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CN110704997A - Method for establishing flicker noise model based on MIT high electron mobility transistor model and application thereof - Google Patents

Method for establishing flicker noise model based on MIT high electron mobility transistor model and application thereof Download PDF

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CN110704997A
CN110704997A CN201910493721.3A CN201910493721A CN110704997A CN 110704997 A CN110704997 A CN 110704997A CN 201910493721 A CN201910493721 A CN 201910493721A CN 110704997 A CN110704997 A CN 110704997A
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flicker noise
mit
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noise model
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罗浩瑞
郭健
姚鸿
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Suzhou Core Micro Electronics Co Ltd
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Abstract

The invention discloses a flicker noise model establishing method based on an MIT high electron mobility transistor model and application thereof. The method comprises the following steps: measuring necessary physical parameters of the transistor and the DC IV characteristic curve, fitting the DC IV characteristic curve with MIT model to obtain drain current
Figure DEST_PATH_IMAGE002
Density of drain charge
Figure DEST_PATH_IMAGE004
And source charge density
Figure DEST_PATH_IMAGE006
The expression of (1); then, a series of derivation and simplification are carried out on the original flicker noise model, and then the expressions of the distance and the charge density which are specific to the MIT model are introduced,so that the original flicker noise model can be measured by the drain current in the MIT model
Figure 527996DEST_PATH_IMAGE002
Density of drain chargeDensity of source charge
Figure 788656DEST_PATH_IMAGE006
Some basic physical parameters and some fitting parameters; the last specification uses some measurement data to verify the effectiveness of the modeling method. The method fills the blank that the MIT model which is applied industrially has no corresponding flicker noise model, enlarges the application range of the MIT model and improves the efficiency of the industrial modeling of the flicker noise model.

Description

Method for establishing flicker noise model based on MIT high electron mobility transistor model and application thereof
Technical Field
The invention relates to a flicker noise model establishing method based on an MIT high electron mobility transistor model and application thereof.
Background
The explosive development of the semiconductor industry has prompted a great deal of modeling requirements of semiconductor devices, and compared with the traditional empirical model, the physical model is more and more emphasized by the industry because the physical model can reflect the real physical characteristics of the devices, for example, the MIT high-electron-mobility transistor model based on charge modeling, which has recently become the industrial standard, has the remarkable advantages of accurate modeling, easy adjustment, solid physical significance, less measured data required in modeling and the like. Meanwhile, among various performance indexes of the semiconductor device, flicker noise is an extremely important parameter, and whether the flicker noise is accurately modeled or not is related to the success or failure of the design of devices such as an amplifier or a receiver.
However, at present, there is no corresponding flicker noise model under the MIT model, that is, for a transistor that has been modeled by the MIT method, if the flicker noise performance is to be modeled continuously, tedious and complicated data measurement needs to be performed again and a large number of optimal fitting needs to be performed, which hinders the comprehensiveness of the MIT model in industrial application and also reduces the production efficiency in industry.
Disclosure of Invention
The invention develops a flicker noise model suitable for an MIT model aiming at the condition that the MIT high electron mobility transistor model lacks a corresponding flicker noise model. The model is established on the basis of the MIT model and is an effective extension of the MIT model. The method inherits the idea that the MIT model takes charges as a modeling core, eliminates incompatible physical quantity in the flicker noise model by introducing the approximation of positions and charge densities in the MIT model, evolves the physical quantity into the flicker noise model which is based on charge modeling, is convenient to adjust and is suitable for the MIT model.
The technical scheme adopted by the invention is as follows: a flicker noise model establishing method based on an MIT high electron mobility transistor model establishes an MIT high electron mobility transistor model based on charge modeling.
