JP5797446B2 - Surface charge distribution measuring method and surface charge distribution measuring apparatus - Google Patents

Description

  The present invention is a method and apparatus for measuring a charge distribution or potential distribution generated on the surface of a dielectric material with a high resolution on the order of microns, particularly on an electrophotographic photoreceptor, which has been extremely difficult with the prior art. The present invention relates to a method and apparatus for forming an electrostatic latent image under conditions equivalent to those occurring in an electrophotographic process and measuring the electrostatic latent image.

  As is well known, the electric charges are strictly scattered spatially in the sample. For this reason, the “surface charge” described here refers to a state in which the charge distribution state is largely distributed in the in-plane direction compared to the thickness direction. Note that the charge includes not only electrons but also ions. Further, there may be a state in which there is a conductive portion on the surface and a potential distribution is generated on or near the sample surface by applying a voltage to the conductive portion.

  As a method for observing an electrostatic latent image using an electron beam, there is a method described in Patent Document 1, but an LSI chip or an electrostatic latent image is stored as a sample to which the method described in Patent Document 1 can be applied. -Limited to samples that can be held. That is, a normal electrophotographic photoreceptor that causes dark decay cannot be measured. Since a normal dielectric can hold a charge semipermanently, even if measurement is performed over time after forming a charge distribution, the measurement result is not affected.

  However, in the case of an electrophotographic photosensitive member used in an image forming apparatus or the like, since the resistance value is not infinite, the electric charge cannot be held for a long time, and dark decay occurs and the surface potential increases with time. It will decline. The time that the photoconductor can hold the charge is at most several tens of seconds even in the dark room.

  Therefore, even if an electrostatic latent image formed by charging and exposing an electrophotographic photosensitive member is observed in an electron microscope (SEM), the electrostatic latent image disappears at the preparation stage. In addition, in the apparatus described in Patent Document 2, the wavelength used differs from the wavelength used by the electrophotographic photosensitive member by 4 digits or more, and an arbitrary line pattern, latent beam diameter and beam profile latency are obtained. It is impossible to form an image and the object of the present invention cannot be achieved.

  There are methods and measuring apparatuses that can measure an electrostatic latent image even for a photoreceptor sample that causes dark decay (see, for example, Patent Document 3 and Patent Document 4). The principle is as follows. If there is a charge distribution on the sample surface, an electric field distribution corresponding to the surface charge distribution is formed in the space. For this reason, the secondary electrons generated by the incident electrons are pushed back by this electric field, and the amount reaching the detector is reduced. Therefore, a portion where the electric field intensity is strong is dark and a weak portion is bright and contrasted, and a contrast image corresponding to the surface charge distribution can be detected. Therefore, when exposed, the exposed portion is black and the non-exposed portion is white, so that the electrostatic latent image formed in this way can be measured.

  Further, there is a method of measuring a latent image profile under a condition in which a region where the velocity vector in the sample vertical direction of incident charged particles is inverted exists (see, for example, Patent Document 5). By using this method, it is possible to visualize the latent image profile which has been difficult in the past on the order of microns. However, on the other hand, unlike a normal SEM, the trajectory of incident electrons changes due to a change in the space electric field due to the surface charge. Therefore, it is desirable to correct the startup change of the incident electrons in order to measure with high accuracy.

  As another conventional technique, there is a method of changing the deflection condition by predicting in advance the influence of the voltage applied to the sample, as in the inventions described in Patent Document 6, Patent Document 7, and Patent Document 8. However, when the sample to be measured has a charge or a potential distribution, the influence of the applied voltage cannot be predicted in advance because the bending of the incident electron trajectory is unknown.

  In addition, a method and an apparatus for calculating an electron trajectory and enabling high-precision measurement have been proposed (see, for example, Patent Document 9 and Patent Document 10). In this method and apparatus, the electron trajectory calculated by the simulation is collated with the actual measurement data, but it takes a long time to calculate the electron trajectory.

  Furthermore, a process is performed to convert the electrode potential of the conductor to an apparent charge density at the interface between the dielectric and the sample back electrode, and the direct electric field solution is obtained from the apparent charge density on the conductor and dielectric interface. There is a method using a calculation method (see Patent Document 11). According to this method, high calculation accuracy and short-time calculation can be realized. Therefore, this method can be applied to a shape limited to some extent, such as a similar shape when the aspect ratio of the charge distribution shape is fixed. However, for charge distribution shapes with complicated aspect ratios and distribution shapes, a large number of electron trajectories must be calculated, and further improvement in calculation speed has been demanded.

  To reduce the time required for calculation while ensuring high measurement accuracy, reduce the number of calculation steps required to determine the time interval of the electron orbit, reduce the number of electron orbits that need to be calculated, and compare with the results of the electron orbit calculation Improvement of fidelity of measured data is required.

  In view of the above, an object of the present invention is to provide a surface charge distribution measuring method and apparatus capable of reducing calculation time while ensuring high measurement accuracy.

The present invention is a surface charge distribution measuring method for measuring a surface charge distribution of a sample by scanning a sample having a surface charge distribution with a charged particle beam, and the sample is based on a configuration of an apparatus for measuring the surface charge distribution. A model setting step of setting a surface charge distribution model of the first and a differential value of the acceleration of the charged particle beam at the starting point based on the surface charge distribution model, and determining the next point based on the calculation result A trajectory calculation step of calculating a trajectory of the charged particle beam by setting a time interval from the time point to the time point of the next point, and a surface charge of the sample by a detection signal obtained by scanning the sample with the charged particle beam the measured obtaining a measured value of the distribution, the verification process of the value of the surface charge distribution model, matching with the actual value in the actual process, the in the verification step Error between the value of the surface charge distribution model and the measured value is the most important feature that and a determination step of employing the surface charge distribution model as the actual surface charge distribution is within a predetermined range.

  According to the present invention, it is possible to provide an apparatus for forming an electrostatic latent image on an electrophotographic photosensitive member under the same conditions as in an electrophotographic process and measuring the electrostatic latent image. Further, according to the present invention, it is possible to provide a surface charge distribution measuring method and apparatus capable of shortening calculation time while ensuring high measurement accuracy.

3 is a flowchart illustrating a method for measuring a surface charge distribution according to an embodiment of the present invention. It is a model figure which shows the example of the signal detection apparatus part which can be used for the measuring method and apparatus of the surface charge distribution which concern on this invention. It is a model figure which shows the example of the structure body model used in this invention. It is the model figure which looked at the structure model of FIG. 3 from the side. It is a model figure for demonstrating the apparent charge density of the electrode potential in the measuring method of the surface charge distribution which concerns on this invention. It is a figure which shows the coefficient matrix applied to the measuring method of the surface charge distribution which concerns on this invention. It is a model figure for demonstrating apparent charge density conversion of the conductor in the measuring method of the surface charge distribution which concerns on this invention. It is a graph for demonstrating the setting method of the conventional time interval. It is a flowchart which shows the calculation method of a time interval, (a) shows a present Example, (b) has shown the thing of a prior art example. In order to compare the results of the trajectory calculation with the present embodiment, the graph is shown with the Z coordinate as the horizontal axis, where (a) shows the time interval on the vertical axis and (b) shows the error amount on the vertical axis. It is a model figure which shows the example of the measuring apparatus of the surface charge distribution which concerns on this invention. It is a model figure which shows the relationship between the incident electron and sample which this invention utilizes. It is a graph and a model diagram showing the relationship between the detection signal intensity and the threshold potential Vth when a sample is scanned two-dimensionally. It is a block diagram which shows the information processing part of the surface charge distribution measuring apparatus of FIG. 11 in detail. It is a graph which shows the smoothing spline curve of the data containing an error. It is a graph which shows the curve approximation by a smoothing spline function, (a) shows the undesirable curve approximation, (B) shows the desirable curve approximation. It is a graph which shows the smoothing spline curve of the data which has an area | region where a discrete space | interval is wide. It is a graph which shows the smoothing spline curve created by adding a dummy point to the data which has an area | region with a wide discrete space | interval. It is a graph which shows the addition method of the dummy point by an elliptic equation. It is a model figure which shows the method of the boundary value determination by applied voltage determination. It is a model figure which shows the method of boundary value determination at the time of fixing an applied voltage. It is a flowchart which shows the calculation procedure of the threshold potential Vth which shows the electric charge distribution state of a sample. It is a model figure which shows the bending of the incident electron by the electric potential distribution of a sample. It is a graph which shows the example of the electric potential with respect to the distance from the center of a latent image. 3 is a flowchart illustrating a method for measuring a surface charge distribution according to an embodiment of the present invention. It is a model figure which shows another example of the surface charge distribution measuring apparatus which concerns on this invention. It is a graph which shows the relationship between acceleration voltage and charging, and acceleration voltage and charging potential. It is a perspective view which shows the example of the exposure part applicable to this invention. It is a conceptual diagram which shows the example of a Schottky emission type | mold electron gun.

