四探針法測電阻率要點

1、實驗 四探針法測電阻率1. 實驗目的：學習用四探針法測量半導體材料的體電阻率和擴散薄層的電阻率及方塊電阻。2. 實驗內容 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）,對測量結果進行比較。 薄層電阻率的測量：對不同尺寸的單面擴散片和雙面擴散片的薄層電阻率進行測 量。改變條件進行測量（與相同），對結果進行比較。團1四探常法徘電匡率原理國h卄囚琛護剛唱電率裝暫禹工無勞丸樣品上探纖 電沆的分侖反半味等勢面1<|圧方附排列的凹探甘酰 Mi啟蠟怫列吋也榕針頸書3. 實驗原理：在半導體器件的研制和生產(chǎn)過程中常常要對半導體單晶材料的原始電阻率和經(jīng)過 擴散、外延等工藝

2、處理后的薄層電阻進行測量。測量電阻率的方法很多，有兩探針法， 四探針法，單探針擴展電阻法， 范德堡法等，我們這里介紹的是四探針法。因為這種方法簡便可行，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、4兩個探針通以小電流，然后在2、3兩個探針上用高輸入阻抗的靜電計、電位差計、電子毫伏計或數(shù)字電壓表測量電壓，最后根據(jù)理論公式計算出樣品的電阻率 ：1：I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就是一個常數(shù)；V23為2、3兩探針

3、之間的電壓，單位為伏特；I為通過樣品的電流，單位為安培。半導體材料的體電阻率和薄層電阻率的測量結果往往與式樣的形狀和尺寸密切相 關，下面我們分兩種情況來進行討論。 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。因為四探針對半導體表面的接觸均為點接觸，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的。因而電流在體內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p ,半徑為r，間距為dr的兩個半球

4、等位面間的電阻為PdR 2 dr,2皿2PI它們之間的電位差為 dV = IdR 2 dr。2町2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« P|PIr點形成的電位為Vr 1：片2兀r22可流經(jīng)探針1的電流在2、3兩探針間形成的電位差為V23 1 訣2貳 112丄r13 J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PI11一 1 + 12兀<r12r13r42r43 J由此可得樣品的電阻率為上式就是四探針法測半無限大

5、樣品電阻率的普遍公式。在采用四探針測量電阻率時通常使用圖1(c)的正方形結構(簡稱方形結構)和圖1( d)的等間距直線形結構，假設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12=43=S,13 =42=2S對于方形四探針有r12 = r43 = S,r13 = r42 = 2S2SV232 -、2 In型薄層的無限大硅單晶薄片，1、2、無限禪層樣品電阻率瀕呈圖2無限薄層樣品情形當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。 測樣品為在p型半導體襯底上擴散有 四個探針在硅片表面的接觸

6、點，探 針間距為S,n型擴散薄層的厚度為 t,并且t<<S, 1+表示電流從探針1 流入硅片，I-表示電流從探針4流出 硅片。與半無限大樣品不同的是， 這里探針電流在 n型薄層內近似為 平面放射狀，其等位面可近似為圓 柱面。類似前面的分析，對于任意 排列的四探針，探針1的電流 I 樣品中r處形成的電位為圖中被3、4為式中P為n型薄層的平均電阻率。于是探針1的電流I在2、3探針間所引起的電位差同理，探針4的電流2tri3|H2-tr12I在2、3探針間所引起的電位差為所以探針1和探針4的電流I在2、3探針之間所引起的電位差是r 2 兀 rtV23lni2 兀tr43 T12于是得到四

7、探針法測無限薄層樣品電阻率的普遍公式為43 T12對于直線四探針,利用 r12=43 二 S，13 二p2ltV232ln2上 V23I/In2 I對于方形四探針,利用 r12=r43 = S，ri3 二P =2 二t V23二2S可得2S可得r42In2 I在對半導體擴散薄層的實際測量中常常采用與擴散層雜質總量有關的方塊電阻Rs,它與擴散薄層電阻率有如下關系:P '11Rs 二 二xXj q壯 jNdX qNXj這里Xj為擴散所形成的pn結的結深。這樣對于無限薄層樣品， 方塊電阻可以表示如下:直線四探針：RsV237Xj ln 2 I圖？單面擴散和颶面擴散的薄層(3)單面擴散的理層；

