CN111024745A - Method for measuring and calculating doping concentration of high-doped semiconductor - Google Patents

Method for measuring and calculating doping concentration of high-doped semiconductor Download PDF

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CN111024745A
CN111024745A CN201911144858.4A CN201911144858A CN111024745A CN 111024745 A CN111024745 A CN 111024745A CN 201911144858 A CN201911144858 A CN 201911144858A CN 111024745 A CN111024745 A CN 111024745A
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calculating
room temperature
concentration
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temperature
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陈施施
张新河
温正欣
叶怀宇
张国旗
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Southwest University of Science and Technology
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Shenzhen Third Generation Semiconductor Research Institute
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N24/00Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects
    • G01N24/14Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects by using cyclotron resonance
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00Investigating or analysing materials by the use of electric, electrochemical, or magnetic means

Abstract

The invention belongs to the field of semiconductor material and process test, and discloses a method for measuring and calculating the doping concentration of a high-doped semiconductor. The method at least comprises the following implementation steps: s1, calculating equivalent state density N by using cyclotron resonance experiment*(ii) a S2, measuring the carrier concentration n at room temperature by a room temperature Hall experiment(Room temperature)(ii) a S3, calculating weak ionization energy epsilon of the current carrier in the weak ionization region through a variable-temperature Hall experiment; s4, combining the equivalent state density N obtained in the step*Concentration of carriers n(Room temperature)And weak ionization energy epsilon to calculate the doping concentration N of the highly doped semiconductor. The invention overcomes the limitation of the existing methods for testing the doping concentration of several semiconductors, and can obtain the doping concentration of a high-doped semiconductor, especially a wide-bandgap semiconductor, more simply, conveniently and accurately through basic experiments and simple calculation and fitting.

Description

Method for measuring and calculating doping concentration of high-doped semiconductor
Technical Field
The invention belongs to the field of semiconductor material and process test, and particularly relates to a method for measuring and calculating the doping concentration of a high-doped semiconductor.
Background
As an important branch in the field of microelectronic devices, discrete devices are widely applied in the aspects of military affairs, aerospace, transportation, power transmission and the like, and have very profound influence on the production and life style of people. The performance of semiconductor devices is closely related to the materials used in the devices, and the third generation semiconductor materials mainly including silicon carbide and gallium nitride are receiving more and more attention. The silicon carbide has the excellent characteristics of high thermal conductivity, high electronic saturation rate, high radiation resistance and the like, and is suitable for manufacturing high-temperature, high-frequency, radiation-resistant and high-power devices; gallium nitride has higher breakdown field strength and electron saturation velocity, and is considered as an ideal material for the next generation of microwave radio frequency electronic devices.
Both the power semiconductor device and the microwave radio frequency semiconductor device need to realize ohmic contact on the surface of the device to extract current in the semiconductor, and the ohmic contact area is generally smaller than 20% -30% of the device, so that the contact resistivity of the ohmic contact is required to be 10-6Ω·cm2Within the range. The surface doping concentration can be raised to an order of 1019cm-3 or even higher by means of highly doped epitaxial growth or ion implantation to obtain a concentration lower than 10-6Ω·cm2The contact resistivity of (2) to realize good ohmic contact. Therefore, the method has certain practical significance for accurately measuring the doping concentration of the highly doped silicon carbide, further exploring the mechanism of ohmic contact, improving the ohmic contact efficiency and promoting the development of power semiconductor devices and microwave radio frequency semiconductor devices.
The existing methods for testing the doping concentration of the semiconductor material mainly comprise the following 4 methods: mercury probe C-V method, SIMS test method, Hall experiment method, and four-probe method. The above 4 testing methods are all insufficient for testing the doping concentration of the wide bandgap and high doping semiconductor.
Mercury probe C-V method: the mercury probe C-V method is the most commonly used method for testing the epitaxial doping concentration of silicon carbide and has the doping concentration of more than 2.5 multiplied by 1018cm-3The above wafer, due to its depletion layer width
Figure BDA0002280871650000011
The variation is less than 0.1 μm, the test result is greatly influenced by interface state, interface charge and the like, and the test error is large.