  Embodiments of a charging characteristic evaluation method and a charging characteristic evaluation apparatus according to the present invention will be described below with reference to the drawings.

  Embodiments of a surface charge distribution measuring method and a surface charge distribution measuring apparatus according to the present invention will be described below with reference to the drawings.

  In the present invention, a calculation for obtaining the apparent charge density on the conductor and dielectric interface as a direct solution is used. Specifically, a known electrode potential is converted into an apparent charge density in the space to be analyzed using the geometrical arrangement of the conductor and dielectric structure model and the unknown charge density on the sample as boundary conditions. The spatial electric field is directly determined using the converted apparent charge density. Then, the charge density on the sample is determined while collating the calculated electron orbit simulation calculation data with the measured detection signal data.

  An example of a flow for determining the surface charge and potential distribution is shown in FIG. In FIG. 1, step S1 is a structure model setting, step S2 is an electrode potential setting, step S3 is a surface charge setting, step S4 is an apparent charge density conversion, step S5 is a spatial electric field calculation, step S6 is a time interval setting, step S7 is simulation calculation, and step S8 is collation with actual measurement data. If this collation matches, the process proceeds with the determination of the surface charge in step S9 and the calculation of the surface charge distribution or surface potential in step S10. If it is determined in step S7 that there is a mismatch, the process proceeds to surface charge model correction in step S11, and the process returns to the apparent charge density conversion again in step S4. Each step will be described in detail later.

  In addition, a coefficient matrix determined from the geometrical arrangement of the conductor and dielectric placed in the space to be analyzed is obtained, and the electric field potential coefficient matrix, the potential of the conductor and the charge density on the dielectric interface are used as boundary conditions. , N-ary simultaneous linear equations may be solved. Specifically, the following method is used.

  First, a structure model is set (see FIGS. 3 and 4). FIG. 2 shows a configuration of a measuring device that detects a signal. In FIG. 2, a plate-like insulator 102 made of an insulator is laminated on the upper surface of a grounded plate-like conductor substrate 101, and a conductive plate 103 is laminated thereon to form a sample mounting table. A voltage Vsub is applied to the conductive plate 103 and a photoconductor 110 as a material is placed thereon. An electron beam 104 is irradiated from above toward the photoconductor 110. An objective lens 105 is disposed in the path of the electron beam 4 and is adjusted so that an electron beam having an appropriate cross-sectional shape is irradiated onto the photoconductor 110. A grid mesh 106 is disposed in the vicinity of the upper portion of the photoconductor 110. A detector 107 that detects electrons returning from the photosensitive member 110 repelled by the electron beam 4 is disposed obliquely above the grid mesh 106.

  The shape and film thickness of the sample (photosensitive member), the electrode shape on the back surface of the sample, and the conductor and dielectric near the sample are factors that have a particularly large influence on the electron trajectory. Therefore, these are geometrically arranged (step S1). If necessary, the position of the detector, the configuration of the electron beam optical system, the characteristics of each optical component constituting the electron beam optical system, and the like may be taken into consideration. The dielectric sets the dielectric constant and sets the voltage applied to the conductor. Since the structure at a position away from the sample has less influence on the electron trajectory, it may be simplified or omitted. In the next step, the electrode potential on the back surface of the sample used in the actual measurement is set (step S2).

  In the next step, a charge density distribution is set on the sample surface (step S3). Since the initially set surface charge distribution is changed in comparison with the measurement data, any value may be used. It is desirable that the value be as close as possible to the expected value. The closer to the actually measured value, the shorter the convergence time.

ここで、σ（Ｒ）は、導体面Ｓ上に分布する電荷密度である。 In the next step, the electrode potential applied to the conductor is converted into an apparent charge density only at the sample boundary surface (step S4). Here, the “apparent charge density” refers to the charge density given to the boundary surface of the structure “becomes an equivalent electromagnetic field environment” to the electrode potential given to the conductor. As shown in FIG. 5A, when there is a conductor to which a potential is applied at the coordinate R in the xyz space, the electrostatic potential φ (R0) at the point R0 in the space can be expressed by the equation (1). it can.

Formula (1)

Here, σ (R) is a charge density distributed on the conductor surface S.

そうすることで、既知の電極電位とみかけの電荷密度の関係を、図６（ａ）で示す行列式で表すことができる。ここで、上記行列式の左辺のうちφ１〜φｍが導体面上の既知電位であり、σｒは最終的に計測すべき表面電荷密度である。σｒは、照合前の電荷密度が入力されているため、左辺は既知である。右辺のσは、見かけ電荷密度であり、そのうちσ１〜σｍが導体面上の見かけ電荷になる。 In the calculation, the boundary region is divided into a small area ΔSi (see FIG. 5B). The charge density within a very small area is approximately set to σi, and this is made constant. The electrostatic potential φ (Rj) at the point Rj in space can be expressed by equation (2).

Formula (2)

By doing so, the relationship between the known electrode potential and the apparent charge density can be expressed by the determinant shown in FIG. Here, among the left sides of the determinant, φ1 to φm are known potentials on the conductor surface, and σr is the surface charge density to be finally measured. Since σr is inputted with the charge density before collation, the left side is known. Σ on the right side is the apparent charge density, and σ1 to σm among them is the apparent charge on the conductor surface.

The coefficient matrix Fji, which is an element of the coefficient matrix, is determined from the geometrical arrangement of the conductors and dielectrics arranged in the space to be analyzed, and calculates the equations shown in FIGS. 6B and 6C. Can be realized. here,
Rj: sample point δji on conductor surface or dielectric surface at coordinates (xj, yj, zj): Kronecker delta nj: normal vector of element j ε0: vacuum dielectric constant ε1: dielectric constant ε2 outside dielectric interface: It is the dielectric constant inside the dielectric interface.

  Accordingly, a coefficient matrix Fji including a geometrical arrangement of conductors and dielectrics arranged in a space to be analyzed is determined, and the matrix is determined using the coefficient matrix, the potential of the conductors, and the charge density on the dielectric interface as boundary conditions. The apparent charge density can be obtained by solving the equations using simultaneous linear equations and inverse matrix operations. In this way, the known electrode potentials φ1 to φm can be converted into the apparent charges σ1 to σm (see FIG. 7). This conversion operation corresponds to step S4 shown in FIG.

  Next, a spatial electric field is calculated from the apparent charge density obtained (step S5 in FIG. 1). Since the electric field at an arbitrary point in space is used when calculating the electron trajectory, the calculation accuracy of the electron trajectory depends on the calculation accuracy of the electric field. Therefore, the calculation accuracy of the electric field is important, and the calculation accuracy of the electric field is required to be high.

得られた微小面積毎の見かけの電荷を面積分することで、空間電界Ｅを計算することができる。このようにして、高精度に電子軌道を計算する。 In the present invention, the apparent charge density on the conductor and dielectric interface is determined, so that the electric field at any point in space uses the apparent charge density to divide the conductor and dielectric interface. Thus, the equation of motion of electrons can be obtained directly. The following equation (3) is an equation indicating the electric field at an arbitrary point in the space calculated by the apparent charges σ1 to σn.

Formula (3)

The spatial electric field E can be calculated by dividing the apparent charge for each minute area obtained. In this way, the electron trajectory is calculated with high accuracy.

  By the way, the electric field calculation is a time-consuming process, and it is important to reduce the time required for the electric field calculation in order to shorten the calculation time of the surface charge distribution and improve the calculation accuracy.

  Conventionally, in an electron orbit calculation program, it has been common to calculate with a constant time step of the electron orbit. In this case, since the time interval is set in accordance with a place where the spatial electric field changes drastically, the time interval is set to be short, resulting in wasteful calculation. If the time interval is increased to shorten the calculation time, the calculation accuracy is greatly reduced. That is, it is not easy to achieve both calculation time and calculation accuracy. It is desirable to set the time interval appropriately according to the electric field environment.

  As shown in FIG. 8, in the method described in Patent Document 11, the time interval is set to Δt when the starting point is P0 as the electron trajectory calculation for solving the equation of motion of the charged particle from the apparent charge density. Then, the coordinate P1 after Δt from the starting point P0 when the electron trajectory is calculated and the coordinate P2 when the electronic trajectory is calculated with the time interval set to 1/2 × Δt are once again set as the time interval 1/2. Calculate the relative error between the starting point P0 and the coordinate P3 after Δt when the electron trajectory is calculated with × Δt, and the time interval is appropriately determined according to the magnitude of the change in the spatial electric field based on the determination result. The electron orbit was calculated.

