电学半导体材料的霍尔效应

1、实验 17 半导体材料的霍尔效应霍尔效应是一种磁电效应，由AHHall（1855-1938）于1879年在研究金属的导电机理时发现。后来发现半导体、导电液等也有这种作用。这种影响对金属来说并不显着，但对半导体来说却非常显着。利用这种效应制成的各种霍尔元件广泛应用于工业自动化技术、检测技术和信息处理等领域。霍尔效应是研究半导体材料特性的基本方法。通过霍尔效应实验，可以测量半导体材料的霍尔系数，从而判断样品的导电类型，计算载流子浓度、载流子迁移率等重要参数。【预览思考题】1、霍尔效应是如何产生的？2、霍尔元件的材料如何选择？实验目的1、了解霍尔效应的实验原理及霍尔元件相关参数的含义和作用；2. 使

2、用“对称测量法”消除副作用的影响，绘制样本总和曲线图；和曲线；3. 测定样品的导电类型、载流子浓度和迁移率。【实验仪器】Th-h 霍尔效应实验仪器。【实验原理】Fig. 1 schematic diagram of hall effect experiment principle: a) carrier is electron (n-type) b) carrier is hole (p-type)Fig. 1 schematic diagram of hall effect experiment principle: a) carrier is electron (n-type) b) ca

3、rrier is hole (p-type)ab1.霍尔效应霍尔效应本质上是磁场中洛伦兹力引起的运动带电粒子的偏转。当带电粒子（电子或空穴）被限制在固体材料中时，这种偏转导致正负电荷在垂直电流和磁场方向上的积累，从而形成一个额外的横向电场，即霍尔电场。对于图 1 所示的半导体样品，如果沿 X 方向施加电流，沿 Z 方向施加磁场，则样品中的载流子将受到洛伦兹力的影响。 。如图1展示的半导体样品，若沿 ，则样品中的载流子将受洛伦兹力的作用（1）在Y方向，即在样品A和A/电极两侧积累了相同数量的不同符号的电荷，从而产生霍尔电场。电场的方向取决于样品的导电类型。对于 N 型（即载流子为电子）样品（图

4、1a），霍尔电场与 Y 方向相反，而 P 型（即载流子为空穴）样品沿 Y 方向（图 1b）。有以下几种类型。Obviously, the Hall electric field will prevent the carrier from shifting sideways. When the force of the Hall electric field on the carrier is equal to the Lorentz force, the charge accumulation on both sides of the sample will reach a dynamic b

5、alance, so将阻止载流子继续向侧面偏移，当载流子所受的霍尔电场力与洛伦兹力相等时，样品两侧电荷的积累就达到动态平衡，故（2）Where Hall electric field is the average drift velocity of carriers in the current direction.为霍尔电场，是载流子在电流方向上的平均漂移速度。Let the width of the sample be B, the thickness be D, and the carrier concentration be N, then(3)It can be obtained f

6、rom two formulas (2) and (3):(4)That is, the Hall voltage (voltage between A and A/electrodes) is proportional to the product and inversely proportional to the thickness of the sample. Proportion coefficient is called Hall coefficient, which is an important parameter reflecting the strength of Hall

7、effect of materials. As long as (V) is measured and (A), (Gauss) and (cm) are known, the following formula can be used to calculate (cm3/coulomb):（乘积成正比，与试样厚度成反比。比例系数称为霍尔系数，它是反映材料霍尔效应强弱的重要参数。只要测出 （安）、（高斯）和（厘米），可按下式计算（厘米RH （5） （5）2. The relationship between Hall coefficient and other parameters与其它参数间

8、的关系The following parameters can be further determined according to:可进一步确定以下参数：(1) Judging the conductivity type of the sample by the sign of (or the positive and negative of Hall voltage).的符号（或霍尔电压的正负）判断样品的导电类型。According to the direction of I and B shown in Figure 1, if the measured value (that is,

9、the potential of the point is higher than the potential of the point) is negative, the sample is N-type, otherwise it is P-type.和（即点的电位高于点的电位），则为负，样品属(2) Find the carrier concentration n from RH.It can be seen that when RH is known, it can be obtained. It should be pointed out that this relation is

10、obtained on the assumption that all carriers have the same drift velocity. Strictly speaking, if the statistical distribution of carrier velocity is considered, a correction factor should be introduced (see Huang Kun and Sids Semiconductor Physics).可知，当。应该指出，这个关系式是假定所有载流子都具有相同的漂移速度得到的，严格一点，如果考虑载流子的速

