四探针法测电阻率实验原理.doc

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，

2、所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 IVC23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，drR2它们之间的电位差为 。IIdV考虑样品为半无限大，在 r 处的电位为 0，所以图（a）中流经探针

4、的电流 I在 r 点形成的电位为 。rIr21流经探针的电流在、两探针间形成的电位差为 ；132123rIV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 。432423rIV于是流经探针、之间的电流在探针、之间形成的电位差为。43213223 rrI由此可得样品的电阻率为 112432323rrIV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，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 SrSr2,413431222IV对于方形

5、四探针有 rr,42134312 3IS 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 t800 0.01 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。 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

6、。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 91参 考平 均参 考 TC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；C T 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附录附录 1A 样品厚度修正系数 G（ ）WS样品厚度较薄： =0.0011 见表 5WSW：样品厚度（m）：S ：探针间距（ mm）W/S W 0 1 2 3 4 5 6 7 8 90.000.010.020.030.040.050.060.070.080.090.100.110.120.130.140

7、.150.160.170.180.190.200.210102030405060708090100110120130140150160170180190200210.000.007.014.022.029.036.043.051.058.065.072.079.087.094.101.108.115.123.130.137.144.151.001.008.015.022.030.037.044.051.058.066.073.080.087.095.102.109.116.123.131.138.145.152.001.009.016.023.030.038.045.052.059.066.0

8、74.081.088.095.102.110.117.124.131.139.145.153.002.009.017.024.031.038.045.053.060.067.074.082.089.096.103.110.118.125.132.139.146.154.003.010.017.025.032.039.046.053.061.068.075.082.089.097.104.111.118.126.133.140.147.154.004.011.018.025.032.040.047.054.061.069.076.083.090.097.105.112.119.126.133.1

9、41.148.155.004.012.019.026.033.040.048.055.062.069.077.084.091.098.105.113.120.127.134.141.149.156.005.012.019.027.034.041.048.056.063.070.077.084.092.099.106.113.120.128.135.142.149.157.006.013.020.027.035.042.049.056.063.071.078.085.092.100.107.114.121.128.136.143.150.157.006.014.021.028.035.043.0

10、50.057.064.071.079.086.093.100.107.115.122.129.136.144.151.1580.220.23220230.159.166.159.167.160.167.161.168.162.169.162.170.163.170.164.171.164.172.165.172W/S W 0 1 2 3 4 5 6 7 8 90.240.250.260.270.280.290.300.310.320.330.340.350.360.370.380.390.400.410.420.430.440.450.460.470.480.49240250260270280

11、290300310320330340350360370380390400410420430440450460470480490.173.180.188.1953202.209.216.224.231.238.245.252.260.267.274.281.288.296.303.310.317.324.331.338.346.353.174.181.188.195.203.210.217.224.232.239.246.253.260.268.275.282.289.296.303.311.318.325.332.339.346.353.175.182.189.19.203.211.218.2

12、25.232.239.247.254.261.268.275.283.290.297.304.311.319.326.333.340.347.354.175.183.190.197.204.211.219.226.233.240.247.255.262.269.276.283.291.298.305.312.319.326.333.341.348.355.176.183.190.198.205.212.219.227.234.241.248.255.263.270.277.284.291.298.306.313.320.327.334.341.348.355.177.184.191.199.2

13、05.213.220.227.234.242.249.256.263.270.278.285.292.299.306.314.321.328.335.342.349.356.177.185.192.199.206.214.221.228.235.242.250.257.264.271.278.286.293.300.307.314.321.329.336.343.350.357.178.185.193.200.207.214.221.229.236.243.250.257.265.272.279.286.293.301.308.315.323.329.336.343.351.358.197.1

14、86.193.201.208.215.222.229.237.244.251.258.265.273.280.287.294.301.308.316.323.330.337.344.351.358.180.187.194.201.208.216.223.230.237.245.252.259.266.273.281.289.295.302.309.316.324.331.338.345.352.3590.50 500 .360 .360 .361 .362 .363 .363 .364 .365 .365 3.68W/S W 0 1 2 3 4 5 6 7 8 90.510.520.530.5

15、40.550560.570.580.590.600.610.620.630.640.650.660.670.680.690.700.710.720.730.740.750.76510520530540550560570580590600610620630640650660670680690700710720730740750760.367.374.381.388.395.402.409.416.422.429.436.443.450.456.463.470.476.483.489.496.502.508.515.521.527.533.368.375.382.389.396.402.409.4