  This method is certainly an effective means for shortening the time, but when calculating the electron trajectory in one step, if the time interval is changed at least three times to set one time interval, In addition, many times the electron trajectory had to be calculated, and there was room for improvement in order to shorten the calculation time.

における電子の加速度の微分値から時間間隔Δtを算出する算定式を考案した。なお、この動作は図１に示すステップＳ６に該当する。

式（４）

但し、

式（５）

なお、

Therefore, in this embodiment, where the differential value of the acceleration of the electron is large, the law is found that it is desirable to calculate with a small time interval, and the electronic position is found.

We have devised a calculation formula to calculate the time interval Δt from the differential value of the acceleration of electrons in. This operation corresponds to step S6 shown in FIG.

Formula (4)

However,

Formula (5)

In addition,

The electron velocity may be such that the differential value of the acceleration of the electron is not more than ε times the electron velocity. ε is a weighting factor. When ε is small, the time interval is shortened and the calculation accuracy is improved, but the calculation time is increased accordingly. Although it depends on the requirements of calculation time and calculation accuracy, it is generally preferable that ε = 5e ⁻⁹ or more and 5e ⁻⁵ or less.

  By accelerating the molecule to the electron velocity, the unit system of the physical quantity on the right side can be made the unit of “time”.

  FIG. 9A shows a time interval setting flow of the present invention, and FIG. 9B shows a conventional time interval setting flow.

  In the conventional method, as shown in FIG. 9B, there are a step of calculating electric field calculation at least three times and a step of determining an error. Specifically, first, the time interval is set to Δt, and the electron trajectory is calculated in only one step. Next, under the same conditions, the time interval Δt is halved and the same calculation is performed in two steps. The time interval Δt is dynamically varied from these two results and calculated.

  This method will be described in detail. When the next step position (Xi + 1, Yi + 1, Zi + 1) is calculated from the position of the starting point P0 (Xi, Yi, Zi), the coordinates obtained by the calculation of the first step at the time interval Δt. P1 (Xa, Ya, Za) (this is defined as (a) calculation), and the coordinate P2 when the electron trajectory is calculated at Δt / 2 which halved the time interval is set as a new starting point, and the time interval is once again The coordinates P3 (Xb, Yb, Zb) (defined as (b) calculation) obtained by the calculation of the second step for calculating the electron trajectory at 1/2 × Δt are compared, and both are compared with the respective coordinates. The value is evaluated by relative error P3-P1. If these errors are smaller than the set accuracy, (Xb, Yb, Zb) is adopted as the solution (Xi + 1, Yi + 1, Zi + 1). Then, the value of Δt is doubled from the calculation in the next step, and (a) calculation and (b) calculation are executed again. On the other hand, if the accuracy is less than the accuracy, the same calculation is performed once again by halving the time interval Δt and performing both the calculations (a) and (b). If the accuracy is still not reached, the time interval is halved again and both calculations (a) and (b) are executed.

  In this way, the time interval Δt is halved until the set accuracy is reached, and when the set accuracy is reached, the value of (Xb, Yb, Zb) is adopted as the solution (Xi + 1, Yi + 1, Zi + 1). To do. Even when the time interval Δt is doubled, the calculation accuracy is determined. If the set accuracy is not reached, the time interval Δt is immediately reduced to half and the calculation is restarted. By doing so, it is possible to cope with the case where a predetermined accuracy cannot be obtained because the step width is doubled.

  Further, not the position but the absolute value of the vector may be used for the relative error determination. By doing so, even if the solution crosses zero, it is possible to correctly determine the error, and the trajectory calculation can be executed efficiently while maintaining a certain accuracy. By setting an appropriate step time (Δt) by such a method, it becomes possible to calculate the electron trajectory with high accuracy and high speed.

  On the other hand, in the method according to the embodiment of the present invention, the electric field calculation is performed only once, and no branch for determining the error is required. Specifically, the electric field at the initial position (starting point) is calculated in step S41, the velocity of electrons at the starting point is calculated in step S42, the differential value of the acceleration at the starting point is calculated in step S43, and the next point is calculated in step S44. The step time (time interval) is calculated. By using such a method, it is possible to reduce the time interval calculation process to 1/3 or less of the conventional method.

The equation of motion of charged particles is

Formula (6)
F = qE
And the acceleration of electrons is

Formula (7)
F = mα
It is represented by

  Since the relationship of α = q / mE is established from the equations (6) and (7), the acceleration of electrons can be easily calculated if the above-described spatial electric field E is known.

  By the way, although the frequency is very rare stochastically, the differential value of the acceleration of the denominator of Equation 4 may become zero. When the differential value of acceleration approaches 0, the denominator becomes 0, which may be caused by the time interval diverging.

In order to solve this inconvenience, an average acceleration differential value before and after the starting point may be calculated. As shown in Equation 10, the probability of occurrence can be greatly reduced by taking an average using the differential value of the acceleration of the electron at the previous coordinate P _i−1 .

Formula (8)

ここで、 Ｑｍａｘ＝７．３５５ｅ^−４（Ｃ／ｍ^２） ＱＤ＝３．０ｅ^−４（Ｃ／ｍ^２） σｘ＝４．０ｅ^−５（ｍ） σｙ＝５．６６ｅ^−５（ｍ） α＝１．４ Ｖｓｕｂ＝１１００Ｖ Ｖａｃｃ＝１．８ｋＶ ε＝５ｅ^−７である。 If Δt takes an abnormally large value, the factor of diverging can be further reduced by using a method of averaging at three or more points including the previous value. However, in this case, since the reaction time is gradually dull, it is desirable to optimize according to the conditions. FIG. 10 shows the result of calculation using the equation (8). The result of the electron trajectory analysis from the position of x = 100 μm 35 mm above the sample surface is a comparison between the method according to this example and the conventional method. In the calculation of the charge density distribution, the following functional formula was used.

Formula (9)

Here, Qmax = 7.355e ⁻⁴ (C / m ² ) QD = 3.0e ⁻⁴ (C / m ² ) σx = 4.0e ⁻⁵ (m) σy = 5.66e ⁻⁵ (m) α = 1.4 Vsub = 1100 V Vacc = 1.8 kV ε = 5e ⁻⁷ .

  As the horizontal axis approaches the sample (z = 35) in the z-coordinate, it is common in that the electric field change is large and the time interval is shortened. However, the surface charge distribution measurement method according to the present invention is adapted to the electric field change. You can see that it is finely set.

FIG. 10B shows the relationship between the z coordinate and the set error amount. The amount of error is the difference from the total energy of the previous step on the assumption that the energy conservation law holds when the sum of kinetic energy (1/2 mV ² ) and potential energy (eV) is the total energy (En). It is expressed by (ΔEn). As shown in FIG. 10B, the error amount is greatly reduced in the surface charge distribution measuring method according to the present invention as compared with the conventional method. This indicates that the time step is set appropriately. It can be seen that the present invention not only shortens the calculation step but also improves the calculation accuracy.

  As described above, it was confirmed that both the calculation time and the calculation accuracy were improved as compared with the conventional surface charge distribution measuring method. Under the above conditions, the calculation time was 30 seconds and the error was about 1V. The charge density distribution function formula is not limited to Formula 11, and any formula that can be expressed by a function formula close to the measurement object can be used.

  Next, a means for detecting a signal by scanning a charged particle beam on a sample having a surface charge distribution will be described.

  FIG. 11 shows the configuration of a measuring device that detects a signal. In FIG. 11, the measurement apparatus includes a charged particle irradiation unit that irradiates a charged particle beam, and a detection unit such as an exposure unit, a sample placement unit, primary inverted charged particles, secondary electrons, and reflected electrons as main components. Yes. The charged particles herein refer to particles that are affected by an electric field or a magnetic field, such as an electron beam or an ion beam.

  The embodiment described below is an example in which an electron beam is irradiated. In FIG. 11, the measuring device includes a charged particle beam irradiation device 108. The charged particle beam irradiation apparatus 108 is configured by incorporating components into the vacuum chamber 140 as follows. An electron gun 141 that irradiates a charged particle beam is attached near the upper end of the vacuum chamber 140, and an extractor, that is, an extraction electrode 143, an acceleration electrode 144, a condenser lens 145, a beam blanking electrode 146, a gate valve 147, movable below the electron gun 141. A diaphragm 148, a stigmator, that is, a correction electrode 149, a deflection electrode (corresponding to a scanning lens) 150, an electrostatic objective lens 151, and a beam exit aperture 152 are arranged in this order.

