四探針法測電阻率試驗(yàn)原理

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1．試驗(yàn)?zāi)康模?/p>

學(xué)習(xí)用四探針法測量半導(dǎo)體材料的體電阻率和擴(kuò)散薄層的電阻率及方塊電阻。

2．試驗(yàn)內(nèi)容

①硅單晶片電阻率的測量：選不同電阻率及不同厚度的大單晶圓片，改變條件（光照

與否），對測量結(jié)果進(jìn)行比較。

②薄層電阻率的測量：對不同尺寸的單面擴(kuò)散片和雙面擴(kuò)散片的薄層電阻率進(jìn)行測

量。改變條件進(jìn)行測量（與①一致），對結(jié)果進(jìn)行比較。

3．試驗(yàn)原理：

在半導(dǎo)體器件的研制和生產(chǎn)過程中往往要對半導(dǎo)體單晶材料的原始電阻率和經(jīng)過擴(kuò)散、外延等工藝處理后的薄層電阻進(jìn)行測量。測量電阻率的方法好多，有兩探針法，四探針法，單探針擴(kuò)展電阻法，范德堡法等，我們這里介紹的是四探針法。由于這種方法簡便可行，適于批量生產(chǎn)，所以目前得到了廣泛應(yīng)用。

所謂四探針法，就是用針間距約1毫米的四根金屬探針同時(shí)壓在被測樣品的平整表面上如圖1a所示。利用恒流源給1、4兩個(gè)探針通以小電流，然后在2、3兩個(gè)探針上用高輸入阻抗的靜電計(jì)、電位差計(jì)、電子毫伏計(jì)或數(shù)字電壓表測量電壓，最終根據(jù)理論

［１］

公式計(jì)算出樣品的電阻率

??CV23I式中，C為四探針的修正系數(shù)，單位為厘米，C的大小取決于四探針的排列方法和針距，

探針的位置和間距確定以后，探針系數(shù)C就是一個(gè)常數(shù)；V23為2、3兩探針之間的電壓，單位為伏特；I為通過樣品的電流，單位為安培。

半導(dǎo)體材料的體電阻率和薄層電阻率的測量結(jié)果往往與式樣的形狀和尺寸密切相關(guān)，下面我們分兩種狀況來進(jìn)行探討。

⑴半無限大樣品情形

圖1給出了四探針法測半無窮大樣品電阻率的原理圖，圖中(a)為四探針測量電阻率的裝置；(b)為半無窮大樣品上探針電流的分布及等勢面圖形；(c)和(d)分別為正方形排列及直線排列的四探針圖形。由于四探針對半導(dǎo)體表面的接觸均為點(diǎn)接觸，所以，對圖１（b）所示的半無窮大樣品，電流I是以探針尖為圓心呈徑向放射狀流入體內(nèi)的。因而電流在體內(nèi)所形成的等位面為圖中虛線所示的半球面。于是，樣品電阻率為ρ，半徑為r，間距為dr的兩個(gè)半球等位面間的電阻為

dR?它們之間的電位差為dV?IdR??dr，2?r2?Idr。2?r2考慮樣品為半無限大，在r→∞處的電位為0，所以圖１（a）中流經(jīng)探針１的電流I在r點(diǎn)形成的電位為?Vr?1???r?I?I。dr?22?r2?r?I?11??流經(jīng)探針１的電流在２、３兩探針間形成的電位差為?V23?1?；???2??r12r13??流經(jīng)探針４的電流與流經(jīng)探針１的電流方向相反，所以流經(jīng)探針４的電流I在探針２、３之間引起的電位差為

?V23?4???I???11???。

2??r42r43??于是流經(jīng)探針１、４之間的電流在探針２、３之間形成的電位差為

V23?由此可得樣品的電阻率為

?I?1111??????。??2??r12r13r42r43??12?V23?1111?????????I?r12r13r42r43???1?

上式就是四探針法測半無限大樣品電阻率的普遍公式。

在采用四探針測量電阻率時(shí)尋常使用圖１（c）的正方形結(jié)構(gòu)（簡稱方形結(jié)構(gòu)）和圖１（d）的等間距直線形結(jié)構(gòu)，假設(shè)方形四探針和直線四探針的探針間距均為S，則對于直線四探針有r12?r43?S,r13?r42?2S

???2?S?V23I?2?

