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This paper describes novel design concepts and some advanced techniques proposed for increasing the accuracy of low cost impedance measuring devices without reduction of operational speed. The proposed structural method for algorithmic error correction and iterating correction method provide linearization of transfer functions of the measuring sensor and signal conditioning converter, which contribute the principal additive and relative measurement errors. Some measuring systems have been implemented in order to estimate in practice the performance of the proposed methods. Particularly, a measuring system for analysis of
In spite of the strong efforts to develop and design high accuracy sensors these are devices which still contribute the most significant error to measurement results due to imperfections of the sensor transfer functions [
Actually, measuring devices and systems for analysis of complex parameters (impedance and admittance of electrical circuits on alternate current) are used in different applications due to their high speed (0.01–0.001 s) and low relative measurement error (0.01–0.1%) [
A sensing element is the most critical piece of any measuring system. The different physical nature of operations in a passive (modulating) or an active (selfgenerating) sensing element permits measurement of a wide variety of electrical and nonelectrical values. For instance, impedance measurements are based on the proportional changing of electrical properties of sensing element, such as resistivity, permittivity, and permeability in function of input measured force, displacement, torque, pressure, thickness, temperature, speed, humidity,
The signal conditioning element converts the output of the sensing element (with certain error) into a form suitable for further processing. Among the many methods for designing signal conditioning elements the most efficient for particular applications are the bridge iterating methods, the equal deflection methods, the network analysis or substitution methods for comparative measurements, highspeed direct conversion methods, the dynamic counting and resonant methods for capacitance and inductance measurements, and the oscillating methods for feedback systems [
The signal processing element is implemented using analog to digital converters (ADC) and microcomputers that are highaccuracy devices that do not reduce the precision of the measurements. Other important functions of the processing element are error reduction or compensation, control and synchronization of sensing and conditioning element, and data visualization.
There are some wellknown methods used for error correction by signal processing elements. They may be subdivided in the groups of compensative methods (a measurement result is used as a feedback compensation action on sensing or conditioning elements); differential methods [a measured parameter presented by an active value (voltage or current) is compared with a highlystable reference voltage or current computing deviation of a measured parameter with respect to a reference one]; direct conversion methods (the measured parameter is treated in a sequential process of corresponding active value conversion) [
Any measured value can be represented by an equivalent circuit, which consists of serial and parallel connections of resistance, inductance, and capacitance. The equivalent or substitution circuit is varied according to the magnitude and frequency of the test exciting signal. Impedance measurements strongly depend on specific characteristics of the sensor and data acquisition process, such as limited power (25 mV) and imperfection of monochromatic sine test signals generating nonlinear distortions, low magnitudes of the parameter to be measured (10^{−3}−10^{2} pF for capacitance and 10^{−4}−10 μS for conductance) requiring high resolution of the impedance meter, variable configurations of equivalent circuits in measuring converters due to wide test signal frequency range from 1 Hz to 1 MHz,
The total accuracy of measurement is defined by additive and multiplicative errors of measuring converters which may be represented as error vectors with corresponding active and reactive components, as shown in
The measuring converter of any sensor is a critical unit of the meter because it introduces the biggest error. Usually passive or active measuring converters are used [
For ideal complex conductance conversion (
The feedback gain
The structural method of error correction is based on insertion into the direct or feedback channel of measuring system of additional highspeed analog or digital units, which linearize the total nonlinear transfer functions of the designed circuit [
Thus, the analysis of errors is reduced to computing the functions
With the obtained
In
Therefore, the improvement of metrological characteristics is achieved by computing components of the systematic error and its compensation by additional operations according to the described algorithm. We propose to name this technique the “structural algorithmic correction method”. The additional arithmetic operations in the
The plots for error behavior without the correction algorithm
In a wide range of frequencies, the errors of the measuring converter sometimes change their sign, so the absolute values of errors
Analysis of errors has been made for cheap OpAmp with a small gain factor
Another unexpected result of implementation of the structural algorithmic correction method is the measurement frequency range extension with the same level of errors. For example, a measurement error of 0.5% without correction (curves
