GB 11297.7-1989 Test method for resistivity and Hall coefficient of indium antimonide single crystal

This method is applicable to the measurement of resistivity and Hall coefficient of rectangular and thin indium antimonide single crystal samples. GB 11297.7-1989 Test method for resistivity and Hall coefficient of indium antimonide single crystal GB11297.7-1989 Standard download decompression password: www.bzxz.net

National Standard of the People's Republic of China
Test method for tesistivity and Hall coefficientIn InSh slngle crystals
UDC 661.868.247
:621. 317. 33
GB 11297. 7 --89
This method is applicable to the measurement of resistivity and Hall coefficient of rectangular and thin indium antimonide single crystal samples. The sample used in this method is cut from indium antimonide single crystal. Electrode contact is made at specific positions. The resistivity and Hall coefficient of the sample are measured by DC method, and then the carrier density and carrier mobility of the sample are calculated. This method is suitable for antimonide steel single product samples with resistivity of 10-3~～10°0·cm. 1 Measurement and Principle
1.1 Measurement of Resistivity of Antimonide Steel Single Crystal
The resistivity of InSb single crystal can be measured directly. It is measured under zero magnetic field conditions. The definition of resistivity is the ratio of the potential gradient parallel to the current in the material to the current density. Figure 1 is the principle circuit for measuring resistivity.
Figure 1 Principle Circuit for Measuring Resistivity
When a constant sample current 1 is applied between the current electrodes 1.2 at both ends of the rectangular standard sample, a conduction voltage is generated between the electrode contact points 3.4 on the side of the sample. The connecting line between them is parallel to the current direction, so the resistivity at the electrode contact point is: Uub.
Rong: β
Sample resistivity, Q*ms
Ran Conductivity, V,
1--Sample current intensity A:
Sample width, m:
-Sample thickness, m!
The distance between the sample electrode contact points 3.4, m. 1.2 Measurement of Hall coefficient of antimonide single crystal
Approved by the Ministry of Machinery and Electronics Industry of the People's Republic of China on October 9, 1988 and implemented on January 1, 1990
GB 11297.789
The Hall coefficient of indium antimonide single crystal material can also be directly measured. When mutually perpendicular electric and magnetic fields are applied to a rectangular standard sample at the same time (Figure 2), the carriers deflect in a direction perpendicular to both the electric and magnetic fields, thus generating a transverse potential difference on both sides of the sample, i.e., Hall voltage. This phenomenon is called the Hall effect. The definition of the Hall coefficient is the ratio of the intensity of the transverse Hall electric field to the product of the density of the sample current and the magnetic flux density.
Formula: KH—
Hall coefficient of the sample, m/C
E—Intensity of the Hall electric field, V/m
J,—Density of sample current, A/m\
B,—Magnetic flux density, T.
For type II samples, the Hall coefficient is negative; for convex samples, the Hall coefficient is positive. n-InSb
p-InSb
Figure 2 Principle diagram of Hall coefficient measurement
Given the sample current intensity I (α direction) and magnetic flux density B (direction), if the hall potential difference UH (y direction) is measured, you can calculate the Hall coefficient Re of the sample:
Wu Zhong: RH
Hall coefficient of the sample, m/C;
Hall voltage, V
Magnetic flux density, Tt
Sample current intensity, A:
Hall electrode spacing of the sample, that is, the width of the sample, mi; the thickness of the sample, m.
1.3 Hall mobility
The ratio of the absolute value of the Hall coefficient to the resistivity is defined as the Hall mobility: h
Where:
Hall mobility, m\/(VS);
-Hall coefficient of the sample, m\/C,
-resistivity of the sample, 2m.
1.4 Carrier concentration and carrier mobility
GB 11297.789
Indium antimonide is a single-carrier extrinsic semiconductor at 77K, with a Hall factor of 1. The carrier concentration of the sample can be calculated from the measured Hall coefficient:
Where: n
Carrier concentration of the sample, m-\
-Hall coefficient of the sample, m/C;
Carrier charge, C.
Carrier mobility is the same as Hall mobility: F = l
Where: -
Carrier mobility of the sample, m\/(V·S): Hall mobility of the sample, m/(V·S). For n-type antimonide steel, the carriers are electrons, and for p-type indium antimonide, the carriers are holes. 2 Measurement method
2.1 Measurement principle circuit
2.1.1 Test circuit of rectangular standard sample 1
Figure 3 Test circuit of rectangular standard sample
S—Electric forging contact selection switch S, current reversing switch, S:—Voltage reversing switch, R. Standard resistor, G constant current source, V potentiometer galvanometer system or digital voltmeter Test circuit for thin-sheet samples
（6）
GB 11297.7—89
() (4)
Figure 4 Test circuit for thin-sheet samples
(33(4)
S--electrode contact selection switch; S.—current reversing switch +S, voltage reversing switch; S voltage selection switch, R.—standard resistor core—constant current source, V—potentiometer galvanometer system or digital voltmeter 2.2 Measuring instruments
2. 2. 1 Magnet
A calibrated magnet, the direction of magnetic flux can be reversed, to ensure that the uniformity of the magnetic flux density in the area where the sample is measured is better than ±1%, and the stability of the magnetic field is ±1%.
