Download Resistivity Measurement

Determining Carrier Density through
Measuring Resistivity
Kathleen Broughton
Ernesto Indacochea
Klaus Attenhofer
Photocathodes 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 = resistivity
Ε = magnitude of electric field
J = magnitude of current density
R = electrical resistance
l = length of material
A = cross-sectional area of material
σ = conductivity
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Current – Voltage Curve
j
j(V)=e(J(h)+J(e))(e^eV/kT -1)
j
v
-e (J(h) + J(e))
Standard I-V curve
Perceived I-V curve of
photocathode

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 Theory
E=ρ*j;
j=σ*E
σ = ne^2τ / m
E = electric field, ρ = resistivity, j = current density
σ = conductivity,
τ = relaxation time (avg. time since its last collision)
n = number of carriers, e = electrical charge, m = mass
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Sample Surface Measurements
R (b)
V
(s)
RR (s)
Sample
Bulk
Surface
V/I = R(b) + R(s)
I
R (surface) << R (bulk)
R(b)
R (s)
Bulk
Surface


V
V/I = (R(b)*R(s)) / (R(b) + R(s))
I
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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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.
7
Chamber Set-up
Signal
Chamber
Zero Volt
Ground
Chamber Wall
Black-Ground
Yellow-Signal
Blue-Reference Potential
Red-High Voltage
SHV
Chamber Wall
Floating
BNC Connector
Triax
Sample
SHV
Triax 1
Triax 2
Triax / BNC Feedthrough Design
Switchbox for Triax and SHV (safety feature)
Sample holder (compatible with Igor’s)
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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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