四探针法测电阻率

1、实验四探针法测电阻率1实验目的：学习用四探针法测量半导体材料的体电阻率和扩散薄层的电阻率及方块电阻。2实验内容硅单晶片电阻率的测量：选不同电阻率及不同厚度的大单晶圆片，改变条件（光照与否），对测量结果进行比较。薄层电阻率的测量：对不同尺寸的单面扩散片和双面扩散片的薄层电阻率进行测量。改变条件进行测量（与相同） ，对结果进行比较。3 实验原理：在半导体器件的研制和生产过程中常常要对半导体单晶材料的原始电阻率和经过扩散、外延等工艺处理后的薄层电阻进行测量。测量电阻率的方法很多，有两探针法，四探针法， 单探针扩展电阻法， 范德堡法等， 我们这里介绍的是四探针法。因为这种方法简便可行，适于批量生产，所

2、以目前得到了广泛应用。所谓四探针法， 就是用针间距约1 毫米的四根金属探针同时压在被测样品的平整表面上如图 1a 所示。利用恒流源给1、 4 两个探针通以小电流，然后在2、 3 两个探针上用高输入阻抗的静电计、电位差计、 电子毫伏计或数字电压表测量电压，最后根据理论公式计算出样品的电阻率C V23I式中，C 为四探针的修正系数，单位为厘米， C 的大小取决于四探针的排列方法和针距，探针的位置和间距确定以后，探针系数C 就是一个常数； V 23为 2、3 两探针之间的电压，单位为伏特； I 为通过样品的电流，单位为安培。半导体材料的体电阻率和薄层电阻率的测量结果往往与式样的形状和尺寸密切相关，下

3、面我们分两种情况来进行讨论。 半无限大样品情形图 1 给出了四探针法测半无穷大样品电阻率的原理图，图中(a) 为四探针测量电阻率的装置； (b) 为半无穷大样品上探针电流的分布及等势面图形；(c)和 (d) 分别为正方形排列及直线排列的四探针图形。因为四探针对半导体表面的接触均为点接触，所以， 对图（ b）所示的半无穷大样品，电流I 是以探针尖为圆心呈径向放射状流入体内的。因而电流在体内所形成的等位面为图中虚线所示的半球面。于是，样品电阻率为， 半径为 r，间距为 dr 的两个半球等位面间的电阻为dR2 r2 dr ，I它们之间的电位差为dVIdR2dr 。r 2考虑样品为半无限大，在r处的电

4、位为0，所以图（ a）中流经探针的电流I 在r 点形成的电位为Vr12I 2 dr2I。rrr流经探针的电流在、两探针间形成的电位差为V23 1I11 ；2r12r13流经探针的电流与流经探针的电流方向相反，所以流经探针的电流I 在探针、之间引起的电位差为V2342I11。r42r43于是流经探针、之间的电流在探针、之间形成的电位差为V23I1111 。2r12r13r42r43由此可得样品的电阻率为2 V23111111Ir12r13r42r43上式就是四探针法测半无限大样品电阻率的普遍公式。在采用四探针测量电阻率时通常使用图（c）的正方形结构（简称方形结构）和图（ d）的等间距直线形结构，

5、假设方形四探针和直线四探针的探针间距均为S，则对于直线四探针有r12r43S,r13r422S2SV232I对于方形四探针有r12r43S,r13r422S2 SV23322I无限薄层样品情形当样品的横向尺寸无限大，而其厚度 t 又比探针间距S 小得多的时候， 我们称这种样品为无限薄层样品。图给出了用四探针测量无限薄层样品电阻率的示意图。图中被测样品为在p 型半导体衬底上扩散有n 型薄层的无限大硅单晶薄片，、为四个探针在硅片表面的接触点，探针间距为 S，n 型扩散薄层的厚度为t，并且 t<<S， I+ 表示电流从探针流入硅片， I-表示电流从探针流出硅片。与半无限大样品不同的是，这

6、里探针电流在n 型薄层内近似为平面放射状，其等位面可近似为圆柱面。类似前面的分析，对于任意排列的四探针，探针的电流I 在样品中 r 处形成的电位为Vr 12I drIln rrrt2t式中为 n 型薄层的平均电阻率。于是探针的电流I 在、探针间所引起的电位差为V23 1Iln r12Iln r132 tr132 tr12同理，探针的电流I 在、探针间所引起的电位差为V234Iln r422tr43所以探针和探针的电流I 在、探针之间所引起的电位差是V232Iln r42r13tr43r12于是得到四探针法测无限薄层样品电阻率的普遍公式为2 tV 23ln r42r134Ir43r12对于直线四

