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1、实验 四探针法测电阻率1.1. 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。2.2. 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。團1 1四探常法徘电匡率原理国h h卄囚琛护剛唱电率装暫禹工无劳丸样品上探纤 电沆的分侖反半味等势面1|1|圧方附排列的凹探甘酰MiMi启蠟怫列吋也榕針頸书3.3. 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
2、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。法简便可行,适于批量生产,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 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 1a1a 所示。利用恒流源给 1 1、4 4 两个探针通以小电流,然后在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,公式计算出样品的电阻率:1:2 2、3 3 两个探针上最后根据理论因为这种方I式中,C C 为四探针的修正系数, 单位为厘米,C C 的大小取决于四探针的排列方法和针距,23探针的位置和间
3、距确定以后,探针系数C C 就是一个常数;V V23为 2 2、3 3 两探针之间的电压,单位为伏特;I 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,下面我们分两种情况来进行讨论。 半无限大样品情形图 1 1 给出了四探针法测半无穷大样品电阻率的原理图,图中率的装置;(b)(b)为半无穷大样品上探针电流的分布及等势面图形;排列及直线排列的四探针图形。图1(b b)所示的半无穷大样品,电流(a)(a)为四探针测量电阻(c)(c)和(d)(d)分别为正方形所以,对因为四探针对半导体表面的接触均为点接触,I I 是以探针尖为圆心呈径向放
4、射状流入体内的。于是,样品电阻率为p,半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。径为 r r,间距为 drdr 的两个半球等位面间的电阻为它们之间的电位差为dV = IdR2 dr。PdR2 dr,2皿2PI2町2考虑样品为半无限大,在r处的电位为 0 0,所以图1(a a)中流经探针1的电流 I I 在 P|r r 点形成的电位为PI:Vr 1片2兀r22可V23 1訣2贰112流经探针1的电流在2、3两探针间形成的电位差为丄r13J流经探针4的电流与流经探针1的电流方向相反,所以流经探针4的电流I I 在探针2、3之间引起的电位差为于是流经探针1、4之间的电流在探针2、3之间形
5、成的电位差为PI12兀 12r1r13一1+1r43 Jr42由此可得样品的电阻率为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1(c c)的正方形结构(简称方形结构)和S S,图1(d 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则对于直线四探针有12=43=S,13=42=2S对于方形四探针有r12 = r43 = S,2SV23r13 = r42 = 2S2 -、2 I23无限薄层样品情形当样品的横向尺寸无限大,而其厚度 t t 又比探针间距 S S 小得多的时候,我们称这种样品为无限薄层样品。 图2给出了用四探针测量无限薄层样品
6、电阻率的示意图。 测样品为在 p p 型半导体衬底上扩散有 四个探针在硅片表面的接触点,探 针间距为 S,nS,n 型扩散薄层的厚度为 t t,并且tStS, 1 1+表示电流从探针1流入硅片,I I-表示电流从探针4流出 硅片。与半无限大样品n n 型薄层的无限大硅单晶薄片,1、2、析,对于任意 排列的四探针,探针1的电流 I I 样品中 r r 处形成的电位为图中被3、4为不同的是, 这里探针电流在 n 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r 2兀rtV23lni图2 2无限禅层样品电阻率濒呈2兀t r43 T12式中P为 n n 型薄层的平均电阻率。于是
7、探针1的电流|HI I 在2、3探针间所引起的电位差2t同理,探针4的电流ri32-tr12I I 在2、3探针间所引起的电位差为I I 在2、3探针之间所引起的电位差是于是得到四探针法测无限薄层样品电阻率的普遍公式为所以探针1和探针4的电流43 T12对于直线四探针,利用r12=43二S,13二r42二2S可得上V23p2ltV232ln2/=r43=S,2二t V23In2 IIIn2 Iri3二对于方形四探针,利用r122S可得P =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R Rs,它与扩散薄层电阻率有如下关系:P 11Rs二 二-XXjq壮NdX qNXjj
8、这里 X Xj为扩散所形成的 pnpn 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:RsV237Xjln 2 I图?单面扩散和飓面扩散的薄层(3)单面扩散的理层;(b)艰面扩散的薄层方形四探针:Rs2 V238Xjln2 I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,因此常常要引入不同的修正系数。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,如图这两种样品的修正系数分别列于附录中的表。3 3 所示。样品的形状也不一定相同,图 4 SZT-2A4 SZT-2A 四探针测试仪4 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
9、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 E1V/cmE1V/cm的弱场下进