16、16.423.430.437.444.450.457.464.470.477.483.490.496.503.509.516.522.528.534.368.375.382.389.396.403.410.417.424.431.437.444.451.458.464.471.477.484.491.497.503.510.516.522.529.535.369.376.383.390.397.404.411.418.425.431.438.445.452.458.465.472.478.485.491.498.504.510.517.523.529.535.370.377.384.391.3

17、98.405.411.418.425.432.439.446.452.459.466.472.479.485.492.498.505.511.517.524.530.536.370.377.384.391.398.405.412.419.426.433.439.446.453.460.466.473.479.486.492.499.505.512.518524.530.537.371.378.385.392.399.406.413.420.427.433.440.447.454.460.467.474.480.487.493.500.506.512.519.525.531.537372.379

18、.386.393.400.407.414.420.427.434.441448454461.468.474.481.488.494.500.507.513.519.525.532.538372.379.386.393.400.407.414.421.428.435.442.448.455.462.468.475.481.488.494.501.507.514.520.526.532.538.373.380.387.394.401.408.415.422.429.435.442.449.456.462.469.476.482.489.495.501.508.514.520.527.533.539

19、0.77 770 .540 .540 .541 .541 .542 .543 .543 .544 .544 .545W/S W 0 1 2 3 4 5 6 7 8 90.780.790.800.810.820.830.840.850.860.870.880.890.900.910.920.930.940.950.960.970.980.991.007807908008108208308408508608708808909009109209309409509609709809901000.546.552.558.564.569.575.581.587.592.598.603.609.614.61

20、9.625.630.635.640.645.650.655.660.665.546.552.558.564.570.576.581.587.593.598.604.609.615.620.625.630.636.641.646.651.656.660.547.553.559.565.571.576.582.588.593.599.604.610.615.621.626631.636.641.646.651.656.661.547.553.559.565.571.577.583.588.594.599.605.610.616.621.626.631.637.642.647.652.657.661

21、.548.554.560.565.572.577.583.589.594.600.605.611.616.622.627.632.637.642.647.652.657.662.549.555.561.567.573.579.584590.596.601.607.612.617.623.628.633.638.643.648.653.658.663.549.555.561.567.573.579.584.590.596.601.607.612.617.623.628.633.638.643.648.653.658.663.550.556.562.568.573.579.585.591.596.

22、602.607.613.618.623.628.634.639.644.649.654.658.663.550.556.562.568.574.580.585.591.597.602.608.613.618.624.629.634.639.644.649.654.658.664.551.557.563.569.575.580.586.592.597.603.608.614.619.624.629.635.640.645.650.655.659.664附录 1B 样品厚度修正系数 G（ ）WS样品厚度较厚： =0.013.49 见表WSW：样品厚度（m）：S：探针间距（mm）W/S 0.00 0

23、.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.601.701.800.00000.07210.14430.21640.28840.35970.42930.49570.55760.61410.66470.70930.74820.78170.81060.83520.85630.87430.88970.00720.07940.15150.22360.29560.36680.43610.50210.56350.61940.66940

24、.71340.75180.78480.81320.83750.83820.87600.89110.01440.08660.15870.23080.30270.37380.44290.50850.56940.62470.67410.71750.75530.78790.81580.83970.86010.87760.89250.02160.09380.16590.23800.30990.38080.44960.51480.57510.62990.67870.72150.75890.79080.81840.84190.86200.87920.89390.02890.10100.17310.24520

25、.31710.38780.45630.52100.58090.63510.68330.72550.76220.79380.82090.84410.86390.88080.89520.03610.10820.18030.25240.32420.39480.46300.52730.58660.64020.68770.72940.76660.79670.82340.84620.86570.88230.89650.04330.11540.18750.25960.33130.40180.46960.53340.59220.64520.69220.73330.76890.79960.82580.84830

26、.86750.88380.89780.05050.12260.19480.26680.33850.40870.47620.53960.59780.65010.69650.73710.71220.80240.82820.85030.86920.88530.89910.05770.12980.20200.27400.34560.41560.48270.54560.60330.65510.70090.74080.77540.80520.83060.85240.87090.88680.90040.06490.13710.20920.28120.35260.42240.48920.55160.60870.65990.70510.74450.77860.80790.83290.85440.87260.88830.9016