrate of the long channel transistor (for example, Lg is 1 μm or more) It can be determined by examining the concentration.

  Nch can also be determined by a method of estimating Nch from the measured value of Vth of the long channel transistor or a method of estimating Nch from the measurement result of Vth (substrate voltage) dependence of Vth of the long channel transistor. .

によって求めることができる。 The model parameter NDEP is a model parameter representing the channel impurity concentration, and is a parameter directly connected to the physical parameter Nch. When the impurity dose is changed and the physical parameter Nch is changed to the physical parameter Nch ′, the changed model parameter NDEP ′ is expressed by the following equation:

Can be obtained.

  Inverse short channel effect model parameters in BSIM4 are two model parameters LPE0 and LPEB. The model parameter LPE0 is used in the equation (1-3) in Table 1 and represents the magnitude of the effect of increasing Vth with a transistor having a short Lg. On the other hand, the model parameter LPEB is used in the equation (1-2) in Table 1 and represents the magnitude of the effect of enhancing the Vth dependency on Vbs (substrate voltage) with a transistor having a short Lg. Formulas for the model parameters LPE0 and LPEB can be expressed based on the following physical model using the average impurity concentration.

  FIG. 6 is a diagram showing a P-type high concentration region in a region near the source / drain of an N-channel transistor. Referring to FIG. 6, a region near the source / drain of the N-channel transistor has a region having a P-type impurity concentration higher than that of the center of the channel. This region is caused by unintentional abnormal diffusion due to halo impurities intentionally implanted to suppress the short channel effect and crystal defects. The reverse short channel effect is caused by an increase in the proportion of such a high concentration P-type region in the channel region as the gate length is shortened.

すなわち、ゲート長が短くなるにつれＮａｖが増大し、Ｎａｖの増加分はＬｅｆｆの逆数に比例する。 FIG. 7 is a simplified diagram of the impurity distribution inside the transistor. As shown in FIG. 7, the distribution of the P-type impurity in the lateral direction (source / drain direction) is P-type doped with a uniform channel concentration Nch over the entire area, from the source end and the drain end to the position of the distance Lhalo. Assume that the concentration is increased by Nhalo. In FIG. 7, the distribution of N-type impurities is omitted. At this time, the average impurity concentration Nav of the channel region is expressed by the following equation.

That is, Nav increases as the gate length becomes shorter, and the increase in Nav is proportional to the reciprocal of Leff.

On the other hand, in a channel with uniform impurity distribution, Vth increases or decreases according to the 1/2 power of the impurity concentration. Assuming that the channel region is a uniform impurity distribution of concentration Nav, the amount of increase in Vth due to the high concentration P-type region near the source / drain is proportional to the following equation.

  Referring to Equation (5) and the term of Vth increase due to the inverse short channel effect in Equation (1-3) in Table 1, the model parameter LPE0 corresponds to (Nhalo · Lhalo) / Nch. That is, the model parameter LPE0 is proportional to the inverse of Nch.

によって表すことができる。 As described above, when the channel impurity concentration Nch is changed to Nch ′ by changing the channel impurity implantation dose, the model parameter LPE0 ′ corresponding to the changed process is expressed by the following equation:

Can be represented by

によって表すことができる。 Similarly, the model parameter LPEB is given by

Can be represented by

  Note that Vth is determined by the impurity distribution in the substrate depletion layer, and Vbs dependence of Vth is determined by expansion and contraction of the substrate depletion layer. Therefore, LPE0, which is a parameter affecting Vth itself, can be regarded as a parameter related to the impurity distribution near the substrate surface. On the other hand, LPEB, which is a parameter that affects the dependence of Vth on Vbs, can be regarded as a parameter related to the impurity distribution in a slightly deeper portion near the edge of the substrate depletion layer.

  FIG. 8 is a simplified diagram showing the impurity distribution inside the transistor. The simplified impurity distribution model of FIG. 7 can be extended to a model having a depth direction distribution as shown in FIG. In FIG. 8, it is considered that the impurity concentration is high by Nhalo1 in the vicinity of the substrate surface, and by Nhalo2 in a slightly deeper part. The model parameter LPE0 corresponds to (Nhalo1 · Lhalo) / Nch, and the model parameter LPEB corresponds to (Nhalo2 · Lhalo) / Nch.