7、探针，利用r12r43S,r13r422S 可得2 tV23 2ln 2tV235Iln 2I对于方形四探针，利用r12r43S,r13r422S 可得2 tV236ln 2I在对半导体扩散薄层的实际测量中常常采用与扩散层杂质总量有关的方块电阻RS，它与扩散薄层电阻率有如下关系：RS11X jq NX jX jqNdX0这里 X j 为扩散所形成的pn 结的结深。这样对于无限薄层样品，方块电阻可以表示如下：直线四探针：RSV237ln 2 IX j方形四探针：RS2V238ln 2IX j在实际测量中， 被测试的样品往往不满足上述的无限大条件，样品的形状也不一定相同，因此常常要引入不同的修正系

8、数。实际测量中的扩散样片可能有两种情况：单面扩散片和双面扩散片，如图3 所示。这两种样品的修正系数分别列于附录中的表。图 4 SZT-2A 四探针测试仪4实验装置及注意事项 实验装置实验装置如图 4 所示。电路中的恒流源所提供的电流是连续可调的，电压表采用电位差计或数字电压表。实验所用的探针通常采用耐磨的导电硬质合金材料，如钨、碳化钨等。探针要求等间距配置，并使其具有很小的游移误差。在探针上需加上适当的压力，以减小探针与半导体材料之间的接触电阻。 注意事项半无限大样品是指样品厚度及任意一根探针距样品最近边界的距离远大于探针间距，如果这一条件不能得到满足则必需进行修正。为了避免探针处的少数载流子

9、注入，提高表面复合速度，待测样品的表面需经粗砂打磨或喷砂处理。在测量高阻材料及光敏材料时需在暗室或屏蔽盒内进行。因为电场太大会使载流子的迁移率下降，导致电阻率测量值增大，故须在电场强度 E<1V/cm 的弱场下进行测量。为了避免大电流下的热效应，测试电流应尽可能低，但须保证电压的测试精度。不同电阻率样品的电流选择大致为2电阻率范围测量电流（ mA ）（· cm）<0.0121000.080.6100.46014012000.1>8000.01为了满足探针与半导体的接触为欧姆接触，探针上须加上一定的压力。对于体材料，一般取12kg；对于薄层材料或外延材料选取200g。

10、当室温有较大波动时，最好将电阻率折算到 23时的电阻率。因为半导体的电阻率对温度很敏感。如果有必要考虑温度对电阻率的影响，可用下面的公式进行计算参考平均1 CTTT参考9式中 参考 为修正到某一参考温度 ( 例如 23 )下的样品电阻率 ; 平均 为测试温度下样品的平均电阻率； CT 为温度系数， 它随电阻率变化的曲线示于图5；T 为测试温度；T 参考 为某一指定的参考温度。5附录W附录 1A样品厚度修正系数G（ S）W样品厚度较薄：S =0.0011见表 5W：样品厚度（ m）： S：探针间距（ mm）W/SW01234567890.000.000.001.001.002.003.004.0

11、04.005.006.0060.0110.007.008.009.009.010.011.012.012.013.0140.0220.014.015.016.017.017.018.019.019.020.0210.0330.022.022.023.024.025.025.026.027.027.0280.0440.029.030.030.031.032.032.033.034.035.0350.0550.036.037.038.038.039.040.040.041.042.0430.0660.043.044.045.045.046.047.048.048.049.0500.0770.051

12、.051.052.053.053.054.055.056.056.0570.0880.058.058.059.060.061.061.062.063.063.0640.0990.065.066.066.067.068.069.069.070.071.0710.10100.072.073.074.074.075.076.077.077.078.0790.11110.079.080.081.082.082.083.084.084.085.0860.12120.087.087.088.089.089.090.091.092.092.0930.13130.094.095.095.096.097.097

13、.098.099.100.1000.14140.101.102.102.103.104.105.105.106.107.1070.15150.108.109.110.110.111.112.113.113.114.1150.16160.115.116.117.118.118.119.120.120.121.1220.17170.123.123.124.125.126.126.127.128.128.1290.18180.130.131.131.132.133.133.134.135.136.1360.19190.137.138.139.139.140.141.141.142.143.1440.

