Techniques and Methods of Hall Measurements · 2018-06-20 · Measurement 1 positive field (B) and...

| Lake Shore Cryotronics, Inc.| Lake Shore Cryotronics, Inc.

Techniques and Methods of Hall Measurements

Jeffrey LindemuthLake Shore CryotronicsMay 29,2018

| Lake Shore Cryotronics, Inc.

Outline

General introduction to the Hall Effect Sample Considerations

– Geometry– Contact size effects

Ohmic contactsMeasurement of high mobility materials – DC field HallMeasurement of low mobility materials – AC field HallMulti-Carrier systemsMeasurements of Magnetic materials - anomalous Hall effect


Techniques and Methods of Hall Measurements

Edwin Hall 1855-1938


Electronic transport in semiconductors

Four parameters of interest– Conductivity or resistivity – Carrier concentration– Carrier type sign of hall voltage– Mobility

Temperature dependency can help determine basic properties of the material, like scattering mechanisms, Fermi level and excitation energies.

𝜎𝜎0 = 𝑛𝑛𝑛𝑛𝜇𝜇

𝑛𝑛 =1

𝑛𝑛 𝑅𝑅𝐻𝐻

𝜇𝜇 = 𝑅𝑅𝐻𝐻/𝜌𝜌


Sample Considerations


Van der Pauw Sample

Current flow is two dimensional4 point contacts on the edge of the sampleSample is simply connectedOnly thickness is required to convert resistance measurements to resistivity


Van der Pauw Samples

R. Chwang, B. J. Smith, and C. R. Crowell, "Contact size effects on the van der Pauw method for resistivity and Hall coefficient measurement," Solid-State Electronics, vol. 17, pp. 1217-1227, 12// 1974.

Common van der Pauw Sample Geometries.

Most common sample geometryFinite size of contacts introduce errors in the resistivity and hall voltage


Resistivity Measurement

𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 =𝑽𝑽𝟏𝟏𝟏𝟏 𝑰𝑰𝟏𝟏𝟏𝟏+ − 𝑽𝑽𝟏𝟏𝟏𝟏 𝑰𝑰𝟏𝟏𝟏𝟏−

𝑰𝑰𝟏𝟏𝟏𝟏+ − 𝑰𝑰𝟏𝟏𝟏𝟏−

𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 =𝑽𝑽𝟏𝟏𝟏𝟏 𝑰𝑰𝟏𝟏𝟏𝟏+ − 𝑽𝑽𝟏𝟏𝟏𝟏 𝑰𝑰𝟏𝟏𝟏𝟏−

𝑰𝑰𝟏𝟏𝟏𝟏+ − 𝑰𝑰𝟏𝟏𝟏𝟏−

𝝆𝝆 =𝝅𝝅𝝅𝝅𝐥𝐥𝐥𝐥(𝟏𝟏)

(𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 + 𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 )𝟏𝟏

𝒒𝒒 − 𝟏𝟏𝒒𝒒 + 𝟏𝟏

=𝝅𝝅 𝒄𝒄𝒄𝒄𝒄𝒄𝒄𝒄−𝟏𝟏(𝒆𝒆

𝒍𝒍𝒍𝒍 𝟏𝟏𝝅𝝅𝟏𝟏 )

𝐥𝐥𝐥𝐥(𝟏𝟏)

𝒒𝒒 =𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

𝒄𝒄𝒐𝒐 𝒒𝒒 =𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝑹𝑹𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏

𝒘𝒘𝒄𝒄𝒘𝒘𝒄𝒄𝒄𝒄 𝒆𝒆𝒆𝒆𝒆𝒆𝒐𝒐 𝒘𝒘𝒄𝒄 𝒍𝒍𝒍𝒍𝒐𝒐𝒍𝒍𝒆𝒆𝒐𝒐


Van der Pauw Sample (Hall voltage)

