Hall Effect Measurement

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Hall Measurement
2005. 11. 10 Song Dong Eon
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C O N T E N T S
1. Introduction 2. Advantage 3. Principle 4.
Van der Pauw Method 5. Hall Measurement
System 6. Calculation Processing 7. Summary
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I. Introduction

• Hall Effect? ??? ?? ??
• Hall Effect?
• Metal?? Semi-conductor ?? ??? ??? ?? ??, ????
• ??? ???? ?? ?? Current? ???, ? ?? ??? ???
• ??? ?? ?? Electric Field? ????, ?? Hall
  Voltage? ??
• ???. ? Hall voltage? ??? ??? Hall Effect?? ?
• Hall Effect? 1987? ??? ?? ??? ???? Henry A.
  Rowland
• ??? ??? ?? Hall? ?? ??

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II. Advantage

• Hall Measurement? ??? ??? ?? ???, ???, ???
• ??, N??? P? ?? ?? ???? ??
• ?? ?? ??? ??? ??? ???? ???? ?????
• ???? ?? ?? ??
• Si?, SiGe?, InGaAs?, InP?, GaN?? ?? ???? ????

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III. Principle
1.The Hall effect and the Lorentz Force
Coordinate System
Lorentz Force F-qv X B
z
y
x
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III. Principle
y ????? ??? Ey? ??? ???? ??
(1)
Z????? ??? B? ??? ???? Lorenz??
(2)
? ?? ??? ????
(3)
???? Lorenz? ??? ??? ???(Hall Voltage)
(4)
N ???(1/cm3) ??? ?? q ??? v ??? ?? d
?? ?? w ?? ?
?? ?? I ? ??? ?? ??
(5)
Hall Voltage? ??? N? ?? ? ??
(6)
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III. Principle
(6)?? ??? ? ??
(7)
? ?? RH? ?? ??? type? ????.
?? n-type semiconductors ?? p-type
semiconductors
Hall Voltage VH? ???? ??? ? ?? ? ??.
(7)
?????? ????
(8)
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IV. Van der Pauw Method

• Van der Pauw ??? ?? ?? ??
• 1) contact? sample? ??? ??.
• 2) contact? ??? ??.
• 3) sample? ??? ????.
• 4) sample? ??? ??? ?? ?? ??. ?, Sample??? ?
  ??? ??.
• 5) Ohmic contact? quality? ?????.
• 6) Photoconductive? photovoltaic effect?
  ????.
• 7) sample? ??? contact? ??? sample? ???? ??.
• 8) sample ??, magnetic field ??, electrical
  current and voltage? ????
• ????.

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IV. Van der Pauw Method

• Sample Geometry

Square or rectangle Contacts at the edges or
inside the perimeter
Square or rectangle Contacts at the corners
Cloverleaf
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IV. Van der Pauw Method

• Conformal Mapping ??

Van der Pauw ??? ?? ?? ??? ????? sample? ??? ???
Sample? ??? ?? ??? ??? ??? 4?? Ohmic contact A,
B, C, D
P,Q,R,S? A,B,C,D? conformal Mapping??? ?? ?????
?? ?? a,b,c??? ??? ??? ??
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IV. Van der Pauw Method
? ?? Sample? R ? ?? ? ??
?? P?-gtQ? S?? R?? ????
(9)
(10)
(11)
b(abc)ca(ab)(bc)
(12)
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IV. Van der Pauw Method
(13)
? ?? ??????.
Van der Pauw ??? ???? ??? ??? (13)??? ?? ??? ??
??? ??
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V. Hall Measurement System

• ?? ??
• - Control box
• - Power supply
• - Gaussmeter
• - Magnet
• - Sample holder

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VI. Calculation Processing

• Sample? ?? R? ???? ??

• A?? B? ?? IAB? ??? ?, C? D?? ???? VCD?? ??? ????
  ?
•                       
• B?? C? ?? IBC? ??? ? D? A?? ???? VDA? ?? ? ?