  The extraction electrode 143 controls the electron beam, the acceleration electrode 144 controls the energy of the electron beam, and the condenser lens 145 focuses the electron beam generated from the electron gun. The beam blanking electrode 146 turns on / off the electron beam, and the gate valve 147 and the movable aperture 148 function as an aperture for controlling the irradiation current of the electron beam. The deflection electrode 150 functions as a scanning lens for scanning the electron beam that has passed through the beam blanking electrode 146. The electron beam that has passed through the deflection electrode 150 is again converged on the surface of the photoreceptor sample 110 by the objective lens 151. A driving power source (not shown) is connected to each lens.

  Below the charged particle beam irradiation apparatus 108, a mounting table for mounting a photoconductor 110 as a sample is disposed. The mounting table can be configured in the same manner as described in FIG. In the vacuum chamber 140, a detector 107 that detects electrons repelled by the photoconductor is disposed near the upper portion of the photoconductor 110. The detection signal output from the detector 107 is subjected to measurement of the surface charge distribution of the photoconductor 110 by passing through a detection circuit, detection signal processing means, and the like.

  When an ion beam is used as the charged particles, a liquid metal ion gun or the like is used instead of the electron gun 141. A scintillator, a photomultiplier tube, or the like can be used as the detector 107 that detects primary inversion electrons.

  FIG. 12 shows the relationship between incident electrons and a sample in signal detection. There is a region where a state in which the velocity vector of the incident charged particles in the sample vertical direction reverses before reaching the sample, and the primary incident charged particles are detected. If the acceleration potential of the electron is Vacc and the potential potential of the sample surface is Vp, the incident electron reaches the sample and the electron does not return depending on the magnitude relationship between Vacc and Vp, and the incident electron is repelled by the sample. May return. Note that the acceleration voltage is generally expressed as positive, but the applied voltage Vacc of the acceleration voltage is negative and has a physical meaning as a potential potential. Is expressed as negative (Vacc <0). The acceleration potential of the electron beam is Vacc (<0), and the potential potential of the sample is Vp (<0).

  A potential is the electrical potential energy of a unit charge. Therefore, incident electrons move at a speed corresponding to the acceleration voltage Vacc at a potential of 0 (V), but the potential increases as the distance to the sample surface approaches, and the speed changes due to the influence of Coulomb repulsion of the sample charge. . Therefore, the following phenomenon generally occurs.

  In the case of | Vacc |> | Vp |, the electron reaches the sample although its speed is reduced (see FIG. 12A).

  In the case of | Vacc | <| Vp |, the velocity of the incident electrons is gradually decelerated under the influence of the potential potential of the sample, the velocity becomes zero before reaching the sample, the moving direction is reversed, and the opposite direction is reached. Proceed (see FIG. 12B).

  In a vacuum with no air resistance, the energy conservation law is almost completely established. Therefore, the potential on the surface of the photosensitive member sample can be measured by measuring the condition where the energy on the sample surface when the energy of the incident electrons is changed, that is, the landing energy is almost zero. Here, the case of primary inversion charged particles, particularly electrons, will be referred to as primary inversion electrons. The secondary electrons generated when the sample reaches the sample and the primary inversion charged particles differ greatly in the amount reaching the detector, so that they can be distinguished from the border of contrast between light and dark (see FIG. 13).

  A scanning electron microscope or the like has a backscattered electron detector. In this case, the backscattered electrons are generally reflected (scattered) on the rear back surface by the interaction with the material of the sample, and the sample. It refers to the electrons that jump out of the surface. The energy of the reflected electrons is comparable to the energy of the incident electrons. The intensity of the reflected electrons is said to increase as the atomic number of the sample increases, and this is a detection method for observing the difference in the composition of the sample and the unevenness. In contrast, primary inversion electrons are electrons that are affected by the potential distribution on the sample surface and reverse before reaching the sample surface, and are used in backscattered electron detectors such as a scanning electron microscope. This is a completely different phenomenon.

Therefore, by changing the acceleration voltage Vacc or the electrode potential Vsub on the back of the sample while scanning the sample surface with electrons and detecting the incident electrons with a detector, the surface potential Vp of the sample can be measured. Become.
Further, when the potential potential Vp of the sample is positive (Vp> 0), positive ions such as gallium and protons may be incident as charged particles.

Thus, when the potential distribution of the sample is Vp (x), the acceleration voltage Vacc is
Min | Vp | ≦ | Vacc | ≦ Max | Vp |
By scanning the sample with the acceleration voltage Vacc of the charged particle within the range, the state where the velocity vector in the sample vertical direction of the incident charged particle is inverted exists, and by detecting the inverted primary inverted charged particle Information on the surface charge distribution of the sample can be acquired.

  The detection signal obtained by scanning the charged particle beam is collated with the result of the electron trajectory simulation when the surface charge is applied (step S8 in FIG. 1). It is determined that the surface charge value used in the electron orbit simulation is an actual value (step S9 in FIG. 1). If it is out of the allowable range, the surface charge is corrected (step S11 in FIG. 1), and the electron orbit simulation is repeatedly executed from the conversion of the apparent charge density (step S4 in FIG. 1) until it falls within the allowable range. To do.

  In this way, the surface charge can be determined by calculating the electron trajectory and collating it with the actual measurement result. When the surface potential is measured, the electrostatic field is determined if the charge distribution is known. Therefore, the physical quantity distribution such as the potential distribution V (x, y) and the electric field strength distribution is measured by solving the electrostatic field such as the Poisson equation. be able to.

  By the way, since the measured detection signal data is discrete, it is necessary to interpolate between the discrete data in order to collate with the simulation result. The measured detection signal data includes a normal error. Depending on the degree of these errors, if you try to interpolate these data using normal linear interpolation or spline functions, the curve will be reproduced in each section in an attempt to faithfully reproduce the data including that error. It becomes vibrational and results away from the true result. If a natural smoothing curve can be drawn in consideration of the above, a more accurate simulation can be expected.

  Here, there is a least square approximation as a conventional method, but the least square approximation reproduces a curve with one function of a certain order over the entire interval. That is, a law property is required so that the measured detection signal data can be expressed by one function. However, it is theoretically impossible to derive a law property that can be expressed by a single function in the measured data. For example, even if the shape is relatively close, if it is forcibly expressed by an existing function like a Gaussian distribution, the error will be enormous because it does not match the actual measurement environment.

  Therefore, the entire measured data becomes a continuous curve function by expressing each section with a polynomial function so that adjacent sections of the measured detection signal data obtained discretely are connected continuously. It is preferable to perform the smoothing calculation as described above.

の多項式関数で近似し、ｘ_ｉからｘ_ｉ＋１の範囲［ｘ_ｉ，ｘ_ｉ＋１］では

式（１１）

という別の多項式関数で近似する。そして、その微分値が等しくなるようにする。

式（１２）

式（１３）

ただし、ｘ＝ｘｉ＋０はｘ＞ｘｉ側の極限値を、ｘ＝ｘｉ−０はｘ＜ｘｉ側の極限値を示している。 An example of such a polynomial function is a smoothing spline function. Specifically, the measured detection signal data points are represented by N of (x ₀ , y ₀ ), (x ₁ , y ₁ )... (X _i , y _i ) (X _n−1 , y _n−1 ). For example, in the range [x _i-1 , x _i ] from x _{i -1} to x _i ,

Formula (10)

In the range [x _i , x _{i + 1} ] from x _i to x _{i + 1}

Formula (11)

Approximate with another polynomial function. The differential values are made equal.

Formula (12)

Formula (13)

However, x = xi + 0 indicates the limit value on the x> xi side, and x = xi-0 indicates the limit value on the x <xi side.

なお、ｆ^（Ｍ）（ｘ）は、ｆ（ｘ）のＭ回微分である。ｇは平滑化係数であり、ｇが大きいと、元のデータに対する忠実度が低く、ｇが小さいと元データに対する忠実度が上がるが、振動する可能性が出てくる。 The actual calculation may be expressed by a smoothing curve function f (x) that minimizes the value of σ in Expression 16.

Formula (14)

Note that f ^(M) (x) is M times differentiation of f (x). g is a smoothing coefficient. When g is large, fidelity to the original data is low, and when g is small, fidelity to the original data is increased, but there is a possibility of vibration.

  The smoothing spline function can be calculated by using a calculation formula that satisfies such conditions. An example of the calculation result is shown in FIG.

  In this way, it is possible to reproduce the shape of the detection signal data that is discrete and includes an error with the most suitable curve and express it as a function of a smoothed continuous curve. The smoothing spline function can flexibly and accurately correspond to curve data of various shapes of measured detection signal data.