XB

𝑽𝑽𝑯𝑯 =𝑹𝑹𝑯𝑯𝑩𝑩 𝑰𝑰𝒕𝒕

𝜇𝜇 = 𝑅𝑅𝐻𝐻/𝜌𝜌𝑛𝑛 =1

𝑛𝑛 𝑅𝑅𝐻𝐻


Hall Bar

6 contacts (other contact arrangements are possible)Current flow is one dimensional

Current flows between contacts 5 and 6Hall voltage measured between contacts 1 and 2 or contacts 4 and 3Resistivity measured between contacts 1 and 4 or contacts 2 and 3

requires knowledge of D and W to calculate resistivity𝜌𝜌 = (𝑅𝑅14+𝑅𝑅23)

2𝑊𝑊𝑊𝑊𝐷𝐷

were t is the thickness.


Errors due to contact size

Square SampleFor c/L = 1/6 Δρ/ρ = 2% for square contacts; <1% for triangle contactsΔRH /RH = 15% for triangle contacts

increase by 3% as µB goes from 0.1 to 0.5

Circular Sample

Δρ/ρ = -1% for 4 contacts and c/l = 1/6

ΔRH /RH = 15% for 4 contacts and c/l = 1/6

Cloverleaf sampleReduces errors by 10 to 20 for resistivity and 3 to 5 for Hall coefficient. Structurally more fragile with smalleractive area.

L/w = 3 c/w = .2 this is a 13% errorAdding contact arms with p > c c ≤ w/3 and L > 4w reduces error to near zero.


Contact to your sample


Sample Preparation Ohmic Contacts

Contact on the sample are used to connect wires to the sample or probe points for measurements.

Measurement with non-ohmic contact can give results that are the properties of the contacts not the bulk material.


Ohmic check

The quality of the contacts is measured by using an IV curve.– Measure current and voltage over a range of currents– Fit the data to a straight line

The IV curve should be linear with correlation coefficient > 0.9999


Understanding ohmic check results

Correlation coefficient = 1High quality ohmic contact

Correlation coefficient = 0.99IV curve indicates self heating


Understanding ohmic check results


High Mobility MaterialsDC Field Hall Methods


Contributions to measured voltage

Voltages that do not depend on I or B but depend on temperature gradients– Thermo-Electric VTE (Seebeck effect)

Voltages that depend on B and temperature gradient– Nernst effect voltage (VN)– Righi-Leduc effect voltage (VR)

Voltages that depends only on I– Misalignment voltage (Ohm’s law V0)

Voltages that depend on the product of B and I– Hall effect voltage (VH)– Ettingshausen effect voltage (VE)


Removing undesirable voltages

Thermal electric voltages: removed using current reversal

Misalignment voltages: removed using field reversal; there will be large errors if the offsets are large compared to the Hall voltage, (low mobility material)

Note: Non-uniformity effects in the sample: removed using geometry averaging (interchange of current source and voltmeter)


Hall measurement recap

There are 4 factors in mobility measurement:– Hall voltage VH

The value we want to measure calculate Hall coefficient RH=VHt/IB and mobility µ=RH/ρ

– Misalignment voltage Error due to imperfect sample geometry Not field dependent Use field reversal to remove by subtraction

– Thermal electric voltage VTE Error due to temperature effects Not current dependent Use current reversal to remove by subtraction

– Noise Error due to experimental & instrumentation limitations

Hall voltage

Misalignment voltage

T/E voltage

Noise


Hall measurement recap

High mobility materials

Hall voltage


T/E voltage

Lower mobility materialsHall voltage


T/E voltage

Very low mobility materials

Hall voltageMisalignment voltage

T/E voltage

Hall voltageDC Field

Hall voltageAC Field

AC Field

time

Misalignment voltage errors become more impactful due

to longer measurement times

time

Noise


Un-cancelled misalignment voltage (error) due to time-dependent changes (self-

heating, etc.)



time


DC field Hall method

𝑉𝑉𝑚𝑚 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 + 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇

An ideal Hall measurement would give zero volts at zero fieldReal measurements always have offset voltages:

𝑽𝑽𝒎𝒎 𝑖𝑖𝑖𝑖 𝑡𝑡𝑡𝑛𝑛 𝑚𝑚𝑛𝑛𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑛𝑛𝑚𝑚 𝑣𝑣𝑣𝑣𝑣𝑣𝑡𝑡𝑚𝑚𝑣𝑣𝑛𝑛𝑹𝑹𝑯𝑯𝑰𝑰𝑩𝑩 𝑖𝑖𝑖𝑖 𝑡𝑡𝑡𝑛𝑛 𝐻𝐻𝑚𝑚𝑣𝑣𝑣𝑣 𝑣𝑣𝑣𝑣𝑣𝑣𝑡𝑡𝑚𝑚𝑣𝑣𝑛𝑛

𝜶𝜶𝝆𝝆𝑰𝑰 𝑖𝑖𝑖𝑖 𝑡𝑡𝑡𝑛𝑛 𝑚𝑚𝑖𝑖𝑖𝑖𝑚𝑚𝑣𝑣𝑖𝑖𝑣𝑣𝑛𝑛𝑚𝑚𝑛𝑛𝑛𝑛𝑡𝑡 𝑣𝑣𝑣𝑣𝑣𝑣𝑡𝑡𝑚𝑚𝑣𝑣𝑛𝑛𝑽𝑽𝑻𝑻𝑻𝑻 𝑖𝑖𝑖𝑖 𝑡𝑡𝑡𝑛𝑛 𝑡𝑡𝑡𝑛𝑛𝑚𝑚𝑚𝑚𝑚𝑚𝑣𝑣 𝑛𝑛𝑣𝑣𝑛𝑛𝑒𝑒𝑡𝑡𝑚𝑚𝑖𝑖𝑒𝑒 𝑣𝑣𝑣𝑣𝑣𝑣𝑡𝑡𝑚𝑚𝑣𝑣𝑛𝑛

𝝆𝝆 is the sheet resistivity 𝜶𝜶 is a dimensionless parameter that

depends on the sample geometry


DC field Hall method

𝑉𝑉𝑚𝑚,1 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 + 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇

4 measurements are required to separate the Hall voltage from the misalignment voltage and thermal electric voltageMeasurement 1 positive field (B) and positive current (I)

Measurement 2 positive field (B) and negative current (-I)

𝑉𝑉𝑚𝑚,3 = −𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 + 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇Measurement 3 negative field (-B) and positive current (I)

Measurement 4 negative field (-B) and negative current (-I)

𝑉𝑉𝑚𝑚,2 = −𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 − 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇

𝑉𝑉𝑚𝑚,4 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 − 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇𝑉𝑉𝑚𝑚,1- 𝑉𝑉𝑚𝑚,2 = 2(𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 + 𝛼𝛼𝜌𝜌𝐼𝐼) 𝑉𝑉𝑚𝑚,4- 𝑉𝑉𝑚𝑚,3 = 2(𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 − 𝛼𝛼𝜌𝜌𝐼𝐼)

𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 = (𝑉𝑉𝑚𝑚,1- 𝑉𝑉𝑚𝑚,2 + 𝑉𝑉𝑚𝑚,4- 𝑉𝑉𝑚𝑚,3)/4 = 𝑉𝑉𝐻𝐻


