JP2000081359A - Measurement method using secondary electron multiplication element and device using secondary electron multiplication element - Google Patents

Abstract

PROBLEM TO BE SOLVED: To maintain accurate measurement without recalibrating a measurement system during use by using the ratio of an initial intensity value where light intensity is measured to light intensity value during use at the initial stage of the installation of a secondary electron multiplication element. SOLUTION: A vacuum measurement part 1 is composed of an ion generation part 3 and an ion detection part 4 that oppose each other via a cylindrical electrode 2. The ion detection part 4 is composed by a secondary electron multiplication element, and a negative high voltage from a DC high-voltage power supply 10 is applied to an entrance part 4b of a trumpet-shaped secondary electron multiplication element. The measurement value of a particle such as a charged particle being measured is multiplied, as a correction coefficient, by a ratio A/B between an initial intensity value A that is obtained by measuring the intensity of light such as soft X rays at the initial stage of the installation of the secondary electron multiplication element and an intensity value B of light being measured during use, thus performing accurate measurement without calibrating a measurement system by stopping measurement. The method can be effectively applied to the measurement of a vacuum pressure and surface analysis, and efficiency is improved by providing an operation device for executing the correction.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for compensating the sensitivity of a secondary electron multiplier used for measuring vacuum pressure, mass spectrometry, and analyzing the surface condition of a sample, and uses the secondary electron multiplier. The present invention relates to a vacuum processing apparatus such as a vacuum deposition apparatus and an ashing apparatus.

[0002]

2. Description of the Related Art Conventionally, various vacuum processing apparatuses such as a sputtering apparatus, a vacuum evaporation apparatus, a CVD apparatus, and an MBE.
Vacuum film forming apparatus such as an ashing apparatus, an ion implantation apparatus, and an oxidation diffusion apparatus include an ionization vacuum pressure gauge,
A vacuum pressure gauge such as a polar mass spectrometer and a surface analyzer such as Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS) and electron loss spectroscopy (EELS) are installed. It plays an important role in maintaining and improving the quality of products such as semiconductors and liquid crystals.

[0003] Such a vacuum pressure gauge or surface analyzer includes a generator for generating charged particles of ions and electrons together with light such as neutral particles, excited neutral particles, and soft X-rays. And a secondary electron multiplier for capturing and amplifying light such as ions, electrons, neutral particles, excited neutral particles, and soft X-rays generated by collision with the sample and the secondary electron multiplier. In the device, incident ions, electrons, neutral particles, excited neutral particles,
A measuring instrument for detecting the number of secondary electrons generated by light such as soft X-rays and measuring the vacuum pressure and surface state is connected. The secondary electron multiplier uses a continuous intensifier type seratron, a channeltron, a multi-stage intensifier, and the like, and a small amount of ions, electrons, neutral particles, excited neutral particles, and soft X-rays. It is used for measurement of light such as. These devices are made of materials such as beryllium oxide, magnesium oxide, and ceramic semiconductors, whose surfaces tend to emit secondary electrons, and charge ions, electrons, and neutral particles, Converts light such as neutral particles and soft X-rays into electrons,
It further amplifies, which is convenient for measuring a very small current value. In surface analyzers and vacuum pressure gauges, charged particles such as ions and electrons
Neutral particles, light, etc. are made incident, and the emitted charged particles, neutral particles, light, etc. are measured. Usually, necessary ones such as charged particles, neutral particles, and light are measured, and others are removed by some method because they cause noise.

[0004]

In recent years, in order to satisfy the demand for further improving the quality of semiconductors and liquid crystals, etc., and to develop new products, quantitative measurement of surface analyzers and vacuum pressure gauges has been required. However, in the conventional vacuum pressure gauge, the state tends to change depending on the environment and the use time, and it is necessary to calibrate the measurement system at intervals of one to three months in order to perform accurate quantitative measurement. The reason is that the secondary electron multiplier element
This is because water, oxygen, hydrogen, etc. adsorb on the surface, changes in the environment such as temperature and humidity, and changes in operating voltage greatly change the detection efficiency and amplification factor. I can't. If the element is calibrated frequently, the accuracy can be maintained, but for that purpose, the vacuum processing device or the like in use is stopped, the element is taken out, and the work of attaching it to the new calibration apparatus is performed, so that time and cost are increased. There was such a drawback.