The method comprises the following steps:
1) fitting a direct current IV image of a certain transistor by using an MIT model to obtain a drain current under the MIT model
Figure RE-RE-DEST_PATH_IMAGE002
Density of drain charge
Figure RE-RE-DEST_PATH_IMAGE004
Density of source charge
Figure RE-RE-DEST_PATH_IMAGE006
Substituting the specific expression into the proposed flicker noise model to obtain a flicker noise model of the transistor;
2) deriving and simplifying a flicker noise model in the semiconductor device using a distance-to-charge density relationship in the MIT model;
3) the improved flicker noise model is used for modeling flicker noise in the semiconductor device and obtaining a series of related simulation results, namely the relationship between the normalized current noise power spectral density of the device and the working frequency thereof, the relationship between the normalized current noise power spectral density of the device and the grid voltage, and the relationship between the voltage power spectral density of the device and the grid voltage.
The flicker noise model is:
charge-based flicker noise power spectral density for MIT models
Figure RE-RE-DEST_PATH_IMAGE008
In the formula:
Figure RE-RE-DEST_PATH_IMAGE010
is the frequencyAs a function of (a) or (b),
Figure RE-RE-DEST_PATH_IMAGE014
are all gate source voltage
Figure RE-DEST_PATH_IMAGE016
And drain-source voltage
Figure RE-DEST_PATH_IMAGE018
A function of (a);
whereinThe parameters of the fit may be adjusted,
Figure RE-132177DEST_PATH_IMAGE004
is the charge density of the drain electrode and,
Figure RE-465069DEST_PATH_IMAGE006
is the charge density of the source electrode,
Figure 100002_RE-DEST_PATH_IMAGE022
in order to be the density of the traps,
Figure RE-DEST_PATH_IMAGE024
in order to achieve the mobility of the carriers,
Figure RE-DEST_PATH_IMAGE026
for the length of the transistor device,adjusting the power spectral density and frequency phase for a singleThe physical quantities that are of relevance,
Figure 100002_RE-DEST_PATH_IMAGE030
represents the probability of electron tunneling to a trap,
Figure 100002_RE-DEST_PATH_IMAGE032
is the drain current.
The flicker noise model is:
Figure 100002_RE-DEST_PATH_IMAGE034
in the formula:
Figure 100002_RE-DEST_PATH_IMAGE036
for the power spectral density of the current flicker noise,is a transconductance, and is,is the power spectral density of the voltage flicker noise.
The flicker noise model is used in semiconductor device testing for evaluating the performance of semiconductor devices.
The invention aims at a specific semiconductor model device, and measures necessary physical parameters of the device, such as the gate width, the gate length, the index, the mobility, the carrier migration speed and the like of the device. Meanwhile, an MIT model corresponding to the semiconductor device is established according to the IV characteristic curve of the device, and drain current is obtained
Figure RE-531639DEST_PATH_IMAGE002
Charge density of drain and source
Figure RE-541052DEST_PATH_IMAGE004
And
Figure RE-745768DEST_PATH_IMAGE006
so as to connectNext, a flicker noise model is calculated.
The method simplifies and deduces the existing flicker noise model, introduces the elements of the MIT model, and obtains the flicker noise model capable of accurately reflecting the power spectral density characteristic of the device noise by adjusting the empirical parameters in the flicker noise model.
The invention has the advantages that: the method fills the blank that the modeling method of the flicker noise is absent under the MIT semiconductor device model which is already applied industrially, and has the advantages of accurate modeling, easy adjustment, solid physical significance, less measured data required during modeling and the like, provides the flicker noise model suitable for the MIT model, and improves the efficiency and the precision of the modeling of the semiconductor device flicker noise model.
Further: the main advantages of the invention are:
1. the blank that a flicker noise model does not exist under an MIT model system is filled;
2. compared with a traditional theoretical flicker noise model, the flicker noise model can work well under an MIT model system, is easy to adjust, has higher precision and is suitable for various devices;
3. compared with a flicker noise model under an empirical model, the flicker noise model modeled based on the physical MIT model greatly reduces the requirement on test data volume, and can better reflect the physical characteristics of the device;
4. compared with a physical flicker noise model under an ASM model taking surface potential as a core, the flicker noise model has better inheritance relation with a parent model, and well inherits the idea that the MIT model takes charge as a modeling core.