DC field Hall low mobility

𝑉𝑉𝑚𝑚,1 = 𝜌𝜌𝐼𝐼(𝜇𝜇𝐼𝐼 + 𝛼𝛼) + 𝑉𝑉𝑇𝑇𝑇𝑇

𝑉𝑉𝑚𝑚,2 = −𝜌𝜌𝐼𝐼(𝜇𝜇𝐼𝐼 + 𝛼𝛼) + 𝑉𝑉𝑇𝑇𝑇𝑇

𝑉𝑉𝑚𝑚,3 = 𝜌𝜌𝐼𝐼(−𝜇𝜇𝐼𝐼 + 𝛼𝛼) + 𝑉𝑉𝑇𝑇𝑇𝑇

𝑉𝑉𝑚𝑚,4 = 𝜌𝜌𝐼𝐼(𝜇𝜇𝐼𝐼 − 𝛼𝛼) + 𝑉𝑉𝑇𝑇𝑇𝑇

𝑉𝑉𝑚𝑚,1 − 𝑉𝑉𝑚𝑚,2 = 2𝜌𝜌𝐼𝐼(𝜇𝜇𝐼𝐼 + 𝛼𝛼)𝑉𝑉𝑚𝑚,3 − 𝑉𝑉𝑚𝑚,4 = 2𝜌𝜌𝐼𝐼 −𝜇𝜇𝐼𝐼 + 𝛼𝛼

𝑉𝑉𝑚𝑚,1 − 𝑉𝑉𝑚𝑚,2 − 𝑉𝑉𝑚𝑚,3 + 𝑉𝑉𝑚𝑚,4 = 4𝜌𝜌𝜇𝜇𝐼𝐼𝐼𝐼


How big is α? an example

Rectangular Van der Pauw sample with point contacts on corners

w

l

w/l α μ (cm2/(Vs)) = α/B=α/(1T)

1 00.99 0.014 1400.9 0.14 14000.5 1.11 11100


Low mobilities and the DC field method

Consideration #2—both Vma and VTE change with temperature and timeAny change in the offset voltage between the two field measurements appears as a Hall voltage

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0 200 400 600 800 1000 1200

Volta

ge [v

olts

]

Time (sec)

-0.7020

-0.7015

-0.7010

-0.7005

-0.7000

-0.6995

-0.6990

-0.6985

-0.6980

-0.6975

0 200 400 600 800 1000 1200

Volta

ge [v

olts

]

Time (sec)


DC field Hall effect: equations

Raw data:

After current reversal:

After field reversal:

𝑉𝑉𝑚𝑚 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 + 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇

𝑉𝑉𝑚𝑚 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 + 𝛼𝛼𝜌𝜌𝐼𝐼

𝑉𝑉𝑚𝑚 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼 = 𝑉𝑉𝐻𝐻


T/E voltage

Hall voltageDC Field Misalignment voltage


Low Mobility MaterialsAC Field Methods


AC Field Methods

The DC field method works well on materials with mobility ~ 10 cm2/(V s).

For lower mobility materials other methods are used. One such method is to use AC fields.

In this method the DC field is replaced with an AC field. The AC field may be generated by a rotating magnet or an AC current driving an electromagnet.


AC field method

When the B field becomes an AC field, the raw data equation gets a new term proportional the time derivative of the B field—this term is due to the inductance of the system

The DC voltage can be separated from the AC voltage by the AC method.

For high resistance samples there are additional terms proportional to the capacitance of the system; we will consider these later

𝑉𝑉𝑚𝑚 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼𝑒𝑒𝑣𝑣𝑖𝑖 𝜔𝜔𝑡𝑡 − 𝛽𝛽𝐼𝐼𝜔𝜔sin(𝜔𝜔𝑡𝑡) + 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇

AC voltage DC voltage


AC field method

The DC voltage can be removed with a capacitor and measured with a lockin amplifier with reference to the magnetic field.

LIA

𝑉𝑉𝑚𝑚 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼𝑒𝑒𝑣𝑣𝑖𝑖 𝜔𝜔𝑡𝑡 − 𝛽𝛽𝐼𝐼𝜔𝜔sin(𝜔𝜔𝑡𝑡) + 𝛼𝛼𝜌𝜌𝐼𝐼 + 𝑉𝑉𝑇𝑇𝑇𝑇

No current reversal

𝑉𝑉𝑚𝑚 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼𝑒𝑒𝑣𝑣𝑖𝑖 𝜔𝜔𝑡𝑡 − 𝛽𝛽𝐼𝐼𝜔𝜔sin(𝜔𝜔𝑡𝑡)


AC field method

Consideration #1—inductive pickup term: using phase spaceIn the case of the AC field hall signal, the input signal contains two terms