SIMS test method: the SIMS test is a destructive test, and the test results are the ratio and concentration of each element in the semiconductor, which correspond to the gap doping concentration and the substitutional doping concentration. Typically, substitutional doping is the effective doping in the semiconductor material, and thus the results of the SIMS test do not accurately reflect the actual effective doping concentration of silicon carbide.
Hall experiment method: the test results are only carrier concentration and not the actual doping concentration of epitaxy or ion implantation. In general, hall effect experiments can be used to measure the doping concentration in semiconductors under strong ionization, while for wide bandgap semiconductor materials, such as silicon carbide and gallium nitride, the ionization energy is higher, and at higher doping concentrations, often in weak ionization state, the carrier concentration measured by the hall effect is much smaller than the actual doping concentration of the semiconductor material.
The four-probe method: the test result is the product of carrier concentration and mobility. The four-probe method is often used for testing the resistivity of a semiconductor material, and as can be seen from a conductivity formula, the result of the four-probe method is the product of the carrier concentration and the mobility in the semiconductor material, and since the mobility is influenced by scattering and changes with the doping concentration and the temperature, and meanwhile, the carrier concentration is the same as the actual doping concentration in the semiconductor only under strong ions, the method cannot accurately reflect the actual doping concentration of the semiconductor material.
Disclosure of Invention
The invention aims to provide a method for measuring and calculating the doping concentration in a high-doped semiconductor, which is convenient and accurate, aiming at the defects of the existing method for measuring the doping concentration of the high-doped semiconductor, and comprises the following steps:
s1, calculating equivalent state density N by using cyclotron resonance experiment*
S2, measuring the carrier concentration n at room temperature by a room temperature Hall experiment(Room temperature)
S3, calculating weak ionization energy epsilon of a current carrier in a weak ionization region through a variable-temperature Hall experiment;
s4, obtaining the equivalent state density N through the steps*Concentration of carriers n(Room temperature)And weak ionization energy epsilon to calculate the doping concentration N of the highly doped semiconductor.
Preferably, the step S1 includes measuring the electromagnetic field frequency ω and the magnetic field strength B during the cyclotron resonance absorption by the cyclotron resonance experiment, and calculating the carrier effective mass m*From which the equivalent density of states N is calculated*
Preferably, the method for measuring and calculating the effective mass of the current carrier is
Figure BDA0002280871650000021
Where q is the charge carrier amount.
Preferably, the equivalent density of states is calculated by
Figure BDA0002280871650000022
Wherein k isBBoltzmann constant, T temperature, h planck constant.
Preferably, the room-temperature carrier concentration n in S2(Room temperature)The measuring and calculating method comprises
Figure BDA0002280871650000023
Wherein IxFor the current applied across the semiconductor, BzFor the intensity of the applied magnetic field perpendicular to the direction of the current, UH (Room temperature)Is the hall potential and d is the semiconductor width.
Preferably, the S3 includes:
s3.1 gradient-reducing ambient temperature of Hall experiment, keeping semiconductor in weak ionization region, and testing Hall potential U corresponding to each temperatureHAnd calculating to obtain the carrier concentration n corresponding to each temperature.
S3.2 the carrier concentration n obtained from S3.1 is calculated by the formula
Figure BDA0002280871650000024
To carry out
Figure BDA0002280871650000025
Linear fitting to obtain slope k, and calculating weak ionization energy epsilon-2 k.kBWherein k isBBoltzmann constant.
Preferably, the S4 includes a carrier concentration passing through a weak ionization region
Figure BDA0002280871650000026
Wherein g is the carrier spin degeneracy, and is substituted into the room-temperature carrier concentration n(Room temperature)And calculating to obtain the doping concentration N of the high-doped semiconductor.