11、度统计分布，需引入的修正因子（可参阅黄昆、希德著半导体物理学）。(3) Combining with the measurement of conductivity, find the mobility of carriers.。There is the following relationship between conductivity, carrier concentration n and mobility:与载流子浓度之间有如下关系：(6) That is, =, the value measured by experiment can be obtained.，通过实验测出值即可求

12、出。3. The relationship between Hall effect and material propertiesAccording to the above, the key to obtain a large Hall voltage is to choose materials with large Hall coefficient (i.e. high mobility and high resistivity). Because, as far as metal conductors are concerned, the sum is very low, while

13、the bad conductor is high, but very small, so the Hall coefficients of the above two materials are very small, so they cant be used to manufacture Hall elements. The semiconductor material is high and moderate, which is an ideal material for manufacturing Hall elements. Because the mobility of elect

14、rons is larger than that of holes, Hall elements are mostly made of N-type materials. Secondly, the Hall voltage is inversely proportional to the thickness of the material, so the output voltage of the thin-film Hall element is much higher than that of the sheet. As far as the Hall element is concer

15、ned, its thickness is certain, so it is practically used to represent the sensitivity of the device, which is called Hall sensitivity, and the unit is or.亦较高）的材料。因，就金属导体而言，和均很低，而不良导体虽高，但极小，因而上述两种材料的霍尔系数都很小，不能用来制造霍尔元件。半导体材料高，适中，是制造霍尔元件较理想的材料。由于电子的迁移率比空穴迁移率大，所以霍尔元件多采用来表示器件的灵敏度，称为霍尔灵敏度，单位为或。【实验能力】1、熟悉仪

16、器性能，连接好测试仪和实验仪器之间的各组导线。图2 实验电路连接装置示意图(1) 为准确测量，开机或关机前，应将测试仪归零，即IS，将测试仪的“IS调节”和“IM调节”旋钮调到零（即逆时针转动至结尾）。（2）按图2将测试仪与实验仪器对应的IS、VH、IM连线接好，IS、IM换向开关向上拨动，表示IS、IM均为正向（即IS沿x方向和z方向），反之亦然，它们是负的。 “VH、V输出”双极开关调高测量VH，调低测量V。沿Z方向），反之为负值。“(3)接通电源，预热10分钟左右，电流表显示“.000”（表示按下“测量选择”键显示励磁电流IM值）或“0.00”（表示松开“测量选择”键显示导通电流IS值）

17、；电压表（此时测试仪上的“”功能转换开关拨到VH侧，实验仪器上的“输出”双极开关也拨到VH侧）显示“0.00”。如果VH不显示“0.00”，则可以通过面板左下孔中的“调零”电位器实现调零。当显示器的数字前面出现“-”时，被测电压的极性为负。 功能切换开关投向输出双刀开关亦置（4）将“测量选择”设置到IS位置（松开键），电流表显示的数值随着“IS调节”旋钮顺时针旋转而增大，变化范围为0-10mA。此时，如果电压表显示的读数不为0，则会显示“不等电位”电压值（见附录不等电位电压V0），该值会随着IS的增加而增加。测量时，可通过“对称测量法”消除“不等电位”电压值。 IS=2mA。 (5) 将“测量

18、选择”设置到互调位置（键），电流表显示的数值随着“互调调节”旋钮顺时针旋转而增加，变化范围为0-1A。此时该值随IM的增加而增加，IM反向，极性改变符号（其绝对值随IM的流动方向而变化，这是由副作用引起的，可以通过“对称测量法”消除） .取IM=00A随值随改号（其绝对值随值）。(6) Release the measurement selection key, measure and adjust again, then turn the function switch on the tester to the V side, and set the output double-pole s

19、witch on the experimental instrument to the V side to measure the voltage (voltage between electrodes); Change direction, also change number. It shows that all electrodes of these Hall samples work normally and can be measured. Return the switch on the tester and experimental instrument to the side.