10、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。2不同电阻率样品的电流选择大致为cmcm)0.012800800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 12kg12kg ;对于薄层材料或外延材料选取当室温有较大波动时,最好将电阻率折算到200g200g。2323C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 行计算参考二平均1CT -TT参考1平均i9为测试温度下样 品的平均电阻式中P参考为修正到某一参考温度( (例如 2323C) )下的样品电阻率;p率;CT为温度系数,
11、它随电阻率变化的曲线示于图 5 5; T T 为测试温度; T T参考为某一指定的参考温度。10r10r1-0.21L -1 - 1 -1-1 -1 - L.(a)(a)曲L0L0J J 10 101 1 Ilf Ilf101010103 3 IO IO3 31屮KT IS3-1 1M 1。10210J图5 N-Si(a)和F-Si(b)的电阻率温度莠数随电阻率的变化5 5.附录附录 1A1A 样品厚度修正系数 G G)样品厚度较薄: =0.0011 见表 5WW:样品厚度(卩 mm) : S S:探针间距(mmmm)W/S0.000.010.020.030.040.050.060.070.0
12、80.090.100.110.120.130.140.150.160.170.180.190.20W01020304050607080901001101201301401501601701801902002100.000.007.014.022.029.036.043.051.058.065.072.079.087.094.101.108.115.123.130.137.144.1511.001.008.015.022.030.037.044.051.058.066.073.080.087.095.102.109.116.123.131.138.145.1522.001.009.016.023
13、.030.038.045.052.059.066.074.081.088.095.102.110.117.124.131.139.145.1533.002.009.017.024.031.038.045.053.060.067.074.082.089.096.103.110.118.125.132.139.146.1544.003.010.017.025.032.039.046.053.061.068.075.082.089.097.104.111.118.126.133.140.147.1545.004.011.018.025.032.040.047.054.061.069.076.083.
14、090.097.105.112.119.126.133.141.148.1556.004.012.019.026.033.040.048.055.062.069.077.084.091.098.105.113.120.127.134.141.149.1567.005.012.019.027.034.041.048.056.063.070.077.084.092.099.106.113.120.128.135.142.149.1578.006.013.020.027.035.042.049.056.063.071.078.085.092.100.107.114.121.128.136.143.1
15、50.1579.006.014.021.028.035.043.050.057.064.071.079.086.093.100.107.115.122.129.136.144.151.1580.210.22 220 .159 .159 .160 .161 .162 .162 .163 .164 .164 .1650.23230.166.167.167.168.169W/SW012340.24240.173.174.175.175.1760.25250.180.181.182.183.1830.26260.188.188.189.190.1900.27270.195.195.19.197.198
16、0.282803202.203.203.204.2050.29290.209.210.211.211.2120.30300.216.217.218.219.2190.31310.224.224.225.226.2270.32320.231.232.232.233.2340.33330.238.239.239.240.2410.34340.245.246.247.247.2480.35350.252.253.254.255.2550.36360.260.260.261.262.2630.37370.267.268.268.269.2700.38380.274.275.275.276.2770.3
17、9390.281.282.283.283.2840.40400.288.289.290.291.2910.41410.296.296.297.298.2980.42420.303.303.304.305.3060.43430.310.311.311.312.3130.44440.317.318.319.319.3200.45450.324.325.326.326.3270.46460.331.332.333.333.3340.47470.338.339.340.341.3410.48480.346.346.347.348.3480.49 490 .353 .353 .354 .355 .355
18、 .356 .357 .358 .358 .359.170.17056.177.177.184.185.191.192.199.199.205.206.213.214.220.221.227.228.234.235.242.242.249.250.256.257.263.264.270.271.278.278.285.286.292.293.299.300.306.307.314.314.321.321.328.329.335.336.342.343.349.350.171.17278.178.197.185.186.193.193.200.201.207.208.214.215.221.22
19、2.229.229.236.237.243.244.250.251.257.258.265.265.272.273.279.280.286.287.293.294.301.301.308.308.315.316.323.323.329.330.336.337.343.344.351.351.1729.180.187.194.201.208.216.223.230.237.245.252.259.266.273.281.289.295.302.309.316.324.331.338.345.3520.50 500 .360 .360 .361 .362 .363 .363 .364 .365 .