  By the way, there is a problem that the measured detection signal data is discrete and includes errors, and the interval between the discrete data is not always constant. There is a concern that an abnormal value is exhibited in a place where the discrete interval is wide.

  More specifically, the measured detection signal data should be expressed by a function of a curve as shown in FIG. 16B, but the smoothing described above as shown in FIG. When interpolating with the normalized spline, as shown in FIG. 17, there is a case where the actual measurement data is lost and an unnatural vibration occurs in a region where the discrete interval is wide. As a result, a maximum value exists in the middle of the data, not at both ends, and a large error may occur with actual measurement.

  However, in spite of the fact that the spline function is unavoidable in an area with a large discrete interval, it is inevitable due to the nature of the spline function. is there.

  In particular, in the detected signal data that is measured, the data from the rise of the Vth distribution to the asymptotic tendency tends to be lost.

  In order to solve these problems, as shown in FIG. 18, it is preferable to add a dummy point to an area having a wide discrete interval. In this case, the regularity of the measured detection signal data may be used. That is, it is known that the measured detection signal data has a regularity that monotonously increases with distance from the center of the charge distribution sample and has maximum values at both ends. Therefore, it is desirable to add a dummy point using a function having the law that is most fitted to a portion where the discrete interval is wide. For example, an exponential function such as a Gaussian function, a logarithmic function, or a part of a trigonometric function may be used. Here, a method for adding a dummy point using an elliptic equation will be described.

両辺をxで微分して整理すると、式（１６）となる。

式（１６）

The elliptic equation at this time is shown in Equation 15.

Formula (15)

When both sides are differentiated by x and arranged, Expression (16) is obtained.

Formula (16)

  As shown in FIG. 19, the tangent line at (x1, y1), (x1, y1) becomes a straight line passing through (x0, y0), (x1, y1), and the slope of the tangent line at (x2, y2) is An ellipse that becomes 0 is applied to determine the coefficients a, b, c, and d, and dummy points are added along the ellipse. A feature in which dummy points are added along the elliptic equation is characterized in that a natural curve can be obtained without a steep change because a slope can be specified.

  FIG. 16B shows the result of smoothing spline processing after adding dummy points to the measured detection signal data along the elliptic equation.

  By placing the dummy points along the elliptic equation that satisfies the above-described conditions, it is possible to suppress the vibration as shown in FIG. 16A and obtain a smoothing spline result faithful to the data. And it becomes easy to collate with simulation data, and it becomes possible to improve accuracy and reduce time.

  Since the amount of electrons reaching the detector differs depending on whether or not incident electrons reach the dielectric surface, the surface charge state can be estimated by detecting the boundary value. A boundary value between the sample inversion region and the sample arrival region is calculated from the electron trajectory calculation by detecting the boundary between the region where the primary charged particles are reversed without reaching the sample and the region where the sample reaches the sample.

  In the calculations so far, the applied voltage on the back of the sample is fixed and the coordinates of the incident charged particle trajectory are changed to calculate the spatial boundary value. However, a large number of calculations are required to identify the spatial position. In addition, all the results of the analysis may reach the sample, or all of the sample may be inverted. Under such conditions, a result cannot be obtained unless the calculation is performed to the end, and the boundary position cannot be calculated even in the final result, resulting in a useless calculation and a long calculation time.

  Therefore, the boundary value between the sample reversal region and the sample arrival region is calculated from the electron trajectory calculation by detecting the boundary between the region where the primary charged particles are reversed without reaching the sample and the region where the primary charge particles reach the sample. That is, the charged particle trajectory is calculated by setting the applied voltage between the applied voltage at which the charged particle beam reaches the sample and the applied voltage at which the charged particle beam is reversed without reaching the sample as a new applied voltage. To calculate the boundary value between the sample arrival region and the sample inversion region.

  Specifically, the incident start coordinates of the primary charged particles are fixed, and the applied voltage on the back surface of the sample under the condition that the primary charged particles reach the sample is reversed without Vsub1 and the primary charged particles reaching the sample. When the applied voltage on the back surface of the sample under non-reaching conditions is Vsub2, the boundary value is determined to be between Vsub1 and Vsub2, as shown in FIGS. 20 (a) and 20 (b).

  Further, the boundary value is narrowed down using the following method. As shown in FIG. 20 (c), the electron trajectory is calculated using the intermediate point (Vsub1 + Vsub2) / 2 between Vsub1 and Vsub2 as a new applied voltage Vsub3 on the back surface of the sample.

Then, as shown in FIG. 20D, when the primary charged particle trajectory reaches the sample under the Vsub3 condition, the following value is given as a new applied voltage Vsub4 on the back surface of the sample.
Vsub4 = (Vsub2 + Vsub3) / 2

As shown in FIG. 20E, when the primary charged particle orbit is reversed without reaching the sample under the Vsub3 condition, the following value is given as a new applied voltage Vsub4 on the back surface of the sample.
Vsub4 = (Vsub1 + Vsub3) / 2

  By repeatedly executing the above operation, the interval between the injection positions can be reduced by ½ in one trajectory calculation. Then, the problem that the analysis results are all in the region where the sample reaches the sample or the region where the sample is inverted is solved, the boundary value can be narrowed down with a small number of trajectory calculations, and the calculation time can be greatly shortened. In this method, a charge model with a small charge density near the center and a charge model with a large charge density around the periphery, such as around the charge distribution when the charge model is assumed to be measured, Thus, this is particularly effective because the number of trajectory calculations is reduced in a region where the horizontal electric field is small. That is, it can be said that it is particularly effective when calculating the maximum value and the minimum value of the applied voltage Vsub.

  Note that, between the maximum value and the minimum value of the applied voltage Vsub, the spatial boundary value may be calculated by fixing the applied voltage on the back surface of the sample and changing the coordinates of the incident charged particle trajectory. In other words, the incident start coordinate parallel to the sample surface under the condition that the primary charged particle is reversed without reaching the sample is xi, and the incident start coordinate parallel to the sample surface under the condition where the primary charged particle reaches the sample is xj. Then, the boundary value is determined by repeating the electron trajectory calculation using the intermediate point (xi + xj) / 2 between xi and xj as the incidence start coordinate.

  Assuming that there is a reflection region between the electron trajectory at the injection position reaching the sample and the electron trajectory at the injection position by reversing before reaching the sample, electrons are injected from the injection position between them and the reflection region is further narrowed down. By repeatedly executing the above operation, the interval between the injection positions can be reduced by ½ in one trajectory calculation.

  As shown in FIG. 21A, since the electron trajectory of xj reaches the sample and the electron trajectory of xi is reversed, a boundary value exists between xi and xj. Therefore, as shown in FIG. 21B, new electrons are injected from the emission position between the electron trajectories xi and xj, and the position of the boundary value is narrowed down depending on whether or not the electrons reach the sample.

  As described above, when the applied voltage on the back surface of the sample is fixed, the coordinate of the incident charged particle trajectory is changed, and the method is used in combination with the method of calculating the spatial boundary value, it is effective in shortening the calculation time.

  In the surface charge distribution measuring method according to the present embodiment, the surface charge distribution of the sample calculated by the surface charge distribution measuring method according to each of the embodiments described above is used as the threshold potential Vth (x, Since correction is performed using y), the surface charge distribution can be obtained with higher accuracy. Hereinafter, only the correction of the surface charge distribution using the threshold potential Vth (x, y) will be described, and the calculation of the surface charge distribution prior to the correction is the same as in each of the embodiments described above. Is omitted.

The threshold potential Vth is Vacc as the acceleration voltage of the electron beam and Vsub as the voltage applied to the conductor.
Vth = Vacc−Vsub
It is a value represented by the expression. Vth (x, y) represents the value of Vth at the coordinates (x, y) on the sample surface.

  First, a method for obtaining Vth (x, y) by measurement will be described. FIG. 23 shows the result of measuring Vth (x, y) by signal detection. The acceleration voltage of the electron gun that scans two-dimensionally is set to −1800V. The curve in FIG. 23A shows the detection result of the Vth distribution generated by the charge distribution on the sample surface. The Vth value at the center (x = y = 0) is about −600V. This indicates that the center landing energy is almost zero when Vsub = −1200V.

  Further, the Vth value increases in the negative direction from the center toward the outside, and the Vth value in the peripheral region exceeding the radius of 75 μm from the center is about −850V. The ellipse shown in FIG. 13B is an image of the detector output when the back surface of the sample is set to Vsub = −1150V. At this time, Vth = Vacc−Vsub = −650V. The ellipse shown in FIG. 13C is an image of the detector output obtained under the same conditions as above except that Vsub = −1100V. At this time, Vth is -700V.