SUMMARY OF THE INVENTION The present invention provides a method for maintaining accurate measurement without recalibrating a measurement system of a secondary electron multiplier during use, and for calibrating the sensitivity of a secondary electron multiplier. It is an object of the present invention to provide a vacuum processing apparatus whose operation is not stopped.

[0006]

According to the present invention, an initial intensity value A obtained by measuring the intensity of light such as soft X-rays at the initial stage of installing a secondary electron multiplier provided in a vacuum, The measurement is stopped and the measurement system is calibrated by multiplying the ratio A / B of the light intensity value B measured therein to the measured value of particles such as charged particles measured by the element as a correction coefficient. The measurement can be performed accurately without the above, and the above-mentioned object is achieved. The means of the present invention can be effectively applied to vacuum pressure measurement and surface analysis, and performs this correction on a measuring device provided in a vacuum processing device for measuring the intensity of electrons, ions, neutral particles, and excited neutral particles. By providing an arithmetic device that performs the processing, the processing device can be operated efficiently.

[0007]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described with reference to the drawings. FIG. 1 shows the present invention applied to an ultrahigh vacuum ionization gauge provided in an ultrahigh vacuum and measuring the vacuum pressure. In this embodiment, reference numeral 1 denotes a cylindrical electrode 2
Vacuum measuring units 5, 5 and 5 composed of an ion generating unit 3 and an ion detecting unit 4 which face each other are disk electrodes provided at both ends of the cylindrical electrode 2.

The ion generator 3 is made of, for example, a Pt clad Mo wire and has a diameter of about 12 m with both ends open.
m, a collector electrode 6 of a cylindrical grid having a length of about 15 mm,
A hot cathode type electron beam source 8 composed of a W filament provided on the outer side of the current collecting electrode 6 heated by a direct current from a heating power source 7. The cylindrical electrode 2 is referred to as a Bessel-Box type energy filter, and is provided so as to coincide with the central axis of the current collecting electrode 6. Part 3
To remove light, neutral particles, high-speed ions, and soft X-rays emitted together with charged particles such as ions and electrons from the disk, the disk shape is slightly larger than the ion introduction hole 5a formed in the disk electrode 5. The baffle 9 is provided, and the same potential as that of the cylindrical electrode 2 is applied to the baffle 9.

The ion detector 4 is composed of a secondary electron multiplier such as a channeltron, a seratron, or a multi-channel plate (MCP) as shown in the figure. A negative high voltage was applied to the inlet 4b of the multiplier 4 by the DC high-voltage power supply 10, and the output from the outlet 4a of the secondary electron multiplier 4 was connected to the pulse counter measuring device 12 via the preamplifier 11. . The secondary electron multiplier 4 has a beryllium oxide, a magnesium oxide, whose inner surface easily emits secondary electrons,
Electrons, ions, excited neutral particles, and light that are formed of a material such as a ceramic semiconductor collide with the surface and are converted into two or more electrons. Each time the electrons collide with the surface, It is multiplied to two or more electrons. In front of or behind each disk electrode 5, an ion extraction electrode 1 having a ground potential
3 and 13 are provided.

The collector electrode 6 is connected to the ground via a first DC power supply 14 of, for example, 10 V and a second DC power supply 15 of, for example, 100 V, and is connected between the collector electrode 6 and the electron beam source 8. A potential difference of the second DC power supply 15 was given to attract thermoelectrons generated by the electron beam source 8 into the collector electrode 6. In order to adjust the potential difference between the cylindrical electrode 2, the disk electrode 5 and the baffle plate 9 and the ground, these are connected to a ground via a variable DC power supply 16, and the cylindrical electrode 2 and the baffle plate 9 are connected to the ground. Bias power supply 17 between electrode 5
Thus, a potential difference of, for example, 225 V is applied.