20、，调节，然后将测试仪上“”功能切换开关投向输出”双刀开关亦置电压（电极间电压）；换向，亦改号。这些说明霍尔样品的各电极工作均正常，可进行测量。将测试仪及实验仪上的 “”开关均恢复侧。注意事项： 试样各电极引线与对应双极开关的连接已由厂家连接好。请不要再移动！ 严禁将测试仪的励磁电源IM输出端接在IS输入端（IS和IM的值相差1000倍量级）或实验仪器的输出端，否则会导致霍尔样品通电后损坏！输出 样品中有三对电极，其中A、A/或C、C/用于测量霍尔电压，A、C或A/、C/用于测量电导，D、E工作样品的电流电极。仪器出厂前，霍尔片已调至中心位置。霍尔易碎易碎，电极很薄，容易折断。不要用手敲打或触摸

21、它，否则很容易损坏！霍尔片放置在电磁铁间隙的中间。当需要调整霍尔片的位置时，必须注意不要随意改变Y轴方向的高度，以免霍尔片与磁极表面摩擦而损坏。 ， 为不因过热损坏通电线圈，或影响测量精度，其余时间最好关闭励磁电流开关，短时间读取相关数据并通过励磁除外当前即时消息。 同一个数字电压表通过功能开关测量；并通过测量选择键（“键”表示IM值，“释放键”表示IS值）用同一个电流表测量IS和IM。和通过数字功能表切换开关由同一个电压进行测量；2、掌握仪器的测试方法，用对称法测量霍尔电压VH。It should be noted that the Hall effect is accompanied by

22、 various side effects, so that the experimentally measured voltage between the two electrodes is not equal to the real Hall voltage value, but contains additional voltages caused by various side effects, so it must be eliminated. According to the mechanism of the side effect (see appendix), it can b

23、e known that the symmetrical measurement method of current and magnetic field commutation can basically eliminate the influence of the side effect from the measurement results. The specific method IS that the magnitude of IS and (i.e., IM) is constant. After the positive and negative directions of c

24、urrent and magnetic field are specified, the following four groups of different directions and combinations (potential difference between two points) are measured in turn:、两电极间的电压并不等于真实的霍尔电压值，而是包含着各种副效应所引起的附加电压，因此必须设法消除。根据副效应产生的机理（参阅附录）可知，采用电流和磁场换向的对称测量法，基本上能把副效应的影响从测量结果中消除。具体的做法是(即和组合的（、两点的电位差）即：，

25、， ， ， Then find the algebraic average of, and.、和的代数平均值。 （） Although all the side effects cant be eliminated by the symmetrical measurement method, the error introduced by it is small and can be neglected.，虽然还不能消除所有的副效应，但其引入的误差不大，可以略而不计。3. Mapping curves曲线Turn the function switch on the tester to the

26、 VH side, and the output double-pole switch on the experimental instrument is also placed on the VH side, and the reversing switch is thrown up, indicating that both sum and are positive (that is, along the X direction and along the Y direction); otherwise, they are negative. Keep the value unchange

27、d (take = 0.300A), and change the value. The value range is. The values measured by symmetry method are recorded in Table 1.”功能切换开关投向输出”双刀开关亦置及换向开关掷向上方，表明及均为正值（即沿沿值不变（取的值，取值围为。用对称法分别测量的值，将实验测量值记入表1中。表1 IM =0。 3 00AI s（ mA ）1 伏（毫伏）V（毫伏）V（毫伏）V（毫伏）+IS 、 +B+IS 、 -B-为B-IS 、 +B1 .001.502.002.503.003.504.0

28、04. 映射曲线曲线The switch positions of the experimental instrument and tester are unchanged. Keep the value unchanged (take = 3.00mA), change the value, and take the value around. The values measured by symmetry method are recorded in Table 2.值不变（取的值，取值围为。用对称法分别测量的值，将实验测量值记入表2中。2 IS=3.00mAI (a) _V 1 (m V

29、 )V 2 (m V )V 3 (m V )V 4 (m V )+I S 、 +B+I S 、 -B-I S 、 -B-I S 、 +B0.3000.3200.3400.3600.3800.4005. Measured values值Turn the function switch on the tester to the V side, and the output double-pole switch on the experimental instrument is also placed on the V side. Under the zero magnetic field (a),

30、 take = 0.2mA and measure (i.e. voltage between electrodes). Note: the value should not be greater than, so as not to make the millivolt meter exceed the range (at this time, the first digit is displayed as 1, and the last three digits are turned off).”功能切换开关投向输出”双刀开关亦置A），取0.2（即,电极间电压）。注意：取值不要大于，以免过

31、大使毫伏表超量程（此时首位数码显示为6. Determine the conductivity type of the sample.Throw all three groups of double-pole switches of the experimental instrument upward, that is, along the X direction and along the Z direction, and the voltage measured by the millivoltmeter is (i.e.). Take, measure the size and pola

32、rity, and judge the conductivity type of the sample.沿沿（即）。取，测量大小及极性，由此判断样品导电类型。Data Processing Requirements1. Draw curves and curves according to the data in Table 1 and Table 2, respectively, to verify the linear proportional relationship between Hall voltage VH and sum.曲线和曲线，以验证霍尔电压V和之间的线性正比关系。2.

