A method for modeling flicker noise in small size semiconductor devices

Abstract

The application discloses a modeling method of flicker noise of a small-size semiconductor device, which comprises the following steps: measuring flicker noise of the small-size semiconductor device under different gate voltages to obtain device noise data; separating the noise obtained by testing under different gate voltages in a frequency domain to obtain noise spectrum caused by RTN defect charge state change and noise spectrum caused by mobility fluctuation; processing the noise spectrum caused by RTN defect charge state change to obtain S vg，I ; processing the noise spectrum caused by mobility fluctuation to obtain S id，II / III ; and obtaining a total current noise intensity model, which is expressed as: S id =S id，I +S id，II / III The model established by the application can accurately describe frequency, voltage dependence and fluctuation of flicker noise of the small-size device; can be applied to different processes; and the model can be applied to a circuit simulator.

Description

Technical Field

[0001] This invention relates to the field of semiconductor devices, and more particularly to a method for modeling flicker noise in small-sized semiconductor devices. Background Technology

[0002] As integrated circuit dimensions shrink, the impact of flicker noise (1 / f noise) on analog and mixed-signal circuits becomes significant, and device noise fluctuations further increase. How to model the flicker noise of advanced process devices and accurately describe its frequency, voltage dependence, and fluctuations is a critical problem that urgently needs to be solved. Currently, there are two main traditional methods for describing flicker noise: carrier number fluctuation models and mobility fluctuation models.

[0003] Traditional carrier number fluctuation models posit that flicker noise originates from defects in the gate dielectric layer of the device. These defects trap and release carriers, causing changes in their charge, which in turn alter the device threshold voltage and lead to fluctuations in the transistor's drain-source current. Through the superposition of numerous defects, the noise spectrum intensity superimposes into a 1 / f form. The defect state changes are described by elastic tunneling.

[0004] The mobility fluctuation model posits that the source of flicker noise is the scattering of carriers in the channel region (lattice scattering, surface roughness scattering, impurity scattering, etc.), described by empirical formulas of the Hooge model, with the noise intensity reflected by the magnitude of the Hooge coefficient.

[0005] Existing BSIM noise models describe noise based on traditional carrier number fluctuation theory, assuming that changes in defect charge not only affect the transistor threshold voltage but also influence mobility through mechanisms such as Coulomb scattering. Three fitting parameters are used to describe the voltage dependence of noise intensity.

[0006] As device size decreases, the number of effective defects in the dielectric layer decreases, and the 1 / f form of flicker noise in the frequency domain cannot be explained by the superposition of a large number of defects, indicating that transistor noise is not entirely caused by defects. The voltage dependence of noise test results on advanced process devices also does not conform to existing models and exhibits large fluctuations. To correctly assess the impact of noise on circuit performance during circuit design, a new and accurate flicker noise model is needed. Summary of the Invention

[0007] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is that the flicker noise phenomenon of advanced process transistors becomes complicated. The present invention aims to establish a physics-based noise model to accurately describe the noise phenomenon and to be used for circuit simulation.

[0008] To achieve the above objectives, the present invention provides a method for modeling flicker noise in small-sized semiconductor devices, comprising the following steps:

[0009] The flicker noise of a small-sized semiconductor device under different gate voltages is measured to obtain device noise data.

[0010] The noise obtained from tests at different gate voltages is separated in the frequency domain to obtain the noise spectrum caused by the change in the charged state of RTN defects and the noise spectrum caused by mobility fluctuations.

[0011] The noise spectrum caused by the change in the charged state of the RTN defect is processed to obtain S. vg,I ;

[0012] The noise spectrum caused by mobility fluctuations is processed to obtain S. id,II / III ;

[0013] The overall current noise intensity model is obtained, and its expression is:

[0014] S id =S id,I +S id,II / III

[0015] S id,I =g m 2 S vg,I

[0016] Among them, g m It is the transconductance of the transistor, S vg,I It is the equivalent voltage noise intensity originating from the dielectric region, S id,II / III It refers to the current noise intensity in the channel region and the source / drain region.

[0017] A further improvement of the present invention is that, in the process of measuring the flicker noise of small-sized semiconductor devices under different gate voltages, a semiconductor parameter analyzer and a low-frequency noise tester are used to measure the small-sized semiconductor devices.

