Determining Carrier Density through Measuring Resistivity

1. Determining Carrier Density through Measuring Resistivity Kathleen Broughton Ernesto Indacochea Klaus Attenhofer Photocathodes Group

2. 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 Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"

3. Current – Voltage Curve j(V)=e(J(h)+J(e))(e^eV/kT -1) • 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 ; E = electric field, ρ = resistivity, j = current density j = 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 -e (J(h) + J(e)) Standard I-V curve Perceived I-V curve of photocathode j j v

4. 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) V/I = R(b) + R(s) R (s) R (s) V/I = (R(b)*R(s)) / (R(b) + R(s)) Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All" R (b) V Sample R (s) Bulk Surface I R (surface) << R (bulk) V R(b) Bulk Surface I

5. 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) Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"

6. 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.

7. 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.

8. Chamber Set-up Floating BNC Connector Triax • Triax / BNC Feedthrough Design • Switchbox for Triax and SHV (safety feature) • Sample holder (compatible with Igor’s) Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All" Signal Zero Volt Chamber Ground Chamber Wall Chamber Wall Black-Ground Yellow-Signal Blue-Reference Potential Red-High Voltage SHV Sample SHV Triax 1 Triax 2

9. 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 Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"