CN110927458B - Testing and fitting method of multi-carrier system - Google Patents
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Abstract
The invention discloses a method for testing and fitting a multi-carrier system, which comprises the following steps: placing the sample in a low-temperature variable magnetic field, and measuring the transverse conductivity sigma of the samplexxAnd longitudinal conductivity σxy(ii) a Fitting operation is carried out on the measured sigma xx and sigma xy, and the mobility of various carriers in the sample is calculated; and determining the concentration ni of each type of carrier in the sample based on the calculated mobility of each type of carrier in the sample. By adopting the invention, relatively accurate material electrical parameter information can be obtained, the design capability of the detector structure can be improved, the carrier concentration and the mobility of each conductive type in the material are optimized through guiding the process, the dark current of the device is reduced, and the performance of the detector assembly is improved.
Description
Technical Field
The invention relates to the technical field of infrared detector materials, in particular to a method for testing and fitting a multi-carrier system.
Background
The mercury cadmium telluride is used as a material with multiple carriers participating in electric conduction, the electric transport behavior is complex, and the transport behavior of various carriers has great influence on the performance of the device, so that it becomes more important to find a scientific and reasonable way to represent the transport behavior of the carriers.
In the related technology, the Hall effect is used for representing the transport characteristics in the HgCdTe, the conduction type in the material is judged to be n-type or p-type through the positive sign of Hall voltage, however, for the HgCdTe material, holes and electrons are often conducted together in the material, and therefore, for a material system with multiple carriers participating in conduction together, the real electrical property of the material system cannot be accurately represented by a conventional magnetic transport measurement result. For example, for p-type tellurium-cadmium-mercury materials, at 77K, mu p is approximately equal to 1 × 103cm 2/V-s, mu n is approximately equal to 2 × 105cm 2/V-s, mu n/mu p is greater than 102, the mobility of holes and electrons is different by two orders of magnitude, when the conventional magnetic transport measurement is adopted, the test result shows that the n-type materials with poor performance (low mobility mu is approximately equal to 1 × 103cm 2/V-s) are actually p-type materials with excellent performance, so the test result becomes unreliable, even wrong results are obtained, the screening of the materials cannot be carried out, and finally, great waste and low device yield are caused.
Disclosure of Invention
The embodiment of the invention provides a method for testing and fitting a multi-carrier system, which is used for solving the problem of inaccurate measurement of carrier transport behavior in the prior art.
The embodiment of the invention provides a method for testing and fitting a multi-carrier system, which comprises the following steps:
placing a sample in a low-temperature variable magnetic field, and measuring the transverse conductivity sigma of the samplexxAnd longitudinal conductivity σxy；
Calculating the mobility of each type of carriers in the sample by performing fitting operation on the measured σ xx and σ xy according to formula 1 and formula 2,
wherein q is the type number of carriers in the sample, B is magnetic induction intensity, sigma i is the conductivity of the ith type of carriers, and mu i is the mobility of the ith type of carriers;
determining the concentration ni of each type of carrier in the sample according to formula 3 based on the calculated mobility of each type of carrier in the sample,
σi＝μinie the values of the equations 3 are,
wherein e is the electron electric quantity.
According to some embodiments of the invention, the sample is placed in a varying magnetic field, and the lateral conductivity σ of the sample is measuredxxAnd longitudinal conductivity σxyThe method comprises the following steps:
putting the sample in a low-temperature variable magnetic field, and introducing current I to the sample through an electrode of the samplexRecording the voltage V of the sample in the direction of the current flowxAnd a voltage V in the direction perpendicular to the current flowy；
Based on the IxThe VxAnd said VyCalculating the transverse resistance R of the samplexyAnd a longitudinal resistance Rxx；
Testing the length, width and height of the sample and based on the RxyAnd said RxxCalculating the transverse resistivity rho of the samplexyAnd longitudinal resistivity ρxx；
According to the rhoxyAnd the rhoxxCalculating the transverse conductivity σ of the samplexxAnd longitudinal conductivity σxy。
Further, the step of placing the sample in a low-temperature and variable-magnetic field comprises:
the sample was placed in an environment at a temperature of 77K and a magnetic field of ± 10T.
