Van Der Pauw Van Der Pauw measurement and

半導體專題實驗 實驗三 Van Der Pauw量測與霍爾效應 Van Der Pauw measurement and Hall effect 1

Hall effect have got two Nobel Prize in Physics Klaus von Klitzing 1985 "the quantized Hall effect" Robert B. Laughlin Horst L. Störmer Daniel C. Tsui 1998 " the fractional quantum Hall effect " 2

實驗目的 o 利用 Van Der Pauw 四點探針法和霍爾效應 (Hall effect)，量測半導體中多數載子濃度與 遷移率μ (mobility) 。 The Van Der Pauw Method Original paper by L. J. van der Pauw in 1958 http: //electron. mit. edu/~gsteele/vanderpauw. pdf 3

霍爾效應 (Hall Effect) For p-type: Remember, Hall effect is used to measure majority carrier density. For minority carrier density, we use Haynes-Shockley experiment. 6

霍爾效應 (Hall Effect) 由Lorentz force balance: 得到 (positive for ptype) 又 其中 故 稱 Hall coefficient (positive for ptype) （d為導體厚度） : Hall voltage : Hall field : Hall coefficient 7

霍爾效應 (Hall Effect) For n-type: 同理可得 (for n-type) (negative for ntype) 8

vs. Original quote: 17

B=0. 55 T 地磁 400 m Gause 1 T=104 Gause 方程式 , , 可求出 (1) (2) (3) 由量測中得到 可求出 (majority carrier density) 可求出 19

結報問題 1. Calculate r、n、m from measurement data for n-type and p-type 2. Compare with the hall mobility we already have. 3. Hall coefficient RH 22

BACK UP 23

n-type ρ=6. 119Ω·cm n=5. 804 E+14/cm 3 μ=1. 757 E+3 cm 2/Vs 24

p-type ρ=8. 467Ω·cm n=1. 918 E+15/cm 3 μ=3. 849 E+2 cm 2/Vs 25