20、365 3.68W/SW012340.51510.367.368.368.369.3700.52520.374.375.375.376.3770.53530.381.382.382.383.3840.54540.388.389.389.390.3910.55550.395.396.396.397.398056560.402.402.403.404.4050.57570.409.409.410.411.4110.58580.416.416.417.418.4180.59590.422.423.424.425.4250.60600.429.430.431.431.4320.61610.436.43
21、7.437.438.4390.62620.443.444.444.445.4460.63630.450.450.451.452.4520.64640.456.457.458.458.4590.65650.463.464.464.465.4660.66660.470.470.471.472.4720.67670.476.477.477.478.4790.68680.483.483.484.485.4850.69690.489.490.491.491.4920.70700.496.496.497.498.4980.71710.502.503.503.504.5050.72720.508.509.5
22、10.510.5110.73730.515.516.516.517.5170.74740.521.522.522.523.5240.75750.527.528.529.529.5300.76 760 .533 .534 .535 .535 .536 .537 .537 .538 .538 .53956.370.371.377.378.384.385.391.392.398.399.405.406.412.413.419.420.426.427.433.433.439.440.446.447.453.454.460.460.466.467.473.474.479.480.486.487.492.
23、493.499.500.505.506.512.512.518.519524.525.530.53178372372.379.379.386.386.393.393.400.400.407.407.414.414.420.421.427.428.434.435.441.442448.448454.455461.462468.468.474.475.481.481.488.488.494.494.500.501.507.507.513.514.519.520.525.526.532.5329.373.380.387.394.401.408.415.422.429.435.442.449.456.
24、462.469.476.482.489.495.501.508.514.520.527.5330.77 770 .540 .540 .541 .541 .542 .543 .543 .544 .544 .545W/SW0.787800.797900.808000.818100.828200.838300.848400.858500.868600.878700.888800.898900.909000.919100.929200.939300.949400.959500.969600.979700.989800.999901.00 1000 .66501.546.546.552.552.558.
25、558.564.564.569.570.575.576.581.581.587.587.592.593.598.598.603.604.609.609.614.615.619.620.625.625.630.630.635.636.640.641.645.646.650.651.655.656.660.66023.547.547.553.553.559.559.565.565.571.571.576.577.582.583.588.588.593.594.599.599.604.605.610.610.615.616.621.621.626.626631.631.636.637.641.642
26、.646.647.651.652.656.657.661.66145.548.549.554.555.560.561.565.567.572.573.577.579.583.584.589590.594.596.600.601.605.607.611.612.616.617.622.623.627.628.632.633.637.638.642.643.647.648.652.653.657.658.662.66367.549.550.555.556.561.562.567.568.573.573.579.579.584.585.590.591.596.596.601.602.607.607.
27、612.613.617.618.623.623.628.628.633.634.638.639.643.644.648.649.653.654.658.658.663.66389.550.551.556.557.562.563.568.569.574.575.580.580.585.586.591.592.597.597.602.603.608.608.613.614.618.619.624.624.629.629.634.635.639.640.644.645.649.650.654.655.658.659.664.664W:样品厚度(口 m): S:探针间距(mm)附录 1B样品厚度较厚:
28、W =0.013.49样品厚度修正系数见表W/S0.000.010.000.00000.00720.100.07210.07940.200.14430.15150.300.21640.22360.400.28840.29560.500.35970.36680.600.42930.43610.700.49570.50210.800.55760.56350.900.61410.61941.000.66470.66941.100.70930.71341.200.74820.75181.300.78170.78481.400.81060.81321.500.83520.83751.600.85630.
