CN115906723A - Circuit Simulation Method for Metal Work Function Fluctuation of Nanosheet Gate-Round Field-Effect Transistor - Google Patents

Abstract

The invention discloses a method for simulating a metal work function fluctuation circuit of a nanosheet ring gate field effect transistor, and belongs to the field of microelectronic devices. According to the circuit simulation method, firstly, a global model extraction is carried out on IV and CV data of a nanosheet gate-all-around field effect transistor based on a BSIM-CMG model, then a calculation formula is utilized to obtain the mean value and standard deviation of parameter PHIG fluctuation in the model under the influence of metal work function fluctuation, the mean value and the standard deviation are embedded into a simulation netlist of circuit simulation software to carry out circuit simulation, and then circuit performance parameters caused by metal work function fluctuation can be obtained. The device characteristic fluctuation influence which can be accurately obtained by adopting the invention is consistent with the result precision obtained by TCAD simulation. The traditional TCAD simulation volatility method is slow in speed and high in cost, and the circuit simulation method established by the invention is fast in speed and small in error.

Description

Circuit Simulation Method for Metal Work Function Fluctuation of Nanosheet Gate-Round Field-Effect Transistor

technical field

The invention belongs to the field of microelectronic devices, and in particular relates to a method for simulating a metal work function fluctuation circuit of a nanosheet ring gate field effect transistor.

Background technique

On the one hand, the gate-all-around field effect transistor is one of the current research hotspots. Compared with FinFET, the ring gate field effect transistor has more superior performance. Its gate material surrounds the three-dimensional channel region, which can better suppress the short channel effect, achieve a better switching ratio and carry current in the channel. The electrons can be transported along the quasi-one-dimensional ballistic trajectory, which can better improve the driving current of the device. Under the 3nm technology node, the gate-all-around field effect transistor will become the mainstream device for research.

得到器件有效功函数

的涨落大小。目前应用于平面MOSFET和FinFET的金属功函数波动的仿真无法直接应用于环栅场效应晶体管，主要是由于环栅场效应晶体管的结构更加复杂，原本的公式无法直接套用，需要进行修正，其次对于每个不同栅长的环栅场效应晶体管都需要做单独集约模型提取，耗费大量时间，而使用同时校准多个栅极长度器件的全局模型能够有效的解决这个问题。But on the other hand, because the fabrication process of gate-all-round field effect transistors has become more complex, the influence of random fluctuations in the device has become more important. The random fluctuation of the device is due to the influence of the electrical characteristics of the device caused by the inevitable process uncertainty during the device manufacturing process, such as the fluctuation of parameters such as threshold voltage. In the gate-all-around field effect transistor, the random fluctuation sources mainly include metal work function fluctuation (WFV), line edge roughness (LER), and line width edge roughness (LWR). For metal work function fluctuations, there is currently an effective intensive model, which regards the influence of WFV as the influence on the effective work function of the device. function distribution

Get the effective work function of the device

fluctuation size. The current simulation of metal work function fluctuations applied to planar MOSFETs and FinFETs cannot be directly applied to gate-all-around field-effect transistors, mainly because the structure of gate-all-around field effect transistors is more complex, and the original formula cannot be directly applied and needs to be corrected. Secondly, for Each gate-all-around field-effect transistor with different gate lengths requires a separate intensive model extraction, which consumes a lot of time, and using a global model that simultaneously calibrates devices with multiple gate lengths can effectively solve this problem.

It is very important to correctly study the fluctuation of the metal work function of the device to improve the stability of the electrical performance of the device and evaluate the circuit performance of the device. At present, the TCAD simulation used by most metal work function fluctuation researches has the problems of slow speed and high cost, so it is very necessary to establish an accurate and predictable metal work function fluctuation circuit simulation method.

Contents of the invention

The object of the present invention is to provide a kind of circuit simulation method for metal work function fluctuation in ring gate field effect transistor based on predictability intensive model, this method can accurately obtain the influence of device characteristic fluctuation, and the TCAD simulation currently used Compared with the speed, the result obtained by simulation is consistent with the accuracy of TCAD, and the error is small.