  The bright part and the dark part in FIGS. 13B and 13C represent the difference in the detection signal intensity, and the bright part indicates that the detection signal amount is larger. That is, the bright part is an area where the incident electrons are reversed without reaching the sample, and the dark part is an area where the incident electrons reach the sample. The boundary between the bright part and the dark part indicates that the landing energy is almost zero.

  The boundary value between the bright part and the dark part is defined as a Vth value, and Vth (x, y) is measured by using a method of repeatedly scanning the sample surface with electrons while changing the acceleration voltage Vacc or the applied voltage Vsub. Data can be acquired on a micron scale.

  A flow of Vth (x, y) measurement by signal detection is shown in FIG. That is, the threshold potential Vth is set (S51), the contrast image is captured (S52), the binarization process (S53), and the latent image diameter calculation (S54), and the process up to this point is performed until a predetermined number of times (S55, S57), Vth (x, y) is calculated (S56).

Next, a method for obtaining Vth (x, y) by simulation will be described. The primary charged particles are incident on the sample at an acceleration voltage Vacc (<0) from an initial coordinate z0 away from the sample surface. As the simulation condition at that time, when the applied voltage on the back surface of the sample is Vsub, it is determined whether the trajectory of the primary charged particles is reversed without reaching the sample or reaches the sample, and the primary that becomes the boundary is determined. Determine the initial coordinates (x0, y0, z0) of the charged particles;
Vth (x0, y0) = Vacc−Vsub
It is said.

  The simulation model shown in FIGS. 3 and 4 and an unknown surface charge are set to calculate the trajectory of the primary charged particle. The applied voltage on the back side of the sample is Vsub.

  Here, electrons are used as the primary charged particles. The condition may be that the light enters the sample perpendicularly from a distance z0 away from the sample surface. It is desirable to arrange z0 so that it is farther than the distance from the upper grid to the sample. An initial coordinate and an acceleration voltage are applied to the incident electrons as Vacc (<0) or an initial velocity equivalent to Vacc, and is incident on the sample.

  Although it may be analyzed whether or not the trajectory of the incident electrons finally reaches the detector, in this case, the time required for calculation increases. On the other hand, sufficient accuracy can also be obtained by a method of determining whether the incident electrons are reversed without reaching the sample or whether the sample reaches the sample.

Therefore, it is determined whether the trajectory of the primary charged particle is reversed without reaching the sample or the sample, and the initial coordinate (x0, y0, z0) of the primary charged particle serving as the boundary is determined.
Vth (x0, y0) = Vacc−Vsub
The boundary region can be determined as follows. In this way, Vth (x, y) equivalent to Vth (x, y) obtained from the detection signal can be calculated.

  In the following, for convenience, Vth (x, y) calculated is distinguished from Vth_s (x, y), and Vth (x, y) measured is distinguished from Vth_m (x, y). As an example, FIG. 24A shows the relationship between the surface potential calculated in the X-axis direction and the scanning position. Check if Vth_s (x, y) is equal to Vth_m (x, y). As a method for collation, a method for obtaining a difference (Δ (x, y)) between Vth_s (x, y) and Vth_m (x, y) may be used. As an example, in FIG. 24B, the measured surface potential and the calculated surface potential in the X-axis direction are shown superimposed.

In the next step, it is determined whether or not Δ (x, y) is equal to or less than a preset evaluation value M. For example, the difference may be executed for all Vth_m (x, y) groups, and Vth_m (x, y) having the minimum value may be selected. Further, the sum of squares of differences as shown in the following expression may be used as the evaluation value.
M = Σ (Vth_s (x, y) −Vth_m (x, y)) ^ 2

  If Δ (x, y) exceeds M, the determination here is denied. In this case, the charge distribution model is corrected according to the determination result Δ (x, y). For example, when Δ (x, y) has a bias component, it is determined that the average potential is different, and the bias component is added to each potential in the charge distribution model. Further, when Δ (x, y) is an uneven shape, it is determined that the distribution shape of the surface charge, for example, depth and width, is different, and the shape in the charge distribution model is brought close to the uneven shape. This provides a more appropriate charge distribution model.

  The above steps are repeated until the result of the collation is affirmed. Thereby, an unknown electric charge can be determined.

  As described above, the actual measurement value of the detection signal obtained by the detector 24 when actually irradiating the electron beam is compared with the calculated value of the detection signal obtained by the electron trajectory calculation, and the actual measurement value and the calculated value match. Alternatively, if it is within the allowable range, the surface charge distribution model is estimated to be an actual charge distribution. If the measured value and the calculated value are outside the allowable range, the apparent charge density is calculated again to correct the surface charge distribution. This series of steps is repeated until the measured value and the calculated value are within the allowable range. A flowchart of this series of steps is shown in FIG.

  First, in step S61, the shape of the sample (photoconductor), the film thickness, the electrode shape on the back surface of the sample, and the like, which are the charge distribution shape parameters to be substituted as the values of the coefficient matrix shown in FIG.

  Next, in step S62, a structure model is set.

  Next, in step S <b> 63, an applied voltage Vsub to the conductor 60 on which the sample 23 is placed is set, and a voltage is applied to the conductor 60.

  Next, in step S64, the known electrode potential is set as a boundary condition using the algebraic geometric arrangement of the conductor and dielectric structure model in the space to be analyzed and the unknown charge density on the sample. A process of converting to an apparent charge density is performed.

  Next, in step S65, a spatial electric field is calculated using the converted apparent charge density.

  Next, in step S66, the differential value of the acceleration of the charged particle beam at the starting point is calculated based on the surface charge distribution model, and from the time point of the starting point for determining the next point based on the calculation result to the time point of the next point. A time interval is set.

  Next, in step S67, the trajectory analysis of electrons incident on the sample is performed based on the apparent charge density.

  Next, in step S68, a boundary value that determines whether or not incident electrons reach the sample is obtained using the electron trajectory analysis result. Specifically, the simulation condition when the primary charged particles are made to enter the sample from the initial coordinate separated by z0 from the sample surface at the acceleration voltage Vacc (<0) is Vsub. At this time, it is determined whether the trajectory of the primary charged particle is reversed without reaching the sample or the sample is reached, and the initial coordinate (x0, y0, z0) of the primary charged particle serving as the boundary is determined.

  Next, in step S69, it is determined whether or not the number of repetitions i of steps S63 to S69 has reached a predetermined number N. For Vsub and Vacc, values equivalent to the actual measurement conditions described later are used, and Vsub and Vacc are sequentially changed and simulation is executed as many times as necessary. If i has not reached N, the process proceeds to step S75, the applied voltage Vsub to the conductor 60 is changed, and the processes from step S63 are performed again. On the other hand, if i has reached N, the process proceeds to the next step S70.

In step S70,
Vth (x0, y0) = Vacc−Vsub
Vth (x, y) is calculated based on the following equation.

  By the way, although not shown in the flowchart of FIG. 25, Vth (x, y) is obtained by actual measurement separately from the value Vth_s (x, y) calculated in step S70. Vth (x, y) obtained by actual measurement is defined as Vth_m (x, y). In step S71, whether or not the calculated value Vth_s (x, y) matches the actual measurement value Vth_m (x, y) is checked. If the calculated value Vth_s (x, y) and the measured value Vth_m (x, y) do not match as a result of the collation, the surface charge distribution model is corrected in step S76, and the series of steps from step S63 is performed again. Done. On the other hand, if the calculated value Vth_s (x, y) matches the actual measurement value Vth_m (x, y), the process proceeds to step S72.

  In step S72, it is determined that the charge distribution shape parameter provisionally determined in step S62 is correct, and the shape of the surface charge is determined based on this parameter.

  Next, in step S73, a surface charge distribution is calculated based on the determined shape of the surface charge. In addition, since the electrostatic field is determined if the charge distribution is known, by analyzing the electrostatic field using the Poisson equation or the like, the physical quantity distribution such as the potential distribution and the electric field strength distribution can also be measured.

  Next, in step S74, the calculation result is displayed on a display (not shown) or the like of the surface charge distribution measuring apparatus, and all the processes are completed.

  In this way, the surface charge can be determined by calculating the electron trajectory and collating it with the actual measurement result. When measuring the surface potential, if the charge distribution is known, the electrostatic field is determined. Therefore, by solving the electrostatic field such as the Poisson equation, the physical quantity distribution such as the potential distribution V (x, y) and the electric field strength distribution is measured. can do.

