四探針?lè)y(cè)電阻率

1、實(shí)驗(yàn)四探針?lè)y(cè)電阻率1實(shí)驗(yàn)?zāi)康模簩W(xué)習(xí)用四探針?lè)y(cè)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實(shí)驗(yàn)內(nèi)容硅單晶片電阻率的測(cè)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(duì)測(cè)量結(jié)果進(jìn)行比較。薄層電阻率的測(cè)量：對(duì)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(cè)量。改變條件進(jìn)行測(cè)量（與相同） ，對(duì)結(jié)果進(jìn)行比較。3 實(shí)驗(yàn)原理：在半導(dǎo)體器件的研制和生產(chǎn)過(guò)程中常常要對(duì)半導(dǎo)體單晶材料的原始電阻率和經(jīng)過(guò)擴(kuò)散、外延等工藝處理后的薄層電阻進(jìn)行測(cè)量。測(cè)量電阻率的方法很多，有兩探針?lè)ǎ奶结樂(lè)ǎ?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?lè)?。因?yàn)檫@種方法簡(jiǎn)便可行，適于批量生產(chǎn)，所

2、以目前得到了廣泛應(yīng)用。所謂四探針?lè)ǎ?就是用針間距約1 毫米的四根金屬探針同時(shí)壓在被測(cè)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(cè)量電壓，最后根據(jù)理論公式計(jì)算出樣品的電阻率C V23I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)； V 23為 2、3 兩探針之間的電壓，單位為伏特； I 為通過(guò)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(cè)量結(jié)果往往與式樣的形狀和尺寸密切相關(guān)，下

3、面我們分兩種情況來(lái)進(jìn)行討論。 半無(wú)限大樣品情形圖 1 給出了四探針?lè)y(cè)半無(wú)窮大樣品電阻率的原理圖，圖中(a) 為四探針測(cè)量電阻率的裝置； (b) 為半無(wú)窮大樣品上探針電流的分布及等勢(shì)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。因?yàn)樗奶结槍?duì)半導(dǎo)體表面的接觸均為點(diǎn)接觸，所以， 對(duì)圖（ b）所示的半無(wú)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， 半徑為 r，間距為 dr 的兩個(gè)半球等位面間的電阻為dR2 r2 dr ，I它們之間的電位差為dVIdR2dr 。r 2考慮樣品為半無(wú)限大，在r處的電

4、位為0，所以圖（ a）中流經(jīng)探針的電流I 在r 點(diǎn)形成的電位為Vr12I 2 dr2I。rrr流經(jīng)探針的電流在、兩探針間形成的電位差為V23 1I11 ；2r12r13流經(jīng)探針的電流與流經(jīng)探針的電流方向相反，所以流經(jīng)探針的電流I 在探針、之間引起的電位差為V2342I11。r42r43于是流經(jīng)探針、之間的電流在探針、之間形成的電位差為V23I1111 。2r12r13r42r43由此可得樣品的電阻率為2 V23111111Ir12r13r42r43上式就是四探針?lè)y(cè)半無(wú)限大樣品電阻率的普遍公式。在采用四探針測(cè)量電阻率時(shí)通常使用圖（c）的正方形結(jié)構(gòu)（簡(jiǎn)稱方形結(jié)構(gòu)）和圖（ d）的等間距直線形結(jié)構(gòu)，

5、假設(shè)方形四探針和直線四探針的探針間距均為S，則對(duì)于直線四探針有r12r43S,r13r422S2SV232I對(duì)于方形四探針有r12r43S,r13r422S2 SV23322I無(wú)限薄層樣品情形當(dāng)樣品的橫向尺寸無(wú)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(wú)限薄層樣品。圖給出了用四探針測(cè)量無(wú)限薄層樣品電阻率的示意圖。圖中被測(cè)樣品為在p 型半導(dǎo)體襯底上擴(kuò)散有n 型薄層的無(wú)限大硅單晶薄片，、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 t<<S， I+ 表示電流從探針流入硅片， I-表示電流從探針流出硅片。與半無(wú)限大樣品不同的是，這

6、里探針電流在n 型薄層內(nèi)近似為平面放射狀，其等位面可近似為圓柱面。類(lèi)似前面的分析，對(duì)于任意排列的四探針，探針的電流I 在樣品中 r 處形成的電位為Vr 12I drIln rrrt2t式中為 n 型薄層的平均電阻率。于是探針的電流I 在、探針間所引起的電位差為V23 1Iln r12Iln r132 tr132 tr12同理，探針的電流I 在、探針間所引起的電位差為V234Iln r422tr43所以探針和探針的電流I 在、探針之間所引起的電位差是V232Iln r42r13tr43r12于是得到四探針?lè)y(cè)無(wú)限薄層樣品電阻率的普遍公式為2 tV 23ln r42r134Ir43r12對(duì)于直線四