The concrete technical scheme that realizes the object of the invention is:

A nanosheet ring gate field effect transistor metal work function fluctuation circuit simulation method, the method includes the following steps:

1) Based on the BSIM-CMG model, the global parameters of the nanosheet ring gate field effect transistor are extracted, and the global model and the key parameter PHIG of all Targets within the industrial error range and which can be applied to a series of devices with channel length Lg changes are obtained;

2) Correct the key parameter PHIG; metal work function fluctuations mainly affect the core parameter PHIG in the BSIM-CMG model, using the formula

μ(PHIG)=PHIG (1)

为有效功函数的涨落，能够直接反映在PHIG的变化上；D为金属晶粒的直径，nstack为纳米片的层数，W为沟道宽度，L为沟道长度，

为金属栅材料两种晶向对应的功函数之差，使用金属TiN<100>和<111>所对应的功函数之差，根据对晶粒统计分布的结果，两种晶向的比例为60％和40％，分别对应公式中晶向比例p₁和1-p₁的值；μ(PHIG)为PHIG涨落的均值，σ(PHIG)为PHIG涨落的标准差；所使用的计算公式修正了器件栅面积的算法，与目前已有的金属功函数波动计算公式相比更加贴和纳米片环栅场效应晶体管的结构；The mean value and variance of PHIG fluctuations under the influence of the metal work function are respectively obtained, where PHIG in the formula is the core parameter PHIG under no fluctuation in the extracted global model,

is the fluctuation of the effective work function, which can be directly reflected in the change of PHIG; D is the diameter of the metal grain, nstack is the number of layers of nanosheets, W is the channel width, L is the channel length,

is the difference between the work functions corresponding to the two crystal orientations of the metal gate material, using the difference between the work functions corresponding to the metal TiN<100> and <111>, according to the results of the statistical distribution of the crystal grains, the ratio of the two crystal orientations is 60 % and 40%, respectively corresponding to the value of the crystal orientation ratio p ₁ and 1-p ₁ in the formula; μ(PHIG) is the mean value of PHIG fluctuation, σ(PHIG) is the standard deviation of PHIG fluctuation; the calculation formula used The algorithm of the gate area of the device is revised, which is more suitable for the structure of the nanosheet ring gate field effect transistor compared with the existing metal work function fluctuation calculation formula;

3) Embed the global model obtained by extracting the global parameters and the mean value and variance of PHIG fluctuation into the simulation netlist of the circuit simulation software, and use the circuit simulation software to perform circuit simulation to obtain the device drain current variation under the influence of metal work function fluctuations. Gate voltage variation curve Id-Vg diagram.

The present invention is different from the current metal work function fluctuation circuit simulation method that uses a single length intensive model, but uses a global model based on the BSIM-CMG model, and the same model can be used to simulate devices with multiple gate lengths , instead of intensive model extraction for each length.

When the present invention calculates the core parameter PHIG, the variance calculation formula of the main influence value PHIG of the metal work function fluctuation is corrected for the structure of the nanosheet ring gate field effect transistor, and the area is calculated by nstack W L, so that the result is closer to the real device metal Work function fluctuation results.

Compared with the TCAD simulation used in the current metal work function fluctuation research, the invention can accurately obtain the influence of the device characteristic fluctuation, and the result obtained by the simulation is consistent with the TCAD accuracy and the error is small. Compared with the existing metal work function fluctuation circuit simulation method, the present invention is more suitable for nanosheet gate-all-around field effect transistors, and adopts a global model instead of a single length-intensive model, which is faster and more efficient.

Description of drawings

Fig. 1 is a schematic flow sheet of the present invention;

Fig. 2 is the three-dimensional structure of the gate-all-around field effect transistor used in the present invention;

Fig. 3 is a sectional view along the y direction of the gate-all-around field effect transistor used in the present invention;

Fig. 4 is a schematic diagram of the global model extraction process of the present invention;

Fig. 5 is the comparison diagram of the threshold voltage Vtsat in the saturation region obtained by simulating the device circuit characteristics under the metal particle diameter of 3nm with traditional TCAD and the present invention using Hspice for adding metal work function fluctuations;

Fig. 6 is the comparison diagram of the linear region threshold voltage Vtlin obtained by simulating the device circuit characteristics under the metal particle diameter of 3nm with traditional TCAD and the present invention using Hspice for adding metal work function fluctuation;

Fig. 7 adds metal work function fluctuation with traditional TCAD and the present invention uses Hspice to simulate the circuit characteristics of the device under the metal particle diameter of 3nm, and the saturation region sub-threshold swing SS is compared with the saturation region threshold voltage Vtasat change;

Fig. 8 adds metal work function fluctuation and uses traditional TCAD and the present invention uses Hspice to simulate the device circuit characteristics under the metal particle diameter of 3nm, and the turn-on current Ion is compared with the saturation region threshold voltage Vtsat variation diagram;

Fig. 9 adds metal work function fluctuation with traditional TCAD and the present invention obtains with the simulation device circuit characteristic of Hspice and is respectively 3nm, 5nm, 7nm, the comparison chart of the fluctuation standard deviation change of saturation region threshold voltage Vtsat under 10nm;

Fig. 10 is a comparison chart of fluctuation standard deviation variation of turn-on current Ion under 3nm, 5nm, 7nm, and 10nm diameters of metal particles obtained by adding metal work function fluctuations using traditional TCAD and the present invention using Hspice simulation device circuit characteristics.