  The short channel effect and DIBL are caused by the drain electric field entering the channel region and lowering the channel potential. These effects are modeled by using a parameter called characteristic length and increasing the influence exponentially as the ratio of effective channel length to characteristic length decreases. The characteristic length is determined by the gate insulating film thickness and the substrate depletion layer width. BSIM4 is also based on the same concept, and lt0 included in the term of the cosh function of the denominator of the DIBL model equation (equation (1-5) in Table 1) is the characteristic length.

lt0 is represented by an equation proportional to the 1/2 power of the depletion layer width Xdep0 as shown in Equation (2-3) in Table 2. Xdep0 is expressed by an equation proportional to the −1/2 power of the channel concentration parameter NDEP as shown in equation (2-4) in Table 2. At this time, lt0 is proportional to NDEP to the -1/4 power. However, the lt0 expression does not incorporate the effect of increasing the average impurity concentration in the region with a short Lg. In the formula (2-3) and (2-4), when the replaces the NDEP at Nav and LT0 ^*, found the following LT0 ^* than LT0, considered close to the original characteristic length. Therefore, the characteristic length is modeled not as NDEP but as being proportional to -1/4 of Nav.

である。ＮｃｈがＮｃｈ’に変化したときのＤＳＵＢの値をＤＳＵＢ’とすると、ＤＳＵＢ’は、次の式

によって表される。 The term cosh (DSUB · Leff / lt0) of the cosh function includes a model parameter DSUB. Therefore, the influence of the increase in impurity concentration not taken into account in lt0 can be corrected by DSUB. That is,

It is. If the value of DSUB when Nch is changed to Nch ′ is DSUB ′, DSUB ′ is expressed by the following equation:

Represented by

Here, assuming that only the average impurity concentration in the vicinity of the substrate surface is considered as DSUB ′ is DSUB1 ′, and only when the average impurity concentration in a slightly deep portion is considered as DSUB ′ is DSUB2 ′, the inverse short channel effect parameter Thus, DSUB1 ′ and DSUB2 ′ can be expressed as follows.

である。最も簡単なパラメータの推定としては、η＝１／２とすればよい。さらに、Ｌｅｆｆの値は、テクノロジの最小寸法付近のゲート長における値（Ｌｅｆｆ＿ｍｉｎ）で代表させる。すなわち、

とすればよい。式（１３）は、ＤＳＵＢ以外に２種類のパラメータＬＰＥ０（ＬＰＥ０’）及びＬＰＥＢ（ＬＰＥＢ’）含み、ＤＳＵＢはＬＰＥ０及びＬＰＥＢと連動して変化する。短チャネル効果モデルパラメータであるＤＶＴ１についても、同様の議論から

となる。 Actual DIBL is affected not only by the vicinity of the substrate surface but also by the wraparound of the electric field that passes through a deep portion of the substrate. Therefore, it is considered that an appropriate value of DSUB ′ is an intermediate value between DSUB1 ′ and DSUB2 ′. That is,

It is. The simplest parameter estimation may be η = 1/2. Further, the Leff value is represented by a value (Leff_min) in the gate length near the minimum dimension of the technology. That is,

And it is sufficient. Expression (13) includes two types of parameters LPE0 (LPE0 ′) and LPEB (LPEB ′) in addition to DSUB, and DSUB changes in conjunction with LPE0 and LPEB. The same discussion applies to DVT1, which is a short channel effect model parameter.

It becomes.

  The model parameter was determined by the model parameter determination apparatus of the present invention for a transistor manufactured under the condition that the channel impurity implantation dose was lower than the manufacturing process condition before the change. According to the model parameter group of the manufacturing process before the change, the gate length dependency of Vth in the device manufactured by the manufacturing process before the change is accurately reproduced.

  First, a process simulation of a transistor having a gate length of 10 μm was performed by simulating each manufacturing process condition, and a device simulation was performed based on the process simulation result to obtain a substrate depletion layer width. Xdep0 in the equation (2-4), which is the theoretical formula of the substrate depletion layer width, is the substrate depletion layer width obtained from the simulation, and Nch and Nch ′ are calculated with NDEP = Nch. Further, NDEP ′ = Nch ′ was set.

  FIG. 9 is a diagram showing the gate length dependence of Vth in this embodiment. FIG. 9 is a graph plotting the difference between Vth at each Lg and Vth for a transistor with a long Lg against the gate length. By reducing the dose, the reverse short channel effect is relatively strengthened.

  “No parameter change” indicates a result of calculating Vth from the model when only the value of NDEP is changed, and LPE0, LPEB, DVT1, and DSUB are left as model parameter values of the manufacturing process before the change. At this time, the Lg dependency of Vth is significantly different from the measurement data. In the conventional parameter determination method, it is necessary to start the fitting operation from this state.