2.2,2 Instrument for measuring magnetic flux density
The resolution of the instrument for measuring magnetic flux density is not less than 0.0001T, and the measurement error is less than ±1%. 2.2.3 Sample current source
It is required to provide the sample with a stable current with a stability better than ±0.5% during the measurement process. 2.2. 4 Standard resistor
It is a standard resistor with the same order of magnitude as the resistance of the sample to be tested, with an accuracy of ±0.1%. 2.2.5 Voltage measuring instrument
It is recommended to use a high-precision and high-input impedance digital voltmeter with a sensitivity of 1μV and an accuracy better than ±0.5%. 2.2.6 Dewar flask and sample rack
It is required that the Dewar flask and sample rack are made of non-ferromagnetic materials, and their existence cannot cause the change of the magnetic flux density at the location of the sample to exceed ±1%.
2.2.7 Hall effect tester
It is required to be able to realize the conversion of the contact between the relevant instruments, samples and electrodes, control the size and direction of the sample current, magnetic flux density, and measure the relevant voltages according to the "fixed program".
2.2.8 Sample geometric dimension measuring equipment
GB 11297. 7—89
The geometrical dimensions of the sample can be measured by micrometer, outside micrometer and distance microscope, etc., with an accuracy of not less than 1%. 2.3 Measurement conditions
2.3.1 Measurement environment
The measurement environment has no strong electromagnetic interference to ensure the normal operation of the measurement system. 2.3.2 Test sample
2.3.2.1 Geometric shape of the sample
The test sample is a six-contact rectangular standard sample (Figure 5) or a square thin sheet sample (Figure 6). The sample is cut from a single crystal ingot of stepped steel, carefully ground, degreased and rinsed with deionized water. The sample has a regular shape, a flat surface, no scratches and no holes. 5
Figure 5 Six-contact rectangular standard sample
1. 0 cm<,L<1. 5 cm
1+226h
ar = ai ± 0, 005 cm
1s4 = Inb ± 0. 005 cm
w=a2± 0. 005 cm
f≤o.1cm
1 and 2 are current electrode contacts, 3, 4, 5 and 6 are ear electrode contacts. It is required that the angle error of the perpendicular surfaces of the samples is less than ±0.5, and the difference between the length of the parallel sides and their average value is less than ±1%. Figure 6 Square thin sheet sample
L> 1. 5 cm t ≤0. 1 cm
is the perimeter of the sample, t is the thickness of the sample, and the change in the sample thickness is required not to exceed ±1% of its average thickness. 2.3.2.2 Electrode contact of the sample
All electrode contacts should be ohmic contacts, and indium is generally used as electrode contact. The two end faces of the six-contact rectangular standard sample are the sample current electrode contacts. The entire end face should be coated with metal steel and then welded with electrode leads. The mixed electrode contact should be a strip electrode with a width not greater than 0.02cm, or a diameter less than 0.0.2cm small steel ball electrode. For square thin samples, the electrode contacts should be symmetrically distributed on the edges. If the electrode contacts must be made on one of the two planes with a thickness of t, the electrode contacts should be as close to the edge of the sample as possible, usually distributed on the four corners. 2.3.3 Sample current
GB 11297.7—89
The size of the sample current should ensure that the injection of minority carriers is avoided during the measurement process, and the electric field generated in the sample should be less than 1V/cm to ensure that Ohm's law holds.
2.3.4 Magnetic field
Magnetic flux density should meet the weak field condition: μB≤ 10*T cm\/(V -S)
Where: μ carrier current mobility, cm=/(V+S); B—magnetic flux density, T,
2.3.5 Precautions
2. 3.5.1 In order to avoid the influence of photoconductivity and photovoltaic effect on resistivity measurement, the sample to be measured should be shielded from light. 2.3.5.2 In order to eliminate the influence of side effects other than Ettinghausen effect, the sample current and magnetic field can be measured by reversing, and the measured Hall voltage can be appropriately averaged. The error introduced by Ettinghausen effect is small, especially when the sample has good thermal contact with its surrounding diagram, it can be ignored.
2.3.5-[3. Sometimes false electromotive force is generated during measurement, such as thermal electromotive force, which should be carefully checked and eliminated. 2.4 Test steps
2.4.1 Sample installation
Weld the sample to be tested to the sample holder, and then place the sample holder in a Dewar flask containing liquid nitrogen, connect the test circuit, select a suitable standard resistor, connect the circuit, and adjust the sample current. 2.4.2 Resistivity measurement
2.4.2.1 Measure under zero magnetic field and constant current conditions. 2.4.2.2 Six-contact rectangular standard sample
In the case of forward sample current, measure the voltages Us (+I), Us (+I) between electrode contacts 3, 4 and 5, 6, and measure the voltage on the standard resistor. (+I).