[0018] A further improvement of the present invention lies in that, during the process of separating the noise obtained from tests at different gate voltages in the frequency domain, the noise spectrum S is calculated. id The product of the frequency f and the number of peaks in the product is taken as the number of RTN defects; the noise spectrum S is obtained by fitting. id The noise spectrum is separated into the noise spectrum caused by mobility fluctuations and the noise spectrum caused by changes in the charged state of each RTN defect; wherein, the noise spectrum caused by mobility fluctuations is in the form of 1 / f, and the noise spectrum caused by changes in the charged state of each RTN defect is in the form of... Where A is the coefficient obtained from the fitting, and τ is the equivalent time constant.

[0019] A further improvement of the present invention is that the noise spectrum caused by the change in the charged state of the RTN defect is processed to obtain S. vg,I During the process:

[0020] The energy levels Et and relaxation energies S of RTN defects in multiple small-sized semiconductor devices are obtained, and the distribution of the defect energy levels Et and relaxation energies S of each RTN defect is obtained.

[0021] The defect trapping time constant τ of the corresponding RTN defect is calculated using the NMP nonradiative multiphonon transition model, based on the defect energy level Et and relaxation energy S. c Defect release time constant τ e The threshold voltage change ΔV caused by a single defect th Obtained from the charge layer approximation:

[0022] ΔV th =mq / (WLC) ox )

[0023] The total noise caused by the overall defects is the sum of the noise from each individual RTN defect:

[0024]

[0025] Where: m is a coefficient describing the magnitude of the threshold voltage change caused by the change in defect charge, q is the unit charge size, and WLC ox These represent the transistor width, length, and gate oxide capacitance, respectively; N is the number of RTN defects; τ c,i and τ e,i Let represent the defect capture time constant and the defect release time constant of the i-th RTN defect, respectively.

[0026] A further improvement of this invention lies in the process of obtaining the defect energy level Et and relaxation energy S of a small-sized semiconductor device: based on the NMP model formula for the defect time constant, Et and S are calculated from the equivalent time constant τ and its variation with the gate voltage; the time constant expression of the defect NMP model is:

[0027] ε 12 =(S+E) 21 ) 2 / 4S

[0028]

[0029]

[0030]

[0031]

[0032] Where: ε12 E represents the potential barrier when the defect transitions from state 1 to state 2, where state 1 indicates that the defect has not captured carriers, and state 2 indicates that the defect has captured carriers. 21 E represents the energy level difference between state 1 and state 2. t For defect energy levels, E is the potential difference between the defect location and the channel caused by the applied voltage. v Valence band energy level at the channel. p is the hole concentration in the channel region, σ is the reaction cross section, and v th τ is the thermal velocity of charge carriers, k is the Boltzmann constant, T is the thermodynamic temperature, and τ is the thermal velocity of charge carriers. c τ is the defect capture time constant. e E is the defect release time constant. f This refers to the Fermi level in the channel region.

[0033] A further improvement of the present invention is that the noise spectrum caused by mobility fluctuations is processed to obtain S. id,II / III During the process, the noise spectrum caused by mobility fluctuations is separated into noise caused by carrier scattering in the channel region and noise caused by drain-source contact resistance; where:

[0034] The noise caused by carrier scattering in the channel region is described by the Hooge model, and its expression is:

[0035]

[0036] Among them: I D α represents the magnitude of the drain-source current. H Here, f is the Hooge coefficient, fN is the frequency and the number of inversion carriers, respectively, and V is the inversion coefficient. D Where μ is the source-drain voltage, μ is the mobility, and L is the channel length; μ and L are known device parameters.

[0037] The expression for the noise caused by the drain-source contact resistance is:

[0038]

[0039] Among them, K r It is the resistance noise intensity factor;

[0040] Using small-signal analysis, the expression for the overall noise caused by mobility fluctuations when the transistor is operating in the linear region is obtained as follows:

[0041]

[0042] R tot =V D / I D

[0043] Among them, Rtot R is the resistance between the source and drain of the transistor. access It is the magnitude of the drain-source contact resistance; the test data S obtained under different voltages id,II / III By fitting the changes, the Hooge coefficient α can be obtained. H and the resistance noise intensity coefficient K r By performing statistical tests on multiple devices, the coefficient α can be obtained. H and K r The mean and distribution of.

