CN113702451A - Defect state space position determination method for excitation energy level capacitance analysis method - Google Patents

Defect state space position determination method for excitation energy level capacitance analysis method Download PDF

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CN113702451A
CN113702451A CN202110957687.8A CN202110957687A CN113702451A CN 113702451 A CN113702451 A CN 113702451A CN 202110957687 A CN202110957687 A CN 202110957687A CN 113702451 A CN113702451 A CN 113702451A
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trap
frequency
dlcp
energy level
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陈小青
张鑫
严辉
张永哲
孙召清
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Beijing University of Technology
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Abstract

A defect state space position measuring method for an excitation energy level capacitance analysis method belongs to the field of semiconductor material testing. Recording the state density of a trap state with the energy level depth shallower than E as N (E, V) under the condition that the DLCP voltage is V; when the DLCP voltage is V (corresponding to a specific spatial position), the state density in the unit position and energy space is represented as g (E, V). Calculating (x) at different energies, spatial positionse(ETi,Vk),N(ETi,Vk) ); finally, according to the formula (1), the state density g (E) of the trap state in the unit position and energy space can be calculatedTi,Vk) I.e. by
Figure DDA0003220114180000011
Figure DDA0003220114180000012
Thus can be arranged into (x)e(ETi,Vk),g(ETi,Vk) Data table of (b), where xe(ETi，Vk) I.e. the trap position solved.