8、(b)艱面擴散的薄層方形四探針：Rs2 V238Xj ln2 I在實際測量中，被測試的樣品往往不滿足上述的無限大條件，樣品的形狀也不一定相同，因此常常要引入不同的修正系數(shù)。實際測量中的擴散樣片可能有兩種情況：單面擴散片和雙面擴散片，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四探針測試儀4 實驗裝置及注意事項實驗裝置實驗裝置如圖4所示。電路中的恒流源所提供的電流是連續(xù)可調的，電壓表采用電 位差計或數(shù)字電壓表。實驗所用的探針通常采用耐磨的導電硬質合金材料，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?shù)膲毫?以減小探針與半導體材料

9、之間的接觸電阻。注意事項 半無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大于探針 間距，如果這一條件不能得到滿足則必需進行修正。 為了避免探針處的少數(shù)載流子注入，提高表面復合速度，待測樣品的表面需經(jīng) 粗砂打磨或噴砂處理。 在測量高阻材料及光敏材料時需在暗室或屏蔽盒內進行。 因為電場太大會使載流子的遷移率下降，導致電阻率測量值增大，故須在電場 強度E<1V/cm的弱場下進行測量。 為了避免大電流下的熱效應，測試電流應盡可能低，但須保證電壓的測試精度。不同電阻率樣品的電流選擇大致為2電阻率范圍 (Q cm)測量電流(mA)<0.0121000.080.6100.46014

10、012000.1>8000.01 為了滿足探針與半導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12kg ;對于薄層材料或外延材料選取200g。 當室溫有較大波動時，最好將電阻率折算到23C時的電阻率。因為半導體的電阻率對溫度很敏感。如果有必要考慮溫度對電阻率的影響，可用下面的公式進 行計算"參考二"平均1 Ct T - T參考1i9式中p參考為修正到某一參考溫度(例如23C )下的樣品電阻率；p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。10r-0.21l1111

11、1L.L0J 10'1 Ilf 10103 IO3(a) 曲1 o1 屮 KT3 IS-1 1M 1。10210J圖5 N-Si(a)和F-Si(b)的電阻率溫度莠數(shù)隨電阻率的變化5.附錄附錄1A 樣品厚度修正系數(shù)G）樣品厚度較?。?=0.0011 見表5W:樣品厚度（卩m） : S:探針間距（mm）W/SW01234567890.000.000.001.001.002.003.004.004.005.006.0060.0110.007.008.009.009.010.011.012.012.013.0140.0220.014.015.016.017.017.018.019.019.0

12、20.0210.0330.022.022.023.024.025.025.026.027.027.0280.0440.029.030.030.031.032.032.033.034.035.0350.0550.036.037.038.038.039.040.040.041.042.0430.0660.043.044.045.045.046.047.048.048.049.0500.0770.051.051.052.053.053.054.055.056.056.0570.0880.058.058.059.060.061.061.062.063.063.0640.0990.065.066.066

13、.067.068.069.069.070.071.0710.10100.072.073.074.074.075.076.077.077.078.0790.11110.079.080.081.082.082.083.084.084.085.0860.12120.087.087.088.089.089.090.091.092.092.0930.13130.094.095.095.096.097.097.098.099.100.1000.14140.101.102.102.103.104.105.105.106.107.1070.15150.108.109.110.110.111.112.113.1

14、13.114.1150.16160.115.116.117.118.118.119.120.120.121.1220.17170.123.123.124.125.126.126.127.128.128.1290.18180.130.131.131.132.133.133.134.135.136.1360.19190.137.138.139.139.140.141.141.142.143.1440.20200.144.145.145.146.147.148.149.149.150.1510.21210.151.152.153.154.154.155.156.157.157.1580.22 220

15、 .159 .159 .160 .161 .162 .162 .163 .164 .164 .1650.23230.166.167.167.168.169.170.170.171.172.172W/SW01234567890.24240.173.174.175.175.176.177.177.178.197.1800.25250.180.181.182.183.183.184.185.185.186.1870.26260.188.188.189.190.190.191.192.193.193.1940.27270.195.195.19.197.198.199.199.200.201.2010.