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VI. Calculation Processing

• Current measurement
• -Sample? 1?? 2? ??? ??? ?? I12
• -?? ?? ??? ??? ??
• I23, I34, I41, I21, I14, I43, I32
• -in Amperes, A
• Voltage measurement
• -Sample? 1?? 2? ??? ??? ?? V12
• -?? ?? ??? ??? ??
• V23, V34, V41, V21, V14, V43, V32
• -in Volts, V

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VI. Calculation Processing

• Resistivity Measurements

- ??? ???? ??? ?? ??? ????? ??? Hall Voltage?
???? ?? R? ?? R21,34 V34/I21, R12,43 V43/I12
R32,41 V41/I32, R23,14 V14/I23 R43,12
V12/I43, R34,21 V21/I34 R14,23 V23/I14,
R41,32 V32/I41 - ?? ???? ???? ???? ??? ?? ????
Hall Voltage? ?? ?? R?? ? ?? ??? ? R21,34
R12,43 R43,12 R34,21 R32,41 R23,14
R14,23 R41,32 -??? ?? ?????
?? R21,34R12,43 R43,12R34,21
R32,41R23,14 R14,23R41,32
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VI. Calculation Processing
-Sample? ??? 2?? ??(RA, RB)? ????
RA(R21,34R12,43R43,12 R34,21)/4
RB(R32,41R23,14R14,23 R41,32 )/4 -Van der
pauw equation? ?? RS? ?? ? ?? exp(-p RA/RS)
exp(-p RB/RS)1 -Electrical resistivity
?Rsd (d? ??? ??)
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VI. Calculation Processing
-????? ??? sample, sample? ??, ??? ?? ??? ?? ???
?? ?? -??? ???? ???? ?? positive ???? negative
???? ???? ??
-Positive ??? B? ??? ?? I13 ?? ? ?? V24p? ??
?? I31 ?? ? ?? V42p? ?? (I24? ? V13p??, I42? ?
V31p??) -Negative ??? B? ??? ?? I13 ?? ? ??
V24n? ?? ?? I31 ?? ? ?? V42n? ?? (I24? ?
V13n??, I42? ? V31n??)
 (a)-(d)? ??? ???? ???? ?? ??? ??? ?? ??? ???
?????? ? 8?? ???? ?? ?? (e)? (f)? Hall ??? ????
???? ??? ??? ??? ??? ??? ?? 8?? ?????? ??
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VI. Calculation Processing
-V24p, V42p, V13p, V31p, V24n, V42n, V13n, V31n ?
?? type (p or n)? Sheet Carrier
Concentration (/cm-2) ? ?? VC V42p-V42n, VD
V42p-V42n, VE V13p- V13n, VF V31p- V31n ?? -???
?(VC VD VE VF)? ??? p-type, ?? ??? n-type
-Sheet Carrier Concentration (1/cm2) ???? ???
?? Positive ?? Ps 8 X 10-8
IB/q(VCVDVEVF) ??? ?? Negative ?? Ns
8 X 10-8 IB/q(VCVDVEVF) -Bulk
Carrier Concentration (1/cm3) ? ?? d? ??? ????
??? ?? positive ?? PBPS/d --------p-type
??? ?? negative ?? NBNS/d--------n-type
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VI. Calculation Processing
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VI. Calculation Processing
Sample index Current Range Magnetic Flux Density(T) Sample Thickness(um ) Concentration (1/cm3) Mobility (cm2/Vs) Coefficient (cm2/C) Resistivity (ohmcm)
1 1.0003 x 1uA 1.0085 x 1uA 1.0161 x 1uA 1.0242 x 1uA 1.0006 x 1uA 0.51 0.51 0.51 0.51 0.51 0.78 0.78 0.78 0.78 0.78 -5.2913E17 -3.5080E17 -2.7242E17 -5.4913E17 -3.0405E17 0.89642 2.75017 3.58316 1.58221 2.9689 -0.89642 -2.75017 -3.58316 -1.58221 -2.9689 4.29624 4.98341 5.55313 6.02138 6.41408
2 1.0081 x 1uA 1.0086 x 1uA 1.0121 x 1uA 1.0042 x 1uA 1.0026 x 1uA 1.0142 x 1uA 0.51 0.51 0.51 0.51 0.51 0.51 0.47 0.47 0.47 0.47 0.47 0.47 -1.3922E16 -6.7118E15 -7.4078E15 -9.5173E15 -1.6326E16 -6.7915E15 11.77849 23.4951 21.34703 16.63182 9.64707 23.48492 -448.38524 -930.03686 -842.64706 -655.88235 -382.35294 -919.11765 37.42039 39.23378 39.04421 39.56481 39.23695 38.93681
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VII. Summary

• Hall??? ?????? ???
•  
• 1. ??? ??? ???? ??? ???
•   
• 2. Hall??? ????? ?????? ??? ?? ? ??
•   
• 3. ???? Hall ????? ???? ??? ? ??
•  
• 4. ?????? ??? ??? ??? ??? ? ??
• 5. Magnetic Field? ??? ??? ????? ??