33、Check the conductivity of the sample from the measured value.值，验样品的电导率。The conductivity of can be measured by electrodes A and C (or,) shown in Figure 1, assuming that the distance between A and C is, the cross-sectional area of the sample is, and the current flowing through the sample is. Under the

34、 zero magnetic field, if the potential difference between A and C is measured as (i.e.), the的测量可以通过图所示的、（或、）电极进行测量，设、间的距离为，样品的横截面积为，流经样品的电流为。在零磁场下，若测得（即），则由get3. 从实测值判断实验样品的电导率类型，检查RH、N和样品总和值，判断实验样品的电导率类型，并检验样品的电导率。已知：试样的几何尺寸为：D=d=0.5mm，b=4.0mm，A，A、C电极间距L=3.0mm。外加磁场的大小可以用关系式计算，其中K值标注在实验仪器的励磁线圈上，IM为实

35、验中输入的励磁电流大小。大小由关系式计算可得，其中【思考题】1、霍尔效应的机理？2. 测量值是用来做什么的？值是用途的？3.如果样品的方向已知，如何判断样品的导电类型？如何的方向判断样品的导电类型？4、霍尔灵敏度有什么意义？它的单位是什么？可以用这个实验装置测量霍尔系数 RH 吗？5. 如何利用霍尔效应测量磁场？6、如何消除霍尔效应的副作用？附记录霍尔元件的副作用及其消除方法Figure 3 Unequal potential voltage1.电位电压不等Figure 3 Unequal potential voltageThis is because the position of the

36、 electrodes A and A/ for measuring Hall voltage is difficult to be on an ideal equipotential surface. Therefore, when a current passes through, an additional voltage = will be generated even if no magnetic field is applied, where R is the resistance between the two equipotential surfaces where A and

37、 A/ are located (as shown in Figure 3). The symbol is only related to the direction of current, but not the direction of magnetic field, so it can be eliminated by changing the direction.通过时，即使不加磁场也会产生附加的电压，其中的符号只与电流的方向有关，与磁场的方向无关，因此，可以通过改变的方向予以消除。Figure 4 Additional voltage caused by thermoelectric

38、 effect2. Additional voltage caused by thermoelectric effectFigure 4 Additional voltage caused by thermoelectric effectAs shown in fig. 4, because of the different speeds of carriers constituting the current, if the Lorentz force exerted by the carriers with a speed of zero just counteracts the acti

39、on of Hall electric field force, the carriers with a speed greater than or less than zero will each deflect toward the opposite side under the action of electric field and magnetic field, thus causing temperature difference in Y direction, resulting in thermoelectric effect. Additional voltage is in

40、troduced to the electrode, and its sign is the same as the direction of sum, so it cant be eliminated by changing the direction of sum, but its introduced error is small and can be ignored.的载流子所受的洛仑兹力与霍尔电场力的作用刚好抵消，则速度大于或小于的载流子在电场和磁场作用下，将各自朝对立面偏转，从而在，由此产生的温差电效应。在电极上引入附加电压，且，其符号与和的方向关系跟是相同的，因此不能用改变和方向

41、的方法予以消除，但其引入的误差很小，可以忽略。Figure 5 Additional voltage directly caused by thermomagnetic effect3、热磁效应直接引起的附加电压Figure 5 Additional voltage directly caused by thermomagnetic effectFigure 6 Additional voltage caused by temperature difference caused by thermomagnetic effectDue to the unequal contact resista

42、nce of current leads at both ends of the device, different joule heat will be generated at the two contact points after power-on, resulting in a temperature gradient in the X direction, which will cause carriers to diffuse along the gradient direction and generate thermal diffusion current. Under th

43、e action of the magnetic field in the Z direction of heat flow, an additional electric field and corresponding voltage are generated in the Y direction similar to the Hall effect, and the sign of is only related to the direction of, but has nothing to do with, so it can be eliminated by changing the direction. As shown in Figure 5.在，相应的电压，而的符号只与的方向有关，与的方向无关，因此可通过改变的方向予以消除。如图5所示。Figure 6 Additional vo