[0044] The beneficial effects of this invention include:

[0045] 1. This invention solves the problem that traditional noise models cannot describe the noise phenomena of advanced process node devices. The model established by this invention can accurately describe the frequency, voltage dependence and fluctuation of flicker noise in small-sized devices.

[0046] 2. The testing scheme, separation method, and modeling method are universal and applicable to different processes, and the model is applicable to circuit simulators;

[0047] 3. The testing, data processing, and modeling methods of this invention are easy to integrate into testing instruments and have important guiding significance for the development of testing instrument programs.

[0048] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0049] Figure 1 These are flicker noise test data;

[0050] Figure 2 This is a schematic diagram of the separation method;

[0051] Figure 3 This is a schematic diagram of a defect NMP model;

[0052] Figure 4 This is a schematic diagram of the mobility fluctuation noise model;

[0053] Figure 5 This is a schematic diagram of the equivalent circuit;

[0054] Figure 6 This is a schematic diagram of each region of the device. Detailed Implementation

[0055] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0056] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0057] Some exemplary embodiments of the invention have been described for illustrative purposes. It should be understood that the invention may be implemented in other ways not specifically shown in the accompanying drawings.

[0058] like Figure 5 , 6 As shown, an embodiment of the present invention provides a method for modeling flicker noise in small-sized semiconductor devices, which includes the following steps:

[0059] (S1) Measure the flicker noise of the small-sized semiconductor device under different gate voltages to obtain device noise data; in this step, a semiconductor parameter analyzer and a low-frequency noise tester are used to measure the small-sized semiconductor device, and the measurement results are as follows: Figure 1 As shown.

[0060] (S2) The noise obtained from tests under different gate voltages is separated in the frequency domain to obtain the noise spectrum caused by the change in the charged state of the RTN defect and the noise spectrum caused by mobility fluctuation.

[0061] During the process of separating the noise obtained from tests at different gate voltages in the frequency domain, the noise spectrum S measured in step S1 is calculated. id The product of the frequency f and the number of peaks in the product is taken as the number of RTN defects; the noise spectrum S is obtained by fitting. id The noise spectrum is separated into the noise spectrum caused by mobility fluctuations and the noise spectrum caused by changes in the charged state of each RTN defect; wherein, the noise spectrum caused by mobility fluctuations is in the form of 1 / f, and the noise spectrum caused by changes in the charged state of each RTN defect is in the form of... like Figure 2 The figures show the separation results for cases with one RTN defect and cases with two RTN defects, respectively.

[0062] (S3) The noise spectrum caused by the change in the charged state of the RTN defect is processed to obtain S. vg,I ;

[0063] like Figure 3 As shown, the RTN defect energy levels Et and relaxation energies S in multiple small-sized semiconductor devices are obtained, and the distribution of defect energy levels Et and relaxation energies S is obtained. In this process: according to the NMP model formulas for the defect time constant (Formulas 1-5), the equivalent time constant τ and its variation with the gate voltage V are obtained. G The changes in Et and S are calculated; the time constant expression for the defect NMP model is:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Where: ε 12 E represents the potential barrier when the defect transitions from state 1 to state 2, where state 1 indicates that the defect has not captured carriers, and state 2 indicates that the defect has captured carriers. 21 E represents the energy level difference between state 1 and state 2. t For defect energy levels, E is the potential difference between the defect location and the channel caused by the applied voltage. v Valence band energy level at the channel. p is the hole concentration in the channel region, σ is the reaction cross section, and v th τ is the thermal velocity of charge carriers, k is the Boltzmann constant, T is the thermodynamic temperature, and τ is the thermal velocity of charge carriers. c τ is the defect capture time constant. e E is the defect release time constant. f This refers to the Fermi level in the channel region.

[0070] In solving the above model, the potential difference Hole concentration p in the channel region, Fermi level E in the channel region f This can be determined using the electrostatic model of a transistor. From the above equations, it can be seen that when an applied voltage causes... At this point, the equivalent time constant τ will reach its maximum value. Therefore, based on the experimentally obtained relationship between the RTN defect time constant τ and the applied voltage, the defect energy level E can be obtained. tBased on this, in the above expression, only the relaxation energy S remains unknown. The relaxation energy S can be calculated by inversely from the magnitude of the equivalent time constant τ.