The inductive pickup term, even though it is small, will ultimately determine the highest usable gain of the lock-in amplifier (LIA)

𝑉𝑉𝐻𝐻 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼𝑒𝑒𝑣𝑣𝑖𝑖 𝜔𝜔𝑡𝑡 − 𝛽𝛽𝐼𝐼𝜔𝜔sin(𝜔𝜔𝑡𝑡)

Hall voltage (in phase with the magnetic field)

Inductive pickup (-90° out of phase)


AC field method

Consideration #2—phase errors

If the LIA is phased perfectly, the x and y channel of the LIA will read

𝑉𝑉𝑥𝑥 = 𝑅𝑅𝐻𝐻𝐼𝐼𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅

𝑉𝑉𝑦𝑦 = −𝛽𝛽𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝜔𝜔

If there is an error in the phase of φ then the x and y channel will read

𝑉𝑉𝑥𝑥 = 𝑅𝑅𝐻𝐻𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼 cos φ + 𝛽𝛽𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝜔𝜔 sin φ

𝑉𝑉𝑦𝑦 = −𝛽𝛽𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝜔𝜔 cos φ + 𝑅𝑅𝐻𝐻𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼 sin φ


Phase errors: the fix

Inductive pickup terms: remove these using current reversal

Note: Hall voltage depends on the current but the inductive pickup term does not depend on the current.

𝑉𝑉𝑥𝑥 = 𝑅𝑅𝐻𝐻𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼 cos φ𝑉𝑉𝑦𝑦 = 𝑅𝑅𝐻𝐻𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼 sin φ


Applications Multi-carrier systems


yxxy

yyxx

ρ−=ρ

ρ=ρ

𝐸𝐸𝑥𝑥𝐸𝐸𝑦𝑦

= 𝜌𝜌 −𝑅𝑅𝐻𝐻𝐼𝐼𝑧𝑧𝑅𝑅𝐻𝐻𝐼𝐼𝑧𝑧 𝜌𝜌

𝐽𝐽𝑥𝑥𝐽𝐽𝑦𝑦

ρ−

ρ

+ρ=σ

Hz

Hz2H

2z

2 RBRB

RB1

Resistivity and Conductivity as Tensors

Ohm’s law is often written as a scaler equation for 1D current flow: V = IRFor 2D current flow the relation between electric field and current density


=𝜌𝜌𝑥𝑥𝑥𝑥 𝜌𝜌𝑥𝑥𝑦𝑦𝜌𝜌𝑦𝑦𝑥𝑥 𝜌𝜌𝑦𝑦𝑦𝑦


The Onsager relations reduce the four elements of the resistivity tensors to two elements

For Hall effect with a B field in the z direction


Single-Carrier System

(both parameters are field independent)

(n, µ)

n: carrier densityµ : carrier mobilityq: charge of a carrier

𝜌𝜌𝑥𝑥𝑥𝑥 = 𝜌𝜌𝑦𝑦𝑦𝑦 = 𝜌𝜌 = 1/(neµ)𝜌𝜌𝑥𝑥𝑦𝑦= - 𝜌𝜌𝑥𝑥𝑦𝑦 = 𝑅𝑅𝐻𝐻𝐼𝐼𝑧𝑧 = 𝐵𝐵𝑧𝑧

ne

𝜎𝜎 =𝜎𝜎0

1 + µ𝐼𝐼𝑍𝑍 21 𝜇𝜇𝐼𝐼𝑧𝑧

−𝜇𝜇𝐼𝐼𝑧𝑧 1


=𝜌𝜌𝑥𝑥𝑥𝑥 𝜌𝜌𝑥𝑥𝑦𝑦𝜌𝜌𝑦𝑦𝑥𝑥 𝜌𝜌𝑦𝑦𝑦𝑦



Multi-Carrier System

(n1, µ1)(n2, µ2)

(n3, µ3 ) … ...

Examples: heterostructure devices, indirect band gap semiconductors, etc.