7、探針，利用r12r43S,r13r422S 可得2 tV23 2ln 2tV235Iln 2I對(duì)于方形四探針，利用r12r43S,r13r422S 可得2 tV236ln 2I在對(duì)半導(dǎo)體擴(kuò)散薄層的實(shí)際測(cè)量中常常采用與擴(kuò)散層雜質(zhì)總量有關(guān)的方塊電阻RS，它與擴(kuò)散薄層電阻率有如下關(guān)系：RS11X jq NX jX jqNdX0這里 X j 為擴(kuò)散所形成的pn 結(jié)的結(jié)深。這樣對(duì)于無(wú)限薄層樣品，方塊電阻可以表示如下：直線四探針：RSV237ln 2 IX j方形四探針：RS2V238ln 2IX j在實(shí)際測(cè)量中， 被測(cè)試的樣品往往不滿足上述的無(wú)限大條件，樣品的形狀也不一定相同，因此常常要引入不同的修正系

8、數(shù)。實(shí)際測(cè)量中的擴(kuò)散樣片可能有兩種情況：?jiǎn)蚊鏀U(kuò)散片和雙面擴(kuò)散片，如圖3 所示。這兩種樣品的修正系數(shù)分別列于附錄中的表。圖 4 SZT-2A 四探針測(cè)試儀4實(shí)驗(yàn)裝置及注意事項(xiàng) 實(shí)驗(yàn)裝置實(shí)驗(yàn)裝置如圖 4 所示。電路中的恒流源所提供的電流是連續(xù)可調(diào)的，電壓表采用電位差計(jì)或數(shù)字電壓表。實(shí)驗(yàn)所用的探針通常采用耐磨的導(dǎo)電硬質(zhì)合金材料，如鎢、碳化鎢等。探針要求等間距配置，并使其具有很小的游移誤差。在探針上需加上適當(dāng)?shù)膲毫?，以減小探針與半導(dǎo)體材料之間的接觸電阻。 注意事項(xiàng)半無(wú)限大樣品是指樣品厚度及任意一根探針距樣品最近邊界的距離遠(yuǎn)大于探針間距，如果這一條件不能得到滿足則必需進(jìn)行修正。為了避免探針處的少數(shù)載流子

9、注入，提高表面復(fù)合速度，待測(cè)樣品的表面需經(jīng)粗砂打磨或噴砂處理。在測(cè)量高阻材料及光敏材料時(shí)需在暗室或屏蔽盒內(nèi)進(jìn)行。因?yàn)殡妶?chǎng)太大會(huì)使載流子的遷移率下降，導(dǎo)致電阻率測(cè)量值增大，故須在電場(chǎng)強(qiáng)度 E<1V/cm 的弱場(chǎng)下進(jìn)行測(cè)量。為了避免大電流下的熱效應(yīng)，測(cè)試電流應(yīng)盡可能低，但須保證電壓的測(cè)試精度。不同電阻率樣品的電流選擇大致為2電阻率范圍測(cè)量電流（ mA ）（· cm）<0.0121000.080.6100.46014012000.1>8000.01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(duì)于體材料，一般取12kg；對(duì)于薄層材料或外延材料選取200g。

10、當(dāng)室溫有較大波動(dòng)時(shí)，最好將電阻率折算到 23時(shí)的電阻率。因?yàn)榘雽?dǎo)體的電阻率對(duì)溫度很敏感。如果有必要考慮溫度對(duì)電阻率的影響，可用下面的公式進(jìn)行計(jì)算參考平均1 CTTT參考9式中 參考 為修正到某一參考溫度 ( 例如 23 )下的樣品電阻率 ; 平均 為測(cè)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(cè)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樣品厚度較薄：S =0.0011見(jiàn)表 5W：樣品厚度（ m）： S：探針間距（ 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附錄 1B樣品厚度修正系數(shù)G（ S）樣品厚度較厚：W=0.013.49見(jiàn)表SW：樣品厚度（ m）： S：探針間距（ 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如需所測(cè)值更精確，請(qǐng)查下表d附錄 2 樣品形狀和測(cè)量位置的修正系數(shù)D（ s ）（1）圓形薄片探針位置直徑 d距圓心位置距邊緣位置(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