14、20200.144.145.145.146.147.148.149.149.150.1510.21210.151.152.153.154.154.155.156.157.157.1580.22220.159.159.160.161.162.162.163.164.164.1650.23230.166.167.167.168.169.170.170.171.172.172W/SW01234567890.24240.173.174.175.175.176.177.177.178.197.1800.25250.180.181.182.183.183.184.185.185.186.1870.2626

15、0.188.188.189.190.190.191.192.193.193.1940.27270.195.195.19.197.198.199.199.200.201.2010.282803202.203.203.204.205.205.206.207.208.2080.29290.209.210.211.211.212.213.214.214.215.2160.30300.216.217.218.219.219.220.221.221.222.2230.31310.224.224.225.226.227.227.228.229.229.2300.32320.231.232.232.233.2

16、34.234.235.236.237.2370.33330.238.239.239.240.241.242.242.243.244.2450.34340.245.246.247.247.248.249.250.250.251.2520.35350.252.253.254.255.255.256.257.257.258.2590.36360.260.260.261.262.263.263.264.265.265.2660.37370.267.268.268.269.270.270.271.272.273.2730.38380.274.275.275.276.277.278.278.279.280

17、.2810.39390.281.282.283.283.284.285.286.286.287.2890.40400.288.289.290.291.291.292.293.293.294.2950.41410.296.296.297.298.298.299.300.301.301.3020.42420.303.303.304.305.306.306.307.308.308.3090.43430.310.311.311.312.313.314.314.315.316.3160.44440.317.318.319.319.320.321.321.323.323.3240.45450.324.32

18、5.326.326.327.328.329.329.330.3310.46460.331.332.333.333.334.335.336.336.337.3380.47470.338.339.340.341.341.342.343.343.344.3450.48480.346.346.347.348.348.349.350.351.351.3520.49490.353.353.354.355.355.356.357.358.358.3590.50500.360.360.361.362.363.363.364.365.3653.68W/SW01234567890.51510.367.368.36

19、8.369.370.370.371372372.3730.52520.374.375.375.376.377.377.378.379.379.3800.53530.381.382.382.383.384.384.385.386.386.3870.54540.388.389.389.390.391.391.392.393.393.3940.55550.395.396.396.397.398.398.399.400.400.401056560.402.402.403.404.405.405.406.407.407.4080.57570.409.409.410.411.411.412.413.414

20、.414.4150.58580.416.416.417.418.418.419.420.420.421.4220.59590.422.423.424.425.425.426.427.427.428.4290.60600.429.430.431.431.432.433.433.434.435.4350.61610.436.437.437.438.439.439.440.441.442.4420.62620.443.444.444.445.446.446.447448.448.4490.63630.450.450.451.452.452.453.454454.455.4560.64640.456.

21、457.458.458.459.460.460461.462.4620.65650.463.464.464.465.466.466.467468.468.4690.66660.470.470.471.472.472.473.474.474.475.4760.67670.476.477.477.478.479.479.480.481.481.4820.68680.483.483.484.485.485.486.487.488.488.4890.69690.489.490.491.491.492.492.493.494.494.4950.70700.496.496.497.498.498.499.

22、500.500.501.5010.71710.502.503.503.504.505.505.506.507.507.5080.72720.508.509.510.510.511.512.512.513.514.5140.73730.515.516.516.517.517.518.519.519.520.5200.74740.521.522.522.523.524524.525.525.526.5270.75750.527.528.529.529.530.530.531.532.532.5330.76760.533.534.535.535.536.537.537.538.538.5390.77

23、770.540.540.541.541.542.543.543.544.544.545W/SW01234567890.78780.546.546.547.547.548.549.549.550.550.5510.79790.552.552.553.553.554.555.555.556.556.5570.80800.558.558.559.559.560.561.561.562.562.5630.81810.564.564.565.565.565.567.567.568.568.5690.82820.569.570.571.571.572.573.573.573.574.5750.83830.