According to some embodiments of the invention, 3 ≦ q ≦ 7.
According to some embodiments of the invention, q is 6.
According to some embodiments of the invention, the method further comprises:
according to said μiThe type of the carrier is judged.
By adopting the embodiment of the invention, relatively accurate material electrical parameter information can be obtained, the design capability of the detector structure can be improved, the carrier concentration and the mobility of each conductive type in the material are optimized by guiding the process, the dark current of the device is reduced, and the performance of the detector assembly is improved.
The foregoing description is only an overview of the technical solutions of the present invention, and the embodiments of the present invention are described below in order to make the technical means of the present invention more clearly understood and to make the above and other objects, features, and advantages of the present invention more clearly understandable.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
fig. 1 is a flow chart of a method for testing and fitting a multi-carrier system according to an embodiment of the invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
Aiming at the problem of inaccuracy of characterization of transport characteristics in mercury cadmium telluride by using the Hall effect in the related art. Researchers have improved the traditional fixed magnetic field hall measurement methods, and mobility spectrometry has emerged. The mobility spectrometry technology is developed by magnetic transport measurement of a variable magnetic field and is an evaluation means for analyzing the electrical properties of a material with multiple carriers participating in electric conduction. The mobility spectrometry method overcomes the defects of the traditional method, can obtain more and more accurate electrical information, but the result given by the mobility spectrometry is only qualitative or semi-quantitative, and in order to more accurately obtain the electrical parameters of the material, methods such as maximum entropy mobility spectrometry and the like are sequentially appeared. However, the conclusion obtained from the actual processing result is not completely credible, and the analysis result often appears many unnecessary peaks which are easy to appear and have no physical significance, so that many false images are caused to the analysis of the test result, and the data cannot be quantitatively analyzed. In order to analyze which useful peaks are, researchers often need to change experimental parameters through various means to perform comparison experiments so as to make reasonable explanations for various peaks, which undoubtedly increases the uncertainty of the analysis and various human factors.
The embodiment of the invention provides a method for testing and fitting a multi-carrier system, as shown in fig. 1, the method comprises the following steps:
s1, placing the sample in a low-temperature and variable magnetic field, and measuring the transverse conductivity sigma of the samplexxAnd longitudinal conductivity σxy；
It should be noted that "low temperature" mentioned herein may be understood as an environment with a temperature below 90K, and "variable magnetic field" may be understood as an environment with a changing magnetic field strength, where the changing magnetic field strength may be continuous or discontinuous.
S2, fitting the measured sigma xx and sigma xy according to the formula 1 and the formula 2, calculating the mobility of various carriers in the sample,
wherein q is the type number of carriers in the sample, B is magnetic induction intensity, sigma i is the conductivity of the i-th type carriers, and mu i is the mobility of the i-th type carriers;
it can be understood that, assuming that a sample contains q carriers, each of which forms a channel, the conductivity formed by the q carriers is calculated by the equation to the right of the equal sign of equation 1, and then the lateral conductivity obtained on the actual side is fitted thereto, and similarly, the conductivity formed by the q carriers is calculated by the equation to the right of the equal sign of equation 2, and then the longitudinal conductivity obtained on the actual side is fitted thereto. When the fitting is successful through both the formula 1 and the formula 2, the fact that the sample contains the q carriers can be determined.
S3, determining the concentration ni of each carrier in the sample according to the formula 3 based on the calculated mobility of each carrier in the sample,
σi＝μinie the values of the equations 3 are,
wherein e is the electron electric quantity.
By adopting the embodiment of the invention, relatively accurate material electrical parameter information can be obtained, the design capability of the detector structure can be improved, the carrier concentration and the mobility of each conductive type in the material are optimized by guiding the process, the dark current of the device is reduced, and the performance of the detector assembly is improved.