Advantageous results of the invention
The invention discloses a method for measuring and calculating the doping concentration in a highly doped semiconductor, which respectively measures the equivalent state density N through a cyclotron resonance experiment and a variable-temperature Hall experiment*And weak ionization energy epsilon, so that the effective doping concentration in a weak ionization state is calculated more accurately, the calculation mode is not influenced by an interface state and interface charges, the calculated substitutional doping concentration in the semiconductor material is calculated, the accuracy is high, and the method has certain practical significance for further exploring an ohmic contact mechanism, improving ohmic contact efficiency and promoting the development of high-power, radio frequency and microwave devices.
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FIG. 1 is a flowchart of the measurement and calculation method according to embodiments 1 and 2 of the present invention;
FIG. 2 is a schematic diagram of the cyclotron resonance experiment of examples 1 and 2 of the present invention;
fig. 3 is a schematic diagram of a hall experiment in the measurement and calculation of the doping concentration of the N-type highly doped silicon carbide material in embodiment 1 of the present invention;
fig. 4 is a schematic diagram of a hall experiment in the measurement and calculation of the doping concentration of the P-type highly-doped gallium nitride material in embodiment 2 of the present invention.
Detailed Description
In order that the objects, technical solutions and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings in conjunction with the following specific embodiments.
Example 1
The present embodiment provides a method for measuring and calculating a doping concentration of N-type highly doped silicon carbide, as shown in fig. 1, the method includes the steps of:
s1, obtaining conduction band equivalent state density N by using cyclotron resonance experimentCAs shown in fig. 2, the specific experimental steps of the cyclotron resonance test are as follows: a constant magnetic field B is applied to a silicon carbide sample, an alternating electromagnetic field is applied, and an electric component E is perpendicular to the constant magnetic field B. Because electrons in the semiconductor do spiral motion around the magnetic field under the action of Lorentz force and are influenced by the alternating electromagnetic field, when the frequency omega of the electromagnetic field and the cyclotron frequency of the electrons
Figure BDA0002280871650000031
At the same time, the electrons will be constantly accelerated by the alternating electromagnetic field, thereby gaining energy, causing resonant absorption. The effective mass of electrons is obtained by measuring the frequency omega of electromagnetic field and the magnetic field intensity B during the absorption of cyclotron resonance
Figure BDA0002280871650000032
In the formula, q is the charge quantity, and the obtained effective mass of electrons is substituted into the equivalent state density formula to calculate the equivalent state density of the conduction band
Figure BDA0002280871650000033
As shown in fig. 3, a schematic diagram of a hall experiment in the present embodiment is shown, and the present embodiment includes a normal temperature hall experiment and a variable temperature hall experiment:
s2, obtaining the electron concentration n at room temperature by room temperature Hall experiment(Room temperature)The specific experimental steps are as follows:
at room temperature, a current I is applied to N-type silicon carbide with the thickness dxAnd applying a magnetic field B perpendicular to the current directionzA lateral hall potential difference U is generated in a direction perpendicular to the current and magnetic field directionsH. Testing Hall potential U at both ends of semiconductor at room temperatureH (Room temperature)And calculating to obtain the Hall coefficient at room temperature
Figure BDA0002280871650000041
Substituting into the relation between Hall coefficient and carrier concentration to obtain the value at room temperatureCarrier concentration of electrons
Figure BDA0002280871650000042
n(Room temperature)And UH (Room temperature)In a relationship of
Figure BDA0002280871650000043
Wherein q is the amount of charge;
s3, measuring donor weak ionization energy epsilon by temperature-changing Hall experimentDThe method comprises the following specific steps:
reducing the temperature of the Hall experiment according to a certain gradient, keeping the silicon carbide in a weak ionization region, and testing the corresponding Hall potential U at each temperatureHCalculating the electron carrier concentration n corresponding to each temperature, and calculating the electron carrier concentration n under weak current
Figure BDA0002280871650000044
The curve chart is fitted, and the concentration of electron carriers under weak ionization and the temperature have the following relationship:
Figure BDA0002280871650000045
wherein g isDIs the degree of donor spin degeneracy, and is obtained by taking the logarithm of both sides of the formula
Figure BDA0002280871650000046
Description (lnn) with
Figure BDA0002280871650000047
In a linear function relationship with a slope of
Figure BDA0002280871650000048
The weak current is ionized
Figure BDA0002280871650000049