  FIG. 26 shows an example of a surface potential distribution measuring apparatus having a function of forming a latent image. In FIG. 26, an electrophotographic photoreceptor is used as a sample. An organic photoreceptor (OPC) has a charge generation layer (CGL) and a charge transport layer (CTL) on a conductive support. When exposed in a state where the surface charge is charged, Light is absorbed by the charge generation material (CGM), and positive and negative charge carriers are generated. One of these carriers is injected into the CTL and the other into the conductive support by an electric field. The carriers injected into the CTL move to the surface of the CTL by an electric field through the CTL, and combine with the charge on the surface of the photoreceptor to disappear. Thereby, a charge distribution, that is, an electrostatic latent image is formed on the surface of the photoreceptor.

  In this surface potential distribution measuring apparatus 200, a pattern forming apparatus 220 that scans the surface of a sample with light and forms a latent image pattern is added to the surface potential distribution measuring apparatus 200 in the above embodiment. In FIG. 26, the control system is omitted. A pattern forming apparatus 220 in FIG. 26 includes a semiconductor laser 201 having a wavelength of 400 nm to 1000 nm, a collimator lens 203, an aperture 205, and an imaging lens including three lenses (207, 209, 211), which the photosensitive member has sensitivity. ing. Further, in the vicinity of the sample 71, an LED 213 for discharging the surface of the sample is disposed. The pattern forming device 220 and the LED 213 are controlled by a control system (not shown).

  A method for forming a latent image in the surface potential distribution measuring apparatus 200 will be briefly described. The surface of the photoreceptor sample is uniformly charged. Here, by setting the acceleration voltage to a voltage higher than the voltage at which the secondary electron emission ratio becomes 1, the amount of incident electrons exceeds the amount of emitted electrons, so that electrons are accumulated in the sample and charge up occurs. As a result, the sample is negatively charged. In addition, it can be charged to a desired potential by controlling the acceleration voltage and the irradiation time.

  The photoreceptor sample 71 is irradiated with an electron beam emitted from the electron gun 10. When the acceleration voltage | Vacc | is set to an acceleration voltage higher than the acceleration voltage at which the secondary electron emission ratio is 1, the amount of incident electrons exceeds the amount of emitted electrons, so that electrons are accumulated in the sample and charge up occurs. (FIG. 27 (a)). As a result, the sample can be negatively charged uniformly. The acceleration voltage and the saturation charging potential have a relationship as shown in FIG. 27B, and by setting or controlling the acceleration voltage and the irradiation time appropriately, the same charging potential as that of an actual machine in electrophotography can be formed. it can. When the irradiation current is large, the target charging potential can be reached in a short time, and therefore it is preferable to irradiate with 1 nA or more.

  Thereafter, the amount of incident electrons is reduced to 1/100 to 1/1000 so that the electrostatic latent image can be observed. In this state, the semiconductor laser 201 of the pattern forming apparatus 220 is caused to emit light. Laser light from the semiconductor laser 201 becomes substantially parallel light by the collimator lens 203, is made a prescribed beam diameter by the aperture 205, and is then condensed on the surface of the sample 71 by the imaging lenses 207, 209, and 211. As a result, a latent image pattern is formed on the sample surface.

  In the organic photoconductor (OPC), the charge decays with time due to dark decay. Therefore, it is necessary to complete data acquisition by signal detection within 10 seconds after the latent image is formed at the latest. As in the example shown in FIG. 26, by providing a function of charging and exposing the photoconductor sample in the vacuum chamber 30, it is possible to start data acquisition immediately after the formation of the latent image, which is necessary for acquiring the latent image profile. Even when measurement is performed by changing a plurality of applied voltages, data acquisition within 10 seconds can be completed. The latent image profile information can be acquired by changing the applied voltage as described above.

  If necessary, an upper electrode may be added above the photoconductor sample. By disposing the upper electrode, the influence of the spatial electric field due to the charge distribution of the sample can be localized in the range up to the upper electrode, so that the structure model can be further simplified.

  Moreover, although the said embodiment demonstrated the case where a sample was plate shape, the sample which this invention makes object is not limited to this, For example, a sample may be cylindrical shape. When the sample has a cylindrical shape, the sample can be applied as it is to a photosensitive drum used in an electrophotographic image forming apparatus such as a laser printer or a digital copying machine. Therefore, by feeding back the measurement result of the surface potential distribution for the cylindrical photoconductor sample to the design of the image forming apparatus, the process quality of each process related to image formation can be improved, and the image quality is improved and the durability is high. , High stability and energy saving can be realized.

  When the photosensitive member sample is cylindrical as described above, as an example of the exposure unit, as shown in FIG. 28, as shown in FIG. 28, the semiconductor laser 110, the collimating lens 111, the aperture 112, the cylinder lens 113, the optical path bending mirror. 114, a polygon mirror 115, two scanning lenses 116 and 117, an optical path bending mirror 118, and the like, an exposure unit 76 formed of an optical scanning device may be used.

  The semiconductor laser 110 emits laser light for exposure. The collimating lens 111 makes the laser light emitted from the semiconductor laser 110 substantially parallel light. The aperture 112 defines the beam diameter of the light that has passed through the collimating lens 111. Here, it is possible to generate an arbitrary beam diameter in the range of 20 μm to 200 μm by changing the size of the aperture 112. The cylinder lens 113 shapes the light transmitted through the aperture 112 only in one direction. The mirror 114 bends the optical path of light from the cylinder lens 113 in the direction of the polygon mirror 115. The polygon mirror 115 has a plurality of deflection surfaces, and deflects light from the mirror 114 at a constant angular velocity within a predetermined angular range. The two scanning lenses 116 and 117 convert the light deflected by the polygon mirror 115 into constant speed light. The mirror 118 bends the optical path of the light from the scanning lens 117 in the direction of the sample 71.

  The operation of the exposure unit 76 will be briefly described. The light emitted from the semiconductor laser 110 is once imaged near the deflection surface of the polygon mirror 115 via the collimating lens 111, the aperture 112, the cylinder lens 113, and the mirror 114. The polygon mirror 115 is rotated in the direction of the arrow in FIG. 21 at a constant speed by a polygon motor (not shown), and the light imaged in the vicinity of the deflecting surface is deflected at a constant angular velocity with the rotation. The deflected light further passes through two scanning lenses 116 and 117, and is converted into light that scans the longitudinal direction of the mirror 118 at a constant angular range within a predetermined angular range. This light is reflected by the mirror 118 toward the sample 71 and scans the surface of the sample 71. That is, the light spot moves in the generatrix direction of the sample 71. Thereby, an arbitrary latent image pattern including a line pattern can be formed in the bus line direction of the sample 71. The light source may be a multi-beam scanning optical system such as a VCSEL.

  Moreover, although the case where an electron beam was used as a charged particle beam was demonstrated in the said embodiment, not only this but an ion beam may be used. In this case, an ion gun is used instead of the electron gun. For example, when a gallium (Ga) liquid metal ion gun is used as the ion gun, the acceleration voltage is a positive voltage, and a bias voltage is applied to the sample 71 so that the surface potential is positive.

  In the above embodiment, the case where the surface potential of the sample is negative has been described. However, the surface potential of the sample may be positive. That is, the surface charge may be a positive charge. In this case, the sample may be irradiated with a positive ion beam such as gallium.

  In the embodiment shown in FIG. 26, the gate valve 40 is disposed on the −Z side of the beam blanking electrode 37, but the present invention is not limited to this. In short, the gate valve 40 may be disposed between the electron gun 10 and the sample stage 81.

  In the above embodiment, the case where a field emission electron gun is used as the electron gun has been described. However, the present invention is not limited to this, and a thermionic emission electron gun may be used. As shown in FIG. A Schottky emission (SE) type electron gun may be used. This Schottky emission type electron gun has an emitter 11, a suppressor electrode 12, a lead electrode 31, an acceleration electrode 33, and the like. If is a filament current, Ie is an emission current, and Vs is a suppressor voltage. The SE type electron gun is also called a hot cathode field emission electron gun.

  In the above-described embodiment, the surface potential distribution is obtained by detecting the primary repulsive electrons. However, the present invention is not limited to this. For example, when there is no risk of being affected by the material or surface shape of the sample, The surface potential distribution may be obtained by detecting secondary electrons.

  According to the present invention, it is possible to provide an apparatus for forming an electrostatic latent image on an electrophotographic photosensitive member under the same conditions as in an electrophotographic process and measuring the electrostatic latent image. Further, according to the present invention, it is possible to provide a surface charge distribution measuring method and apparatus capable of shortening calculation time while ensuring high measurement accuracy.

  In addition, according to the present invention, it is possible to greatly reduce the influence of time interval divergence by taking an average using the differential value of the acceleration of the electron at the previous coordinate.