16、282803202.203.203.204.205.205.206.207.208.2080.29290.209.210.211.211.212.213.214.214.215.2160.30300.216.217.218.219.219.220.221.221.222.2230.31310.224.224.225.226.227.227.228.229.229.2300.32320.231.232.232.233.234.234.235.236.237.2370.33330.238.239.239.240.241.242.242.243.244.2450.34340.245.246.247.

17、247.248.249.250.250.251.2520.35350.252.253.254.255.255.256.257.257.258.2590.36360.260.260.261.262.263.263.264.265.265.2660.37370.267.268.268.269.270.270.271.272.273.2730.38380.274.275.275.276.277.278.278.279.280.2810.39390.281.282.283.283.284.285.286.286.287.2890.40400.288.289.290.291.291.292.293.29

18、3.294.2950.41410.296.296.297.298.298.299.300.301.301.3020.42420.303.303.304.305.306.306.307.308.308.3090.43430.310.311.311.312.313.314.314.315.316.3160.44440.317.318.319.319.320.321.321.323.323.3240.45450.324.325.326.326.327.328.329.329.330.3310.46460.331.332.333.333.334.335.336.336.337.3380.47470.3

19、38.339.340.341.341.342.343.343.344.3450.48480.346.346.347.348.348.349.350.351.351.3520.49 490 .353 .353 .354 .355 .355 .356 .357 .358 .358 .3590.50 500 .360 .360 .361 .362 .363 .363 .364 .365 .365 3.68W/SW01234567890.51510.367.368.368.369.370.370.371372372.3730.52520.374.375.375.376.377.377.378.379.

20、379.3800.53530.381.382.382.383.384.384.385.386.386.3870.54540.388.389.389.390.391.391.392.393.393.3940.55550.395.396.396.397.398.398.399.400.400.401056560.402.402.403.404.405.405.406.407.407.4080.57570.409.409.410.411.411.412.413.414.414.4150.58580.416.416.417.418.418.419.420.420.421.4220.59590.422.

21、423.424.425.425.426.427.427.428.4290.60600.429.430.431.431.432.433.433.434.435.4350.61610.436.437.437.438.439.439.440.441.442.4420.62620.443.444.444.445.446.446.447448.448.4490.63630.450.450.451.452.452.453.454454.455.4560.64640.456.457.458.458.459.460.460461.462.4620.65650.463.464.464.465.466.466.4

22、67468.468.4690.66660.470.470.471.472.472.473.474.474.475.4760.67670.476.477.477.478.479.479.480.481.481.4820.68680.483.483.484.485.485.486.487.488.488.4890.69690.489.490.491.491.492.492.493.494.494.4950.70700.496.496.497.498.498.499.500.500.501.5010.71710.502.503.503.504.505.505.506.507.507.5080.727

23、20.508.509.510.510.511.512.512.513.514.5140.73730.515.516.516.517.517.518.519.519.520.5200.74740.521.522.522.523.524524.525.525.526.5270.75750.527.528.529.529.530.530.531.532.532.5330.76 760 .533 .534 .535 .535 .536 .537 .537 .538 .538 .5390.77 770 .540 .540 .541 .541 .542 .543 .543 .544 .544 .545W/

24、SW01234567890.78780.546.546.547.547.548.549.549.550.550.5510.79790.552.552.553.553.554.555.555.556.556.5570.80800.558.558.559.559.560.561.561.562.562.5630.81810.564.564.565.565.565.567.567.568.568.5690.82820.569.570.571.571.572.573.573.573.574.5750.83830.575.576.576.577.577.579.579.579.580.5800.8484

25、0.581.581.582.583.583.584.584.585.585.5860.85850.587.587.588.588.589590.590.591.591.5920.86860.592.593.593.594.594.596.596.596.597.5970.87870.598.598.599.599.600.601.601.602.602.6030.88880.603.604.604.605.605.607.607.607.608.6080.89890.609.609.610.610.611.612.612.613.613.6140.90900.614.615.615.616.6

26、16.617.617.618.618.6190.91910.619.620.621.621.622.623.623.623.624.6240.92920.625.625.626.626.627.628.628.628.629.6290.93930.630.630631.631.632.633.633.634.634.6350.94940.635.636.636.637.637.638.638.639.639.6400.95950.640.641.641.642.642.643.643.644.644.6450.96960.645.646.646.647.647.648.648.649.649.