Slope k of the fitted curve and
Figure BDA00022808716500000410
comparing, calculating the donor weak ionization energy epsilon of the obtained N-type highly doped silicon carbideD=-2k·kB
S4, calculating and solvingDoping concentration of highly doped silicon carbide: by the formula of carrier concentration under weak current
Figure BDA00022808716500000411
Figure BDA00022808716500000412
Substituted donor spin degeneracy gDConduction band equivalent density of states
Figure BDA00022808716500000413
Ionization energy of donor ∈DAnd a carrier concentration n at room temperature(Room temperature)Calculating to obtain the doping concentration N of the highly doped silicon carbideD
Example 2
The embodiment provides a method for measuring and calculating the doping concentration of P-type highly-doped gallium nitride, which comprises the following steps:
and S1, measuring and calculating valence band equivalent state density by using a cyclotron resonance experiment, wherein the cyclotron resonance experiment specifically comprises the steps of adding a constant magnetic field B on a gallium nitride sample, applying an alternating electromagnetic field, and enabling an electric component E to be perpendicular to the constant magnetic field B. The holes in the semiconductor will make a spiral motion around the magnetic field, and will be influenced by the alternating electromagnetic field when the frequency of the electromagnetic field is omega and the convolution frequency of the holes
Figure BDA00022808716500000414
At the same time, the holes will be constantly accelerated by the alternating electromagnetic field, thereby gaining energy, causing resonant absorption. Obtaining the effective mass of the cavity by measuring the frequency omega of the electromagnetic field and the magnetic field intensity B during the absorption of the cyclotron resonance
Figure BDA00022808716500000415
Substituting the effective mass of the cavity into the equivalent density formula to obtain the equivalent density of valence band
Figure BDA00022808716500000416
As shown in fig. 3, a schematic diagram of a hall experiment in the present embodiment is shown, and the present embodiment includes a normal temperature hall experiment and a variable temperature hall experiment:
s2 obtaining hole concentration p at room temperature by room temperature Hall experiment(Room temperature)The method comprises the following specific steps: passing current I to P-type gallium nitride with thickness dxAnd applying a magnetic field B perpendicular to the current directionzA lateral hall potential difference U is generated in a direction perpendicular to the current and magnetic field directionsH. Hall potential U at two ends of gallium nitride under room temperature is testedH (Room temperature)And calculating to obtain the Hall coefficient at room temperature
Figure BDA0002280871650000051
Substituting into the relation between Hall coefficient and carrier concentration to obtain the carrier concentration of hole at room temperature
Figure BDA0002280871650000052
Wherein q is the amount of charge.
S3 temperature-changing Hall experiment, after the Hall experiment at room temperature is completed, the temperature of the Hall experiment is reduced according to a certain gradient, gallium nitride is kept in a weak ionization region, and Hall potential U corresponding to each temperature is testedHAnd calculating to obtain the corresponding hole carrier concentration p at each temperature. For weak ionization
Figure BDA0002280871650000053
The curve chart is fitted, and the concentration of hole carriers under weak ionization and the temperature have the following relationship:
Figure BDA0002280871650000054
taking logarithm on both sides of formula
Figure BDA0002280871650000055
Description (lnp) with
Figure BDA0002280871650000056
In a linear function relationship with a slope of
Figure BDA0002280871650000057
The weak current is ionized
Figure BDA0002280871650000058
Slope k of the fitted curve and
Figure BDA0002280871650000059
comparing, and calculating the acceptor weak ionization energy epsilon of the P-type highly-doped silicon carbideA=-2k·kB
S4, calculating and solving the doping concentration of the highly doped silicon carbide: by the formula of carrier concentration under weak current
Figure BDA00022808716500000510
Figure BDA00022808716500000511
Substituted acceptor spin degeneracy gAValence band equivalent density of states
Figure BDA00022808716500000512
Acceptor ionization energy epsilonAAnd a carrier concentration p at room temperature(Room temperature)Calculating to obtain the doping concentration N of the highly doped gallium nitrideA
The above examples have donor electron doping concentrations N for N-type doped semiconductorsDAnd acceptor hole doping concentration N of p-type doped semiconductorAThe method is different from the traditional method which only can measure the carrier concentration n in the strong ionization state as the doping concentration, the method measures and calculates the weak ionization energy more accurately by combining the cyclotron resonance method, the room temperature Hall experiment and the variable temperature Hall experiment on the basis of measuring the carrier concentration n, thereby measuring the effective doping concentration in the weak ionization state, and the method is more accurate and reasonable and has wider application range compared with the traditional method.