The above configuration is the same as the configuration of a conventional vacuum pressure gauge having a secondary electron multiplier, and
Is provided in a vacuum, and when the electron beam source 8 is heated, the thermoelectrons generated by this are collected in the cylinder of the collector electrode 6,
Gas ions are generated by colliding with gas molecules existing there, and the ions are generated by the ion extraction electrode 13.
To the entrance 4b of the secondary electron multiplier 4 of the ion detector 4. The electrons are amplified by the incidence of ions in the secondary electron multiplier 4, and the ion intensity (ion current) is measured by the measuring device 12 by a pulse count method or a direct current method, and is converted into a pressure to obtain a vacuum. The pressure is measured.

As described above, the surface of the secondary electron multiplier 4 is made of a material such as beryllium oxide which easily emits secondary electrons, and water, oxygen, hydrogen and the like are adsorbed thereon. For example, the detection efficiency and amplification factor may change significantly due to changes in the environment such as temperature, humidity, etc., or the operating voltage may change.To perform accurate measurement, stop the measurement and Calibration is required, but according to the present invention,
Initially, when the secondary electron multiplier 4 is installed and started to be used, that is, while the surface is fresh, only the soft X-ray light emitted from the ion generator 3 emits the secondary electron multiplier. The initial intensity value A under the condition of incidence on the secondary electron multiplier 4 is measured, and this value is multiplied by the intensity value B under the condition that only the light is incident on the secondary electron multiplier 4 during the measurement of the vacuum pressure. By measuring the ratio A / B by measuring with the element 4 and multiplying the measured intensity value of particles such as charged particles measured with the element 4 as a correction coefficient, the detection efficiency and the amplification factor of the element 4 can be improved. Accurate measurement can be performed even if it changes.

More specifically, in the ion generator 3, gas molecules in the collector electrode 6 are ionized by the impact of thermionic electrons accelerated and emitted from the electron beam source 8, and gas ions to be measured are generated. However, at the same time, the surface of the collector electrode 6 is bombarded with thermionic electrons to emit soft X-ray light. When this light is reflected directly or inside the cylindrical electrode 2 and enters the secondary electron multiplier 4, secondary electrons are emitted inside the secondary electron multiplier 4 by the photoelectric effect, and this is generated as a pseudo ion current other than the ion for measurement. Measured. The pseudo ion current intensity due to this soft X-ray does not depend on the vacuum pressure in the vacuum vessel and is a noise to be measured and should be removed. However, as shown in FIG. , That is, linearly proportional to the surface state of the secondary electron multiplier 4. The present invention uses this phenomenon to eliminate the inconvenience that the measurement sensitivity changes due to a change in the surface state or the like of the secondary electron multiplier 4. First, the state in which the vacuum pressure can be measured or as described below. At the initial stage of installing the secondary electron multiplier 4 in a state where the surface analysis can be performed, the variable DC power supply 16 is adjusted to change the potentials of the electrodes 3 and 9 of the measurement system, and ions are incident on the element 4. When control is performed so that soft X-rays enter, the light generated by the ion generator 3 is
And the intensity of the light can be measured as an initial intensity value A. Then, ions are guided from the ion generation unit 3 to the element 4, the secondary electrons amplified in the element 4 are measured by a pulse count method or the like, and converted into pressure to convert the pressure into a normal vacuum pressure measurement or surface analysis. Perform the measurement. Since the detection efficiency and the secondary electron amplification factor of the element 4 change with the measurement environment and the passage of time, the sensitivity changes and the accuracy of the measurement is lost. When the power supply 16 is adjusted so that soft X-rays enter the element 4 without entering ions, the intensity of the soft X-rays at this time can be measured. The ratio A / B of the intensity value B and the initial intensity value A is a ratio of sensitivity, and if this is used as a correction coefficient and multiplied by a measured intensity value when a vacuum pressure is measured by subsequently injecting ions, the sensitivity becomes It is possible to obtain an accurate vacuum pressure corrected for the change in the pressure. The intensity value B can be measured only by temporarily changing the voltage of the power supply 16, and the operation of multiplying the correction coefficient by the measured intensity value can be performed by attaching the arithmetic device 18 to the measuring device 12, so that the sensitivity can be increased as in the conventional case. There is no need to remove the secondary electron multiplier having changed and recalibrate the sensitivity, saving time and money. It is desirable that the intensity value B is frequently measured after an appropriate time that does not hinder the measurement of the vacuum pressure.