24、575.576.576.577.577.579.579.579.580.5800.84840.581.581.582.583.583.584.584.585.585.5860.85850.587.587.588.588.589590.590.591.591.5920.86860.592.593.593.594.594.596.596.596.597.5970.87870.598.598.599.599.600.601.601.602.602.6030.88880.603.604.604.605.605.607.607.607.608.6080.89890.609.609.610.610.611

25、.612.612.613.613.6140.90900.614.615.615.616.616.617.617.618.618.6190.91910.619.620.621.621.622.623.623.623.624.6240.92920.625.625.626.626.627.628.628.628.629.6290.93930.630.630631.631.632.633.633.634.634.6350.94940.635.636.636.637.637.638.638.639.639.6400.95950.640.641.641.642.642.643.643.644.644.64

26、50.96960.645.646.646.647.647.648.648.649.649.6500.97970.650.651.651.652.652.653.653.654.654.6550.98980.655.656.656.657.657.658.658.658.658.6590.99990.660.660.661.661.662.663.663.663.664.6641.001000.665.W附录 1B样品厚度修正系数G（ S）样品厚度较厚：W=0.013.49见表SW：样品厚度（ m）： S：探针间距（ mm）W/S0.000.010.020.030.040.050.060.070

27、.080.090.000.00000.00720.01440.02160.02890.03610.04330.05050.05770.06490.100.07210.07940.08660.09380.10100.10820.11540.12260.12980.13710.200.14430.15150.15870.16590.17310.18030.18750.19480.20200.20920.300.21640.22360.23080.23800.24520.25240.25960.26680.27400.28120.400.28840.29560.30270.30990.31710.3

28、2420.33130.33850.34560.35260.500.35970.36680.37380.38080.38780.39480.40180.40870.41560.42240.600.42930.43610.44290.44960.45630.46300.46960.47620.48270.48920.700.49570.50210.50850.51480.52100.52730.53340.53960.54560.55160.800.55760.56350.56940.57510.58090.58660.59220.59780.60330.60870.900.61410.61940

29、.62470.62990.63510.64020.64520.65010.65510.65991.000.66470.66940.67410.67870.68330.68770.69220.69650.70090.70511.100.70930.71340.71750.72150.72550.72940.73330.73710.74080.74451.200.74820.75180.75530.75890.76220.76660.76890.71220.77540.77861.300.78170.78480.78790.79080.79380.79670.79960.80240.80520.8

30、0791.400.81060.81320.81580.81840.82090.82340.82580.82820.83060.83291.500.83520.83750.83970.84190.84410.84620.84830.85030.85240.85441.600.85630.83820.86010.86200.86390.86570.86750.86920.87090.87261.700.87430.87600.87760.87920.88080.88230.88380.88530.88680.88831.800.88970.89110.89250.89390.89520.89650

31、.89780.89910.90040.90161.900.90290.90410.90530.90640.90760.90870.90990.91100.91210.9131W/S0.000.010.020.030.040.050.060.070.080.092.000.91420.91520.91620.91720.91820.91920.92020.92110.92210.92302.100.92390.92480.92570.92660.92740.92830.92910.92990.93070.93152.200.93230.93310.93380.93460.93530.93610.

32、93680.93750.93820.93892.300.93960.94020.94090.94150.94220.94280.94350.94410.94470.94532.400.94590.94020.94700.94760.94820.94870.94930.94980.95030.95092.500.95140.95190.95240.95290.95340.95380.95430.95480.95530.95572.600.95620.95660.95710.95750.95790.95830.95880.95920.95960.96002.700.96040.96080.9612

33、0.96160.96190.96230.96270.96300.96340.96372.800.96410.96440.96480.96520.96550.96580.96610.96640.96670.96712.900.96740.96770.96800.96830.96860.96890.96920.96940.96970.97003.000.97030.97050.97080.97110.97130.97160.97180.97210.97240.97263.100.97280.97310.97330.97360.97380.97400.97420.97450.97470.97493.

34、200.97510.97530.97560.97580.97600.97620.97640.97660.97680.97703.300.97720.97740.97760.97780.97790.97810.97830.97850.97870.97883.400.97900.97920.97940.97950.97970.97990.98000.98020.98030.9805如需所测值更精确，请查下表d附录 2 样品形状和测量位置的修正系数D（ s ）（1）圆形薄片探针位置直径 d距圆心位置距边缘位置(mm)0mm1/4 d5 mm4 mm3 mm2 mm200.97880.96330.96330.95080.92630.8702230.98390.97190.96620.95380.92950.8739250.98630.97610.96770.95530.93120.8758270.98820.97940.96880.95650.93250.8773300.99040.98320.97020.95800.93