On the basis of the above-described embodiment, various modified embodiments are further proposed, and it is to be noted herein that, in order to make the description brief, only the differences from the above-described embodiment are described in the various modified embodiments.
According to some embodiments of the invention, the sample is placed in a varying magnetic field and the transverse conductivity σ of the sample is measuredxxAnd longitudinal conductivity σxyThe method comprises the following steps:
putting the sample in a low-temperature variable magnetic field, and introducing current I to the sample through an electrode of the samplexRecording the voltage V of the sample in the direction of the current flowxAnd a voltage V in the direction perpendicular to the current flowy；
Based on Ix、VxAnd VyCalculating the transverse resistance R of the samplexyAnd a longitudinal resistance Rxx；
Length, width and height of the test specimen and based on RxyAnd RxxCalculating the transverse resistivity rho of the samplexyAnd longitudinal resistivity ρxx；
According to rhoxyAnd ρxxCalculating the transverse conductivity σ of the samplexxAnd longitudinal conductivity σxy。
Further, placing the sample in a low-temperature, varying magnetic field, comprising:
the sample was placed in an environment at a temperature of 77K and a magnetic field of + -10T.
According to some embodiments of the invention, 3 ≦ q ≦ 7.
According to some embodiments of the invention, q is 6.
According to some embodiments of the invention, the method further comprises:
according to μiThe type of the carrier is judged.
The following describes a method for testing and fitting a multi-carrier system according to an embodiment of the present invention in detail. It is to be understood that the following description is illustrative only and is not intended to be in any way limiting. All similar structures and similar variations thereof adopted by the invention are intended to fall within the scope of the invention.
Because the conventional magnetic transport measurement result cannot accurately represent the real electrical property of the magnetic transport measurement result, the mobility spectrometry and other methods are easy to generate a plurality of redundant peaks without physical significance, so that a plurality of false images are caused for the analysis of the test result, and the method is very unfavorable for accurately analyzing the transport behavior of the current carrier. Meanwhile, the mobility spectrum is difficult to carry out quantitative analysis on the concentration of the current carrier, the specific concentration is often calculated through integration, and the obtained result still has high uncertainty. The reason for the deep analysis of the problems exposed by the mobility spectrometry technology is that in the analysis and fitting processes of the mobility spectrometry, carriers with each mobility are considered, which is undoubtedly very blind in the fitting process, and a huge calculation process often covers many physical essences and cannot accurately position the true mobility ranges of electrons and holes. When iteration is performed based on the principle of maximum entropy, the iteration is usually corresponding to a plurality of completely different mobility distribution results near the maximum value of the entropy, so that a large number of mixed peaks appear in a fitting result, and meanwhile, the uncertainty of a certain mobility analysis result becomes large.
In order to better analyze the transport behavior of multiple carriers in mercury cadmium telluride, the embodiment of the invention provides a method for testing and fitting a multi-carrier system, which can be used for analyzing the transport behavior of the multi-carrier system in mercury cadmium telluride materials, and specifically comprises the following steps:
(1) and leading out electrodes on the surface of the sample by pressing indium so as to perform Hall test. The sample is placed in a low-temperature high-intensity magnetic field environment for variable magnetic field testing, the current introduced during the testing is recorded as x, the size of the current is 1mA, namely Ix is 1mA, the testing temperature is 77K, the size of the magnetic field is +/-10T, and meanwhile, the voltage Vx in the current direction and the voltage Vy in the direction perpendicular to the current direction, namely the Hall voltage, are recorded.
(2) The lateral magnetic resistance, namely the hall resistance Rxy is Vy/Ix, but the experimental raw data often includes a real hall resistance and an unequal resistance which has interference to analysis, and the lateral residual resistance when the magnetic field is zero needs to be deducted, so that the real hall resistance is obtained. The longitudinal resistance of the sample Rxx is Vx/Ix.
(3) And converting Rxy and Rxx by the geometrical parameters of the sample, namely the length, the width and the height of the sample, wherein rho is RS/L, wherein S is the area of the material, and L is the length, so as to obtain the Hall resistivity rhoxy and the longitudinal resistivity rhoxx.