Drawings
FIG. 1 is a 75 μm gate width AlGaN/GaN device，
Figure RE-DEST_PATH_IMAGE044
Under the condition of (1), the modeling result and the actual measurement result of the flicker noise power spectrum density and the working frequency of the current sourceAnd (6) comparing.
FIG. 2 shows GaN/Al with a gate width of 50 μm0.15Ga0.85N device at
Figure RE-DEST_PATH_IMAGE046
Under the condition, the modeling results of the flicker noise power spectral density of the voltage source and the grid source voltage under different working frequencies are compared with the actual measurement results.
FIG. 3 is an AlGaAs/InGaAs device with a gate width of 1.7 μm in
Figure RE-DEST_PATH_IMAGE048
，Under the condition of (3), a modeling result between the noise power spectral density and the grid source voltage of the normalized current source is compared with an actual measurement result.
Detailed Description
The invention is explained by starting from an original flicker noise model, and obtaining a flicker noise model which is based on an MIT model and is suitable for a high electron mobility transistor through a series of derivation and simplification. The specification selects three devices to respectively verify the effectiveness of the noise model, wherein the three devices are respectively an AlGaN/GaN device with the gate width of 75 mu m and a GaN/Al device with the gate width of 50 mu m0.15Ga0.85N device, and an AlGaAs/InGaAs device with a gate width of 1.7 μm.
The specific implementation method corresponding to the invention comprises the following steps:
1. building MIT model
The MIT model is a model of high electron mobility transistors built based on the virtual source concept, which uses charge density as a modeling core. To accurately model the MIT model, we need to first measure some basic physical parameters of the strip-modeled device, such as the gate width of the deviceLength of gridIndex of
Figure RE-DEST_PATH_IMAGE056
Mobility of carrier
Figure RE-DEST_PATH_IMAGE058
Carrier transfer speed
Figure RE-DEST_PATH_IMAGE060
Unit area capacitance between strong reverse time grid and channel of device
Figure RE-DEST_PATH_IMAGE062
And the like. Next, we need to measure the DC IV data of the device, and fit the DC IV data using the drain expression of the MIT model to get the MIT model suitable for the device.
Specifically, drain current of MIT model
Figure RE-DEST_PATH_IMAGE064
The expression is as follows:
Figure RE-DEST_PATH_IMAGE066
wherein
Figure RE-DEST_PATH_IMAGE068
Is the width of the gate of the transistor,
Figure RE-DEST_PATH_IMAGE070
is the index of the gate electrode(s),
Figure RE-DEST_PATH_IMAGE072
to be the rate at which the carriers migrate,
Figure RE-DEST_PATH_IMAGE074
and
Figure RE-DEST_PATH_IMAGE076
representing the charge density of the drain and source respectively,
Figure RE-DEST_PATH_IMAGE078
then is a transfer function given in the form:
Figure RE-DEST_PATH_IMAGE080
wherein
Figure RE-DEST_PATH_IMAGE082
The capacitance per unit area between the gate and the channel under the strongly inverted region,is the value of the saturation voltage of the transistor,
Figure RE-DEST_PATH_IMAGE086
is a for adjusting
Figure RE-DEST_PATH_IMAGE088
The fitting parameters of the velocity are switched. In particular, the amount of the solvent to be used,
Figure RE-DEST_PATH_IMAGE090
and
Figure RE-DEST_PATH_IMAGE092
can be expressed as
Figure RE-DEST_PATH_IMAGE094
In the above-mentioned formula, the compound of formula,
Figure RE-DEST_PATH_IMAGE096
which represents a thermal voltage, represents the voltage of heat,
Figure RE-DEST_PATH_IMAGE098
to adjust for
Figure RE-DEST_PATH_IMAGE100
The physical quantity of the degree of saturation at carrier velocity saturation, which may be combined with their associated formulaeIs expressed as follows
Figure RE-DEST_PATH_IMAGE102
Figure RE-DEST_PATH_IMAGE104
And
Figure RE-DEST_PATH_IMAGE106
are Fermi functions, they have the following morphology
Figure RE-DEST_PATH_IMAGE108
Therefore, the direct current IV of the measured device can be fitted based on the expression, the MIT model corresponding to the direct current IV is established, and the direct current IV required by the subsequent flicker noise modeling is obtained
Figure RE-DEST_PATH_IMAGE110
The specific expression of (1).