對于方形四探針有r12?r43?S,r13?r42?2S

?2?SV23???2?2I?3?

⑵無限薄層樣品情形

當(dāng)樣品的橫向尺寸無限大，而其厚度t又比探針間距S小得多的時(shí)候，我們稱這種樣品為無限薄層樣品。圖２給出了用四探針測量無限薄層樣品電阻率的示意圖。圖中被測樣品為在p型半導(dǎo)體襯底上擴(kuò)散有n型薄層的無限大硅單晶薄片，１、２、３、４為四個(gè)探針在硅片表面的接觸點(diǎn)，探針間距為S，n型擴(kuò)散薄層的厚度為t，并且t800

⑥為了滿足探針與半導(dǎo)體的接觸為歐姆接觸，探針上須加上一定的壓力。對于體

材料，一般取1~2kg；對于薄層材料或外延材料選取200g。

⑦當(dāng)室溫有較大波動時(shí)，最好將電阻率折算到23℃時(shí)的電阻率。由于半導(dǎo)體的電

阻率對溫度很敏感。假使有必要考慮溫度對電阻率的影響，可用下面的公式進(jìn)行計(jì)算

測量電流（mA）1001010.10.01?參考??平均?1?CT?T?T參考???9?

式中ρ參考為修正到某一參考溫度(例如23℃)下的樣品電阻率;ρ平均為測試溫度下樣品的平均電阻率；CT為溫度系數(shù)，它隨電阻率變化的曲線示于圖5；T為測試溫度；T參考為某一指定的參考溫度。

5．附錄

W

附錄1A樣品厚度修正系數(shù)G（）

S

W

樣品厚度較?。篠=0.001~1見表5

W：樣品厚度（μm）：S：探針間距（mm）

W/SW0.0000.01100.02200.03300.04400.05500.06600.07700.08800.09900.101000.111100.121200.131300.141400.151500.161600.171700.181800.191900.202000.21

210

01.000.001.007.008.014.015.022.022.029.030.036.037.043.044.051.051.058.058.065.066.072.073.079.080.087.087.094.095.101.102.108.109.115.116.123.123.130.131.137.138.144.145.151

.152

23.001.002.009.009.016.017.023.024.030.031.038.038.045.045.052.053.059.060.066.067.074.074.081.082.088.089.095.096.102.103.110.110.117.118.124.125.131.132.139.139.145.146.153

.154

45.003.004.010.011.017.018.025.025.032.032.039.040.046.047.053.054.061.061.068.069.075.076.082.083.089.090.097.097.104.105.111.112.118.119.126.126.133.133.140.141.147.148.154

.155

67.004.005.012.012.019.019.026.027.033.034.040.041.048.048.055.056.062.063.069.070.077.077.084.084.091.092.098.099.105.106.113.113.120.120.127.128.134.135.141.142.149.149.156

.157

89.006.006.013.014.020.021.027.028.035.035.042.043.049.050.056.057.063.064.071.071.078.079.085.086.092.093.100.100.107.107.114.115.121.122.128.129.136.136.143.144.150.151.157

.158

0.222200.23230W/SW0.242400.252500.262600.272700.282800.292900.303000.313100.323200.333300.343400.353500.363600.373700.383800.393900.404000.414100.424200.434300.444400.454500.464600.474700.484800.49

490

.159.159.166.16701.173.174.180.181.188.188.195.1953202.203.209.210.216.217.224.224.231.232.238.239.245.246.252.253.260.260.267.268.274.275.281.282.288.289.296.296.303.303.310.311.317.318.324.325.331.332.338.339.346.346.353

.353

.160.161.167.16823.175.175.182.183.189.190.19.197.203.204.211.211.218.219.225.226.232.233.239.240.247.247.254.255.261.262.268.269.275.276.283.283.290.291.297.298.304.305.311.312.319.319.326.326.333.333.340.341.347.348.354

.355

.162.162.169.17045.176.177.183.184.190.191.198.199.205.205.212.213.219.220.227.227.234.234.241.242.248.249.255.256.263.263.270.270.277.278.284.285.291.292.298.299.306.306.313.314.320.321.327.328.334.335.341.342.348.349.355

