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Nanotechnology and Nanoelectronics - Materials, Devices, Measurement Techniques Part 6

Tham khảo tài liệu 'nanotechnology and nanoelectronics - materials, devices, measurement techniques part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 90 4 Nanolayers Fig. 4.59 Specific resistance as a function of the doping Fig. 4.60 Experimental setup of the Hall effect schematic develops due to an electric field caused by the accumulation of the electrons on the cuboid s surface this field must not be mistaken with the field causing the current I . In the stationary case the forces are equal so that q v B q EH or after multiplying by the electron density n qnv B qn Eh . 4.38 The product q n v represents the current density. The term RH determined from the measurements is known as the Hall constant Rh T 4.39 j B qn The electron density n the hole density p for a hole semiconductor is obtained from this term. From the sign of the Hall constant the information whether electrons or holes are present is obtained. This procedure can be extended to a simultaneous measurement of the resistivity p and the Hall mobility pH. The four contacts A B C and D are mounted on 4.2 Characterization of Nanolayers 91 Fig. 4.61 Measurement setup according to van der Pauw 90 the edge of a thin sample that can have an arbitrary form Fig. 4.61 . The resistance Rab cd is defined as the quotient of the potential drop VD - VC and the feed current between the contacts A and B causing the voltage drop. The resistance Rbc da is defined analogously. The resistivity nd Rab cd Rbc da z. I Rab cd P --1 f I ln2 2 Rbc da 4.40 The factor f is obtained from the implicit equation cos Rab cd Rbc da 1 ln2 Rab cd Rbc da 1 f ln2 p f 2 e 4.41 The Hall mobility is determined by measuring the change in the resistance Rbd AC by an applied magnetic field n d RRCHD. 4.42 B p The method described above is named after van der Pauw 90 . Another way of determining the doping level is the use of an MOS diode. A typical cross section of such a device has already been shown in Fig. 4.27. A bias is applied between the two metal contacts and an alternating voltage modulation usually 25 mV is superimposed on it. In our case an alternating voltage frequency of 1 MHz is .