Description

Defect state space position determination method for excitation energy level capacitance analysis method
Technical Field
The invention belongs to the field of semiconductor material testing, and particularly provides a method for measuring a defect state space position by using a Drive-level capacitance analysis method (Drive-level capacitance profiling)
Background
In order to improve the performance of semiconductor devices, defects and interface defects of semiconductor materials have attracted extensive attention in academia and industry. The capacitance testing technology is an important means for researching the matrix defect and the interface defect of a semiconductor device, and has been widely applied to the fields of solar cells and light emitting diodes. The basic method of this technique is to apply a perturbation voltage signal to the semiconductor device to measure the capacitance of the device, and since the trapping or emission of carriers in the defect state affects the capacitance of the device, the capacitance measurement can be used to analyze the information about the defect state. Based on basic physical images of the semiconductor device, defect states of different spatial positions and energy level depths in a semiconductor can be respectively researched by changing conditions such as bias voltage, frequency and the like during capacitance measurement, so that a series of defect state analysis methods based on capacitance measurement are formed, wherein the method comprises the following steps: Capacitance-Voltage (Capacitance-Voltage), Deep-level transient spectrum (Deep-level transient spectrum), and Drive-level Capacitance profiling (Drive-level Capacitance profiling). Excitation level capacitance analysis (hereinafter DLCP) is used to obtain the spatial distribution information and energy distribution information of the defects of the material, and the measurement principle, related assumptions and operation method thereof are described in j.appl.phys.95, 1000-1010 (2004). However, the DLCP method is limited in that the spatial position (x) of the defect cannot be accurately givene) Only one and x can be giveneRelative "quasi-position" ((ii))<x>). According to J.appl.Phys.95, 1000-1010 (2004), xeAnd<x>there is a theoretical correlation, i.e.
Figure BDA0003220114160000021
Wherein epsilon is the dielectric constant of the semiconductor material, F is the position x of the defect in the measurement processeElectric field of (E)T,xe) Is xeIs shallower than ET(according to J.appl.Phys.95, 1000-1010 (2004), ETDepending on the frequency used in the capacitive test). So far, since there is no measurementOr analysis of F (E)T,xe) And therefore cannot be effectively determined according to the measured<x>Solving for xeEven more fail to obtain xeEnergy level and DLCP voltage. In order to solve the problem of the DLCP technology, the invention provides a method for testing the defect state position based on the DLCP principle.
Disclosure of Invention
Basic physical images and assumptions adopted by the DLCP technology are described in j.appl.phys.95, 1000-1010 (2004), and measurement devices thereof include various types of variable-frequency and variable-dc-bias capacitance test equipment, such as LCR testers, impedance testers, semiconductor parameter analyzers and other devices, and test systems composed of other devices. This method analyzes different frequencies and voltages V (i.e. the voltage V) systematically
Figure BDA0003220114160000022
Wherein VDCIs a direct current bias voltage and is used for controlling the voltage,
Figure BDA0003220114160000023
is AC bias) to study the state density (dimension is' number/(cm)3eV) "). Wherein the frequency determines the deepest trap state energy level that can be detected; v together with frequency (or energy level) influences the spatial position x of the trap states that can be detectedeThis dependency is the problem addressed by the present invention.
For convenience of description, the state density of a trap state with an energy level depth shallower than E under the condition that the voltage of the DLCP is V (corresponding to a specific spatial position) is recorded as N (E, V), and is defined as the difference between the shallow acceptor impurity concentration and the shallow donor impurity concentration, and the dimension is "unit/(cm3) "; under the condition that the DLCP voltage is V (corresponding to a specific space position), the state density (dimension is' number/(cm))3eV) ") as g (E, V). It is obvious that
Figure BDA0003220114160000031
The measurement method is used for providing a test method of defect state space distribution for the DLCP technology. The basic physical images, assumptions and experimental set-up are the same as for the DLCP technique, described in j.appl.phys.95, 1000-1010 (2004). The basic analysis principle is shown in fig. 1, the basic implementation flow chart is shown in fig. 2, and the implementation steps are briefly described as follows:
1) finding the highest frequency ω that can be used to analyze the device internal carrier behavior through the capacitance-frequency relationship of the devicedevice(because when the frequency ω is>ωdeviceIn time, the capacitance is mainly derived from device geometry capacitance), and the analytical method is referred to as j.app.phys.118,205504 (2015). Will omegadeviceHighest available frequency omega with capacitance measuring equipmentinstrumentComparison, let omegamaxIs omegadeviceAnd ωinstrumentThe smaller of them.
