23and4intoe eq1yields s j e current i c 4 5

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Unformatted text preview: esistance o I = Current Recall R and I J A 1 l l A A V El and In nsertion of E Eq. (2), (3), and (4) into E Eq. (1) yields s J E Current = I = C (4) (5) e number of electron r ns e n v Area unit time u J e nv o o o o (3) e nu umber of electrons charge unit time e unit time Current densi = J C ity (2) e = ele ementary ch harge = 1.602 2 × 10–19 C n = co oncentration n of electrons per cm3 v = av verage veloci ity of electro ons = co onductivity Chapter 1 – page 3 (6) Derivation of: D J e nv (7) o Consid der electron ns in a volum me V = A dx o N elec ctrons are in nside the volume N o Conce entration = n A dx dx o The av verage veloc city of carrie ers is = v dt e N e N dx o Current density: = J = e n v A dt A dx dt o … wha at was to be shown Chapter 1 – page 4 Conductiv vity and resi stivity Resistivity = Conductivity = dimension ( () = cm dimension ( () = –1 cm–1 = S cm–1 m y shows a large variation n The resistivity How many or H rders of mag gnitude? Reason for th he large varia ation: Conce entration of electrons: o Insula ator: All elec ctrons are tig ghtly bound to atoms o Metal l: Electrons can freely y move abou ut the metal o Semic conductor: Some e electrons can n freely mov ve about the e crystal o What is the reaso on for these c conductivity y differences s? Chemical n nature of ele ement or compound es in the chemical bond Difference Differe ence in numb ber of free e electrons o Examp ples: 3 Metal: n = 1022 cm–3 3 Semicondu uctor: n = 1015 – 1 20 cm–3 10 5 –3 Insulator: n = 10 cm 3 Chapter 1 – page 5 Free ele ectrons in a s solid Chemical model: Electron n is not local lized in a par rticular chem mical bond Ex xamples: acuum = truly free e electron Electron in va Electron in a solid = quasi‐free electron Free electron ns = fre ee to move a...
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