[0071] The defect trapping time constant τ is calculated using the NMP nonradiative multiphonon transition model, based on the defect energy level Et and the relaxation energy S. c Defect release time constant τ e The threshold voltage change ΔV caused by a single defect th Obtained from the charge layer approximation:

[0072]

[0073] The total noise caused by the overall change in the charged state of RTN defects is the sum of the noise from each individual RTN defect:

[0074]

[0075] Where: m is a coefficient describing the magnitude of the threshold voltage change caused by the change in defect charge, q is the unit charge size, and WLC ox These represent the width, length, and gate oxide capacitance of the transistor (a small-sized semiconductor device), respectively, where N is the number of defects; τ c,i and τ e,i Let represent the defect capture time constant and the defect release time constant of the i-th RTN defect, respectively.

[0076] (S4) Process the noise spectrum caused by mobility fluctuations to obtain S id,II / III ;

[0077] In this process, the noise spectrum caused by mobility fluctuations is separated into noise caused by carrier scattering in the channel region and noise caused by drain-source contact resistance; wherein:

[0078] The noise caused by carrier scattering in the channel region is described by the Hooge model, and its expression is:

[0079]

[0080] Among them: I D α represents the magnitude of the drain-source current. H Here, f is the Hooge coefficient, fN is the frequency and the number of inversion carriers, respectively, and V is the inversion coefficient. D Where μ is the source-drain voltage, μ is the mobility, and L is the channel length; μ and L are known device parameters.

[0081] The expression for the noise caused by the drain-source contact resistance is:

[0082]

[0083] Among them, Kr It is the resistance noise intensity factor;

[0084] Using small-signal analysis, the expression for the overall noise caused by mobility fluctuations when the transistor is operating in the linear region is obtained as follows:

[0085]

[0086]

[0087] Among them, R tot The resistance between the source and drain of a transistor (the voltage V between the source and drain) D Divide by the source-drain current I D ); R access It is the magnitude of the drain-source contact resistance; such as Figure 4 As shown, the test data S obtained under different voltages id,II / III By fitting the changes, the Hooge coefficient α can be obtained. H and the resistance noise intensity coefficient K r By performing statistical tests on multiple devices, the coefficient α can be obtained. H and K r The mean and distribution of.

[0088] (S5) The overall current noise intensity model is obtained, and its expression is:

[0089] S id =S id,I +S id,II / III (12)

[0090] S id,I =g m 2 S vg,I (13)

[0091] Among them, g m It is the transconductance of the transistor, S vg,I It is the equivalent voltage noise intensity originating from the dielectric region, S id,II / IiI It refers to the current noise intensity in the channel region and the source / drain region. Figure 5 The diagram shown is a schematic of the model.

[0092] The solution in this embodiment has the following advantages:

[0093] 1. This invention solves the problem that traditional noise models cannot describe the noise phenomena of advanced process node devices. The model established by this invention can accurately describe the frequency, voltage dependence and fluctuation of flicker noise in small-sized devices.

[0094] 2. The testing scheme, separation method, and modeling method are universal and applicable to different processes, and the model is applicable to circuit simulators;

[0095] 3. The testing, data processing, and modeling methods of this invention are easy to integrate into testing instruments and have important guiding significance for the development of testing instrument programs.

[0096] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A method for modeling flicker noise in small-sized semiconductor devices, characterized in that... Includes the following steps: The flicker noise of a small-sized semiconductor device under different gate voltages is measured to obtain device noise data. The noise obtained from tests at different gate voltages is separated in the frequency domain to obtain the noise spectrum caused by the change in the charged state of RTN defects and the noise spectrum caused by mobility fluctuations. The noise spectrum caused by the change in the charged state of the RTN defect is processed to obtain S. vg，I ; The noise spectrum caused by mobility fluctuations is processed to obtain S. id，II / III ; The overall current noise intensity model is obtained, and its expression is: S id =S id,I +S id,II / III S id，I =g m 2 S vg，I Among them, g m It is the transconductance of the transistor, S vg，I It is the equivalent voltage noise intensity originating from the dielectric region, S id，II / III It refers to the current noise intensity in the channel region and the source / drain region.

2. The method for modeling flicker noise in a small-size semiconductor device as described in claim 1, characterized in that, In measuring the flicker noise of small-sized semiconductor devices under different gate voltages, a semiconductor parameter analyzer and a low-frequency noise tester are used to measure the small-sized semiconductor devices.