2) At a fixed DLCP voltage of V1(i.e. the
Figure BDA0003220114160000032
Wherein VDCIs a direct current bias voltage and is used for controlling the voltage,
Figure BDA0003220114160000033
is ac bias) is constant, the following operations are performed in sequence.
2.1 from ωmaxInitially, according to the DLCP method, solve for (1) ωmaxCorresponding trap energy level ET0(2) under the specific conditions (E)T0,V1) Lower trap "quasi-position"<x>(ET0,V1) And (3) the depth of the energy level is shallower than ET0State density of trap states (N (E)T0,V1) Defined as the difference between the shallow acceptor impurity concentration-the shallow donor impurity concentration); will (E)T0,V1) Under conditions, the location of the excited defect state is marked xe(ET0,V1) The electric field here is F (x)e(ET0,V1) Is marked as F)0(ii) a From the physical classical image of a semiconductor device, F (x)e(ET0,V1) Can be reasonably assumed to be 0, and thus
Figure BDA0003220114160000034
Further, the derivative of the electric field (F (x)) with respect to the spatial location (x) may be solved according to Gauss's law
Figure BDA0003220114160000041
Where q is the elementary charge and e is the dielectric constant.
2.2 on the basis of the previous step, by reducing the frequency to ω1＝ωmax/m1(1<m1<E, E is a natural logarithmic base) to study the trap level E with deeper trap levelsT1(ii) a According to the theory of DLCP, E can be calculatedT1I.e. ET1＝ET0+dET＝ET0+kTlnm1Where k is the boltzmann constant and T is the temperature; following the 2.1 steps, the depth of the energy level is found to be shallower than ET1Density of trap states (N (E)T1,V1) ); if N (E)T1,V1) Compare N (E)T0,V1) Cannot be ignored (e.g., N (E)T1,V1)-N(ET0,V1)>10％N(ET0，V1) M) is reduced moderately1Up to N (E)T1,V1) Compare N (E)T0,V1) The amount of change of (c) is negligible; due to N (E)T1,V1)≈N(ET0,V1) In (x)e(ET0,V1),xe(ET1,V1) In the interval), the position of any one point can be written as xe(ET0,V1) -x' (where 0<x′<[xe(ET0,V1)-xe(ET1,V1)]) (ii) a Electric field (F (x)) at this pointe(ET0,V1) -x')) can be expressed by formula (3) as
Figure BDA0003220114160000042
From the formula (4), in xe(ET1,V1) Here, the electric field is denoted as F1Is composed of
Figure BDA0003220114160000043
Wherein
Figure BDA0003220114160000044
Is defined as xe(ET0,V1)-xe(ET1,V1) And is and
Figure BDA0003220114160000045
wherein
Figure BDA0003220114160000051
From equation (6), one can obtain
Figure BDA0003220114160000052
And finally can also obtain
Figure BDA0003220114160000053
2.3 on the basis of the previous step, following the mode of operation of 2.2, continue by reducing the frequency to ω1/m2To study the trap level E with deeper trap levelsT2，m2Selection method and m1The selection modes are the same; and obtain ET2＝ET0+kTln(m1m2) And
Figure BDA0003220114160000054
Figure BDA0003220114160000055
2.4 following the above stepsStep three, continuously reducing the frequency to
Figure BDA0003220114160000056
(where i is the number of frequency reductions) and all of the required (E) are calculatedTi,xe(ETi,V1),N(ETi,V1) Combinations of (a) and (b); wherein
Figure BDA0003220114160000057
Figure BDA0003220114160000058
N(ETi,V1) Solving by a DLCP method;
3) for other voltages V, as with the DLCP methodkRepeating all steps of 1.1 to calculate (x) at different energies and spatial positionse(ETi,Vk),N(ETi,Vk) ); finally, according to the formula (1), the state density g (E) of the trap state in the unit position and energy space can be calculatedTi,Vk) I.e. by
Figure BDA0003220114160000059
Thus can be arranged into (x)e(ETi,Vk),g(ETi,Vk) Data table of (b), where xe(ETi,Vk) I.e. the trap position solved.
Drawings
FIG. 1 is a schematic diagram of the basic analysis principle of the present invention.
Fig. 2 is a flow chart of the basic implementation of the present invention.
Detailed Description
For the sake of understanding, a specific simple measurement example will be described below in conjunction with the schematic diagram and the measurement data, but the present invention is not limited to the following embodiments.
Example 1
The test sample is a laboratory self-made perovskite solar cell and has the structure of (ITO/SnO)2/CH3NH3PbI3Periro-OMeTAD/Au), dielectric of perovskiteConstant of about 2.7X 10-10F/m is 31X vacuum dielectric constant. This case will measure at V10.4V, the spatial position of the defect state with a depth of 0.396eV, i.e., xe(0.396eV,0.4V)。
The test equipment used in this case was Keysight B1500, omega of whichinstrumentIs 31.4MHz (5 MHz. times.2 π), ωdeviceIs 126 kHz. Thus omegamaxAt 126kHz, the corresponding trap energy level E can be obtained according to the classical DLCP technologyT0About 0.370 eV. At V1At 0.4V, N (E) is measured according to the classical DLCP techniqueT0,V1)＝3×1015/cm3，xe(ET0,V1)＝337nm，
Figure BDA0003220114160000061
Figure BDA0003220114160000062
On the basis of the previous step, the frequency is reduced to
Figure BDA0003220114160000063
In this case the depth of the trap level to be investigated becomes ET1＝0.396eV，
Figure BDA0003220114160000064
Obtaining N (E) according to classical DLCP techniqueT1,V1)＝3.2×1015/cm3. Obtained according to the formula (6)
Figure BDA0003220114160000065
Figure BDA0003220114160000066
To obtain finally
Figure BDA0003220114160000067
Figure BDA0003220114160000068
If the trap state space positions at other voltages and other energy level depths need to be further solved, the frequency and the voltage only need to be continuously changed.

