Summary electrons in solids eb o o?8cos8oo 9690969090090066 F(E F(E At low temperature all electrons are in the lowest possible energy level below the fermi level As the temperature increase some electrons will go above the fermi level But only those with an energy above the fermi level greater than the work function are "free
16 Summary: electrons in solids • At low temperature all electrons are in the lowest possible energy level, below the Fermi level. • As the temperature increase some electrons will go above the Fermi level. • But only those with an energy above the Fermi level greater than the work function are “free”. (image source: http://cnx.org/content/m13458/lates t/
Thermionic emissⅰon The richardson-Dushman equation gives the electronic current density j(A/m )emitted by a material as a function of the temperatur = ATe 2 With a the richardson constant. 4mk e A =1.2.10 h'3 m-K k了=a/100 0.8 E0 0.6 0.4 0.2 kT=站 (image source kT=/10 Masao Kuriki,∥ LC schoo 0 0 1 2 3
17 Thermionic emission • The Richardson-Dushman equation gives the electronic current density J (A/m-2 ) emitted by a material as a function of the temperature: With A the Richardson constant: (image source: Masao Kuriki, ILC school)
Thermionic cathode material Two parameters are important when considering a thermionic cathode material W=Work function ( as low as possible) Te=Operation Temperature(preferably high Cesium has a low work function ( W2ev but a low operation temperature(Te=320K not good for high current Metals: Ta(4.1ev, 2680K), W(4.5eV, 2860K Bao has good properties (lev; 1000k but can oxidize by exposure to air = sinter of Ba0+W Bao provided slowly to the surface
18 Thermionic cathode material • Two parameters are important when considering a thermionic cathode material: – W=Work function (as low as possible) – Te=Operation Temperature (preferably high) • Cesium has a low work function (W~2eV) but a low operation temperature (Te=320K) => not good for high current • Metals: Ta (4.1eV, 2680K), W(4.5eV, 2860K) • BaO has good properties (1eV; 1000K) but can oxidize by exposure to air => sinter of BaO+W BaO provided slowly to the surface
field enhanced thermionic emission Under a very intense electric vacuum level field some electrons will be able to tunnel across the Fermi level potential barrier and become E tunnel distance free This is known as field effect emission (image source: answers. com)
19 field enhanced thermionic emission (image source: answers.com) ⚫ Under a very intense electric field some electrons will be able to tunnel across the potential barrier and become free. ⚫ This is known as field effect emission
Electric field bias Once the electrons are free they may fall back on the cathode To avoid this an electric field needs to be applied If a negative potential is applied to the cathode the electrons will be attracted away from the cathode after being emitted However this field affects the work functⅰon 6o609oos Ooo F(E 20
20 Electric field bias • Once the electrons are free they may fall back on the cathode. • To avoid this an electric field needs to be applied. • If a negative potential is applied to the cathode the electrons will be attracted away from the cathode after being emitted. • However this field affects the work function