  “Parameter change by mathematical expression” indicates a case where the values of LPE0, LPEB, DVT1, and DSUB are changed and calculated based on the mathematical expression of the model parameter determination device 1 of the present invention. Referring to FIG. 9, the Lth dependence of Vth close to actual transistor measurement data is predicted by the model. This model parameter is determined without using measurement data of a transistor with a short Lg in the process after the change. According to the model parameter determination device 1 of the present invention, the change in characteristics can be predicted with high accuracy. Can do.

  Although there is an error of several tens of mV compared with the measured value, the error can be reduced by further fitting. According to the model parameter determination device 1 of the present invention, the fitting can be started from a situation sufficiently close to the measured value. Therefore, the amount of parameter fluctuation in the fitting process can be reduced compared to the conventional case, and the amount of work required for fitting can also be reduced.

  FIG. 10 is a diagram showing the dependency of DIBL on the gate length Lg in this embodiment. Here, the difference between Vth when the drain voltage is 0.05 V and Vth when the drain voltage is 1.2 V is defined as the DIBL value. As a result of device measurement, DIBL is strengthened by decreasing the dose.

  “No change in parameter DSUB” in FIG. 10A shows a case where only the value of NDEP is changed, and LPE0, LPEB, DVT1, and DSUB are left as model parameter values of the manufacturing process before the change. Since the correction due to the increase in the average impurity concentration is not performed, DIBL is excessive. When the DSUB value is changed by a function, since the impurity concentration is corrected, the DIBL size close to the actual measurement is obtained.

  FIG. 10B shows a case where DSUB ′ = DSUB′1, DSUB ′ = DSUB′2, or DSUB ′ = (DSUB′1 + DSUB′2) / 2 (that is, a function for setting parameters (10) ) To (12)), the dependency of DIBL on the gate length Lg is shown.

  Referring to FIG. 10B, when the value of the model parameter DSUB is changed based on the equation (13) which is a model that takes into account the influence of both the vicinity of the substrate surface and a slightly deeper portion, the size of the DIBL Is best predicted. There is a slight error in DIBL, but the error can be further reduced by performing fitting after this.

  The model parameters LPE0, LPEB, DVT1, and DSUB are all model parameters originally introduced as fitting parameters in the BSIM4 model. Therefore, changes in these model parameters according to changes in channel impurity concentration are not explicitly taken into account in the BSIM4 model. According to the model parameter determination apparatus of the present invention, the model parameter can be easily determined by functionalizing effects that are not considered in the original device model.

表１ ＢＳＩＭ４モデルにおけるＶｔｈモデル式

Table 1 Vth model formula in BSIM4 model

表２ ＢＳＩＭ４ Ｖｔｈモデルに含まれるｌｔなどの値の計算式

Table 2 Formulas for values such as lt included in the BSIM4 Vth model

  FIG. 11 is a block diagram illustrating a configuration of the model parameter determination device 1 according to the present embodiment. The model parameter determination device 1 of this embodiment is obtained by adding a function input unit 7 by a user to the model parameter determination device 1 of FIG. The user can appropriately set the format of the function used for determining the model parameter corresponding to the changed manufacturing process by inputting the function to the function input unit 7 of the model parameter determining apparatus 1 as necessary.

  As an example, the user can change the value of η included in the expression (12) in the second embodiment. If the optimal value of η is found by refinement of the physical model or empirical means, the user can input the value and modify the function.

  In the model parameter determination apparatus 1, a plurality of functions may be prepared in advance so that the function to be used can be changed depending on the device model and device structure (bulk substrate, SOI substrate, FinFET, etc.). At this time, the estimation accuracy of the model parameters can be improved, and the convenience of the model parameter determination device is also improved.

  Furthermore, the user may be able to freely input a function composed of a combination of arbitrary functions. It has been found that the prediction accuracy of the model parameters is improved when the device model specifications are changed and new model parameters are added, or by modifying the function in consideration of the physical model that was not originally assumed. In this case, the user can freely describe the function to expand the function or improve the estimation accuracy of the model parameter.