2. Introduction and derivation of flicker noise
Here we get a flicker noise model based on the MIT model through a series of simplifications, substitutions and approximations starting from the most basic flicker noise model.
First, the power spectral density corresponding to the mean square fluctuation of the number of occupied traps in a unit area is given
Figure RE-DEST_PATH_IMAGE112
Figure RE-DEST_PATH_IMAGE114
(1)
Wherein
Figure RE-DEST_PATH_IMAGE116
In order for the trap density to be measurable,
Figure RE-DEST_PATH_IMAGE118
is aA physical quantity that adjusts the frequency dependence of the power spectral density,
Figure RE-DEST_PATH_IMAGE120
representing the probability of electron tunneling to a trap, a common value for the devices discussed in this invention is 1e10 m-1。
Based on this, assume again that a HEMT device has a length
Figure RE-DEST_PATH_IMAGE122
Width of
Figure RE-DEST_PATH_IMAGE124
Index of grid
Figure RE-DEST_PATH_IMAGE126
Then its power spectral density of flicker noise can be expressed as
Figure RE-RE-DEST_PATH_IMAGE128
(2)
A modified current ripple expression is introduced here. The expression considers the ratio of the current change as the charge density at a certain point of the channel
Figure RE-DEST_PATH_IMAGE130
Change rate of (2) and low field mobility
Figure RE-DEST_PATH_IMAGE132
Adding or subtracting rates of change of
Figure RE-DEST_PATH_IMAGE134
(3)
Where a plus sign corresponds to a situation where the trap is electrically neutral when filled and a minus sign corresponds to a situation where the trap is electrically charged when filled. Followed by introducing a trap density in the above formula
Figure RE-DEST_PATH_IMAGE136
The above formula can be derived to
Figure RE-DEST_PATH_IMAGE138
(4)
By bringing (4) into (2), can be obtained
(5)
Based on the relevant contents of the MIT model, the drain current and the capacitance between the channel and the gate are respectively
Wherein
Figure RE-DEST_PATH_IMAGE144
Representing the potential energy of the gate electrode,
Figure RE-DEST_PATH_IMAGE146
representing the position of a certain point of the channel,
Figure RE-DEST_PATH_IMAGE148
which represents the source of the light emitting diode,
Figure RE-DEST_PATH_IMAGE150
representing the drain. Thus, the relationship of position to charge density can be expressed as
Figure RE-DEST_PATH_IMAGE152
(8)
By bringing (8) into (5) and integrating along the channel length, the current spectral density and charge density are related by
Figure RE-DEST_PATH_IMAGE154
Wherein
Figure RE-DEST_PATH_IMAGE156
Is the charge density of the drain electrode and,is the charge density of the source. Based on previous work, if the device is operated in a strong inversion region, the ratio of the fluctuation of the number of carriers to the fluctuation of the number of occupied traps will be a constant value, and therefore, the ratio of the fluctuation of the number of occupied traps will be a constant value
Figure RE-DEST_PATH_IMAGE160
Quadratic equation as argument
Figure RE-DEST_PATH_IMAGE162
Can be used to replace that in (9)
Figure RE-DEST_PATH_IMAGE164
Wherein
Figure RE-DEST_PATH_IMAGE166
For the adjustable fitting parameters, as shown below
Integrating (10) to obtain the flicker noise power spectral density based on the charge and suitable for the MIT model
Figure RE-DEST_PATH_IMAGE170
In the above-mentioned formula, the compound of formula,
Figure RE-DEST_PATH_IMAGE172
is the frequency
Figure RE-DEST_PATH_IMAGE174
As a function of (a) or (b),are all gate source voltage
Figure RE-DEST_PATH_IMAGE178
And drain-source voltage
Figure RE-DEST_PATH_IMAGE180
The expression of which may be given by a previously established MIT model. Thus, the power spectral density of the device can be determined by adjusting the fitting parameters in the model (11), such as
Figure RE-DEST_PATH_IMAGE182
Etc. to accurately fit. If the power spectral density of the equivalent voltage flicker noise is desired, divide (11) by transconductanceWherein the transconductance can be obtained by observing the amount of change in current after applying a slight voltage increment to the obtained MIT model
Figure RE-DEST_PATH_IMAGE186
(12)
Thus, (11) or (12) is a flicker noise model based on the MIT model.