29、83821.700.87430.87601.800.8897 0.89110.020.030.01440.02160.08660.09380.15870.16590.23080.23800.30270.30990.37380.38080.44290.44960.50850.51480.56940.57510.62470.62990.67410.67870.71750.72150.75530.75890.78790.79080.81580.81840.83970.84190.86010.86200.87760.87920.8925 0.89390.040.050.02890.03610.1010
30、0.10820.17310.18030.24520.25240.31710.32420.38780.39480.45630.46300.52100.52730.58090.58660.63510.64020.68330.68770.72550.72940.76220.76660.79380.79670.82090.82340.84410.84620.86390.86570.88080.88230.8952 0.89650.060.070.04330.05050.11540.12260.18750.19480.25960.26680.33130.33850.40180.40870.46960.4
31、7620.53340.53960.59220.59780.64520.65010.69220.69650.73330.73710.76890.71220.79960.80240.82580.82820.84830.85030.86750.86920.88380.88530.8978 0.89910.080.090.05770.06490.12980.13710.20200.20920.27400.28120.34560.35260.41560.42240.48270.48920.54560.55160.60330.60870.65510.65990.70090.70510.74080.7445
32、0.77540.77860.80520.80790.83060.83290.85240.85440.87090.87260.88680.88830.9004 0.90161.90 0.9029 0.9041 0.9053 0.9064 0.9076 0.9087 0.9099 0.9110 0.9121 0.9131W/S0.000.010.020.032.000.9142 0.91520.91620.91722.100.9239 0.92480.92570.92662.200.9323 0.93310.93380.93462.300.9396 0.94020.94090.94152.400.
33、9459 0.94020.94700.94762.500.9514 0.95190.95240.95292.600.9562 0.95660.95710.95752.700.9604 0.96080.96120.96162.800.9641 0.96440.96480.96522.900.9674 0.96770.96800.96833.000.9703 0.97050.97080.97113.100.9728 0.97310.97330.97363.200.9751 0.97530.97560.97583.300.9772 0.97740.97760.97783.400.97900.9792
34、0.97940.97950.040.050.9182 0.91920.9274 0.92830.9353 0.93610.9422 0.94280.9482 0.94870.9534 0.95380.9579 0.95830.9619 0.96230.9655 0.96580.9686 0.96890.9713 0.97160.9738 0.97400.9760 0.97620.9779 0.97810.97970.97990.060.070.080.090.9202 0.92110.92210.92300.9291 0.92990.93070.93150.9368 0.93750.93820
35、.93890.9435 0.94410.94470.94530.9493 0.94980.95030.95090.9543 0.95480.95530.95570.9588 0.95920.95960.96000.9627 0.96300.96340.96370.9661 0.96640.96670.96710.9692 0.96940.96970.97000.9718 0.97210.97240.97260.9742 0.97450.97470.97490.9764 0.97660.97680.97700.9783 0.97850.97870.97880.98000.98020.98030.
36、9805如需所测值更精确,请查下表附录 2 2 样品形状和测量位置的修正系数 D D (d d)(1)圆形薄片(mm)2023252730323538404245505557606365距圆心位置0mm1/4 d0.97880.96330.98390.97190.98630.97610.98820.97940.99040.98320.99160.98520.99290.98760.99400.98940.99460.99040.99510.99130.99570.99240.99650.99380.99710.99190.99730.99520.99760.99570.99780.99610.
37、99790.9963探针位置5 mm0.96330.96620.96770.96880.97020.97090.97180.97250.97290.97330.97380.97440.97490.97510.97520.97550.9757S S距边缘位置4 mm3 mm0.95080.92630.95380.92950.95530.93120.95650.93250.95800.93420.95880.93510.95980.93620.96060.93710.96100.93770.96140.93820.96200.94880.96270.94970.96330.94030.96350.
38、94060.96380.94090.96400.94120.96410.94142 mm0.87020.87390.87580.87730.87930.88040.88170.88290.88350.88410.88490.88590.88680.88710.88750.88790.8881700.99820.99850.99680.99720.97600.97620.96450.96480.94180.94210.88860.88917580900.99860.99890.99910.99760.99810.99840.97640.97680.97700.96500.96540.96570.
39、94240.94290.94330.88950.89010.89041002)矩形薄片正方形d/s1.01.251.51.752.02.53.04.05.07.510.015.020.040.0矩形a/d=2a/d=30.22040.27510.32630.37940.43010.51920.32860.38030.42970.51940.59580.71150.78880.89050.93450.96960.98600.99571.0000a/d=1a/d 40.22050.27020.32860.38030.42970.51940.59580.71150.78880.89050.93450.96960.98300.99571.00000.54220.68700.77440.88460.93120.96820.97880.99551.00000.59570.71150.78870.89050.93450.96960.98300.99571.0000100d:短边长度 a:长边长度 s:探针间距提醒:每次开机启动,仪器会有一个自动校正和自动预热过程,初测试偶有 5 5 到 1010 次测试数值不精确视为正常情况。建议:一般情况下,附表 1A1A 即已完全能足够满足精度。
限制150内