When the sample current is reversed, measure the corresponding voltages Ua (I), Us (-I) and U. (-I). 2.4.23 Square thin sheet sample
When the positive sample current is passed between electrode contacts 1 and 2, 2 and 3, 3 and 4, and 4 and 1, respectively, measure the voltages Ua (+I), Uu+I), Ua+I) and U, (+I) on electrode contacts 4 and 3, 1 and 4, 2 and 1, 3 and 2, and the standard resistor respectively. Reverse the sample current to measure the corresponding voltages (Ua+I), Uu+I), Ua+I), and U, (Ua+I). 2.A.3 Measurement of the ear coefficient
2.4.3.1 Place the sample at liquid nitrogen temperature in a stable and uniform magnetic field so that the sample surface is perpendicular to the direction of the magnetic field. 2.4.3.2 Six-contact rectangular standard sample
Change the direction of sample current and magnetic field, and measure the voltage between Hall electrode contacts 3 and 5 and the standard resistor respectively: Us(+ B, +1), U,(+ B, +1): Us(+ B, -1), U(+ B, -): Us(-B, -1), U(- B, -); U(-H, +1), U,(- B. +). Similarly, measure the voltage between Hall electrode contacts 4 and 6 and the standard resistor: U(+ B, +I), U,(+B, +I), U(+B, -I), U,(+B, -I), U(- B, -I), U B,-1) Us(- B, + I).U.(- B. +1) .2.4.3.3 Square thin sample
Apply sample current between electrode contacts 1 and 3, and measure the voltage between electrode contacts 4 and 2 and on the standard resistor: U(+ B, + I), U,(+ B, +I): U(+ B,-1), U,(+ B, - I): U(- B, -I), U.(-- B, -I), U(-B, + I), Ust-B,+I).
Apply sample current between electrode contacts 2 and 4, and measure the voltage between electrode contacts 1 and 3 and on the standard resistor: Us(+ B,+I), U,(+ B,+ I) + Uu(+ B,- I), U.(+ B, -I); U(- B. -1). U,(- R...comGB 11297.789
- I): Uu(- B,+ 1), U(- B, + I)3 Result calculation
3.1 Six-contact rectangular standard sample
3.1.1 Calculation of resistivity
Calculate the resistivity of the sample from the data obtained in 2.1.2.2: 03-
Where:
U(+,U.(-)
U(+I,U(-)
U.(+ 1),U.(- 1)
1rUu(+I)
(+ + 0.(-
1rU(+1)
Use(-I)Rbh
Resistivity between conductivity electrode contacts 3.4, cmResistivity between conductivity electrode contacts 5.6, cm, standard resistor,
Width of sample, cm;
Thickness of sample, cm,
Gap between electrode contacts 3 and 4, cm,
Gap between electrode contacts 5 and 6, cm,
Conductivity voltage between electrode contacts 3 and 4, μV,Conductivity voltage between electrode contacts 5 and 6, μV,-voltage on standard resistor, μV.
If the ratio of the difference between the resistivity Pa and ps to their average value is less than ±10%, the sample is considered to be uniform, and its average resistivity can be calculated:
(pss + ps6)
wherein: e-
Ps-Oce
the average resistivity of the sample, n·cm;
-two resistivities calculated according to formula (7), 0+c. If the difference between the resistivities pt and Ps exceeds ±10% of their average value, the sample is considered to be uneven. 3.1.2 Calculation of ear coefficient
Calculate the Rayleigh ear coefficient of the sample from the data in 2.4.3.2; .83
[R - 2.50 × 10 [U.(+ B, +)U,(+ B, +I)
Uss(+ B, -I) L Uss(- B, -I)Uas(- B, + I)Reh--B,+B
U,(+ B, - 1) + U,(- B, -I)
Us(+B,-I) Ue(-B,-)Ua-B,+)Rh
rUst+B,+) a1
[R = 2.50 × 10 [U(+ B:+R - D+ BR + U- B: ~ D(-B, +)(9)
Wherein: RR
are the Hall coefficients between electrode contacts 3.5 and 4.6, cm/C; R—standard resistance, 9 yuan
h—sample thickness, cm:
B—magnetic flux density, T
U(+B,+I), Us(+B,-I), Uss(—B,—I), Uss(—B,+I)——Hall voltage between electrode contacts 3 and 5, μVU (+R.+,U(+R,-,U.(-B,-,U4-E,+)-0(+B.+?,U(+B,-0U.(-B,-,U.(-H,Shark ear voltage between electrode contacts 4 and 6, μV; voltage on standard resistor μV.
If the ratio of the difference between Rgood and R to their average value is less than ±10%, the sample is considered uniform, and the average Hall coefficient of the sample can be calculated: RH=
(R+R智)
CB 11297.789
Where: Rh is the average Hall coefficient of a sample, cm~/C; Rback and R
are the two Hall coefficients calculated by formula (9), c\/C. If the difference between R and Rback and their average value exceeds ±10%, the sample is considered to be non-uniform. 3.2 Square thin slice sample
3.2.1 Calculation of resistivity
Calculate two resistivities from the data obtained in 2.4.2.3: U(+)+Un(+ + U-D+U-)Rtf(2A)
PA = 1. 133 1 ×
rUn(+D+Un(+ I + Uns-D+Ua(-D)Ruf(QA)Ps=1.1331×
Wherein, FaP—-the two resistivities measured, -cmR. Standard electrical, 2;
Sample thickness, cmm
U(+ ),U(+I),U(-D,Un(-),Ua(+D,U(+I,Uat-I),U(- 1) -U(+),U,—)——voltage on standard resistor, μVAQF(Q)
Q,,Q related function, that is, Van der Berg correction function. lor
f(Q) is related to Q as follows:
+ Va(-n1- rUu(+n +Un(-n)
+ AR]+ [U(+R + U(-]
(U,(+) +U(-D
arccosh
...(1
a measured conductivity
voltage V
(13）
Figure 7 is the relationship curve between f(Q) and Q. If the Q value obtained from equation (12) is less than 1, take its reciprocal. Appendix B is the table of Vanderbilt modified Han number
白, 8
aace [ exp(g]
The relationship between the modified function f() and eclipse
60RD 100
GB 11297.7—89
If the ratio of the difference between the resistance P and the average value is less than ±10%, the sample is considered to be uniform, and the average resistance of the sample can be calculated as p(+)/(g)
Where: p—average resistivity of the sample, Qcm; PaPm—two resistivities calculated by formula (11), *cm. If the ratio of the difference between P and β and their average value is greater than ±10%, the sample is considered to be non-uniform. 3.2.2 Calculation of Hall coefficient
The two Hall coefficients of the sample can be calculated from the data in 2.4.3.3: 2 0 1 ... B+
U(-B, +I),Rt
U(-B, +]
U.(+ B.-))
f U,(-B, -I) -
（15）
Wu Zhong: R,R
two-level Hall coefficient of sample, cn*/C;
standard resistance, 0+
sample thickness, cm;
B-—magnetic flux density, T;
U4(+ B, +1),U.2(+B, -),U(-B,-I),U42(-B, +I) and U1,(+ B, +1),U(+B, -1),(is(- R. - I),Us(-R, +I) Hall voltage +pV:1,(+ B, + 1),U(+ B,-),U(-B, -),U,(- R, + ) --voltage on standard resistor, μV.
and the ratio of the difference to its average value is less than ±10%, the sample is considered uniform, and the average Hall coefficient of the product can be calculated: RH
the average Shark's ear coefficient of the sample, cm\/C
R,RP --the Shark's ear coefficient calculated by formula (15), cm/C. (R+R)
If the ratio of the difference to its average value is greater than ±10%, the sample is considered non-uniform. 3.3 Hall mobility
After the average Shark's ear coefficient and average resistivity of the sample are calculated, the average Hall mobility of the sample can be calculated: LRul
where: : average Hall mobility of the sample, cm\/(V+S): Rr: : - average Hall coefficient of the sample, cm\/C; p -- average resistivity of the sample, a-cm. 3.4: Carrier concentration and carrier mobility (16)
The carrier concentration (electrons for n-type antimony and holes for β-type indium) and carrier mobility of InSb single crystal at 77 K are:
Carrier concentration, em-3,
Carrier mobility, cm\/(VS);
Hall coefficient, cm/C
Hall mobility, cn\/(VS).
X 1018www.bzxz.net
4 Experimental report
4.1 Arbitration experimental report
GB11297.7—89
4.1.1 Test sample conditions, including material, shape, relevant dimensional data and the location of the sample in the single crystal. 4.1.2 Test temperature.
4.1.3 The size of the standard resistor.
4.4 Sample current and magnetic flux density. 4.1.5 Data of measured Hall voltage, conductance voltage and voltage on standard resistor. 4.1.6 Calculation of average resistivity, average Hall coefficient (including symbol), Hall mobility and carrier concentration and carrier mobility. 4.1.7 Identification of instruments and equipment used to measure current, voltage, flux density and sample size. 4.18 Test environment, such as temperature, humidity, etc. 4.1.9 Test personnel and test date.
4.2 Routine test report
Includes the contents listed in 4.1.1.4.1.2.4.1.4.4.1.5.4.1.6.4.1.9. 5 Test accuracy
The maximum test error of this standard: resistivity ±7%, mil coefficient ±8%. Measurement principle
GB 11297. 7—89
Appendix A
Measurement of resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1 cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
+ Va(-n1- rUu(+n +Un(-n)
+ AR]+ [U(+R + U(-]
(U,(+) +U(-D
arccosh
...(1
The measured conductivity
Voltage V
(13）
Figure 7 is the relationship curve between f(Q) and Q. If the Q value obtained from formula (12) is less than 1, its reciprocal is taken. Appendix B is the table of Vanderbilt modified Han number
白, 8
aace [ exp(g]
The relationship between the modified function f() and the eclipse
60RD 100
GB 11297.7—89
If the ratio of the difference between the resistance P and the average value is less than ±10%, the sample is considered to be uniform, and the average resistance of the sample can be calculated as p(+)/(g)
Where: p—average resistivity of the sample, Qcm; PaPm—two resistivities calculated by formula (11), *cm. If the ratio of the difference between P and β and their average value is greater than ±10%, the sample is considered to be non-uniform. 3.2.2 Calculation of Hall coefficient
The two Hall coefficients of the sample can be calculated from the data in 2.4.3.3: 2 0 1 ... B+
U(-B, +I),Rt
U(-B, +]
U.(+ B.-))
f U,(-B, -I) -
（15）
Wu Zhong: R,R
two-level Hall coefficient of sample, cn*/C;
standard resistance, 0+
sample thickness, cm;
B-—magnetic flux density, T;
U4(+ B, +1),U.2(+B, -),U(-B,-I),U42(-B, +I) and U1,(+ B, +1),U(+B, -1),(is(- R. - I),Us(-R, +I) Hall voltage +pV:1,(+ B, + 1),U(+ B,-),U(-B, -),U,(- R, + ) --voltage on standard resistor, μV.
and the ratio of the difference to its average value is less than ±10%, the sample is considered uniform, and the average Hall coefficient of the product can be calculated: RH
the average Shark's ear coefficient of the sample, cm\/C
R,RP --the Shark's ear coefficient calculated by formula (15), cm/C. (R+R)
If the ratio of the difference to its average value is greater than ±10%, the sample is considered non-uniform. 3.3 Hall mobility
After the average Shark's ear coefficient and average resistivity of the sample are calculated, the average Hall mobility of the sample can be calculated: LRul
where: : average Hall mobility of the sample, cm\/(V+S): Rr: : - average Hall coefficient of the sample, cm\/C; p -- average resistivity of the sample, a-cm. 3.4: Carrier concentration and carrier mobility (16)
The carrier concentration (electrons for n-type antimony and holes for β-type indium) and carrier mobility of InSb single crystal at 77 K are:
Carrier concentration, em-3,
Carrier mobility, cm\/(VS);
Hall coefficient, cm/C
Hall mobility, cn\/(VS).
X 1018
4 Experimental report
4.1 Arbitration experimental report
GB11297.7—89
4.1.1 Test sample conditions, including material, shape, relevant dimensional data and the location of the sample in the single crystal. 4.1.2 Test temperature.
4.1.3 The size of the standard resistor.
4.4 Sample current and magnetic flux density. 4.1.5 Data of measured Hall voltage, conductance voltage and voltage on standard resistor. 4.1.6 Calculation of average resistivity, average Hall coefficient (including symbol), Hall mobility and carrier concentration and carrier mobility. 4.1.7 Identification of instruments and equipment used to measure current, voltage, flux density and sample size. 4.18 Test environment, such as temperature, humidity, etc. 4.1.9 Test personnel and test date.
4.2 Routine test report
Includes the contents listed in 4.1.1.4.1.2.4.1.4.4.1.5.4.1.6.4.1.9. 5 Test accuracy
The maximum test error of this standard: resistivity ±7%, mil coefficient ±8%. Measurement principle
GB 11297. 7—89
Appendix A
Measurement of resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1 cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
+ Va(-n1- rUu(+n +Un(-n)
+ AR]+ [U(+R + U(-]
(U,(+) +U(-D
arccosh
...(1
The measured conductivity
Voltage V
(13）
Figure 7 is the relationship curve between f(Q) and Q. If the Q value obtained from formula (12) is less than 1, its reciprocal is taken. Appendix B is the table of Vanderbilt modified Han number
白, 8
aace [ exp(g]
The relationship between the modified function f() and the eclipse
60RD 100
GB 11297.7—89
If the ratio of the difference between the resistance P and the average value is less than ±10%, the sample is considered to be uniform, and the average resistance of the sample can be calculated as p(+)/(g)
Where: p—average resistivity of the sample, Qcm; PaPm—two resistivities calculated by formula (11), *cm. If the ratio of the difference between P and β and their average value is greater than ±10%, the sample is considered to be non-uniform. 3.2.2 Calculation of Hall coefficient
The two Hall coefficients of the sample can be calculated from the data in 2.4.3.3: 2 0 1 ... B+
U(-B, +I),Rt
U(-B, +]
U.(+ B.-))
f U,(-B, -I) -
（15）
Wu Zhong: R,R
two-level Hall coefficient of sample, cn*/C;
standard resistance, 0+
sample thickness, cm;
B-—magnetic flux density, T;
U4(+ B, +1),U.2(+B, -),U(-B,-I),U42(-B, +I) and U1,(+ B, +1),U(+B, -1),(is(- R. - I),Us(-R, +I) Hall voltage +pV:1,(+ B, + 1),U(+ B,-),U(-B, -),U,(- R, + ) --voltage on standard resistor, μV.
and the ratio of the difference to its average value is less than ±10%, the sample is considered uniform, and the average Hall coefficient of the product can be calculated: RH
the average Shark's ear coefficient of the sample, cm\/C
R,RP --the Shark's ear coefficient calculated by formula (15), cm/C. (R+R)
If the ratio of the difference to its average value is greater than ±10%, the sample is considered non-uniform. 3.3 Hall mobility
After the average Shark's ear coefficient and average resistivity of the sample are calculated, the average Hall mobility of the sample can be calculated: LRul
where: : average Hall mobility of the sample, cm\/(V+S): Rr: : - average Hall coefficient of the sample, cm\/C; p -- average resistivity of the sample, a-cm. 3.4: Carrier concentration and carrier mobility (16)
The carrier concentration (electrons for n-type antimony and holes for β-type indium) and carrier mobility of InSb single crystal at 77 K are:
Carrier concentration, em-3,
Carrier mobility, cm\/(VS);
Hall coefficient, cm/C
Hall mobility, cn\/(VS).
X 1018
4 Experimental report
4.1 Arbitration experimental report
GB11297.7—89
4.1.1 Test sample conditions, including material, shape, relevant dimensional data and the location of the sample in the single crystal. 4.1.2 Test temperature.
4.1.3 The size of the standard resistor.
4.4 Sample current and magnetic flux density. 4.1.5 Data of measured Hall voltage, conductance voltage and voltage on standard resistor. 4.1.6 Calculation of average resistivity, average Hall coefficient (including symbol), Hall mobility and carrier concentration and carrier mobility. 4.1.7 Identification of instruments and equipment used to measure current, voltage, flux density and sample size. 4.18 Test environment, such as temperature, humidity, etc. 4.1.9 Test personnel and test date.
4.2 Routine test report
Includes the contents listed in 4.1.1.4.1.2.4.1.4.4.1.5.4.1.6.4.1.9. 5 Test accuracy
The maximum test error of this standard: resistivity ±7%, mil coefficient ±8%. Measurement principle
GB 11297. 7—89
Appendix A
Measurement of resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1 cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
(A5)7—89
If the ratio of the difference between the resistance P and the average value is less than ±10%, the sample is considered to be uniform, and the average resistance of the sample can be calculated as pa+g)
where: p—average resistivity of the sample, Qcm; PaPm—two resistivities calculated by formula (11), *cm. If the ratio of the difference between \, and β and their average value is greater than ±10%, the sample is considered to be non-uniform. 3.2.2 Calculation of Hall coefficient
U(-B, +I),Rt
U(-B, +]
U.(+ B.-))
f U,(-B, -I) 3.2.2 Calculation of Hall coefficient
U(-B, +I),Rt
U(-B, +I),Rt
U(-B, +]
U.(+ B.-))
f U,(-B, -I) -
（15）
Wu Zhong: R, R
Two-level Hall coefficient of sample, cn*/C;
Standard resistance, 0+
Sample thickness, cm;
B-—magnetic flux density, T;
U4(+ B, +1),U.2(+B, -),U(-B,-I),U42(-B, +I) and U1,(+ B, +1),U(+B, -1),(is(- R. - I),Us(-R, +I) Hall voltage +pV:1,(+ B, + 1),U(+ B,-),U(-B, -),U,(- R, + ) --The voltage on the standard resistor, μV.
If the ratio of the difference with the standard resistor to its average value is less than ±10%, the sample is considered to be uniform, and the average Hall coefficient of the product can be calculated: RH
The average Shark's ear coefficient of the sample, cm\/C
R,RP -~The Shark's ear coefficient calculated according to formula (15), cm/C. (R+R)
If the ratio of the difference with the standard resistor to its average value is greater than ±10%, the sample is considered to be non-uniform. 3.3 Hall mobility
After the average shark's ear coefficient and average resistivity of the sample are calculated, the average Hall mobility of the sample can be calculated: LRul
Where: : The average Hall mobility of the sample, cm\/(V+S): Rr: : - The average Hall coefficient of the sample, cm\/C; p - The average resistivity of the sample, a-cm. 3.4: Carrier concentration and carrier mobility (16)
Indium antimonide single crystal at 77 The carrier concentration (electrons for n-type antimonide and holes for β-indium) and carrier mobility of K are:
Carrier concentration, em-3,
Carrier mobility, cm\/(VS);
Hall coefficient, cm/C
Hall mobility, cn\/(VS).
X 1018
4 Experimental report
4.1 Arbitration experimental report
GB11297.7—89
4.1.1 Test sample conditions, including material, shape, relevant size data and the location of the sample in the single crystal. 4.1.2 Test temperature.
4.1.3 The size of the standard resistor.
4.4 The size of the sample current and magnetic flux density. 4.1.5 The data of the measured plug voltage, conductivity voltage and voltage on the standard resistor. 4.1.6 Calculation of average resistivity, average Hall coefficient (including symbol), Hall mobility, carrier concentration, and carrier mobility 4.1.7 Identification of instruments and equipment used to measure current, voltage, contact density, and sample size. 4.18 Test environment, such as temperature, humidity, etc. 4.1.9 Test personnel and test date.
4.2 Routine test report
Include the contents listed in 4.1.1.4.1.2.4.1.4.4.1.5.4.1.6.4.1.9. 5 Test accuracy
The maximum test error of this standard: resistivity ±7%, mil coefficient ±8%. Measurement principle
GB 11297. 7—89
Appendix A
Measurement of resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1 cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
(A5)7—89
If the ratio of the difference between the resistance P and the average value is less than ±10%, the sample is considered to be uniform, and the average resistance of the sample can be calculated as pa+g)
where: p—average resistivity of the sample, Qcm; PaPm—two resistivities calculated by formula (11), *cm. If the ratio of the difference between \, and β and their average value is greater than ±10%, the sample is considered to be non-uniform. 3.2.2 Calculation of Hall coefficient
U(-B, +I),Rt
U(-B, +]
U.(+ B.-))
f U,(-B, -I) 3.2.2 Calculation of Hall coefficient
U(-B, +I),Rt
U(-B, +I),Rt
U(-B, +]
U.(+ B.-))
f U,(-B, -I) -
（15）
Wu Zhong: R, R
Two-level Hall coefficient of sample, cn*/C;
Standard resistance, 0+
Sample thickness, cm;
B-—magnetic flux density, T;
U4(+ B, +1),U.2(+B, -),U(-B,-I),U42(-B, +I) and U1,(+ B, +1),U(+B, -1),(is(- R. - I),Us(-R, +I) Hall voltage +pV:1,(+ B, + 1),U(+ B,-),U(-B, -),U,(- R, + ) --The voltage on the standard resistor, μV.
If the ratio of the difference with the standard resistor to its average value is less than ±10%, the sample is considered to be uniform, and the average Hall coefficient of the product can be calculated: RH
The average Shark's ear coefficient of the sample, cm\/C
R,RP -~The Shark's ear coefficient calculated according to formula (15), cm/C. (R+R)
If the ratio of the difference with the standard resistor to its average value is greater than ±10%, the sample is considered to be non-uniform. 3.3 Hall mobility
After the average shark's ear coefficient and average resistivity of the sample are calculated, the average Hall mobility of the sample can be calculated: LRul
Where: : The average Hall mobility of the sample, cm\/(V+S): Rr: : - The average Hall coefficient of the sample, cm\/C; p - The average resistivity of the sample, a-cm. 3.4: Carrier concentration and carrier mobility (16)
Indium antimonide single crystal at 77 The carrier concentration (electrons for n-type antimonide and holes for β-indium) and carrier mobility of K are:
Carrier concentration, em-3,
Carrier mobility, cm\/(VS);
Hall coefficient, cm/C
Hall mobility, cn\/(VS).
X 1018
4 Experimental report
4.1 Arbitration experimental report
GB11297.7—89
4.1.1 Test sample conditions, including material, shape, relevant size data and the location of the sample in the single crystal. 4.1.2 Test temperature.
4.1.3 The size of the standard resistor.
4.4 The size of the sample current and magnetic flux density. 4.1.5 The data of the measured plug voltage, conductivity voltage and voltage on the standard resistor. 4.1.6 Calculation of average resistivity, average Hall coefficient (including symbol), Hall mobility, carrier concentration, and carrier mobility 4.1.7 Identification of instruments and equipment used to measure current, voltage, contact density, and sample size. 4.18 Test environment, such as temperature, humidity, etc. 4.1.9 Test personnel and test date.
4.2 Routine test report
Include the contents listed in 4.1.1.4.1.2.4.1.4.4.1.5.4.1.6.4.1.9. 5 Test accuracy
The maximum test error of this standard: resistivity ±7%, mil coefficient ±8%. Measurement principle
GB 11297. 7—89
Appendix A
Measurement of resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1 cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
(A5)-I),U42(-B, +I) and U1,(+ B, +1),U(+B, -1),(is(- R. - I),Us(-R, +I) Hall voltage +pV:1,(+ B, + 1),U(+ B,-),U(-B, -),U,(- R, + ) --The voltage on the standard resistor, μV.
and the ratio of the difference to its average value is less than ±10%, then the sample is considered uniform, and the average Hall coefficient of the product can be calculated: RH
The average Hall coefficient of the sample, cm\/C
R,RP -~The Shark's ear coefficient calculated by formula (15), cm/C. (R+R)
If the difference between the magnetic field and its average value is less than ±10%, the sample is considered to be non-uniform. 3.3 Hall mobility
After the average shark's ear coefficient and average resistivity of the sample are obtained, the average Hall mobility of the sample can be calculated: LRul
Where: : The average Hall mobility of the sample, cm\/(V+S): Rr: : - The average Hall coefficient of the sample, cm\/C; p—-—The average resistivity of the sample, a-cm. 3.4: Carrier concentration and carrier mobility (16)
Indium antimonide single crystal at 77 The carrier concentration (electrons for n-type antimonide and holes for β-indium) and carrier mobility of K are:
Carrier concentration, em-3,
Carrier mobility, cm\/(VS);
Hall coefficient, cm/C
Hall mobility, cn\/(VS).
X 1018
4 Experimental report
4.1 Arbitration experimental report
GB11297.7—89
4.1.1 Test sample conditions, including material, shape, relevant size data and the location of the sample in the single crystal. 4.1.2 Test temperature.
4.1.3 The size of the standard resistor.
4.4 The size of the sample current and magnetic flux density. 4.1.5 The data of the measured plug voltage, conductivity voltage and voltage on the standard resistor. 4.1. 6 Calculation of average resistivity, average Hall coefficient (including symbol), Hall mobility, carrier concentration, and carrier mobility 4.1.7 Identification of instruments and equipment used to measure current, voltage, contact density, and sample size. 4.18 Test environment, such as temperature, humidity, etc. 4.1.9 Test personnel and test date.
4.2 Routine test report
Include the contents listed in 4.1.1.4.1.2.4.1.4.4.1.5.4.1.6.4.1.9. 5 Test accuracy
The maximum test error of this standard: resistivity ±7%, mil factor ±8%. Measurement principle
GB 11297. 7-89
Appendix A
Measurement of resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference part)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
(A5)-I),U42(-B, +I) and U1,(+ B, +1),U(+B, -1),(is(- R. - I),Us(-R, +I) Hall voltage +pV:1,(+ B, + 1),U(+ B,-),U(-B, -),U,(- R, + ) --The voltage on the standard resistor, μV.
and the ratio of the difference to its average value is less than ±10%, then the sample is considered uniform, and the average Hall coefficient of the product can be calculated: RH
The average Hall coefficient of the sample, cm\/C
R,RP -~The Shark's ear coefficient calculated by formula (15), cm/C. (R+R)
If the difference between the magnetic field and its average value is less than ±10%, the sample is considered to be non-uniform. 3.3 Hall mobility
After the average shark's ear coefficient and average resistivity of the sample are obtained, the average Hall mobility of the sample can be calculated: LRul
Where: : The average Hall mobility of the sample, cm\/(V+S): Rr: : - The average Hall coefficient of the sample, cm\/C; p—-—The average resistivity of the sample, a-cm. 3.4: Carrier concentration and carrier mobility (16)
Indium antimonide single crystal at 77 The carrier concentration (electrons for n-type antimonide and holes for β-indium) and carrier mobility of K are:
Carrier concentration, em-3,
Carrier mobility, cm\/(VS);
Hall coefficient, cm/C
Hall mobility, cn\/(VS).
X 1018
4 Experimental report
4.1 Arbitration experimental report
GB11297.7—89
4.1.1 Test sample conditions, including material, shape, relevant size data and the location of the sample in the single crystal. 4.1.2 Test temperature.
4.1.3 The size of the standard resistor.
4.4 The size of the sample current and magnetic flux density. 4.1.5 The data of the measured plug voltage, conductivity voltage and voltage on the standard resistor. 4.1. 6 Calculation of average resistivity, average Hall coefficient (including symbol), Hall mobility, carrier concentration, and carrier mobility 4.1.7 Identification of instruments and equipment used to measure current, voltage, contact density, and sample size. 4.18 Test environment, such as temperature, humidity, etc. 4.1.9 Test personnel and test date.
4.2 Routine test report
Include the contents listed in 4.1.1.4.1.2.4.1.4.4.1.5.4.1.6.4.1.9. 5 Test accuracy
The maximum test error of this standard: resistivity ±7%, mil factor ±8%. Measurement principle
GB 11297. 7-89
Appendix A
Measurement of resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference part)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
(A5)7—89
Appendix A
Measurement of the resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1 cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
where the electrode contacts at 1, the distance between the electrodes, and the diameter of the InSb single crystal at this point, m. By the same method, the Hall coefficient at the electrode contacts at 7+1 and 1+1 can be obtained, RnUn
where the Hall coefficient m/cm is measured at the electrode contacts at 1, 1+1 and 1+1. 1, V; the crystal diameter at that location, m;
sample current intensity, A;
phosphorus flux density, T
; the average Hall coefficient of the antimonide steel single crystal in this section is: Ri-
where R is -
average Hall coefficient, m\/C:
(RH+ R')
- the Hall coefficient measured at electrode contact j,\ m/Ct; the Mil coefficient measured at electrode contact +1,\ +1, m/C. Similarly, the resistivity expression between electrode contact, i and 1 can be derived: a+d\
resistivity between electrode contact j+1, Q·!
U. — conductance voltage between electrode contact ii+1, V; (A3)
(A5)7—89
Appendix A
Measurement of the resistivity and flat coefficient of cylindrical indium antimonide single crystal (reference)
Assume that the antimonide steel single crystal is a cylinder, and its two ends are sample current contacts. On both sides of a certain imaginary section, a pair of electrode contacts are symmetrically welded every 1 cm (see Figure A1).
Apply a constant magnetic field and a constant sample current between the rows as shown in the figure. 2
A1 Schematic diagram of antimonide single crystal ingot test
At the electrode contact point, the Hall electric field is: E, = Rhj,B
Where: E, Hall electric field, V/m
RH-Hall coefficient m/C;
-sample current density, A/m:
Magnetic flux density, T.
The relationship between the Hall electric field and the Hall voltage U measured at the electrode contact point is: E,
. (A1)
Where: E,-—Hall electric field, V/mt
Un--Hall voltage, V:
GB 11297: 789
d--the distance between the electrode contact points, that is, the diameter of the single crystal here, m. The sample current density J is:
sample current density.A/m
sample current intensity, A;
-the area of ​​the crystal cross section at the electrode contact j,\, m. Because the antimonide single crystal is a cylinder, the area of ​​the crystal cross section S can be expressed as S
wuzhongs
electrode contact, the cross-sectional area of ​​the crystal at the electrode contact, n, the spacing of the "electrode contact", that is, the diameter of the antimonide single crystal here. The magnetic field is in the direction, so
z-direction magnetic flux density, that is, the magnetic flux density of the applied magnetic field, T. Where:
Substituting equations (A2)~(45) into equation (41) to get the expression of the mil coefficient, R = RH
where the electrode contacts at 1, the Hall coefficient measured at 1, m/cm; the Hall voltage measured between the electrodes being contacted, V; the current intensity of the sample, A;
the magnetic flux density, T;
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