阅读说明：本技术 一种利用扫描探针探测材料介电常数的方法 (Method for detecting dielectric constant of material by using scanning probe ) 是由 许杰 陈剑锋 陈龙 于天祺 蔡远凌云 于 2019-11-07 设计创作，主要内容包括：本发明公开了一种利用扫描探针显微技术探测材料介电常数的方法。本发明包括如下步骤：首先,利用静电力显微镜的电场梯度探测获得探针与试样间电容梯度的实验值；然后利用镜像电荷法建立探针试样间电容随试样介电常数变化的理论模型；最后将实验值与理论模型进行比较,推断出试样的介电常数。本发明能够获知试样在纳米尺度下的介电常数信息,且具有无损伤探测的优点,适用于各种电介质如绝缘体或半导体等材料的表征。(The invention discloses a method for detecting dielectric constant of a material by using a scanning probe microscopy technology. The invention comprises the following steps: firstly, acquiring an experimental value of capacitance gradient between a probe and a sample by utilizing electric field gradient detection of an electrostatic force microscope; then, establishing a theoretical model of capacitance between the probe samples changing along with the dielectric constant of the samples by using a mirror charge method; and finally, comparing the experimental value with a theoretical model to deduce the dielectric constant of the sample. The method can obtain the dielectric constant information of the sample under the nanoscale, has the advantage of nondestructive detection, and is suitable for characterization of various dielectric substances such as insulators or semiconductors.)

1. A method for detecting the dielectric constant of a material by utilizing a scanning probe microscopy technology is characterized by comprising the following steps:

(1) using an electrostatic force microscope: under the DC bias, keeping the distance z between the probe and the sample unchanged, detecting the deviation delta f of the resonance frequency of the probe, and calculating the second derivative d of the capacitance between the probe and the sample according to the deviation delta f²C/dz²；

(2) Using a mirror charge method: constructing a relation model of the acting force and the capacitance between the probe and the sample along with the change of the dielectric constant epsilon in the sample to obtain a C' -epsilon curve;

(3) d in the step (1)²C/dz²And (3) comparing the calculated experimental value with the theoretical curve of C' -epsilon in the step (2) to obtain a final dielectric constant value.

2. The method according to claim 1, wherein the electrostatic force between the probe and the sample capacitor is set as V when the DC bias voltage in step (1) is set as V

the electrostatic force microscope signal is proportional to the electrostatic force gradient, i.e.

Wherein f is₀Is the probe natural frequency, k is the probe stiffness coefficient, and dF/dz is the first derivative of the electrostatic force; obtaining the signal of the electrostatic force microscope in proportion to the second derivative d of the capacitance of the probe and the sample through the two formulas²C/dz²I.e. by

Therefore, the experimental value of the second derivative of the capacitance of the probe and the sample can be obtained from the signal of the electrostatic force microscope.

3. The method for detecting the dielectric constant of a material by using the scanning probe microscopy as claimed in claim 1, wherein the force acting between the probe and the sample in the step (2) is calculated by using an equivalent charge method and a mirror charge method; wherein the equivalent charges of the probe are distributed on the central axis, and N equivalent charges q are taken₁,q₂,…q_NPosition coordinate is r₁,r₂,…r_NThen the mirror charge in the sample having the dielectric constant ε is- β q₁,-βq₂,…-βq_NPosition coordinate is-r₁,-r₂,…-r_N；

The probe is an equipotential body, the potential is V, and then N position points r are arranged on the boundary of the probe_kThe potential of (c):

wherein k is 1,2.. N; the above equation is a set of N equations from which N are solvedEquivalent charge q_iA value of (d); after the charge amounts of the equivalent charge and the mirror charge are determined, the theoretical values of the sample and the electrostatic force are calculated as follows:

in the formula q_j'＝-βq_jAnd r_j'＝-r_jThe size and the position of the mirror image charge are shown, j and i in the subscript are distinguished to indicate that the sum needs to be respectively summed; the first derivative of the acting force can be obtained by derivation of the formula,

then according to

Finally, the second derivative d of the capacitance can be obtained according to the value of beta ═ epsilon-1)/(epsilon +1²C/dz²Theoretical relationship with the dielectric constant epsilon of the sample.

4. The method for detecting the dielectric constant of a material by using the scanning probe microscopy as claimed in claim 1, wherein the step (3) is to apply d in the step (1)²C/dz²Experimental values and d in step (2)²C/dz²And comparing theoretical values to obtain a beta value corresponding to the experimental value, and obtaining the dielectric constant of the sample to be measured according to a relation beta ═ epsilon-1)/(epsilon + 1).