.356

.163.164.170.17167.177.178.185.185.192.193.199.200.206.207.214.214.221.221.228.229.235.236.242.243.250.250.257.257.264.265.271.272.278.279.286.286.293.293.300.301.307.308.314.315.321.323.329.329.336.336.343.343.350.351.357

.358

.164.165.172.17289.197.180.186.187.193.194.201.201.208.208.215.216.222.223.229.230.237.237.244.245.251.252.258.259.265.266.273.273.280.281.287.289.294.295.301.302.308.309.316.316.323.324.330.331.337.338.344.345.351.352.358

.359

0.50

500

W/SW0.515100.525200.535300.545400.555500565600.575700.585800.595900.606000.616100.626200.636300.646400.656500.666600.676700.686800.696900.707000.717100.727200.737300.747400.757500.76

760

.360.36001.367.368.374.375.381.382.388.389.395.396.402.402.409.409.416.416.422.423.429.430.436.437.443.444.450.450.456.457.463.464.470.470.476.477.483.483.489.490.496.496.502.503.508.509.515.516.521.522.527.528.533

.534

.361.36223.368.369.375.376.382.383.389.390.396.397.403.404.410.411.417.418.424.425.431.431.437.438.444.445.451.452.458.458.464.465.471.472.477.478.484.485.491.491.497.498.503.504.510.510.516.517.522.523.529.529.535

.535

.363.36345.370.370.377.377.384.384.391.391.398.398.405.405.411.412.418.419.425.426.432.433.439.439.446.446.452.453.459.460.466.466.472.473.479.479.485.486.492.492.498.499.505.505.511.512.517.518.524524.530.530.536

.537

.364.36567.371372.378.379.385.386.392.393.399.400.406.407.413.414.420.420.427.427.433.434.440.441.447448.454454.460461..467468.474.474.480.481.487.488.493.494.500.500.506.507.512.513.519.519.525.525.531.532.537

.538

.3653.68

89372.373.379.380.386.387.393.394.400.401.407.408.414.415.421.422.428.429.435.435.442.442.448.449.455.456.462.462.468.469.475.476.481.482.488.489.494.495.501.501.507.508.514.514.520.520.526.527.532.533.538

.539

0.77

770

W/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

.540.54001.546.546.552.552.558.558.564.564.569.570.575.576.581.581.587.587.592.593.598.598.603.604.609.609.614.615.619.620.625.625.630.630.635.636.640..641.645.646.650.651.655.656.660.660

.665

.541.54123.547.547.553.553.559.559.565.565.571.571.576.577.582.583.588.588.593.594.599.599.604.605.610.610.615.616.621.621.626.626631.631.636.637.641.642.646.647.651.652.656.657.661

.661

.542.54345.548.549.554.555.560.561.565.567.572.573.577.579.583.584.589590.594.596.600.601.605.607.611.612.616.617.622.623.627.628.632.633.637.638.642.643.647.648.652.653.657.658.662.663

.

.543.54467.549.550.555.556.561.562.567.568.573.573.579.579.584.585.590.591.596.596.601.602.607.607.612.613.617.618.623.623.628.628.633.634.638.639.643.644.648.649.653.654.658.658.663

.663

.544.545

89.550.551.556.557.562.563.568.569.574.575.580.580.585.586.591.592.597.597.602.603.608.608.613.614.618.619.624.624.629.629.634.635.639.640.644.645.649.650.654.655.658.659.664

.664

W

附錄1B樣品厚度修正系數(shù)G（）

S

W

樣品厚度較厚：S=0.01~3.49見表W：樣品厚度（μm）：S：探針間距（mm）W/S0.00

0.000.00000.100.07210.200.14430.300.21640.400.2884

0.500.35970.600.42930.700.49570.800.55760.900.6141

1.000.66471.100.70931.200.74821.300.78171.400.8106

1.500.83521.600.85631.700.87431.800.88970.010.02

0.00720.01440.07940.08660.15150.15870.22360.23080.29560.3027

0.36680.37380.43610.44290.50210.50850.56350.56940.61940.6247

0.66940.67410.71340.71750.75180.75530.78480.78790.81320.8158

0.83750.83970.83820.86010.87600.87760.89110.89250.030.04

0.02160.02890.09380.10100.16590.17310.23800.24520.30990.3171

0.3808