27、6500.97970.650.651.651.652.652.653.653.654.654.6550.98980.655.656.656.657.657.658.658.658.658.6590.99990.660.660.661.661.662.663.663.663.664.6641.00 1000 .665附錄1B樣品厚度修正系數(shù)樣品厚度較厚:W =0.013.49見表W:樣品厚度（口 m）: S:探針間距（mm）W/S0.000.010.020.030.040.050.060.070.080.090.000.00000.00720.01440.02160.02890.03610.04

28、330.05050.05770.06490.100.07210.07940.08660.09380.10100.10820.11540.12260.12980.13710.200.14430.15150.15870.16590.17310.18030.18750.19480.20200.20920.300.21640.22360.23080.23800.24520.25240.25960.26680.27400.28120.400.28840.29560.30270.30990.31710.32420.33130.33850.34560.35260.500.35970.36680.37380.

29、38080.38780.39480.40180.40870.41560.42240.600.42930.43610.44290.44960.45630.46300.46960.47620.48270.48920.700.49570.50210.50850.51480.52100.52730.53340.53960.54560.55160.800.55760.56350.56940.57510.58090.58660.59220.59780.60330.60870.900.61410.61940.62470.62990.63510.64020.64520.65010.65510.65991.00

30、0.66470.66940.67410.67870.68330.68770.69220.69650.70090.70511.100.70930.71340.71750.72150.72550.72940.73330.73710.74080.74451.200.74820.75180.75530.75890.76220.76660.76890.71220.77540.77861.300.78170.78480.78790.79080.79380.79670.79960.80240.80520.80791.400.81060.81320.81580.81840.82090.82340.82580.

31、82820.83060.83291.500.83520.83750.83970.84190.84410.84620.84830.85030.85240.85441.600.85630.83820.86010.86200.86390.86570.86750.86920.87090.87261.700.87430.87600.87760.87920.88080.88230.88380.88530.88680.88831.800.8897 0.89110.8925 0.89390.8952 0.89650.8978 0.89910.9004 0.90161.90 0.9029 0.9041 0.90

32、53 0.9064 0.9076 0.9087 0.9099 0.9110 0.9121 0.9131W/S0.000.010.020.030.040.050.060.070.080.092.000.91420.91520.91620.91720.91820.91920.92020.92110.92210.92302.100.92390.92480.92570.92660.92740.92830.92910.92990.93070.93152.200.93230.93310.93380.93460.93530.93610.93680.93750.93820.93892.300.93960.94

33、020.94090.94150.94220.94280.94350.94410.94470.94532.400.94590.94020.94700.94760.94820.94870.94930.94980.95030.95092.500.95140.95190.95240.95290.95340.95380.95430.95480.95530.95572.600.95620.95660.95710.95750.95790.95830.95880.95920.95960.96002.700.96040.96080.96120.96160.96190.96230.96270.96300.9634

34、0.96372.800.96410.96440.96480.96520.96550.96580.96610.96640.96670.96712.900.96740.96770.96800.96830.96860.96890.96920.96940.96970.97003.000.97030.97050.97080.97110.97130.97160.97180.97210.97240.97263.100.97280.97310.97330.97360.97380.97400.97420.97450.97470.97493.200.97510.97530.97560.97580.97600.97

35、620.97640.97660.97680.97703.300.97720.97740.97760.97780.97790.97810.97830.97850.97870.97883.40 0.9790 0.9792 0.9794 0.9795 0.9797 0.9799 0.9800 0.9802 0.9803 0.9805如需所測值更精確，請查下表附錄2樣品形狀和測量位置的修正系數(shù) D (d )S(1)圓形薄片探針位置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.