∑ +=

N

j j

jjjxx B

qnB 221

)(µ

µσ ∑ +

=N

j j

jjjxy B

BqnB 22

2

1)(

µµ

σ

𝑹𝑹𝑯𝑯 𝑩𝑩 =𝝈𝝈𝒙𝒙𝒙𝒙

𝑩𝑩(𝝈𝝈𝒙𝒙𝒙𝒙𝟏𝟏 + 𝝈𝝈𝒙𝒙𝒙𝒙𝟏𝟏 )𝝆𝝆𝒙𝒙𝒙𝒙 𝑩𝑩 =

𝝈𝝈𝒙𝒙𝒙𝒙𝝈𝝈𝒙𝒙𝒙𝒙𝟏𝟏 + 𝝈𝝈𝒙𝒙𝒙𝒙𝟏𝟏


Finite Number Carrier Fit

Least square fit of Hall data to a preset number of carriers

M: number of data points

N: preset number of carriers (2N fitting parameters)

∑∑ ∑ −+−=N

ji

jxyxy

M

i

N

ji

jxxxx BBBB ]))()((())()([( 2exp2exp2 σσσσχ


Variable Field Hall Data of InP pHEMT

-2.0x106

-1.9x106

-1.8x106

-1.7x106

-1.6x106

0.01 0.1 1 10-200

0

200

400

ρ (300 K)

ρ (100 K)

RH (300 K)

RH (100 K)

B (T)

Shee

t Hal

l Coe

fficie

nt (c

m2 /C

)

Shee

t Res

istivi

ty (Ω

/)


Conductivity Tensor and Fitted Results from QMSA

-0.01

0

0.01

0.02

0.1 1 10

σXX (300 K)

σXY (300 K)

σXX (100 K)

σXY (100 K)

B (T)

Shee

t Con

duct

ivity

Ten

sor (

S)

Markers: data pointsLines: QMSA fitted results


QMSA Spectra

10-8

10-6

10-4

10-2

102 103 104 105 106

Highest mobility2DEG carrier:µ = -4.03e4 cm2/Vsn = -3.14e12 cm-2

2DEG subband carriers

low mobility species(surface or interface carrier)

T = 50 KB = 0.002 - 8.5 T

Mobility (cm2/Vs)

Mob

ility

Spec

tra (a

. u.)

10-7

10-5

10-3

10-1

102 103 104 105 106




T = 100 KB = 0.002 - 8.5 T

Mobility (cm2/Vs)

Mob

ility

Spec

tra (a

.u.)

10-7

10-5

10-3

10-1

102 103 104 105 106




T = 150 KB = 0.002 - 8.5 T

Mobility (cm2/Vs)

Mob

ility

Spec

tra (a

.u.)

10-7

10-5

10-3

10-1

102 103 104 105 106




T = 200 KB = 0.002 - 8.5 T

Mobility (cm2/Vs)

Mob

ility

Spec

tra (a

.u.)


Mobility vs. temperature

Using multi-carrier analysis at different temperatures, the mobility of a carrier vs temperature can be extracted.Each mobility mechanism (phonon scattering, impurity scattering etc.) has a different temperature dependency.


Applications Anomalous Hall Effect


Anomalous Hall Effect


AHE

Ordinary Halleffect V = RH B

Anomalous Hall Effect V = RS M

Ordinary Hall effect can be extracted by fitting the measured data in the saturation region. In the region, the magnetization is a constant Ms. The Hall coefficient is the slope of the line.

Simple Model for AHE in magnetic material


AHE Field Reversal

RH B + RS M(B)

-RH B - RS M(-B)

Similar protocol for DC field Hall effect, except field reversal must reverse both the magnetic field and the magnetic state of the material.

Field Reversal for Magnetic material


Perpendicular recording media


Thanks for your attention.Any questions?

Techniques and Methods of Hall Measurements · 2018-06-20 · Measurement 1 positive field (B) and...

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Transcript of Techniques and Methods of Hall Measurements · 2018-06-20 · Measurement 1 positive field (B) and...