(4) The resistivity is converted to conductivity by the following formula.
(5) Let the total carrier species be denoted as q, i.e. a total of q channels of carriers contribute to the conductance, where the lateral and longitudinal conductivities can be expressed as:
where B is the magnetic induction and μ i is the mobility of the carriers of the ith channel.
(6) Select enough q to fit σ xx and σ xy to get the mobility μ i for each channel. And can judge whether the electron and the hole exist according to the sign of the mu i. Usually, in mercury cadmium telluride, the number of carriers is at most 6, and meaningless stray channels can be avoided by selecting proper q, namely stray peaks in a mobility spectrum, so that data are fitted to obtain the mobility and the conductivity of carriers of different channels.
(7) The concentration ni of the carriers in the corresponding channel can be obtained according to the following formula.
σi＝μinie
Wherein e is the electron charge.
According to the embodiment of the invention, the low-temperature variable magnetic field test is carried out through the high-intensity magnetic field Hall test system, the iteration times are reduced, the calculation time is reduced, the traditional Hall effect analysis method is improved, and the multi-channel fitting is carried out on the experimental data. The obtained conclusion is more reliable, the theoretical fitting value is highly consistent with the experimental test data, and the obtained experimental conclusion is also reasonable.
It should be noted that the above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the present invention, and those skilled in the art can make various modifications and changes. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (6)
1. A method for testing and fitting a multi-carrier system is characterized by comprising the following steps:
placing a sample in a low-temperature variable magnetic field, and measuring the transverse conductivity sigma of the samplexxAnd longitudinal conductivity σxy；
Calculating the mobility of each type of carriers in the sample by performing fitting operation on the measured σ xx and σ xy according to formula 1 and formula 2,
wherein q is the type number of carriers in the sample, B is magnetic induction intensity, sigma i is the conductivity of the ith type of carriers, and mu i is the mobility of the ith type of carriers;
the method for calculating the mobility of various carriers specifically comprises the following steps:
assuming that a sample contains q carriers, calculating the conductivity formed by the q carriers through a formula theory on the right side of the equal sign of a formula 1, fitting the actually measured transverse conductivity with the conductivity, calculating the conductivity formed by the q carriers through the formula theory on the right side of the equal sign of a formula 2 in the same way, fitting the actually measured longitudinal conductivity with the conductivity, and determining that the sample contains the q carriers when the fitting is successful through the formula 1 and the formula 2;
determining the concentration ni of each type of carrier in the sample according to formula 3 based on the calculated mobility of each type of carrier in the sample,
σi＝μinie the values of the equations 3 are,
wherein e is the electron electric quantity.
2. The method of claim 1, wherein the sample is placed in a varying magnetic field and the transverse conductivity σ of the sample is measuredxxAnd longitudinal conductivity σxyThe method comprises the following steps:
putting the sample in a low-temperature variable magnetic field, and introducing current I to the sample through an electrode of the samplexRecording the voltage V of the sample in the direction of the current flowxAnd a voltage V in the direction perpendicular to the current flowy；
Based on the IxThe VxAnd said VyCalculating the transverse resistance R of the samplexyAnd a longitudinal resistance Rxx；
Testing the length, width and height of the sample and based on the RxyAnd said RxxCalculating the transverse resistivity rho of the samplexyAnd longitudinal resistivity ρxx；
According to the rhoxyAnd the rhoxxCalculating the transverse conductivity σ of the samplexxAnd longitudinal conductivity σxy。
3. The method of claim 2, wherein said subjecting said sample to a low temperature, varying magnetic field comprises:
the sample was placed in an environment at a temperature of 77K and a magnetic field of ± 10T.
4. The method of claim 1, wherein 3. ltoreq. q.ltoreq.7.
5. The method of claim 4, wherein q is 6.
6. The method of claim 1, wherein the method further comprises:
according to said μiThe type of the carrier is judged.
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