JPH09135028A - Calculating method for mosfet mobility - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a calculating method for an accurate MOSFET mobility even in a subthreshold region. SOLUTION: When a mobility μ in a channel region where a MOSFET is constituted is calculated, this method is provide with a drain current measuring step (a first step) in which a drain current Id is measured under a predetermined gate voltage Vc and a drain voltage Vd , with a carrier density calculating step (a second step) in which a carrier density N5 is calculated as V5 =Vd =V according to a first relative relation where the carrier density N5 is calculated from the mobility μ, a source voltage V5 and the drain voltage Vd and with a mobility calculating step (a third step) in which mobility μc is calculated from the calculated carrier density Ns the measured drain current Id according to the second relative relation where the mobility μ is calculated from the carrier density Ns and the drain current Id . The channel region mobility μ is decided as μc which is calculated through the drain current measuring step, the carrier density calculating step and the mobility calculating step.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for calculating the mobility of a channel region which constitutes a MOSFET, and more specifically, it is simpler and more accurate than the conventional method, and more particularly, it is possible to accurately measure the mobility even in a subthreshold region. It relates to a method that can be calculated.

[0002]

2. Description of the Related Art Conventionally, the mobility has been measured by the procedure shown in FIG. First, the drain current I _d is measured under a predetermined drain voltage V _d based on the gate voltage V _G dependency (first step). Next, the carrier density N _S is measured by the so-called C (electrostatic capacity) -V (gate voltage) method (hereinafter simply referred to as the CV method) (second step).
The C-V method is a method in which the total carrier amount Q _SC in the surface space charge region is calculated by Q _SC = ∫dQ _SC = −∫C _SC dV _S , and then the carrier density N _S is calculated. Where C _SC
Is a capacitance per unit area, and V _S is a gate voltage. Based on the measured drain current I _d and carrier density N _S , a known relationship, for example, the following equations (1) and (2)
The mobility is calculated by (3rd step). g _d = I _d / V _d (1) μ = (L / W) × {g _d / (qN _S )} (2) where L is the gate length, W is the gate width, and g _d is the conductance. q is an elementary charge.

[0003]

However, in the conventional mobility measuring method, the dimension L × W of the gate electrode is 100 μm.
Even in a sufficiently large MOSFET of about × 100 μm, in the subthreshold region in which the gate voltage is smaller than the threshold voltage, the capacitance C becomes 10 fF or less when measuring the carrier density N _S , so that the influence of disturbance such as noise is large. It was difficult to measure the accurate capacitance. Therefore, it is difficult to measure the accurate carrier density N _S , and thus the accurate mobility. On the other hand, MOSF
Since ET is in the direction of further miniaturization, and the size of the gate electrode is accordingly reduced, it becomes more and more difficult to measure the accurate carrier density N _S , and therefore the accurate calculation of the mobility. Has become difficult.

Therefore, an object of the present invention is to provide a mobility calculating method capable of accurately calculating the mobility, particularly a method capable of accurately calculating the mobility even in the subthreshold region.

[0005]

In order to achieve the above object, the mobility calculating method according to the present invention (hereinafter referred to as the first invention method) is performed when the mobility μ of a channel region constituting a MOSFET is obtained. , A drain current measuring step of measuring a drain current I _d under a predetermined gate voltage V _G and a drain voltage V _d , and a first step of obtaining a carrier density N _S from the mobility μ, the source voltage V _S and the drain voltage V _d . And a carrier density calculation step of obtaining a carrier density N _S with the initial value of the mobility μ _{I and the} source voltage V _S and the drain voltage V _d being V _S = V _d = V according to the correlation of
_According to a second correlation for obtaining the mobility μ from _S and the drain current I _d , a mobility calculating step for obtaining the mobility μ _C based on the calculated carrier density N _S and the measured drain current I _d is provided. The feature is that μ _C obtained in the mobility calculation step is used as the mobility μ of the channel region.

The first correlation for obtaining the carrier density N _S from the mobility μ, the source voltage V _S and the drain voltage V _d is a known relation and is usually incorporated in a process simulator. In the first correlation, under the condition of source voltage V _S = drain voltage V _d = V, the calculated value of the carrier density N _S does not change even if the initial value μ _I of the input mobility fluctuates to some extent. There is a fact that it hardly changes.
The method of the present invention was invented on the basis of this fact, inputs the mobility μ _I that can be assumed to be appropriate, calculates the mobility μ _C based on it, and sets it as the mobility μ.
In carrying out the method of the present invention, V is a normal MOSF.
It may be any value in the range of the voltage applied by ET, but it is preferably 0 or a value close thereto.

That is, in the method of the first invention, a value μ _I that can be generally estimated to be appropriate is set as the initial value of the mobility, and based on this, the carrier density is set under the condition of source voltage V _S = drain voltage V _d = V. Calculate N _S. The mobility μc is calculated from the calculated N _S and the drain current I _d measured in the same manner as the conventional one, based on the known second correlation, and μc is the mobility μ to be calculated.