Specific implementation method

The circuit simulation method of the present invention will be described in detail below through embodiments and in conjunction with the accompanying drawings.

A method for simulating a metal work function fluctuation circuit of a nanosheet ring gate field effect transistor according to the present invention comprises the following steps:

1) Based on the BSIM-CMG model, the global parameters of the nanosheet ring gate field effect transistor are extracted to obtain a global model of all targets that meet the error requirements of the industry, and the model card without fluctuation is embedded in the simulation netlist of the circuit simulation software;

按照以下公式计算得到器件有效功函数

的涨落大小：2) According to the currently established intensive model, the influence of WFV is regarded as the influence on the effective work function of the device. According to the diameter D of the metal grain, the area S of the device gate, and the work function distribution of the grain

Calculate the effective work function of the device according to the following formula

The fluctuation size of :

in

由于环栅场效应晶体管中的面积应该由WL改为nstack·W·L，所以公式改写做：

得到金属功函数波动影响下有效功函数

涨落的均值和方差；then you can get

Since the area in the ring gate field effect transistor should be changed from WL to nstack W L, the formula is rewritten as:

Get the effective work function under the influence of metal work function fluctuation

Mean and variance of fluctuations;

3) The fluctuation of the effective work function can be directly reflected in the fluctuation of the final threshold voltage V _th , which affects the core parameter PHIG in BSIM-CMG, using the formula

μ(PHIG)=PHIG

Obtain the mean value and variance of the fluctuation of PHIG under the influence of metal work function fluctuation;

4) According to the above calculation formula, the mean value and variance of PHIG fluctuations under the influence of metal work function fluctuations are obtained, which are added to the netlist of circuit simulation, and circuit simulation is performed with circuit simulation software to obtain the fluctuations caused by metal work function fluctuations. The influence of the fluctuation of the electrical characteristics of the device, and then the influence of the fluctuation of the circuit performance parameters.

Example

This embodiment considers the influence of metal work function fluctuations in a 3nm gate-all-round field effect transistor on device circuit characteristics. The overall process is shown in FIG. The basic structure of a 3nm gate-all-round field effect transistor is shown in FIG. 2 , and the three-dimensional structure of the surround gate field effect transistor used in the present invention is shown in FIG. 3 along the y-direction cross-sectional view.

Specific steps:

1) As shown in the schematic diagram of the global model extraction process in Figure 4, based on the BSIM-CMG model, the global parameters of the nanosheet ring gate field effect transistor are extracted to obtain a global model that meets the error requirements of the industry for all targets, and the model card without fluctuations is embedded to the simulation netlist of the circuit simulation software;

代入如下公式计算得到器件有效功函数

的涨落大小：2) According to the existing intensive model, according to the diameter D of the metal grain, the area S of the device gate, and the work function distribution of the grain

Substituting the following formula to calculate the effective work function of the device

The fluctuation size of :

The Lg of the gate-all-around field effect transistor adopted in this embodiment is 12nm to 18nm, the W is 21nm, and the nstack is three layers. For TiN, the grain diameter D is 3nm, and the ratio of TiN<111> (work function is 4.6eV) to TiN<100> (work function is 4.4eV) is about 60% and 40%. Therefore, the calculated

3) Using the calculation formula of PHIG in the metal work function fluctuation intensive model of the gate-all-round field effect transistor and the extracted global model, the mean value and variance of PHIG are obtained as follows:

Mean value: μ(PHIG)=4.652421

Variance: σ(PHIG)=0.009562

4) Add the mean value and variance of PHIG fluctuations to the netlist of circuit simulation, and use circuit simulation software to perform circuit simulation to obtain the influence of fluctuations in the electrical characteristics of the device caused by metal work function fluctuations, and then obtain the circuit performance parameters. Fluctuations affect.