3. The method for modeling flicker noise in a small-size semiconductor device as described in claim 1, characterized in that, During the process of separating the noise obtained from tests at different gate voltages in the frequency domain, the noise spectrum S is calculated. id The product of the frequency f and the number of peaks in the product is taken as the number of RTN defects; the noise spectrum S is obtained by fitting. id The noise spectrum is separated into the noise spectrum caused by mobility fluctuations and the noise spectrum caused by changes in the charged state of each RTN defect; wherein, the noise spectrum caused by mobility fluctuations is in the form of 1 / f, and the noise spectrum caused by changes in the charged state of each RTN defect is in the form of... Where A is the coefficient obtained from the fitting. It is the equivalent time constant.

4. The method for modeling flicker noise in a small-size semiconductor device as described in claim 1, characterized in that, The noise spectrum caused by the change in the charged state of the RTN defect is processed to obtain S. vg，I During the process: The energy levels Et and relaxation energies S of RTN defects in multiple small-sized semiconductor devices are obtained to obtain the distribution of the defect energy levels Et and relaxation energies S for each RTN defect. Using the NMP nonradiative multiphonon transition model, the defect trapping time constant τ of the corresponding RTN defect is calculated based on the defect energy levels Et and relaxation energies S. c Defect release time constant τ e The threshold voltage change ΔV caused by a single defect th Obtained from the charge layer approximation: ΔV th =mq / (WLC ox ) The total noise caused by the overall defects is the sum of the noise from each individual RTN defect: Where: m is a coefficient describing the magnitude of the threshold voltage change caused by the change in defect charge, q is the unit charge size, and WLC ox These represent the transistor width, length, and gate oxide capacitance, respectively; N is the number of RTN defects; τ c，i and τ e，i Let represent the defect capture time constant and the defect release time constant of the i-th RTN defect, respectively.

5. The method for modeling flicker noise in a small-size semiconductor device as described in claim 4, characterized in that, In obtaining the defect energy level Et and relaxation energy S of a small-sized semiconductor device: based on the NMP model formula for the defect time constant, Et and S are calculated from the equivalent time constant τ and its variation with gate voltage; the time constant expression of the defect NMP model is: ε 12 =(S+E 21 ) 2 / 4S Where: ε 12 E represents the potential barrier when the defect transitions from state 1 to state 2, where state 1 indicates that the defect has not captured carriers, and state 2 indicates that the defect has captured carriers. 21 E represents the energy level difference between state 1 and state 2. t For defect energy levels, E is the potential difference between the defect location and the channel caused by the applied voltage. v Valence band level at the channel; p is the hole concentration in the channel region, σ is the reaction cross section, v th τ is the thermal velocity of charge carriers, k is the Boltzmann constant, T is the thermodynamic temperature, and τ is the thermal velocity of charge carriers. c τ is the defect capture time constant. e E is the defect release time constant. f This refers to the Fermi level in the channel region.

6. The method for modeling flicker noise in a small-size semiconductor device as described in claim 1, characterized in that, S is obtained by processing the noise spectrum caused by mobility fluctuations. id，II / III During the process, the noise spectrum caused by mobility fluctuations is separated into noise caused by carrier scattering in the channel region and noise caused by drain-source contact resistance; where: The noise caused by carrier scattering in the channel region is described by the Hooge model, and its expression is: Among them: I D α represents the magnitude of the drain-source current. H Here, f is the Hooge coefficient, fN is the frequency and the number of inversion carriers, respectively, and V is the inversion coefficient. D Where μ is the source-drain voltage, μ is the mobility, and L is the channel length; μ and L are known device parameters. The expression for the noise caused by the drain-source contact resistance is: Among them, K r It is the resistance noise intensity factor; Using small-signal analysis, the expression for the overall noise caused by mobility fluctuations when the transistor is operating in the linear region is obtained as follows: R tot =V D / I D Among them, R tot R is the resistance between the source and drain of the transistor. access It is the magnitude of the drain-source contact resistance; the test data S obtained under different voltages id，II / III By fitting the changes, the Hooge coefficient α can be obtained. H and the resistance noise intensity coefficient K r By performing statistical tests on multiple devices, the coefficient α can be obtained. H and K r The mean and distribution of.

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