If μ c is significantly different from μ _I ,
It is preferable to obtain a new mobility μc again in the same manner with μc being a new μ _I. Therefore, in a preferred embodiment of the method of the present invention, μ _C1 obtained through the first carrier density calculating step and the mobility calculating step is used as the initial mobility μ _I2 in the second carrier density calculating step, The second carrier density calculation step and the mobility calculation step are carried out to obtain μ _C2, and the same procedure is repeated until the difference between the obtained mobility μ _Cn and the initial value μ _In of the mobility falls below the allowable value. It is characterized in that the carrier density calculation step and the mobility calculation step are repeated n-2 times.

In another method for calculating the mobility according to the present invention (hereinafter referred to as the second invention method), the gate voltage V _G is the threshold when the mobility μ of the channel region forming the MOSFET is obtained. In the subthreshold region lower than the value V _th, a drain current measuring step of measuring the drain current I _d under a predetermined gate voltage V _G and drain voltage V _d ,
According to the first correlation for obtaining the carrier density N _S from the mobility μ, the source voltage V _S and the drain voltage V _d , the initial value of the mobility is μ _{I and the} source voltage V _S and the drain voltage V _d are V _S = V _The calculated carrier density N _S and the measured drain current I are obtained according to the carrier density calculation step of calculating the carrier density N _S with _d = V and the second correlation for calculating the mobility μ from the carrier density N _S and the drain current I _d. based on the _d, and a mobility calculation step of obtaining the mobility mu _C, a mu _C obtained in mobility calculation step and the mobility mu of the channel region, the gate voltage V _G is higher than the threshold V _th In the region, a predetermined gate voltage V _G and drain voltage V _G
measuring a drain current I _d under _d, measuring a carrier density N _S, in accordance with a second correlation seeking mobility μ from the carrier density N _S and the drain current I _d, the measured carrier density based on the N _S and the drain current I _d, and a mobility calculation step of obtaining a mobility mu _C, is characterized in that the mobility mu of the channel region mu _C obtained in mobility calculation step.

In the method of the second aspect of the invention, in a region where the carrier density N _S is relatively easy to measure and the gate voltage V _G is higher than the threshold value V _th , N _S is measured by a method similar to the conventional method, and mobility is measured. In the subthreshold region where it is difficult to measure the carrier density N _S and the gate voltage V _G is lower than the threshold value V _th , the mobility μ is calculated by the same method as the first invention method.

[0011]

Embodiments of the present invention will be described below in detail with reference to the accompanying drawings. Embodiment 1 This embodiment is an embodiment of the first invention method for calculating the mobility μ _C by obtaining the carrier density N _S by simulation, and FIG. 1 is a flowchart showing the procedure.

As a first step, a predetermined gate voltage V
_The drain current I _d is measured under _G and the drain voltage V _d (drain current measuring step). As the second step,
Using a known simulator that defines the first correlation for obtaining the carrier density N _S from the mobility μ, the source voltage V _S, and the drain voltage V _d , the initial value of the mobility μ _I and the source voltage V _S And drain voltage V _d as V _S = V _d
= V, the carrier density N _S is determined (carrier density calculation step). In setting the initial value μ _I of the mobility μ, the most probable estimated value is μ _I based on the past mobility data. In the carrier density calculation step, it is preferable to set V = 0.

As a third step, the mobility is calculated according to the second correlation (mobility calculation step). Second determination of mobility μ from carrier density N _S and drain current I _d
Is a relationship that has been used in the conventional mobility calculation method. For example, using the following equations (1) and (2), g _d = I _d / V _d (1) μ = ( L / W) × {g _d / (qN _S )} (2) Obtain the mobility μ _C. The calculated mobility μ _C
The mobility μ required for the channel region forming T is set.

Embodiment 2 If μc is significantly different from μ _I, it is preferable to determine μ c as a new μ _I and again obtain a new mobility μ c. The second embodiment is a modification of the first embodiment, and FIG. 2 is a flowchart showing the procedure. First, similarly to the first embodiment, the mobility μ _C1 is obtained through the first carrier density calculation step (second step) and the mobility calculation step (third step). It is determined whether the difference between μ _C1 and μ _I1 (the initial mobility setting value) is less than or equal to the allowable value δ (fourth step). If the difference between μ _C1 and μ _I1 (the initial mobility setting value) is less than or equal to the allowable value δ, μ _C1 is determined as the desired mobility μ.

When the difference between μ _C1 and μ _I1 is equal to or larger than the allowable value δ, μ _C1 is used as the initial value μ _I2 of the mobility, and the second carrier density calculating step and the mobility calculating step are performed. Calculate μ _C2 . Below, the _calculated mobility μ _Cn and the initial mobility μ _In
The carrier density calculation step and the mobility calculation step are repeated n-2 times in the same manner until the difference between and is within the allowable value δ or less. Let the obtained mobility μ _{Cn be} the mobility μ to be obtained. By the above operation, more accurate mobility μ can be obtained.