5. The method for detecting the dielectric constant of a material by using the scanning probe microscopy technology as claimed in claim 1, wherein the distance z between the probe and the sample in the step (1) is expressed as a direction perpendicular to the plane of the sample.

Technical Field

The invention relates to a method for detecting dielectric constant of a material by using a scanning probe.

Background

In the prior art, the dielectric constant is an important intrinsic property of a dielectric material, generally speaking, the relative dielectric constant (abbreviated as dielectric constant) of a metal is large, and the dielectric insulating property is better, the dielectric constant is smaller, and two extreme cases are that: the ideal conductor dielectric constant is infinite, and the vacuum dielectric constant is 1; at present, the conventional means for measuring the dielectric constant is mainly an optical ellipsometer, and the complex refractive index, the extinction coefficient and the dielectric constant of a thin film sample are obtained by analyzing the interference condition of incident light in a thin film material; in general, the ellipsometer spot size requires at least tens of micrometers, and thus it is difficult to perform scanning analysis on a material at a nano-scale; with the development of semiconductor integrated circuits, the characteristic sizes of microelectronic and optoelectronic materials and devices have entered deep submicron and even nanometer levels, and a new method needs to be introduced for the analysis of the dielectric properties of the micro-nano electronic devices; on the other hand, since the atomic force microscope was invented in the last 80 s of the century, the scanning probe microscopy technology has undergone vigorous development, and various extended modes such as kelvin mode, electrostatic force mode, conductive mode, magnetic force mode and piezoelectric force mode have been developed and widely applied to surface analysis of micro-nano electronic materials; the invention provides a novel method for detecting dielectric constant of dielectric materials such as semiconductors and the like in a nanoscale by utilizing a scanning probe based on an electrostatic force microscope technology.

Disclosure of Invention

The object of the present invention is to overcome the drawbacks of the prior art by providing a method for measuring and analyzing the dielectric constant of a dielectric material using a scanning probe.

The technical scheme of the restaurant is as follows: a method for detecting the dielectric constant of a material by utilizing a scanning probe microscopy technology comprises the following steps:

(1) using an electrostatic force microscope: under the DC bias, keeping the distance z between the probe and the sample unchanged, detecting the deviation delta f of the resonance frequency of the probe, and calculating the second derivative d of the capacitance between the probe and the sample according to the deviation delta f²C/dz²(ii) a Said second derivative d²C/dz²May also be represented by C ";

(2) using a mirror charge method: constructing a relation model of the acting force and the capacitance between the probe and the sample along with the change of the dielectric constant epsilon in the sample to obtain a C' -epsilon curve;

(3) d in the step (1)²C/dz²And (3) comparing the calculated experimental value with the theoretical curve of C' -epsilon in the step (2) to obtain a final dielectric constant value.

Further, if the dc bias voltage in the step (1) is V, the electrostatic force between the probe and the sample capacitor is V

Where dC/dz is the first derivative of capacitance,

the electrostatic force microscope signal is proportional to the electrostatic force gradient, i.e.

Wherein f is₀Is the probe natural frequency, k is the probe stiffness coefficient, and dF/dz is the first derivative of the electrostatic force; obtaining the signal of the electrostatic force microscope in proportion to the second derivative d of the capacitance of the probe and the sample through the two formulas²C/dz²I.e. by

Or

Therefore, the experimental value of the second derivative of the capacitance of the probe and the sample can be obtained from the signal of the electrostatic force microscope.

Further, the force acting between the probe and the sample in the step (2) is calculated by adopting an equivalent charge and a mirror charge method; wherein the equivalent charges of the probe are distributed on the central axis, and N equivalent charges q are taken₁,q₂,…q_NPosition coordinate is r₁,r₂,…r_NThen the mirror charge in the sample with dielectric constant of epsilon is q₁',q₂',…q_N', the position coordinate is-r₁,-r₂,…-r_N；

The mirror charge is available q_i'＝-βq_iN, i is 1,2,. N; where β ═ e (e-1)/(e +1) is a parameter related only to the dielectric constant of the sample.

The probe is an equipotential body, the potential is direct current bias voltage V, and then N position points r on the probe boundary_kThe potential of (c):

wherein k is 1,2.. N; the above equation is a system of equations comprising N equations from which N equivalent charges q are solved_iA value of (d); after the charge amounts of the equivalent charge and the mirror charge are determined, the theoretical values of the sample and the electrostatic force are calculated as follows:

in the formula q_j'＝-βq_jAnd r_j'＝-r_jThe size and the position of the mirror image charge are shown, j and i in the subscript are distinguished to indicate that the sum needs to be respectively summed; the first derivative of the acting force can be obtained by derivation of the formula,

then according to

The theoretical relationship between the second derivative of the capacitance and beta is obtained as

Finally, the second derivative d of the capacitance can be obtained according to the value of beta ═ epsilon-1)/(epsilon +1²C/dz²Theoretical relationship with the dielectric constant epsilon of the sample.