  Further, according to the present invention, by calculating the acceleration of electrons from the spatial electric field, the calculation step can be omitted and the calculation time can be shortened.

  Further, according to the present invention, adjacent sections of measured detection signal data obtained discretely are expressed by a polynomial function for each section so as to be connected continuously, thereby being discrete and including errors. The measured detection signal data has the most suitable curve shape, and can be expressed as a function of a smoothed continuous curve. The smoothing spline function can flexibly and accurately handle curve data of various shapes in the measured detection signal data, improving the fidelity of the measured data compared with the electronic trajectory calculation result, and measuring accuracy Both the calculation time and the calculation time can be reduced.

  Further, according to the present invention, using the regularity function of the most fitted law using the regularity function that monotonically increases as the distance from the center of the charge distribution sample and takes the maximum value at the both ends, By adding points, it is possible to obtain smoothing spline results that are faithful to the data without vibration. And it becomes easy to collate with simulation data, and it becomes possible to improve accuracy and reduce time.

  Further, according to the present invention, by the method of determining the boundary value by changing the applied voltage, the region where the charged particle beam reaches the sample or the region where it is all reversed can be excluded from the analyzed region. . Therefore, the boundary value can be narrowed down with a small number of trajectory calculations, and the calculation time can be greatly shortened. This is because the trajectory calculation is reduced in the region where the spatial change of the charge density is small, such as the peripheral region of the charge distribution, or in the region where the spatial frequency of the charge distribution is large but the horizontal electric field is small, such as the charge center. It is particularly effective because it can be done.

  Further, according to the present invention, the boundary between the region where the primary charged particles are reversed without reaching the sample and the region reaching the sample is detected, the difference between the measured value and the calculated value of Vth is calculated, and the difference is reduced. As described above, the electric charge distribution data or the electric potential distribution data on the surface is corrected, and the electric charge distribution data having a high electric field strength such that a potential saddle point is generated by means of sequentially calculating the electron trajectory of the corrected electric charge distribution data. Can be measured with high accuracy. Further, by having means for correcting the scanning position coordinate fluctuation of the scanning electrons generated depending on the potential state of the sample, it is possible to suppress the distortion of the scanning region and to measure the surface charge distribution with high accuracy.

  Further, in the conventional surface charge distribution measuring method, there are a step of calculating the electric field calculation at least three times and a step of determining the error, whereas in the surface charge distribution measuring method according to the present invention, the electric field calculation is performed once. And no branch is required to determine the error. By using such a method, it has become possible to reduce the time interval calculation process to one-third or less of the conventional method. Even when the aspect ratio is different or the charge distribution has a complicated shape, it is possible to measure the surface charge distribution with high resolution on the order of microns in a short time while ensuring measurement accuracy.

  According to the surface charge distribution measuring apparatus according to the present invention, since the charging means and the exposure means necessary for forming the electrostatic latent image are provided, real-time measurement is possible, and the surface charge amount attenuates with time. Can be measured with a high resolution on the order of microns. In particular, in the case of an exposure method using a plurality of light sources such as a VCSEL, the latent image formation and the latent image formation mechanism are complicated as compared with a single light source. Therefore, the surface charge distribution measuring apparatus according to the present invention is effective for measuring the surface charge distribution on the sample surface when an electrostatic latent image is formed using a plurality of light sources such as VCSEL. Further, by measuring the electrostatic latent image on the photoconductor and feeding it back to the design, the process quality of each process is improved, so that high image quality, high durability, high stability, and energy saving can be realized.

DESCRIPTION OF SYMBOLS 1 Conductor base 2 Insulator 3 Conductive plate 4 Electron beam 5 Objective lens 6 Grid mesh 7 Detector 10 Photoconductor (sample)

JP 03-49143 A Japanese Patent Laid-Open No. 3-200100 JP 2003-295696 A JP 2004-251800 A JP 2005-166542 A Japanese Patent Laid-Open No. 10-334844 Japanese Patent Laid-Open No. 03-261057 JP 59-842 JP 2006-344436 A JP 2008-76100 A JP 2009-206074 A

Claims (10)

A surface charge distribution measuring method of scanning a sample having a surface charge distribution with a charged particle beam and measuring the surface charge distribution of the sample,
A model setting step for setting the surface charge distribution model of the sample based on the configuration of the apparatus for measuring the surface charge distribution;
A differential value of the acceleration of the charged particle beam at the starting point is calculated based on the surface charge distribution model, and a time interval from the starting point to the next point is set to determine the next point based on the calculation result A trajectory calculation step for calculating the trajectory of the charged particle beam;
An actual measurement step for obtaining an actual measurement value of the surface charge distribution of the sample from a detection signal obtained by scanning the sample with a charged particle beam;
A collation step of collating the value of the surface charge distribution model with the actual measurement value in the actual measurement step;
A determination step of adopting the surface charge distribution model as an actual surface charge distribution if an error between the value of the surface charge distribution model and the actual measurement value is within a predetermined range in the matching step;
A surface charge distribution measuring method comprising: In the track calculation step, setting of the time interval, the starting point to calculate the average value of the differential value of the acceleration of the charged particle beam between including sky, the time interval based on the calculated the mean value The surface charge distribution measuring method according to claim 1, wherein the method is performed by setting and calculating the trajectory of the charged particle beam.   In the trajectory calculation step, the time interval is set by calculating a spatial electric field at the starting point and determining a differential value of acceleration of the charged particle beam based on the calculated spatial electric field. 2. A method for measuring a surface charge distribution according to 1. The discrete actual measurement values obtained in the actual measurement step are expressed by a polynomial function for each section so that adjacent sections of the actual measurement values are continuously connected, and the entire actual measurement value is a continuous curve function. 2. The surface charge distribution measuring method according to claim 1, wherein after performing a processing operation for smoothing, the collation step collates with the value of the surface charge distribution model .   5. The surface charge distribution according to claim 4, wherein the discrete measured values obtained in the measuring step are monotonously increased as the distance from the charge distribution center increases, and are expressed by a continuous curve function having absolute values at both ends. Measuring method. In the trajectory calculation step, an applied voltage between the applied voltage at which the charged particle beam reaches the sample and the applied voltage at which the charged particle beam is reversed without reaching the sample is set as a new applied voltage. The surface charge distribution measuring method according to claim 1, wherein a boundary value between the sample arrival region and the sample inversion region is calculated by performing an operation of calculating a trajectory of the charged particle beam. When the voltage applied to the back surface of the sample is Vsub, the acceleration voltage of the charged particle beam applied to the sample is Vacc (<0), and the landing energy of the charged particle beam reaching the surface of the sample is 0 A second actual measurement step of obtaining values of Vacc and Vsub by irradiating the surface of the sample with the charged particle beam;
A calculation step of obtaining an actual measurement value of the Vacc-Vsub value Vth from the actually measured Vacc and Vsub values;
A second calculation step of obtaining values of Vacc and Vsub by simulation based on the set surface charge distribution model;
A third calculation step for obtaining a calculated value of Vth from the values of Vacc and Vsub obtained by simulation;
A comparison step of comparing the measured value of Vth with the calculated value;
A correction step of correcting the surface charge distribution model so that an error falls within a predetermined range in the comparison step;
The method for measuring surface charge distribution according to claim 1, further comprising: A surface charge distribution measuring device for a sample having a surface charge,
Charged particle beam scanning means for two-dimensionally scanning the surface of the sample with a charged particle beam;
Model setting means for setting a surface charge distribution model of the sample based on the configuration of the surface charge distribution measurement device;
A differential value of the acceleration of the charged particle beam at the starting point is calculated based on the surface charge distribution model, and a time interval from the starting point to the next point is set to determine the next point based on the calculation result A trajectory calculating means for calculating the trajectory of the charged particle beam;
Actual measurement means for obtaining an actual measurement value of the surface charge distribution of the sample from a detection signal obtained by scanning the sample with a charged particle beam;
Collating means for collating the value of the surface charge distribution model with the actual measurement value in the actual measurement step;
A determination unit that adopts the surface charge distribution model as an actual surface charge distribution if an error between the value of the surface charge distribution model and the measured value is within a predetermined range in the matching step;
A surface charge distribution measuring apparatus comprising: Charging means for charging the sample in a vacuum;
An exposure optical system that includes a light source provided outside a region through which the charged particle beam passes and irradiates the sample charged with a light beam from the light source to expose the surface of the sample;
Light source control means for controlling the light amount and exposure time of the light source;
The surface charge distribution measuring apparatus according to claim 8, further comprising a surface charge forming unit having the following. The surface charge distribution measuring apparatus according to claim 9, wherein a wavelength of a light beam emitted from the light source is 400 nm or more and 800 nm or less.

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