Embodiment 3 This embodiment is an embodiment of the second invention method, and FIG. 3 is a flow chart showing the procedure. In the present embodiment, in the second step, it is determined whether the gate voltage V _G is in the subthreshold region lower than the threshold V _th . In the sub-threshold region where the gate voltage V _G is lower than the threshold value V _th , the mobility is calculated by simulating the carrier density N _S by the simulator in the third step in the same manner as in the first embodiment. In the region where the gate voltage V _G is higher than the threshold value V _th , the carrier density N _S is so-called C− in the third step as in the conventional method.
It is measured by the V method. Then, based on the calculated carrier density N _S or the measured carrier density N _S , the mobility μ
Calculate _C and set it as the required mobility μ.

Calculation Example This calculation example is a specific calculation example of the first embodiment. FIG.
FIG. 4 is a graph showing a result of measuring a drain current I _d under a predetermined gate voltage V _G and drain voltage V _d as a first step. As a second step, FIG. 6 shows an initial mobility value using a known simulator that defines the first correlation for obtaining the carrier density N _S from the mobility μ, the source voltage V _S and the drain voltage V _d. Μ _I , and the source voltage V _S and the drain voltage V _d as V _S = V _d =
6 is a graph showing a result of obtaining a carrier density N _S as V. In setting the initial value μ _I of the mobility μ, the most promising estimated value was set to μ _I based on the past mobility data. Also, V = 0 is set. FIG.
FIG. 6 is a graph showing a result of obtaining mobility with respect to an electric field in the surface vertical direction according to a second correlation as a third step.

[0018]

According to the method of the present invention, even if the mobility is in the subthreshold region of a miniaturized MOSFET whose carrier density is difficult to measure, the carrier density can be calculated by a simulator to obtain accurate mobility. Can be calculated. Further, since the complicated noise countermeasure for suppressing the disturbance, which is required in the conventional method for measuring the carrier density, is unnecessary in the method of the present invention, the mobility can be calculated easily.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a mobility calculation method according to a first embodiment.

FIG. 2 is a flowchart illustrating a mobility calculating method according to a second embodiment.

FIG. 3 is a flowchart illustrating a mobility calculation method according to a third embodiment.

FIG. 4 is a flowchart showing a conventional method of calculating mobility.

FIG. 5 is a graph of gate voltage versus drain current.

FIG. 6 is a graph of gate voltage versus carrier density.

FIG. 7 is a graph of surface vertical field versus mobility.

[Explanation of symbols]

 None

Claims (3)

[Claims] 1. A drain current measuring step of measuring a drain current I _d under a predetermined gate voltage V _G and a drain voltage V _d when determining a mobility μ of a channel region constituting a MOSFET, and a mobility μ. , the source voltage V _S and the drain voltage V in accordance with the first correlation seeking carrier density N _S from _d, the initial value of the mobility mu _I and source voltage V _S and the drain voltage V _d V _S = V _d = V a carrier density calculation step of obtaining a carrier density N _S as the carrier density N _S and the drain current I in accordance with a second correlation seeking mobility μ from _d, the calculated carrier density N
_{Based on S} and the measured drain current I _d , the mobility μ
_The mobility calculation step for obtaining _C is performed, and μ _C obtained in the mobility calculation step is used as the mobility μ of the channel region.
A method for calculating the mobility of a MOSFET, comprising: 2. The method of calculating the mobility of the MOSFET according to claim 1, wherein μ _C1 obtained through the first carrier density calculation step and the mobility calculation step is used to calculate the mobility in the second carrier density calculation step. As the initial value μ _I2 , the second carrier density calculation step and the mobility calculation step are performed to find μ _C2 , and the difference between the obtained mobility μ _Cn and the initial value μ _In of the mobility is the allowable value. The MO is characterized in that the carrier density calculation step and the mobility calculation step are repeated n-2 times in the same manner until the following values are satisfied.
Calculation method of mobility of SFET. When obtaining the wherein the mobility of the channel region constituting the MOSFET mu, a low subthreshold region than the gate voltage V _G is the threshold V _th, under the predetermined gate voltage V _G and drain voltage V _d and the drain current measuring step of measuring the drain current I _d in the mobility mu, in accordance with a first correlation determining carrier density N _S from the source voltage V _S and the drain voltage V _d, the initial value of the mobility mu _I and A carrier density calculation step of obtaining the carrier density N _{S by} setting the source voltage V _S and the drain voltage V _d to V _S = V _d = V, and a second correlation for obtaining the mobility μ from the carrier density N _S and the drain current I _d. According to the calculated carrier density N
_{Based on S} and the measured drain current I _d , the mobility μ
_The mobility calculation step for obtaining _C is performed, and μ _C obtained in the mobility calculation step is used as the mobility μ of the channel region.
And then, at a high gate voltage V _G is the threshold V _th region includes the steps of measuring the drain current I _d under a predetermined gate voltage V _G and drain voltage V _d, and measuring the carrier density N _S , The carrier density N measured according to the second correlation for obtaining the mobility μ from the carrier density N _S and the drain current I _d.
Based on the _S and the drain current I _d, the mobility mu and a mobility calculation step of calculating _C, the mobility of the mu _C obtained in mobility calculation step channel region mu
A method for calculating the mobility of a MOSFET, comprising: