1. experimental name: hall effect principle and its application.
Second, the purpose of the experiment:
1, understand the principle of Hall effect;
2. Measure the curve of Hall element to understand the relationship between Hall voltage, working current of Hall element and excitation current of straight solenoid;
3. Learn the principle and method of measuring magnetic induction intensity with Hall element, and measure the axial magnetic induction intensity and distribution of long straight spiral pipe;
4. Learn to use symmetrical exchange measurement method (different sign method) to eliminate systematic errors caused by negative effects.
Three. Instruments and meters: YX-04 Hall effect experimental instrument (instrument asset number)
Fourth, the experimental principle:
1, Hall effect phenomenon and its physical explanation
The Hall effect is essentially the deflection of moving charged particles by Lorentz force in magnetic field. When charged particles (electrons or holes) are confined in solid materials, this deflection leads to the accumulation of positive and negative charges in the direction perpendicular to the current and magnetic field, thus forming an additional transverse electric field. As shown in figure 1.
If a current is applied to the semiconductor sample in the X direction and a magnetic field is applied to it in the Z direction, charges with different signs will start to accumulate in the Y direction, that is, on both sides of the electrodes of samples A and A', and corresponding electric fields will be generated. The direction of the electric field depends on the conductivity type of the sample. Obviously, when the carriers are subjected to the transverse electric field force, the electric field is constantly strengthened, until the charge accumulation on both sides of the sample reaches a balance, that is, a stable potential difference (Hall voltage) is formed between samples A and A'.
Let it be Hall electric field, which is the average drift velocity of carriers in the current direction; If the sample has a width of, a thickness of and a carrier concentration of, then:
( 1- 1)
Because, and according to, then
( 1-2)
Among them, Hall coefficient is an important parameter reflecting the strength of Hall effect of materials. As long as,, know, can press type calculation:
( 1-3)
( 1—4)
It is that sensitivity of the Hall element. According to RH, the following parameters can be further determined.
(1) The conductivity type of the sample is judged by the sign of (positive and negative Hall voltage). The method of discrimination is based on the direction of sum (i.e.+,+) as shown in +0 in figure 65438. If the measured potential is less than 0 (that is, the potential of a' is lower than that of a), the sample belongs to N type, and vice versa.
(2) By calculating the carrier concentration, that is. It should be pointed out that this relationship is based on the assumption that all carriers have the same drift speed. Strictly speaking, considering the statistical distribution of carrier velocity, a correction factor needs to be introduced (see Semiconductor Physics by Huang Kun and Xie Xide).
(3) Combined with the measurement of conductivity, the mobility of carriers is calculated. The relationship between conductivity and carrier concentration and mobility is as follows:
( 1-5)
2. Side effects of Hall effect and its elimination methods.
The above deduction is based on the ideal situation, and the actual situation is much more complicated. The Hall effect mentioned above is accompanied by four side effects, which will lead to systematic errors in the measurement, as shown in Figure 2.
The potential difference caused by (1) Ettinghausen effect. Because electrons don't actually move in the negative direction along the Y axis at the same speed V, the electrons with high speed have a large radius of gyration and can reach the contact 3 side quickly, which leads to the high-energy electrons being concentrated on the 3 side rather than the 4 side. As a result, there is a temperature difference between the side surfaces 3 and 4, resulting in thermoelectric electromotive force. Can prove it. The symbol of is related to the direction of and.
(2) The potential difference caused by Nernst effect. The contact resistance between the solder joint 1 and 2 may be different, and the degree of heating is different, so the temperature between the two points 1 and 2 may be different, thus generating thermal diffusion current. Similar to the Hall effect, the thermal diffusion current will also form a potential difference between 3 and 4 points. If only the difference of contact resistance is considered, the direction of contact resistance is only related to the direction of magnetic field.
(3) Potential difference caused by Righi-Raducci effect. Due to the different carrier velocities of the above thermal diffusion current, thermoelectric electromotive force will be formed between 3 and 4 points for the same reason as the Ettinghausen effect. The symbol of is only related to the direction of, but not to the direction of.
(4) Potential difference caused by unequal potential effect. Because of the difficulty of manufacturing and the inhomogeneity of materials, it is impossible for 3 points and 4 points to be on the same equipotential surface. As long as there is current flowing in the X direction, there will be a potential difference between 3 o'clock and 4 o'clock even if there is no magnetic field. The positive and negative of is only related to the direction of current, not to the direction of.
To sum up, under a certain magnetic field and current, the actually measured voltage is the algebraic sum of the Hall effect voltage and the additional voltage caused by side effects. The influence of side effects can be eliminated and reduced by changing the direction of magnetic field symmetrically. After the positive and negative directions of current and magnetic field are specified, the following four groups of voltages in different directions can be measured. Namely:
, :
, :
, :
, :
Then find the algebraic average of,,,:
Through the above measurement method, although all the side effects cannot be eliminated, it is very small and the introduced error can be ignored, so the Hall effect voltage can be approximated as:
( 1-6)
3. Distribution of magnetic field in straight solenoid
1. From the above analysis, it can be seen that when the energized Hall element is placed in a magnetic field, the sensitivity of the Hall element is known, and the magnetic induction intensity of the magnetic field can be calculated by measuring its sum.
( 1-7)
2. Theoretical formula of axial magnetic induction intensity at the midpoint of straight spiral pipe:
( 1-8)
Among them, it is the magnetic permeability of the magnetic medium, the number of turns of the spiral tube, the current passing through the spiral tube, the length of the spiral tube, the inner diameter of the spiral tube and the distance from the midpoint of the spiral tube.
When X=0, the magnetic induction intensity at the midpoint of the spiral tube
( 1-9)
Verb (abbreviation of verb) experimental content:
Measuring the relationship between Hall elements;
1. Set the "Adjust" and "Adjust" knobs of the tester to zero (i.e. turn them counterclockwise to the bottom) and set the polarity switch to "0".
2. Turn on the power supply, and the ammeter shows "0.000". Sometimes it is normal to adjust the potentiometer or the starting point of the potentiometer is not zero, and the ammeter will show that the last digit is not zero. The voltmeter shows "0.0000".
3. determine the relationship. Take = =900mA and keep it unchanged; The Hall element is placed at the midpoint of the spiral tube (the horizontal direction of the two-dimensional moving scale 14.00cm is aligned with the reading zero point). Turn the "Adjust" knob clockwise, and the values are 1.00, 2.00, …, 10.00mA in turn. Select "+"and "-"of the polarity switch to change the polarity of the sum, record the corresponding voltmeter reading and fill it in the data record table 1.
4. Draw with abscissa and ordinate, and discuss the curve qualitatively.
5. determine the relationship. Take = 10 mA and keep it unchanged; The Hall element is placed at the midpoint of the spiral tube (the horizontal direction of the two-dimensional moving scale 14.00cm is aligned with the reading zero point). Turn the "Adjust" knob clockwise, and the values are 0,100,200, …, 900 mA in turn. Select "+"and "-"to change the polarity of the sum, record the corresponding voltmeter readings, and fill in the data record table 2.
6. Plot with abscissa and ordinate, and discuss the curve qualitatively.
Measurement of axial magnetic induction intensity of long straight spiral pipe
1, take = 10 mA, = = 900 mA.
2. Move the horizontal adjustment screw to make the position of Hall element in the straight solenoid (read by moving the cursor horizontally), starting from 14.00cm and ending at 0cm. Change the polarity, record the corresponding voltmeter reading, and fill in the data record table 3 to calculate the magnetic induction intensity of the axial corresponding position of the straight spiral pipe.
3. Plot with abscissa and ordinate, and discuss the curve qualitatively.
4. Calculate the theoretical value of the magnetic induction intensity at the center of the long straight spiral pipe with the formula (1-8), and compare it with the measured value of the magnetic induction intensity at the center of the long straight spiral pipe, and show the measured result in the form of percentage error. Type, the other parameters are displayed on the instrument nameplate.
Six, matters needing attention:
1. In order to eliminate the influence of side effects, symmetrical measurement method is adopted in the experiment, that is, the direction of sum is changed.
2. The working current lead and the Hall voltage lead of the Hall element will not be mistaken; The working current of Hall element should be different from the excitation current of solenoid, otherwise it will burn out Hall element.
3. Disconnect the excitation current of solenoid and the working current of Hall element during the experimental interval, that is, set the polarity switch of sum to 0.
4. Hall element and two-dimensional moving ruler are easy to break and deform, so pay attention to protection, avoid extrusion and collision, and don't touch Hall element with your hands.
Seven. Data record: KH=23.09, N=3 150 turns, L=280mm, r= 13mm.
Table 1 relation (=900mA)
mV mV mV mV mV
1.00 0.28 -0.27 0.3 1 -0.30 0.29
2.00 0.59 -0.58 0.63 -0.64 0.6 1
3.00 0.89 -0.87 0.95 -0.96 0.90
4.00 1.20 - 1. 16 1.27 - 1.29 1.23
5.00 1.49 - 1.46 1.59 - 1.6 1 1.54
6.00 1.80 - 1.77 1.90 - 1.93 1.85
7.00 2. 1 1 -2.07 2.22 -2.25 2. 17
8.00 2.4 1 -2.38 2.65 -2.54 2.47
9.00 2.68 -2.69 2.84 -2.87 2.77
10.00 2.99 -3.00 3. 17 -3. 19 3.09
Table 2 Relationship (= 10.00mA)
mV mV mV mV mV
0 -0. 10 0.08 0. 14 -0. 16 0. 12
100 0. 18 -0.20 0.46 -0.47 0.33
200 0.52 -0.54 0.80 -0.79 0.66
300 0.85 -0.88 1. 14 - 1. 15 1.00
400 1.20 - 1.22 1.48 - 1.49 1.35
500 1.54 - 1.56 1.82 - 1.83 1.69
600 1.88 - 1.89 2. 17 -2. 16 2.02
700 2.23 -2.24 2.50 -2.5 1 2.37
800 2.56 -2.58 2.84 -2.85 2.7 1
900 2.90 -2.92 3. 18 -3.20 3.05
Table 3 Relationship = 10.00 mA, = 900 mA
(mV) (mV) (mV) (mV) B × 10-3T
0 0.54 -0.56- 0.73 -0.74 2.88
0.5 0.95 -0.99 1. 17 - 1. 18 4.64
1.0 1.55 - 1.58 1.80 - 1.75 7.23
2.0 2.33 2.37- 2.88 -2.52 10.57
4.0 2.74 -2.79 2.96 -2.94 12.30
6.0 2.88 -2.92 3.09 -3.08 12.90
8.0 2.9 1 -2.95 3. 13 -3. 1 1 13. 10
10.0 2.92 -2.96 3. 13 -3. 13 13. 10
12.0 2.94 -2.99 3. 15 -3.06 13.20
14.0 2.96 -2.99 3. 16 -3. 17 13.3
Eight, data processing: (graphic paper for drawing)
Nine, the experimental results:
Experiments show that the Hall voltage has a linear relationship with the working current of the Hall element and the excitation current of the straight solenoid.
Axial magnetic induction intensity of long straight spiral pipe;
b = UH/KH * IS = 1.33 x 10-2T
The comparison error of theoretical value is: E=5.3%.
X. Problem discussion (or thinking):
References:
Website: There are many.