The principal disadvantage of this method is that a correction unit can be a complex circuit because it must support many arithmetic operations for generation of corrective actions. This problem may be solved by standardization and unification of analog circuits for simple arithmetic operations in highscale integrated circuits. There is no correlation between measured active (real) and reactive (imaginary) components of measured value as well as between the components of systematic errors that appear during impedance measuring processes. This is because the result basically depends on the physical characteristics of the measured value and not on the proportion between real and imaginary parts of measured value. If a measured value is a characteristic of semiconductor structure, the impedance measured components are better used for describing its features, such as substrate doping, flat band voltage, mobile ion concentration, series of resistance effects, charge densities, loss in the MOS structure due to charging and discharging of interface traps,
The structural algorithmic correction method has been introduced for linearization of the transfer function of a complex conductance measuring converter. However it is only the first stage of the measurements. The consecutive vectorscalar and analogtodigital converters introduce nonlinear errors which must be removed by their own correction structures that may occupy more than 30% of all the measuring equipment. As usual, these structures are simple to implement and may be used for incrementing the performance of cheap measuring systems.
In order to explore the power of other error correction techniques an iterating compensation method is also proposed. Iterating methods use error correction units incorporated into the feedback channel which generates correction signals according to the results of previous measurement steps [
The phase sensitive detectors PD_{A}, PD_{R} convert
The digital codes of the measured components are obtained by ADC_{A} and ADC_{R} with their nominal transfer coefficient
The magnitudes of components
Iterating error correction begins with the generation of the first iterating compensation voltage
The voltage from
The first iterating approximation result of
The feedback iterating blocks, which consist of IVRs, IARs, subtractors S_{A}, S_{R}, and adders Σ_{A}, Σ_{R} generate the correction signals:
The iteratingmeasuring process is continued according to the described algorithm (
According to the convergence condition of the iterating correction algorithm, the increment of approximation numbers leads to the fact that
The advantage of the proposed iterating method consists in the generation of correction actions in feedback channels in digital form. That results in a very small error equal to half of the least significant bit of the operating word of the DAC (±0.5/2^{n} where
The experimental results concerning the efficiency of the proposed methods were obtained using an automatic parameter control system which has been constructed for technological process control of chargecoupled device (CCD) manufacturing. The parameter control is used to estimate the accuracy of manufacturing conditions in order to detect deviation limits of the electrical and physical characteristics of the output product. Usually multifrequency VoltFarad, VoltSiemens
Additionally to
The automatic parameter control system for semiconductor manufacturing test has been designed and constructed applying the direct capacitance measurement method with algorithmic error correction of real
The measuring process is started by the connection of a measured structure to three terminals (G, S, D) and selection of measuring ranges, frequencies of test signal, and displacement voltages
In this case, the transfer function of phase detector is analyzed according to the previously proposed error correction algorithm. The principal errors arise from deviations of parasitic angles
To extend the operational functionality of a system the remote control unit (external keyboard) can be included. The constructed measurement system is represented in
Two error correction methods based on linearization of transfer functions of impedance measuring system have been proposed and tested. These methods require simple and cheap electronic components and provide high accuracy measurements without reduction of conversion and data processing speed. Based on the direct conversion method a measurement system for automatic control of semiconductor characteristics during the manufacturing process has been designed and constructed. The system provides the measurement of the
This research is sponsored by Mexican National Council of Science and Technology, CONACyT, Projects: #109115 and #109417. This research also has been partially supported by the Ministry of Science and Innovation (MICINN) of Spain under the research project TEC200763121.
(a) Orthogonal components of the measured complex voltage
Electric circuit of normal active converters: (a) for complex conductance and (b) for complex resistance measurements
(a) Error behavior for active component of conductance measuring converter without (
Block diagram of impedance meter with iterating error correction.
Block diagram of the measurement system for automatic control of semiconductor characteristics.
Relative errors of measurement of active and reactive components without correction.
1  5  10  20  50  100  200  500  1000  

1.96  1.78  1.55  1.09  0.31  2.77  8.06  26.7  64.4  
2.05  2.33  2.66  3.3  5.22  8.33  14.2  29.4  46.7 
Relative errors of measurement on
0  1  2  3  4  5  6  7  8  

24  −16  −1.9  2.5  0.07  −0.38  0.02  0.05  0.01  
−34  −5.7  5.9  −0.38  −0.89  0.02  0.13  −0.01  0.00 
Number of iterating steps for impedance measurement with relative error 0.05%.
1  2  5  10  20  50  100  200  500  1000  
2  2  2  2  2  2  3  4  7  22 
Parameters, measurement intervals, and errors of
C_{X}  1 



C_{X}  2 



C_{X}  3 



G_{X}  1 



G_{X}  2 



G_{X}  3 


