9/1/1 ECE 34 Lecture 6 : Intrinsic and Extrinsic Material I Class Outline: Things you should know when you leave Key Questions What is the physical meaning of the effective mass What does a negative effective mass mean? What is intrinsic material? What is thermal equilibrium? What is extrinsic material? How does doping work? Extrinsic Material At the end of lecture 5, we talked about effective mass Electric Field dv = qe = m dt F We even defined the effective mass We can define the effective mass as: * m = d E / dk Electric Field * dv F = qe = mn dt 1
9/1/1 Let s begin to think about where effective mass comes from Ψ(x) k k Start with the energy-wavevector (dispersion) relation for free electrons: k (6.1) E E k = m 1 de v g = dk (6.) What are the forces that the electron is experiencing? Ψ(x) k k ee δk = where, dk = ee dt field field δt = F E v g δ E = ee v δ t (6.3) field We observe that by using eq. 6. δe 1 d E = F dk de δk = vgδk dk g = (6.4) dv g d E 1 d E dk = = dt dkdt dk dt Simple Example Consider a simple cosine approximation to the band: Sample parameters W (Band Width) ~ 5 ev a (lattice spacing) ~.5 nm 5 E( k) = 1 W ( 1 cos ka) = W sin ka E( k) ev The group velocity goes to zero!! What about the effective mass?.3 π π Effective mass: a a -.3 m m a W ( k) = sec( ka) * v g ( ) 1 de k aw ( k) = = sin( ka) v π g (k) dk a π a
9/1/1 is pure with no additional contaminants But there are more processes at work T = K T = 3 K G = G Generation Rate: + G + G 1 +... cm s th opt mech 3 Since we are in thermal equilibrium, there must be an opposite process In the steady state Recombination Rate: 1 n p cm s R 3 = N number of electrons P number of holes = R n p ni n = p n = p = ni G = 3
9/1/1 Putting numbers to the intrinsic concentrations Extrinsic Semiconductors The great strength of semiconductors Silicon n i ~ 1 1 cm -3 Germanium n i ~ x 1 13 cm -3 GaAs n i ~ x 1 6 cm -3 For silicon 5 x 1 3 atoms/cm 3 4 bonds per atom x 1 3 bonds/cm 3 n i (3 K) ~ 1 1 cm -3 1 broken bond per 1 13 bonds. How does a donor work? Silicon (Si) 4 valence electrons Phosphorous (P) 5 valence electrons How does an acceptor work? Silicon (Si) 4 valence electrons Boron (B) 3 valence electrons Si! B 4
9/1/1 In general, we can modify the materials properties with the introduction of immobile impurity atoms How tightly bound is the extra electron or hole? h + e - Donor Acceptor * 4 mnq EB = 3 π ( ε ε ) r Donor in Si P As Sb Binding energy (ev).45.54.39 r Acceptor in Si B Al Ga In Binding energy (ev).45.67.7.16 M.J. Gilbert ECE 34 Lecture 6 9/1/1 Visualizing donors on the band diagram Extrinsic Material Remember the intrinsic concentrations E c E c Δx E d E a E v E v Let s take a look at Silicon with Phosphorus impurity atoms: Silicon n i ~ 1 1 cm -3 Germanium n i ~ x 1 13 cm -3 E c.45 ev For silicon E d 5 x 1 3 atoms/cm 3 E g = 1.1 ev 4 bonds per atom GaAs x 1 3 bonds/cm 3 n i ~ x 1 6 cm -3 n i (3 K) ~ 1 1 cm -3 E v 1 broken bond per 1 13 bonds. M.J. Gilbert ECE 34 Lecture 6 9/1/1 M.J. Gilbert ECE 34 Lecture 6 9/1/1 5
9/1/1 Revisiting the effect of temperature Extrinsic Material Commonly used terms: Dopants specific impurity atoms that are added to semiconductors in controlled amounts for the express purpose of increasing either the electron or hole concentrations. Intrinsic semiconductor undoped semiconductor; extremely pure semiconductor sample containing an insignificant amount of impurity atoms; a semiconductor whose properties are native to the material. Extrinsic semiconductor doped semiconductor; a semiconductor whose properties are controlled by added impurity atoms. T = K T = 5 K T = 3 K Donor impurity atom that increases the electron concentration; n-type dopant. Acceptor impurity atom that increases the hole concentration; p-type dopant. N-type material a donor doped material; a semiconductor containing more electrons than holes. P-type material an acceptor doped material; a semiconductor containing more holes than electrons. Majority carrier the most abundant carrier in a given semiconductor sample; electrons in n- type and holes in p-type. Minority carrier the least abundant carrier in a given semiconductor sample; electrons in p- type and holes in n-type. M.J. Gilbert ECE 34 Lecture 6 9/1/1 M.J. Gilbert ECE 34 Lecture 6 9/1/1 6