Fig. 5 is the comparison diagram of threshold voltage Vtsat in the saturation region obtained by simulating the circuit characteristics of the device under the metal particle diameter of 3nm with traditional TCAD and the present invention using Hspice for adding metal work function fluctuations, wherein the Vtsat mean value of TCAD simulation is 0.11961V, standard deviation is 9.09344E-4V, the average value of Vtsat simulated by Hspice is 0.11405V, and the standard deviation is 8.55199E-4V.

Fig. 6 is the comparison diagram of the threshold voltage Vtlin in the linear region obtained by using traditional TCAD and Hspice in the present invention to simulate the device circuit characteristics under the metal particle diameter of 3nm for adding metal work function fluctuations, wherein the Vtlin mean value of TCAD simulation is 0.13622V, standard deviation is 9.09322E-4V, the average value of Vtlin simulated by Hspice is 0.13431V, and the standard deviation is 7.58836E-4V.

Fig. 7 adds metal work function fluctuation with traditional TCAD and the present invention uses Hspice to simulate the device circuit characteristics under the metal particle diameter of 3nm and compares the sub-threshold swing SS in the saturation region with the threshold voltage Vtasat in the saturation region. Among them, the TCAD simulated The mean value of SS is 66.381, and the mean value of SS simulated by Hspice is 68.377.

Fig. 8 adds metal work function fluctuation and uses traditional TCAD and the present invention uses Hspice to simulate the circuit characteristics of the device under the metal particle diameter of 3nm. The comparison diagram of the turn-on current Ion obtained by simulating the device circuit characteristics with the threshold voltage Vtsat in the saturation region, wherein the average value of Ion simulated by TCAD is 1.52 E-04, the average Ion value simulated by Hspice is 1.52006E-4A.

Fig. 9 adds metal work function fluctuation and uses traditional TCAD and the present invention uses the simulation device circuit characteristic of Hspice to obtain, and the metal particle diameter is respectively 3nm, 5nm, 7nm, the contrast chart of fluctuation standard deviation change of threshold voltage Vtsat in the saturation region under 10nm.

Fig. 10 is a comparison chart of fluctuation standard deviation variation of turn-on current Ion under 3nm, 5nm, 7nm, and 10nm diameters of metal particles obtained by adding metal work function fluctuations using traditional TCAD and the present invention using Hspice simulation device circuit characteristics.

Claims (3)

1. A method for simulating a metal work function fluctuation circuit of a nanosheet ring gate field effect transistor is characterized by comprising the following steps:

1) Carrying out global parameter extraction on the nanosheet gate all-around field effect transistor based on a BSIM-CMG model to obtain a global model and a core parameter PHIG of all devices with targets within an industrial error range and capable of being applied to channel length Lg variation;

2) Correcting a core parameter PHIG; respectively obtaining the mean value and the variance of the fluctuation of the core parameter PHIG under the influence of the metal work function by using a formula (1) and a formula (2):

μ(PHIG)＝PHIG (1)

wherein, the PHIG in the formula is the core parameter PHIG under no fluctuation in the obtained global model,

the fluctuation of the effective work function can be directly reflected on the change of the PHIG; d is the diameter of the metal crystal grain, nstack is the number of the layers of the nanosheets, W is the width of the channel, L is the length of the channel, and the channel is selected according to the length of the channel>

For the difference of work functions corresponding to two crystal orientations of the metal gate material, metal TiN is used<100>And<111>the corresponding work function difference is that according to the result of statistical distribution of crystal grains, the proportion of two crystal orientations is 60 percent and 40 percent, which respectively correspond to the crystal orientation proportion p in the formula ₁ And 1-p ₁ A value of (d); mu (PHIG) is the mean value of the fluctuation of the PHIG, and sigma (PHIG) is the standard deviation of the fluctuation of the PHIG;

3) And embedding the global model obtained by extracting the global parameters and the mean value and variance of the fluctuation of the core parameter PHIG into a simulation netlist of circuit simulation software, and performing circuit simulation by using the circuit simulation software to obtain a device drain current variation relation curve Id-Vg graph along with the gate voltage under the influence of metal work function fluctuation.

2. The method for simulating a metal work function fluctuation circuit of a nanosheet ring gate field effect transistor of claim 1, wherein the global model is capable of using the same model for simulating devices of multiple gate lengths.

3. The nanosheet gate all-around field effect transistor metal work function fluctuation circuit simulation method of claim 1, wherein when a core parameter PHIG is calculated, a calculation formula of the nanosheet gate all-around field effect transistor is corrected according to the structure of the nanosheet gate all-around field effect transistor, and the area is calculated by nstack W L, so that the result is closer to a real device metal work function fluctuation result.

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