The model parameter determination apparatus of the present invention can be applied to circuit simulation in the design of a semiconductor integrated circuit.
In the present invention, the following modes are possible.
[Form 1]
A first physical parameter group characterizing a semiconductor element manufactured by the first manufacturing method and a model parameter group included in a device model for representing the characteristics of the semiconductor element, the semiconductor element manufactured by the first manufacturing method And a second physical parameter group characterizing the semiconductor element manufactured by the second manufacturing method, and the characteristics of the semiconductor element manufactured by the second manufacturing method are A model that determines a model parameter group to be represented by a device model based on the first physical parameter group, the first model parameter group, and the second physical parameter group, and outputs the model parameter group as a second model parameter group Parameter determination device.
[Form 2]
The model parameters included in the second model parameter group are included in the physical parameters included in the first physical parameter group, the physical parameters included in the second physical parameter group, and the first model parameter group. The model parameter determination device according to aspect 1, wherein the model parameter determination device determines a function based on a physical model including a model parameter as an argument.
[Form 3]
The model parameter determination device according to mode 2, wherein the function is derived based on a function that defines the device model.
[Form 4]
The model parameter according to any one of Embodiments 1 to 3, further comprising a fitting unit that fits the second model parameter group with respect to characteristics measured for the semiconductor element manufactured by the second manufacturing method. Decision device.
[Form 5]
The model according to any one of forms 2 to 4, wherein the function further includes, as an argument, a model parameter that is a model parameter included in the second model parameter group and is determined by the function. Parameter determination device.
[Form 6]
Model parameter for determining the strength of the reverse short channel effect, characteristic length for determining the strength of the short channel effect or a model parameter for correcting the characteristic length, and characteristic length for determining the gate length dependency of DIBL or the characteristics thereof The function that determines each of the model parameters for correcting the length is expressed based on a physical model in which the increase in the average impurity concentration in the region with a short gate length is proportional to the reciprocal of the effective channel length,
The model parameter for determining the strength of the reverse short channel effect is determined by a function including a parameter corresponding to the channel impurity concentration as an argument so that the strength of the reverse short channel effect is proportional to the inverse of the channel impurity concentration,
At least one of a characteristic length that determines the strength of the short channel effect or a model parameter that corrects the characteristic length, and a characteristic length that determines the gate length dependency of DIBL or a model parameter that corrects the characteristic length is The model parameter determination according to the fifth aspect, which is determined by a function including a model parameter as an argument for determining the strength of the inverse short channel effect so that the characteristic length is proportional to the -1/4 power of the average impurity concentration apparatus.
[Form 7]
Determine at least one of a characteristic length for determining the short channel effect or a model parameter for correcting the characteristic length and a characteristic length for determining the gate length dependency of the DIBL or a model parameter for correcting the characteristic length. The model parameter determining apparatus according to the sixth aspect, wherein the function to be expressed is based on a model that considers the influence of impurity distribution in a region near the substrate surface and in a deeper region.
[Form 8]
The model parameter determination device according to any one of Embodiments 2 to 7, further comprising a function input unit that uses a function designated by a user as the function.
[Form 9]
A CPU is a first physical parameter group that characterizes a semiconductor element manufactured by the first manufacturing method, and a model parameter group that is included in a device model for expressing the characteristics of the semiconductor element, and is manufactured by the first manufacturing method. Reading out from the storage device a first model parameter group for representing the semiconductor element and a second physical parameter group characterizing the semiconductor element manufactured by the second manufacturing method;
The first physical parameter group, the first model parameter group, and the second physical parameter are a model parameter group for the CPU to represent characteristics of the semiconductor element manufactured by the second manufacturing method by the device model. And a parameter determining step of determining based on the group and outputting as a second model parameter group.
[Mode 10]
In the parameter determination step, model parameters included in the second model parameter group are converted into physical parameters included in the first physical parameter group, physical parameters included in the second physical parameter group, and the first parameters. The model parameter determination method according to claim 9, wherein the model parameter is determined by a function based on a physical model including a model parameter included in the model parameter group as an argument.
[Form 11]
The model parameter determining method according to claim 10, wherein the function is derived based on a function that defines the device model.
[Form 12]
The model parameter determination method according to any one of Embodiments 9 to 11, further comprising a step of fitting the second model parameter group to characteristics measured for the semiconductor element manufactured by the second manufacturing method.
[Form 13]
A first physical parameter group characterizing a semiconductor element manufactured by the first manufacturing method and a model parameter group included in a device model for representing the characteristics of the semiconductor element, the semiconductor element manufactured by the first manufacturing method A process of reading out from the storage device a first model parameter group for representing and a second physical parameter group characterizing the semiconductor element manufactured by the second manufacturing method;
A model parameter group for representing the characteristics of the semiconductor element manufactured by the second manufacturing method by the device model is defined as the first physical parameter group, the first model parameter group, and the second physical parameter group. A program that causes a computer to execute parameter determination processing that is determined based on and output as a second model parameter group.
[Form 14]
In the parameter determination process, model parameters included in the second model parameter group are converted into physical parameters included in the first physical parameter group, physical parameters included in the second physical parameter group, and the first parameters. The program according to the form 13, which causes a computer to execute a process of determining a function based on a physical model including a model parameter included in a model parameter group as an argument.
[Form 15]
The program according to embodiment 14, wherein the function is derived based on a function that defines the device model.
[Form 16]
The program according to any one of forms 13 to 15, further causing a computer to execute a process of fitting the second model parameter group with respect to characteristics measured for the semiconductor element manufactured by the second manufacturing method.