Claims (1)

1. A method for determining the spatial position of a defect state by excitation energy level capacitance analysis is characterized by comprising the following steps:
1) finding the highest frequency ω that can be used to analyze the device internal carrier behavior through the capacitance-frequency relationship of the devicedeviceBecause when the frequency is ω>ωdeviceThe capacitance mainly comes from the geometrical capacitance of the device; will omegadeviceHighest available frequency omega with capacitance measuring equipmentinstrumentComparison, let omegamaxIs omegadeviceAnd ωinstrumentThe smaller of these;
2) at a fixed DLCP voltage of V1Without change, i.e.
Figure FDA0003220114150000011
Wherein VDCIs a direct current bias voltage and is used for controlling the voltage,
Figure FDA0003220114150000012
is an AC bias, the following operations are performed in sequence:
2.1 from ωmaxInitially, according to the DLCP method, solve for (1) ωmaxCorresponding trap energy level ET0(2) under the specific conditions (E)T0,V1) Lower trap "quasi-position"<x>(ET0,V1) And (3) the depth of the energy level is shallower than ET0State density of trap states (N (E)T0，V1) Defined as the difference between the shallow acceptor impurity concentration-the shallow donor impurity concentration); will (E)T0,V1) Under conditions, the location of the excited defect state is marked xe(ET0,V1) The electric field here is F (x)e(ET0,V1) Is marked as F)0(ii) a From the physical classical image of a semiconductor device, F (x)e(ET0,V1) Can be reasonably assumed to be 0, and thus
Figure FDA0003220114150000013
Further, the derivative of the electric field (F (x)) with respect to the spatial location (x) may be solved according to Gauss's law
Figure FDA0003220114150000014
Wherein q is the elementary charge and e is the dielectric constant;
2.2 on the basis of the previous step, by reducing the frequency to ω1＝ωmax/m1To study the trap level E with deeper trap levelsT1，1<m1<e, e is the natural logarithm base; according to the theory of DLCP, calculate ET1I.e. ET1＝ET0+dET＝ET0+kTlnm1Where k is the boltzmann constant and T is the temperature; following the 2.1 steps, the depth of the energy level is found to be shallower than ET1Density of trap states (N (E)T1,V1) ); if N (E)T1,V1) Compare N (E)T0,V1) Cannot be ignored, m is reduced moderately1Up to N (E)T1,V1) Compare N (E)T0,V1) The amount of change of (c) is negligible; due to N (E)T1,V1)≈N(ET0,V1) In (x)e(ET0,V1),xe(ET1,V1) In the interval), the position of any one point can be written as xe(ET0，V1) -x' (where 0<x′<[xe(ET0,V1)-xe(ET1,V1)]) (ii) a Electric field (F (x)) at this pointe(ET0，V1) -x')) can be expressed by formula (3) as
Figure FDA0003220114150000021
From the formula (4), in xe(ET1,V1) Here, the electric field is denoted as F1Is composed of
Figure FDA0003220114150000022
Wherein
Figure FDA0003220114150000023
Is defined as xe(ET0,F1)-xe(ET1，V1) And is and
Figure FDA0003220114150000024
wherein
Figure FDA0003220114150000025
From equation (6), one can obtain
Figure FDA0003220114150000026
And finally can also obtain
Figure FDA0003220114150000027
2.3 on the basis of the previous step, following the mode of operation of 2.2, continue by reducing the frequency to ω1/m2To study the trap level E with deeper trap levelsT2，m2Selection method and m1The selection modes are the same; and obtain ET2＝ET0+kTln(m1m2) And
Figure FDA0003220114150000028
Figure FDA0003220114150000029
2.4 following the above steps, continue to reduce the frequency to
Figure FDA0003220114150000031
Where i is the number of the frequency reduction, all the required (ET) are calculatedi,xe(ETi,V1)，N(ETi,V1) Combinations of (a) and (b); wherein
Figure FDA0003220114150000032
Figure FDA0003220114150000033
N(ETi,V1) Solving by a DLCP method;
3) for other voltages V, as with the DLCP methodkRepeat all steps of 1.1 to compute different energy, spatial locations for different (x)e(ETi,Vk),N(ETi,Vk) ); finally, according to the formula (1), the state density g (E) of the trap state in the unit position and energy space can be calculatedTi,Vk) I.e. by
Figure FDA0003220114150000034
Thus can be arranged into (x)e(ETi,Vk),g(ETi,Vk) Data table of (b), where xe(ETi,Vk) I.e. the trap position solved.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN88201059U (en) * 1988-01-28 1988-12-14 中国科学院长春物理所 Deep energy level transient optical spectormeter with mini-flasher
WO1990005908A1 (en) * 1988-11-18 1990-05-31 Magyar Tudományos Akadémia Müszaki Fizikai Kutató Intézete Improved method and apparatus for microwave transient spectroscopy of deep levels in semiconductors
CN110907792A (en) * 2019-11-28 2020-03-24 湘潭大学 Method and device for determining GaN irradiation defect energy level by combining DLTS with DLOS
CN114779035A (en) * 2022-04-14 2022-07-22 中国科学院新疆理化技术研究所 GaN power device defect energy level testing method based on low-frequency noise

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