The secondary electron multiplier is an Auger electron spectroscopy type,
X-ray photoelectric spectroscopy, ultraviolet photoelectron spectroscopy, electron loss spectroscopy,
It is also used for surface analysis methods such as electron loss spectroscopy, and in this case, if the sensitivity of the secondary electron multiplier changes, accurate analysis cannot be performed. As shown in FIG. 3, the surface analysis method is based on the method of accelerating ions, electrons, neutral particles, excited neutral particles, and soft X-rays on the surface of a sample 19 placed in a vacuum. The secondary electron multiplier 21 captures and analyzes ions, electrons, neutral particles, excited neutral particles, and soft X-rays emitted from the surface by the impact. In the method, when the surface of the element 21 is freshly installed, light such as soft X-rays emitted from the ion generator 20 or from a separately provided particle source is emitted toward the surface at the initial stage of installation, and the initial intensity is increased. The value A is measured. Thereafter, the original surface analysis, that is, light such as ions, electrons, neutral particles, excited neutral particles, and soft X-rays collide from the ion generating section 20 to the surface, and ions, electrons, and medium emitted from the surface are irradiated. Light such as neutral particles, excited neutral particles, and soft X-rays are made incident on the element 21 for surface analysis. Then, during this surface analysis, the ion generation unit 20 is temporarily adjusted so that light such as soft X-rays is directed toward the surface, or light such as soft X-rays is supplied from a separately provided light source. Irradiate toward the surface, and the device 2
In step 1, the measurement intensity B that can be detected at that time is measured,
In the same manner as described above, an accurate surface analysis can be performed by obtaining an A / B correction coefficient and multiplying the measured intensity value of the surface analysis performed thereafter by the correction coefficient. In addition, different types of sample 1
In the case where the surface analysis of 9 is performed, the initial intensity value A is measured by the same method as described above immediately after performing the surface analysis again after the sample 19 is set, and the correction coefficient is obtained by the same method during the surface analysis. Good.

The method of the present invention can also be applied to the vacuum pressure gauge of the quadrupole mass spectrometer shown in FIG. 4, and in this case, the ion generating unit 22 that generates soft X-rays together with ions. Ions are extracted by the ion extraction electrode 23,
Only predetermined ions are made to enter the secondary electron multiplier 25 by passing between the rod-shaped quadrupoles 24, and the vacuum pressure is measured. By adjusting the potential of the extraction electrode 23 and the quadrupole 24, Since only soft X-rays can be incident on the element 25 except for the ions from the ion generation unit 22, only the soft X-rays can be incident on the element 25 at the initial stage and during the measurement use, respectively, as described above. By measuring the initial intensity value A and the intensity value B and multiplying the ratio of the measured intensity value of the ions as a correction coefficient, a change in the sensitivity of the element 25 can be corrected and an accurate vacuum pressure can be measured.

A vacuum processing apparatus such as a sputtering apparatus, a vacuum deposition apparatus, an etching apparatus, an ashing apparatus, a CVD apparatus, an ion implantation apparatus, an oxidation diffusion apparatus, and a molecular beam epitaxy apparatus has a vacuum for maintaining and improving the quality of products. A pressure gauge and a surface analyzer are incorporated. By incorporating a vacuum pressure gauge having the structure shown in FIG. 1 or a surface analyzer based on FIG. Accurate measurement can be performed even if the sensitivity of the secondary electron multiplier changes, and vacuum processing can be continued without stopping the operation of the vacuum processing apparatus, thereby improving quality and productivity. FIG. 5 shows a vacuum pressure gauge 2 having the configuration shown in FIG. 1 attached to a sputtering device provided with a target 26 attached to an RF electrode 27 and opposed to a substrate 28.
FIG. 6 shows an evaporation source 32 having cells of various elements on a substrate 31 heated by a heater 30.
The vacuum pressure gauge 33 of the quadrupole mass spectrometer having the configuration shown in FIG. 4 and the Auger electron spectroscopy surface analyzer 34 having the configuration shown in FIG. This is an embodiment.