The flicker noise model in this patent is next validated for the examples. Firstly, measuring necessary physical parameters of a transistor, such as the gate width, the gate length, the index, the mobility, the carrier migration speed, the trap density and the like of a device; then, fitting the direct current IV image of the device by using the MIT model to obtain the MIT model suitable for the device, and further obtaining the drain current from the MIT model
Figure RE-DEST_PATH_IMAGE188
Density of drain chargeAnd source charge density
Figure RE-DEST_PATH_IMAGE192
The expression of (1); we then sum the basic physical parameters of the devices
Figure RE-DEST_PATH_IMAGE194
，
Figure RE-DEST_PATH_IMAGE196
And
Figure RE-DEST_PATH_IMAGE198
the flicker noise power spectral density of the current source can be obtained by substituting the expression (11) or (12) and adjusting the fitting parameters given in (11). If the noise power spectral density of the equivalent voltage source is desired to be obtained, a smaller voltage increment can be applied to the modeled MIT model, and the ratio of the current variation and the voltage increment caused by the smaller voltage increment is calculated to obtain the transconductance
Figure RE-DEST_PATH_IMAGE200
Dividing (11) by the transconductance
Figure RE-822964DEST_PATH_IMAGE200
The square of (1) is just required.
FIG. 1 is a graph showing the relationship between the power spectral density of current noise and the operating frequency of an AlGaN/GaN device with a gate width of 75 μm
Figure RE-DEST_PATH_IMAGE202
Under the condition (1), the solid line represents the model proposed by the patent, and the small points represent the measured data; FIG. 2 is a graph showing the relationship between the voltage noise power spectral density and the grid source voltage at different operating frequencies, and the grid width is 50 μm GaN/Al0.15Ga0.85N devices operate in
Figure RE-616477DEST_PATH_IMAGE046
Under the condition (1), the model provided by the patent is represented, and the hollow symbols represent measurement data under various frequencies; FIG. 3 is a graph demonstrating the relationship between normalized current noise power spectral density and gate-source voltage for an AlGaAs/InGaAs device having a gate width of 1.7 μm
Figure RE-298256DEST_PATH_IMAGE048
，
Figure RE-990269DEST_PATH_IMAGE050
Under the condition of (1), the model provided by the patent is realized, and hollow points are measurement data. The parameters corresponding to the specific experiments are shown in table 1. It can be seen from the comparison of modeling result and measuring result, the scintillation noise model that this patent provided can reflect the scintillation noise characteristic of being modeled the device well, has higher precision.
It can be seen from the above embodiment that the flicker noise model of the high electron mobility transistor provided by the invention fills the gap of the MIT model, so that the MIT model has the advantages of accurate modeling, easy adjustment, solid physical significance, less measured data required in modeling, and the like, and can be well inherited to the modeling of flicker noise. Meanwhile, the flicker noise model is convenient to adjust, and the flicker noise performance of the device to be modeled can be accurately fitted only by a small number of fitting parameters. The advantages enable the invention to well improve the flicker noise modeling efficiency of the semiconductor device.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes performed by the present specification and drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.
