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

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 Theory E = ρ * j ; E = electric field, ρ = resistivity, j = current density j = σ * Eσ = conductivity, σ = ne^2τ / mτ = relaxation time (avg. time since its last collision) n = number of carriers, e = electrical charge, m = mass 3 Standard I-V curve Perceived I-V curve of photocathode jj 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) Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All" 4 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)

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" 5

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. 6 th Edition, Keithley. 6

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. 6 th Edition, Keithley. 7

Chamber Set-up Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All" 8 Triax Floating BNC Connector Chamber Wall Chamber Signal Zero Volt Ground Triax 1Triax 2 SHV Sample Black-Ground Yellow-Signal Blue-Reference Potential Red-High Voltage  Triax / BNC Feedthrough Design  Switchbox 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 Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All" 9