[0017]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An ultrahigh vacuum ionization gauge having the configuration shown in FIG. 1 equipped with a brand-new secondary electron multiplier 4 is mounted in a vacuum space of a constant vacuum pressure, and its cylindrical electrode 2, disk electrode 5 and baffle plate 9 are mounted.
When the voltage of the variable DC power supply 16 connected to was scanned, the measurement device 12 measured the ion intensity distribution shown in FIG. When the voltage of the DC power supply 16 is about 70 V, the strength of the gas ions in the vacuum space can be measured, so that it can function as a vacuum pressure gauge. When the voltage is set to 140 V, the ions generated by the ion generator 3 do not enter the secondary electron multiplier 4, and only the intensity by the soft X-ray is measured. The count / second was defined as the initial intensity value A. Thereafter, the voltage was returned to 70 V, and the measurement of the vacuum pressure in the vacuum space was continued. After about 500 hours, the voltage was again set to 140 V and only the soft X-rays were incident on the element 4, and the measured value was 20 counts / sec. B.
Thereafter, the voltage is returned to 70 V, and the measured intensity value of the vacuum pressure is multiplied by a correction coefficient of 1.5 calculated by the arithmetic unit 18 to about 2
The measurement of the vacuum pressure was continued for 000 hours. The measured intensity value during this period was 200 counts / second, and the converted vacuum pressure was 1 × 1.
At 0 ^-9 Pa, there was almost no difference from the set pressure of this vacuum space.

For comparison, an ionization gauge for ultra-high vacuum having the structure shown in FIG.
When the measurement of the vacuum pressure was continued for about 3500 hours while keeping the voltage at 0 V, the pulse count value was initially 200 counts / sec, which was the same as the above-mentioned initial intensity value. And finally at 30 counts / sec. Since the pressure in the vacuum space is kept constant, the decrease is due to a change in the sensitivity of the secondary electron multiplier.

[0019]

As described above, according to the present invention, the initial intensity value A obtained by measuring the intensity of light such as soft X-rays at the initial stage of the installation of the secondary electron multiplier, and the value measured during the use of the device. Since the ratio A / B to the intensity value B due to the light is multiplied as a correction coefficient to the measured intensity value of the element, the change in the sensitivity of the secondary electron multiplier element can be easily performed while the element is in use. It can be corrected, and the time required for the correction is very short, so it has the effect that it hardly disturbs the original measurement.It can be applied to various measuring devices using secondary electron multipliers, There is an effect that the operation efficiency of the processing device can be improved.

[Brief description of the drawings]

FIG. 1 is a diagram showing an embodiment of the present invention.

FIG. 2 is a distribution diagram showing a relationship between soft X-rays and sensitivity of a secondary electron multiplier.

FIG. 3 is an explanatory diagram when the present invention is applied to a surface analyzer.

FIG. 4 is an explanatory diagram when the present invention is applied to a quadrupole mass spectrometer.

FIG. 5 is a cut side view of a sputtering apparatus to which the present invention is applied.

FIG. 6 is a cut side view of a molecular beam epitaxy apparatus to which the present invention is applied.

FIG. 7 is a distribution diagram for obtaining an initial intensity value according to the present invention.

[Explanation of symbols]

2 Cylindrical electrode, 3.20 ion generation section, 4.21 ion detection section (secondary electron multiplier), 5 disk electrode, 6
Collector electrode, 8 electron beam source, 9 baffle plate, 12 measuring device, 13 ion extraction electrode, 16 variable DC power supply, 19 samples, 29/33 vacuum pressure gauge, 31 substrate, 32 evaporation source, 34 Auger electron spectroscopy surface Analysis equipment,

 ────────────────────────────────────────────────── ─── Continued on the front page (72) Inventor Yasushi Yasushi 2500 Hagizono, Chigasaki-shi, Kanagawa Inside ULVAC Corporate Center (72) Inventor Ichiro Arakawa G5-304 F-term 1-2-8 Mejiro, Toshima-ku, Tokyo (Reference) 2F055 AA11 BB01 BB08 CC47 DD20 EE40 FF11 FF45

Claims (6)