Table 1 is the key parameter values corresponding to the 3 modeling results given by the patent.
Figure RE-DEST_PATH_IMAGE204
。

Claims (5)

1. A method for establishing a flicker noise model based on an MIT high electron mobility transistor model is characterized in that the flicker noise model establishes the MIT high electron mobility transistor model based on charge modeling.
2. The flicker noise model establishing method based on the MIT HEMT model according to claim 1, comprising the following steps:
1) fitting a direct current IV image of a certain transistor by using an MIT model to obtain a drain current under the MIT model
Figure RE-DEST_PATH_IMAGE002
Density of drain charge
Figure RE-DEST_PATH_IMAGE004
Density of source charge
Figure RE-DEST_PATH_IMAGE006
Substituting the specific expression into the proposed flicker noise model to obtain a flicker noise model of the transistor;
2) deriving and simplifying a flicker noise model in the semiconductor device using a distance-to-charge density relationship in the MIT model;
3) the improved flicker noise model is used for modeling flicker noise in the semiconductor device and obtaining a series of related simulation results, namely the relationship between the normalized current noise power spectral density of the device and the working frequency thereof, the relationship between the normalized current noise power spectral density of the device and the grid voltage, and the relationship between the voltage power spectral density of the device and the grid voltage.
3. The flicker noise model establishing method based on the MIT HEMT model according to claim 2, wherein the flicker noise model is:
charge-based flicker noise power spectral density for MIT models
Figure RE-DEST_PATH_IMAGE008
In the formula:
Figure RE-DEST_PATH_IMAGE010
is the frequencyAs a function of (a) or (b),are all gate source voltage
Figure RE-RE-DEST_PATH_IMAGE016
And drain-source voltage
Figure RE-RE-DEST_PATH_IMAGE018
A function of (a);
wherein
Figure RE-RE-DEST_PATH_IMAGE020
The parameters of the fit may be adjusted,
Figure RE-128582DEST_PATH_IMAGE004
is the charge density of the drain electrode and,
Figure RE-983406DEST_PATH_IMAGE006
is the charge density of the source electrode,
Figure RE-DEST_PATH_IMAGE022
in order to be the density of the traps,
Figure RE-RE-DEST_PATH_IMAGE024
in order to achieve the mobility of the carriers,
Figure RE-RE-DEST_PATH_IMAGE026
for the length of the transistor device,to a physical quantity that adjusts the frequency dependence of the power spectral density,
Figure RE-DEST_PATH_IMAGE030
represents the probability of electron tunneling to a trap,is the drain current.
4. The flicker noise model establishing method based on the MIT HEMT model according to claim 2, wherein the flicker noise model is:
Figure RE-DEST_PATH_IMAGE034
in the formula:
Figure RE-DEST_PATH_IMAGE036
for the power spectral density of the current flicker noise,
Figure RE-DEST_PATH_IMAGE038
is a transconductance, and is,
Figure RE-DEST_PATH_IMAGE040
is the power spectral density of the voltage flicker noise.
5. Use of a flicker noise model based on the MIT high electron mobility transistor model for evaluating the performance of a semiconductor device in a semiconductor device test.
CN201910493721.3A 2019-06-06 2019-06-06 Method for establishing flicker noise model based on MIT high electron mobility transistor model and application thereof Pending CN110704997A (en)

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CN112434400A (en) * 2020-10-15 2021-03-02 北京交通大学 MOSFET grid source voltage interference conduction path model
CN114355141A (en) * 2021-12-31 2022-04-15 西安电子科技大学 Noise characterization method for trap distribution of Metal Oxide Semiconductor Field Effect Transistors (MOSFETs) gate oxide layer
CN114510895A (en) * 2022-01-24 2022-05-17 北京大学 Monte Carlo simulation flicker noise statistical method

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Application publication date: 20200117