Further, the step (3) is to add d in the step (1)²C/dz²Experimental values and d in step (2)²C/dz²And comparing theoretical values to obtain a beta value corresponding to the experimental value, and obtaining the dielectric constant of the sample to be measured according to a relation beta ═ epsilon-1)/(epsilon + 1).

Further, the distance z between the probe and the sample in the step (1) is expressed as a direction perpendicular to the plane of the sample.

The invention principle is as follows: in the electrostatic force microscope test, the second derivative of the capacitance between the conductive probe and the dielectric sample can be obtained experimentally according to the EFM frequency shift signal, the quantitative relation between the probe acting force and the capacitance and the dielectric constant of the sample can be established theoretically through a mirror charge method, and finally the dielectric constant of the sample can be obtained by comparing the experimental value with the theoretical value.

The invention has the beneficial effects that: (1) compared with an ellipsometer for testing, the diameter of a light spot is dozens to hundreds of micrometers, and the curvature radius of the electrostatic force microscope probe is only about 20 nanometers, so that the dielectric constant of a sample can be observed under the nanoscale, and the micro-area detection is realized; (2) the scanning probe adopts a non-contact mode during detection, so that nondestructive detection can be realized; (3) compared with the complex modeling of the ellipsometer, different materials are suitable for different optical models, and the modeling process is simple and suitable for dielectric materials with various dielectric constants.

Drawings

FIG. 1 is a schematic diagram of an Electrostatic Force Microscope (EFM) signal for measuring a single crystal silicon specimen in accordance with the present invention;

FIG. 2 is a schematic diagram of an EFM test according to the present invention, in which the voltage between the probe and the sample is V, the capacitance is C, and the equivalent charge q on the probe during the modeling process by the mirror charge method_iAnd the image charge q in the sample_i' schematic view;

FIG. 3 is a diagram of the second derivative d of capacitance theoretically obtained by the mirror charge method of the present invention²C/dz²Quantitative relationship with the dielectric constant of the sample (solid line), and d from the EFM signal²C/dz²Experimental values (dotted line, i.e. 3.77X 10)^-4F/m²). The dielectric constant of the monocrystalline silicon sample was found to be 12.6 by comparison.

Detailed Description

Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

A method for detecting the dielectric constant of a material by utilizing a scanning probe microscopy technology comprises the following steps:

(1) using an electrostatic force microscope: under the DC bias, keeping the distance z between the probe and the sample unchanged, detecting the deviation delta f of the resonance frequency of the probe, and calculating the second derivative d of the capacitance between the probe and the sample according to the deviation delta f²C/dz²(ii) a Said second derivative d²C/dz²May also be represented by C ";

(2) using a mirror charge method: constructing a relation model of the acting force and the capacitance between the probe and the sample along with the change of the dielectric constant epsilon in the sample to obtain a C' -epsilon curve;

(3) d in the step (1)²C/dz²And (3) comparing the calculated experimental value with the theoretical curve of C' -epsilon in the step (2) to obtain a final dielectric constant value.

Further, if the dc bias voltage in the step (1) is V, the electrostatic force between the probe and the sample capacitor is V

Where dC/dz is the first derivative of capacitance,

the electrostatic force microscope signal is proportional to the electrostatic force gradient, i.e.

Wherein f is₀Is the probe natural frequency, k is the probe stiffness coefficient, and dF/dz is the first derivative of the electrostatic force; obtaining the signal of the electrostatic force microscope in proportion to the second derivative d of the capacitance of the probe and the sample through the two formulas²C/dz²I.e. by

Or

Therefore, the experimental value of the second derivative of the capacitance of the probe and the sample can be obtained from the signal of the electrostatic force microscope.

Further, the probe and the sample are intercrossed in the step (2)Calculating the force by adopting an equivalent charge and mirror charge method; wherein the equivalent charges of the probe are distributed on the central axis, and N equivalent charges q are taken₁,q₂,…q_NPosition coordinate is r₁,r₂,…r_NThen the mirror charge in the sample with dielectric constant of epsilon is q₁',q₂',…q_N', the position coordinate is-r₁,-r₂,…-r_N；

The mirror charge is available q_i'＝-βq_iN, i is 1,2,. N; where β ═ e (e-1)/(e +1) is a parameter related only to the dielectric constant of the sample.