The above-mentioned embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, and it should be understood that the above-mentioned embodiments are only examples of the present invention and are not intended to limit the present invention. The examples used herein are intended merely to facilitate an understanding of ways in which the embodiments herein may be practiced and to further enable those of skill in the art to practice the embodiments herein. Thus, the examples herein should not be construed as limiting the scope of the embodiments herein, and it is intended to be within the scope of the present invention to replace silicon carbide or gallium nitride materials in embodiments of the present invention with other semiconductor materials, or to use strong or medium ionization calculation formulas for lightly doped semiconductors in the calculation solutions to solve for their actual doping concentrations.

Claims (7)

1. A method for measuring and calculating the doping concentration of a high-doped semiconductor is characterized by comprising the following steps: the method comprises the following steps:
s1, calculating equivalent state density N by using cyclotron resonance experiment*
S2, measuring the carrier concentration n at room temperature by a room temperature Hall experiment(Room temperature)
S3, calculating weak ionization energy epsilon of a current carrier in a weak ionization region through a variable-temperature Hall experiment;
s4, obtaining the equivalent state density N through the steps*Concentration of carriers n(Room temperature)And weak ionization energy epsilon to calculate the doping concentration N of the highly doped semiconductor.
2. The method of claim 1, further comprising: s1 comprises measuring the electromagnetic field frequency omega and the magnetic field intensity B in the process of cyclotron resonance absorption through a cyclotron resonance experiment, and calculating the effective mass m of the current carrier*From which the equivalent density of states N is calculated*
3. The method of claim 2, further comprising: the method for measuring and calculating the effective mass of the current carrier comprises
Figure FDA0002280871640000011
Where q is the charge carrier amount.
4. The method of claim 3, further comprising: the equivalent density of states is calculated by
Figure FDA0002280871640000012
Figure FDA0002280871640000013
Wherein k isBBoltzmann constant, T temperature, h planck constant.
5. The method of claim 1, further comprising: the room temperature carrier concentration n in S2(Room temperature)The measuring and calculating method comprises
Figure FDA0002280871640000014
Wherein IxFor the current applied across the semiconductor, BzFor the intensity of the applied magnetic field perpendicular to the direction of the current, UH (Room temperature)Is the hall potential and d is the semiconductor width.
6. The method according to claim 5, wherein the S3 includes:
s3.1 gradient-reducing ambient temperature of Hall experiment, keeping semiconductor in weak ionization region, and testing Hall potential U corresponding to each temperatureHAnd calculating to obtain the carrier concentration n corresponding to each temperature.
S3.2 the carrier concentration n obtained from S3.1 is calculated by the formula
Figure FDA0002280871640000015
To carry out
Figure FDA0002280871640000016
Linear fitting to obtain slope k, and calculating weak ionization energy epsilon-2 k.kBWherein k isBBoltzmann constant.
7. The method of claim 6, further comprising: the S4 includes passing through weak ionization region carrier concentration
Figure FDA0002280871640000017
Figure FDA0002280871640000018
Wherein g is the carrier spin degeneracy, and is substituted into the room-temperature carrier concentration n(Room temperature)And calculating to obtain the doping concentration N of the high-doped semiconductor.
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