Mobility Chapter 8

Kimmo Ojanperä

S-69.4123, Postgraduate Course in Electron Physics I

Outline•What is mobility?•Different types of mobilities•Hall mobility• Emphasis on the measurement

•MOSFET mobility

Mobility

•Why high mobility is beneficial?

•Higher frequency response

•Higher current

Different types of mobility

• Conductive mobility

• Hall mobility

• Magnetoresistance mobility

• Drift mobility

• MOSFET mobility

• Effective mobility

• Field-effect mobility

• Saturation mobility

Conductive mobility

Hall Mobility

•Hall mobility, carrier concentration and resistivity of the sample from the same measurement

•Van der Pauw measurement

Hall Mobility – theory

Hall Mobility – theory

http://www.nist.gov/pml/div683/hall_resistivity.cfm

Hall Mobility – measurement

http://www.keithley.com/data?asset=55773

Carrier type:•Holes if V_H is positive•Electrons if V_H is negative

Hall effect voltage vs. van der Pauw resistance measurement configurations

Compute the Hall voltage with both positive and negative polarity current and with magnetic field both up and down, and with the two

configurations shown. Then average all voltages.

Hall Mobility – van der Pauw measurement

http://www.keithley.com/data?asset=55773

Van der Pauw requirements•Uniform thickness•No wholes•Contacts at the edge of the sample

Hall Mobility – sample geometry

Symmetrical sample

geometry makes it easier to verify

your measurement

results.

Use the same sample geometry for both the Hall voltage and van Pauw

measurement

Hall Mobility – sample geometry

If you are measuring from a bar make sure it is long enough.

Should be L/W

Hall Mobility – measurement setup

• Not too expensive

• Accurate source meter needed.

• Widely used.

Geometric Magnetoresistance mobility

• Suitable for short and wide transistors with high mobility.• Silicon with µ = 500 – 1300 cm2/Vs is too

slow.

Drift mobility

• Measures minority carrier mobility

MOSFET Mobility

• Device mobility• Hall mobility is bulk material mobility

• Lower than bulk mobility because of all the additional scattering mechanisms• Coulomb scattering from oxide charges and

interface states• Surface roughness scattering

• Three types in the book• Effective mobility • Field-effect mobility• Saturation mobility

• For oxide TFTs also incremental mobility and average mobility have been defined [1]

[1] Hoffman, R. L.; , "ZnO-channel thin-film transistors: Channel mobility," Journal of Applied Physics , vol.95, no.10, pp.5813-5819, May 2004

MOSFET Mobility – effective mobility

• For increased accuracy measure the Qn

MOSFET Mobility – effective mobility

• The effective mobility depends on lattice scattering, ionized impurity scattering, and surface scattering. Ionized impurity and surface scattering depend on the substrate doping density and the gate voltage.

• Additional sources of error• Polysilicon gate

depletion• Gate leakage current• Series resistance • Interface trapped charge

overestimate the Qn

MOSFET Mobility – field effect mobility

MOSFET Mobility – field effect mobility

MOSFET Mobility – saturation mobility

where m is the slope of the (ID,sat )1/2 versus (VGS − VT ) plot.

Strengths and weaknesses

Conductive Mobility+ Defined straight from sample conductivity – no correction factors- Requires independent measurements for sample conductivity and carrier density

Hall effect Mobility+ Is in common use and easy to compare results.- Unknown Hall scattering factor introduces error. Normally assumed to be 1.

Magnetoresistance Mobility+ No special test structures needed for the samples that are applicable to the method- Only for high mobility semiconductors.

Drift Mobility+ Ability to measure mobility and carrier velocity at high electric fields.- Special test structures and high speed electronics needed. Rare.

MOSFET Mobility+ Operational device mobility extracted.- Different values extracted depending on the mobility definition. According to the book saturation and field-effect mobility should not be used. Almost all the papers in my field (solution processed TFTs) use them.