[Claims] 1. An initial intensity value A obtained by measuring the intensity of light such as soft X-rays at the initial stage of installation of a secondary electron multiplier mounted in a vacuum.
Ratio A of the light intensity value B measured during use of the device during use
/ B is multiplied as a correction coefficient by a measured intensity value of particles such as electrons, ions, neutral particles and excited neutral particles measured by the device as a correction coefficient. . 2. A secondary electron multiplier is provided in vacuum with an ion generator for emitting light such as soft X-rays together with particles such as electrons, ions, neutral particles and excited neutral particles, and a secondary electron multiplier. In a method of amplifying electrons, ions, neutral particles, and excited neutral particles generated by an ion generation unit with a secondary electron multiplier, and measuring a vacuum pressure from a signal intensity measured by the element, The ratio A / B of an initial intensity value A obtained by measuring the intensity of light from the ion generating section at the initial stage of the installation of the secondary electron multiplier and the intensity B of the light during measurement of the element. Is multiplied as a correction coefficient by the intensity value of particles such as electrons, ions, neutral particles and excited neutral particles measured by the device as a correction coefficient. 3. A secondary electron multiplying element and an ion generating section for emitting light such as soft X-rays together with electrons, ions, neutral particles and excited neutral particles in a vacuum. An energy filter is provided between the section and the secondary electron multiplier, and electrons, ions,
Neutral particles and excited neutral particles and the like are separated by the energy filter and incident on the secondary electron multiplier, in a method of measuring the vacuum pressure from the signal intensity measured by the element,
The ratio A / B of the initial intensity value A of the light measured at the initial stage of the installation of the secondary electron multiplier and the intensity B of the light measured during the measurement of the device was measured with the device. A measurement method using a secondary electron multiplier, wherein a vacuum pressure is measured by multiplying an intensity value of electrons, ions, neutral particles, excited neutral particles, and the like as a correction coefficient. 4. A surface of a sample provided in a vacuum is irradiated with light such as soft X-rays, particles such as electrons, ions, neutral particles and excited neutral particles, and the surface is radiated by the irradiation. In a method of analyzing the surface by capturing particles such as soft X-rays, light, electrons, ions, neutral particles, and excited neutral particles with a secondary electron multiplier and measuring the intensity thereof, In the initial stage of installation of the secondary electron multiplier, the surface or the surface of a standard sample of the same kind as the sample is irradiated with the light or particles such as electrons, ions, neutral particles, and excited neutral particles, and the emitted soft An initial intensity value A measured by irradiating light such as X-rays on the element; and an intensity value of the light measured by the element by irradiating the light during analysis of the sample using the element. B: multiplying the intensity value measured during analysis with the element by a ratio A / B with B as a correction coefficient. Measurements using multiple elements. 5. A light source such as soft X-rays, together with particles such as electrons, ions, neutral particles and excited neutral particles, is placed in a vacuum vessel communicating with a vacuum processing chamber provided with a substrate for performing film formation and other processing. A radiating ion generator and a secondary electron multiplier are provided to face each other, and electrons, ions, neutral particles and excited neutral particles generated by the ion generator are captured by the secondary electron multiplier. In a vacuum processing apparatus provided with a measuring device for measuring the intensity, the initial intensity value A of the light measured at the initial stage of installation of the secondary electron multiplier and the device are used. Ratio with the intensity value B by the light measured during the measurement
Vacuum processing using a secondary electron multiplier, wherein an arithmetic unit for multiplying B as a correction coefficient by an intensity value of electrons, ions, neutral particles and excited neutral particles measured by the element is provided. apparatus. 6. A vacuum processing chamber provided with a substrate on which film formation or other processing is performed is directed toward a surface of the substrate, such as particles such as electrons, ions, neutral particles, and excited neutral particles, or light such as soft X-rays. Vacuum treatment provided with an irradiation device that emits light and a secondary electron multiplier that captures light, electrons, ions, neutral particles, excited neutral particles, and the like such as soft X-rays emitted from the substrate by this irradiation. In the apparatus, the secondary electron multiplier is irradiated with the light on the surface or the surface of a standard sample of the same kind as the sample at the initial stage of the installation of the secondary electron multiplier, and the soft X-rays emitted from the surface are irradiated. Ratio of the initial intensity value A measured by irradiating the element with light and the intensity value B obtained by measuring light such as soft X-rays emitted from the surface during measurement using the element. B is used as a correction coefficient for the measured values of particles such as electrons, ions, neutral particles and excited neutral particles measured by the device. Vacuum processing apparatus using the secondary electron multiplying device characterized by an arithmetic unit is provided to be multiplied.