Determining Carrier Density through Measuring Resistivity

Kathleen BroughtonErnesto Indacochea

Klaus AttenhoferPhotocathodes Group

Resistivity Measurement

Measurement of how strongly a material resists electrical flow High Resistivity (R ≥ 1 GΩ); Low Resistivity ( R < 1 GΩ)

Ρ = Ε / J = R l / A = 1/σ

Ρ = resistivityΕ = magnitude of electric fieldJ = magnitude of current densityR = electrical resistancel = length of materialA = cross-sectional area of material σ = conductivity

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Current – Voltage Curve

Standard I-V curve– Saturation current is temperature dependant

Perceived I-V curve– Create an internal electric field on material– Question as to whether or not the dopant are a surface barrier and if the electrons that pass though material are equivalent

Drude TheoryE = ρ * j ; E = electric field, ρ = resistivity, j = current densityj = σ * E σ = conductivity, σ = ne^2τ / m τ = relaxation time (avg. time since its last collision)

n = number of carriers, e = electrical charge, m = mass

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Standard I-V curve Perceived I-V curve of photocathode

j j

v

-e (J(h) + J(e))

j(V)=e(J(h)+J(e))(e^eV/kT -1)

Sample Surface Measurements

Passage time through the bulk is much greater than just the surface Temperature Dependant Measurement can provide :

– Carrier density in bulk– Carrier density on surface– Activation energy (chemical potential) of defects and dopants – Work Function (comparison of dark and light measurement)

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Bulk

Surface

R (b)

R (s)V

I

Bulk

Surface

R(b) V

I

R (surface) << R (bulk)

Sample V/I = R(b) + R(s)

V/I = (R(b)*R(s)) / (R(b) + R(s))

R (s)

R (s)

Low Resistivity Measurements (R <1 GΩ)

• 4 Wire Resistance Measurement• Test Current (I) is forced through the test resistance (R) • voltage (Vm) across DMM is measured through sense leads• Voltage drop across sense leads is negligible, so V(m) = V(r)

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High Resistivity Measurements (R ≥1 GΩ)

Guarding Approach– significantly reduces the leakage error – improves measurement accuracy

Voltage across R(L) is essentially zero Test current I(R) flows through R(S) Source resistance can accurately be determined

Source: Low Level Measurements Handbook. 6th Edition, Keithley.

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BNC and Triaxial Connectors

Triaxial Connector– Inner shield can be driven at guard

potential to reduce cable leakage and minimize circuit rise times

Source: Low Level Measurements Handbook. 6th Edition, Keithley.

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Chamber Set-up

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Triax

Floating BNC Connector

Chamber Wall Chamber Wall

Chamber

Signal

Zero Volt

Ground

Triax 1 Triax 2

SHV

SHVSample

Black-GroundYellow-SignalBlue-Reference PotentialRed-High Voltage

Triax / BNC Feedthrough DesignSwitchbox for Triax and SHV (safety feature) Sample holder (compatible with Igor’s)

Conclusion

Literature Review– Basic understanding of conductivity (Drude Theory)– Theoretical understanding of conductivity measurements (Triax system)– Becoming familiar with literature search

Resistivity Measurement of Sample will provide– Carrier Density– Activation Energy of dopant and defects creating free carriers– Work Function with light

Chamber Design has started – Working on Triax / BNC Feedthrough Design– Conceptual work Sample Holder and Safety Features

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