The probe is an equipotential body, the potential is direct current bias voltage V, and then N position points r on the probe boundary_kThe potential of (c):

wherein k is 1,2.. N; the above equation is a system of equations comprising N equations from which N equivalent charges q are solved_iA value of (d); after the charge amounts of the equivalent charge and the mirror charge are determined, the theoretical values of the sample and the electrostatic force are calculated as follows:

in the formula q_j'＝-βq_jAnd r_j'＝-r_jThe size and the position of the mirror image charge are shown, j and i in the subscript are distinguished to indicate that the sum needs to be respectively summed; by taking the derivatives of the above formula, the theoretical value of the first derivative of the applied force or the second derivative of the capacitance can be obtained

The first derivative of the acting force can be obtained by derivation of the formula,

then according toThe theoretical relationship between the second derivative of the capacitance and beta is obtained as

Finally, the second derivative d of the capacitance can be obtained according to the value of beta ═ epsilon-1)/(epsilon +1²C/dz²Theoretical relationship with the dielectric constant epsilon of the sample.

Further, the step (3) is to add d in the step (1)²C/dz²Experimental values and d in step (2)²C/dz²And comparing theoretical values to obtain a beta value corresponding to the experimental value, and obtaining the dielectric constant of the sample to be tested according to the beta ═ epsilon-1)/(epsilon + 1).

Further, the distance z between the probe and the sample in the step (1) is expressed as a direction perpendicular to the plane of the sample.

The invention provides a method for detecting dielectric constant of a dielectric sample under a micro-scale by using an electrostatic force microscope.

The method specifically comprises the following steps:

step (1), under the environment of 20 ℃ and 40% humidity, using a multi-mode atomic force microscope imaging system to perform testing, wherein a Nanoscope 3D multi-mode atomic force microscope imaging system of Bruker, Germany can be adopted, the scanning speed is 1Hz, and the scanning range is a square area with the side length of 0.75 mu m; the probe model used in the test is an SCM-PIT probe produced by the company, the curvature radius of the probe is 25nm, the half cone angle is 20 degrees, the length of the probe is 10 mu m, and the natural frequency of the probe is f₀74.7kHz and 2.8N/m of stiffness coefficient k, wherein the test sample is a P-type monocrystalline silicon material and has the resistivity of about 1 omega-cm; the electrostatic force microscope works in a non-contact mode, the distance between the probe and the surface of the sample is kept at z equal to 50nm, one side of the sample substrate is grounded, the conductive probe is externally applied with V equal to +4V direct current bias voltage,finally, outputting the offset delta f of the working frequency of the probe through a phase-locked loop feedback system; FIG. 1 shows the results of the test of this sample, showing that Δ f is-40.2. + -. 0.4Hz, and negative values indicate that the electrostatic force applied to the probe is an attractive force rather than a repulsive force; according to the formula

Calculating the experimental value of the second derivative of the capacitance as d²C/dz²＝3.77×10^-4F/m²。

Step (2), theoretically establishing a relation model of dielectric constant and probe-sample capacitance by using a mirror charge method; taking the case where the distance between the probe and the sample is 50nm, the dielectric constant of the sample is equal to 10 (in this case, β is 0.8182), 51 points (N is 51) are set in total for the equivalent charge in the probe, and the position r is taken as an example_iTabulated below (Table 1), the location of the mirror charge is-r_iA schematic diagram of which is shown in fig. 2; the surface potential of the conductive probe is equal to the applied direct current voltage, so the charge quantity q of the equivalent charge_i(or mirror charge q)_i'＝-βq_i) Can be represented by formula

Obtaining k is 1,2.. N, r_kRepresenting the position coordinates of any N points on the surface of the probe; calculated equivalent charge q_iAlso shown in Table 1, further based on capacitance formula

Calculating the second derivative d of the capacitance at the moment²C/dz²＝3.20×10^-4F/m²(ii) a By using the same method, the change condition of the second derivative of the capacitance when the dielectric constant of the sample is 3-15 can be calculated, and the calculation result is shown as a solid line in FIG. 3;

table 1, coordinates of equivalent charge and amount of charge when the sample dielectric constant is 10:

step (3), the experimental value of the second derivative of the capacitance obtained in the step (1) is 3.77 multiplied by 10^-4F/m²When compared with the theoretical relationship model, the dielectric constant of the single crystal silicon sample was 12.6 as shown by the broken line in fig. 3.

In conclusion, the capacitance of the probe-sample system is theoretically modeled by a mirror charge method, and the dielectric constant of the dielectric material is detected by utilizing a scanning probe microscopy technology on the basis. The method is simple in principle, can perform nondestructive characterization on a microscale, and is suitable for detecting various insulators or semiconductor materials with different dielectric constants.