1, 101, 501 Model parameter determination device 2, 112 Model parameter group 3, 113 of manufacturing process before change Physical parameter group 4, 114 of manufacturing process before change Physical parameter group 5, 105 of manufacturing process after change After change Manufacturing process model parameter group 6, 122, 502 Device model 7 Function input unit 111 Intermediate model parameter setting unit 121 Fitting unit 123 Intermediate model parameter group 124 Device measurement data 503 of the changed manufacturing process Initial model parameter group 504 Device measurement Data 505 Model parameter group 511 Parameter storage unit 512 Characteristic calculation unit 513 Error determination unit 514 Parameter change unit

Claims (6)

A first physical parameter characterizing a semiconductor element manufactured by the first manufacturing method and a plurality of model parameters included in a device model for representing the characteristics of the semiconductor element, the semiconductor element manufactured by the first manufacturing method A plurality of first model parameters for representing the second physical parameter that characterizes the semiconductor device manufactured by the second manufacturing method are input, and the characteristics of the semiconductor device manufactured by the second manufacturing method are described above. a plurality of second model parameters to represent the device model, determined based on at least one said second physical parameter and the first physical parameter of the plurality of first model parameter,
Each of the plurality of second model parameters is a function including at least one of the plurality of first model parameters, the first physical parameter, and the second physical parameter as arguments; Determined using a function based on the physical model that defines the model,
The function for determining one second model parameter of the plurality of second model parameters further includes another second model parameter of the plurality of second model parameters as an argument.
A model parameter determination device characterized by the above . A fitting unit for fitting the plurality of second model parameters to the characteristics measured for the semiconductor element manufactured by the second manufacturing method;
The model parameter determination apparatus according to claim 1 . A computer includes a first physical parameter that characterizes a semiconductor device manufactured by the first manufacturing method, and a plurality of model parameters included in a device model for representing characteristics of the semiconductor device, and is manufactured by the first manufacturing method. Reading a plurality of first model parameters for representing the semiconductor element and a second physical parameter characterizing the semiconductor element manufactured by the second manufacturing method from the storage device;
A plurality of second model parameters for expressing characteristics of the semiconductor element manufactured by the second manufacturing method by the device model, at least one of the plurality of first model parameters, and the first physical parameter see containing and a step of determining based on said second physical parameter and,
The computer is a function that includes the plurality of second model parameters as arguments each of at least one of the plurality of first model parameters, the first physical parameter, and the second physical parameter. And using a function based on a physical model that defines the device model,
The function for determining one second model parameter of the plurality of second model parameters further includes another second model parameter of the plurality of second model parameters as an argument.
A method for determining model parameters. The computer further comprising fitting the plurality of second model parameters to characteristics measured for a semiconductor device manufactured by the second manufacturing method;
The model parameter determination method according to claim 3 . A first physical parameter characterizing a semiconductor element manufactured by the first manufacturing method and a plurality of model parameters included in a device model for representing the characteristics of the semiconductor element, the semiconductor element manufactured by the first manufacturing method A process of reading from the storage device a plurality of first model parameters for representing and a second physical parameter characterizing the semiconductor element manufactured by the second manufacturing method;
A plurality of second model parameters for expressing characteristics of the semiconductor element manufactured by the second manufacturing method by the device model, at least one of the plurality of first model parameters, and the first physical parameter And a process of determining based on the second physical parameter,
Each of the plurality of second model parameters is a function including at least one of the plurality of first model parameters, the first physical parameter, and the second physical parameter as arguments; Causing the computer to execute a process of determining using a function based on a physical model that defines the model;
The function for determining one second model parameter of the plurality of second model parameters further includes another second model parameter of the plurality of second model parameters as an argument.
A program characterized by that . Causing the computer to further execute a process of fitting the plurality of second model parameters to the characteristics measured for the semiconductor element manufactured by the second manufacturing method;
The program according to claim 5 .

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