Deepak Rajput

Transcription

1 General quetion about eletron and hole: A 1a) What ditinguihe an eletron from a hole? An) An eletron i a fundamental partile wherea hole i jut a onept. Eletron arry negative harge wherea hole are onidered to arry poitive harge. Hole i better undertood a abene of eletron from it poition and annot be explained without eletron. A 1b) Doe a large effetive ma orrepond to a band with large urvature or mall urvature? An) Large effetive ma orrepond to a mall urvature. A 1) If you have an eletri field pointing from left to right, in whih diretion doe a hole move? Whih diretion doe eletron move? An) Hole move from left to right wherea eletron move from right to left. A ) Suppoe we have a ondution band and a valene band with energie (k) and v (k) repetively given by r r h r r ( k ) = ( k ) + ( k k ) * m r r h r r v ( k ) = v ( kv ) + ( k k ) * v m A a) For thee two band, what doe the bandgap equal? An) andgap (E g ) i defined a the differene in energy of highet oupied level and energy of lowet oupied level. r r andgap (E g ) = k ) ( k ) ( v v v A b) What are the mae of the hole and of the eletron? * * An) Ma of hole i repreented by and that for eletron i. m v m A ) At time t = 0 and eletron ha a wave vetor k r 0. It i ubjeted to an eletri field E r for a time Δt. What i it wave vetor at time Δt? What i it hange in energy? (Ignore attering) An) 1 The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee

2 A d) If a magneti field r had been applied intead, what would the fore on the eletron be at time t = 0? An) A ) Some general quetion about emiondutor phyi A a) What i meant by an indiret bandgap? An) An indiret bandgap i a bandgap in whih the minimum energy in the ondution band i hifted by a k-vetor relative to the valene band. Thi hift in k-vetor (q) repreent a differene in momentum. Condution band q E g Valene band K r A b) If a emiondutor with an indiret bandgap aborb a photon, what additional thing i needed to enure rytal momentum i onerved? An) A phonon i needed. It will hange the wave vetor of eletron to onerve it rytal momentum. A ) Are the eletron in the ondution gap uually degenerate? Why? An) No, the eletron in the ondution gap are uually not degenerate beaue μ >> k T. Fermi funtion deribe the oupany of degenerate eletron a β f ( ) = e ( μ ) 1 kβt + 1 The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee

3 A d) In any intrini emiondutor what i the ratio of the number of eletron to the number of hole? An) 1 A e) What i the expreion for the energy of the hallow point defet? An) The expreion for the energy of the hallow point effet i different for donor ( D ) and aeptor ( A ). * me 1 D = X1. 6eV m e r * mh 1 A = v + X1. 6eV m e r A f) Sketh the graph of the logarithm of the eletron onentration againt the phyial explanation of the four region? An) ln(eletron onentration) 1. What are k β T K β 1T A g) How do the relaxation time for impurity and phonon attering vary with temperature? An) For impurity the relaxation time varie a T / wherea for phonon attering it varie a T -/. A h) What i meant by arrier reombination? An) Carrier reombination i an effet where an eletron oupie the tate of a hole and nullifie it effet. The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee

4 A i) What i a heterojuntion? An) Heterojuntion i a juntion made by a p-doped and an n-doped emiondutor. A j) How doe the eletron hemial potential vary with poition in a heterojuntion at equilibrium? An) At equilibrium, there no effet of poition on eletron hemial potential. A k) What i a depletion zone? An) In emiondutor, depletion zone i an inulating region within a ondutive, doped emiondutor material where the harge arrier have been wept away through harge reombination. Charge reombination i an effet where an eletron oupie the tate of a hole and nullifie it effet. A l) In a bipolar tranitor, what i the purpoe of the olletor? An) The main purpoe of the olletor in a bipolar tranitor i to remove the harge arrier introdued by the emitter into the bae. Solid State Phyi Aignment Submitted by: Deepak Rajput 4 The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee

5 1a) What i the relation between magneti field, magneti indution and magnetization? An) = μ(m + H), where μ i the magneti permeability Eletromagneti field ompoe of two part: Eletri field (E) and Magneti field (H). Thu, magneti field i a part of eletromagneti field and i reponible for exerting a fore on a moving harge. It an be aued by a moving harge or a hanging eletri field. It SI unit i Tela (T). Magneti field (H) and Magneti indution () are equal in vauum. Magnetization (M) i defined a the total magneti moment per unit volume. In other word, it i the magneti field whih material itelf produe. Magnetization (M) and Magneti field (H) are related by a term known a Magneti Sueptibility (χ) a: M = χh. Magneti ueptibility i defined a the degree of magnetization of material when plaed in a magneti field. 1b) What i the differene between diamagnetim and paramagnetim? An) Diamagnetim and Paramagnetim are different form of Magnetim. oth of them are exhibited by ubtane in the preene of an externally applied magneti field. Diamagneti material are not affeted when plaed in a magneti field wherea Paramagneti material are weakly affeted i.e. they beome magnetized in the preene of magneti field but loe their magneti propertie when the magneti field i removed. In other word, when plaed in a magneti field, flux denity i more inide a paramagneti material than in a diamagneti material. They an be differentiated by the propertie of magneti ueptibility a well. Diamagneti ueptibility Paramagneti ueptibility Negative i.e. < 0 Poitive i.e. > 0 Typially in range of 10-6 to 10-5 Typially in range of 10-5 to 10 - Temperature independent Temperature dependent 1) Under what ondition doe Curie law apply? An) Curie law an be expreed a: C χ = Or M = C, where χ i the magneti ueptibility, C i Curie ontant, M i T T magnetization, i magneti indution and T i temperature. Curie ontant i material ontant and i different for different material. Thi law i appliable for paramagneti material; it tate that magneti ueptibilitie of mot paramagneti material are inverely proportional to their abolute temperature. It i true only for paramagneti material and hene one of the ondition. It i appliable only when the magneti field i weak. Thi law hold true only at high temperature. 1d) In an atom, whih interation lead to the total pin being maximized? Why i thi relevant to magnetim? An) Exhange interation i the ondition whih favor pin to align parallel and it maximize the total pin. Total pin define the magneti moment of the material and hene it important to magnetim. 5 The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee

6 1e) In the firt tranition erie of the periodi table, why i the magneti moment not well aounted for by Hund rule? An) For the firt tranition erie of the periodi table, atual magneti moment value don t math with thoe alulated uing Hund rule. It happen beaue of rytal field plitting. In eletroni d tate, two tate point diretly toward neighboring ion and three tate point between neighbor. Thee tate have different eletrotati energie. So the d tate are loked to the rytal, and no longer behave like an l= tate with l+1 degenerate m value. Thi phenomenon i alled a quenhing of the orbital angular momentum. It i found that the magneti moment in the firt tranition erie arie almot entirely from pin and angular momentum doen t affet them. 1f) What interation ouple pin together to produe a ferromagnet? An) Poitive exhange interation ouple pin together to produe a ferromagnet. 1g) Why do magneti domain form? An) In hort, magneti domain form in order to redue the total energy of the ytem. a) For a free eletron (l = 0, j = = 1/), what doe the Lande g fator equal? An) The expreion for Lande g fator (g J ) an be written a: For l = 0, j = = ½ g J = S( S + 1) L( L + 1) + J ( J + 1) g J = olution b) Suppoing we ould deribe a free eletron ga with the Curie law (whih we annot), what would the ueptibility be? μ ng J An) The expreion for Curie law an be written a J 0 J μ ( + 1) C χ = (i.e. χ = ) k T T (referred page 19, Chiranjib Mitra). Taking J = ½ and g J = (at room temperature, referred μ0nμ page 190, Chiranjib Mitra), we get χ =. k T β β ) y omparing the reult for the ueptibility you have jut obtained with that derived by Pauli, how that the effetive temperature of the eletron i E F /k β, where E F i the Fermi energy. Why doe thi make ene? An) The expreion for ueptibility given by Pauli an be written a: 6 The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee

7 d) For a pin 1 ytem we have the rillouin funtion being given approximately by J (x) x x, where μ λm M x = kt M and M i the magnetization, λm i the Wei field and M i the aturation magnetization. Hene, uing the mean field ondition M = (x) M J, how that pontaneou magnetization an our provided that k An) M M k T T < μ λm. kβt = x, whih i alo equal to J (x) i.e. x x μ λm β => x = μ λm x x kβt x => x 1 = 0 μ λm kβt x => either x = 0 or 1 = 0 μ λm kβt x => 1 = μ λm k => = ± βt x 1 μ M λ x mut be real and poitive for pontaneou magnetization to our i.e. x > 0 kβt => < 1 μ λ M => kβ T < μλm, hene the ondition for pontaneou magnetization General quetion about uperondutivity: a) What i the prinipal harateriti of uperondutivity? An) A uperondutor ha very high ondutivity and it an behave like a ondutor with no meaurable DC eletrial reitivity. It an behave like a perfet diamagnet. It uually behave a if there were a gap in energy with Δ entered about the Fermi energy, in the et of allowed oneeletron level. Thu an eletron of energy an be aommodated by a uperondutor only if F exeed Δ. The energy gap Δ inreae in ize a the temperature drop, leveling off to maximum value Δ(0) at very low temperature. 7 The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee

8 b) What i Meiner effet and what i the phyial mehanim behind it? An) Meiner effet or Meinner-Ohenfeld effet i the effet by whih a weak magneti field deay rapidly to zero inide a uperondutor. If a metal i kept in a magneti field and ooled below it uperonduting tranition temperature, then the magneti flux inide the metal i abruptly expelled. Thi effet i alled a Meiner effet. ) What i the differene between Type I and Type II uperondutor? An) Type I la of uperondutor mainly onit of metal and metalloid, and how ome ondutivity at room temperature, wherea Type II la of uperondutor mainly onit of metalli ompound and alloy. Type I uperondutor require very low temperature to how uperondutivity and their urfae energy i poitive (λ < ξ) wherea Type II uperondutor have negative urfae energy (λ > ξ). Type II uperondutor have muh higher ritial field and therefore an arry muh higher urrent denitie while remaining in uperonduting tate. Type I: elow a ritial field H (T) that inreae a T fall below T, there i no penetration of flux; when the applied field exeed H (T) the entire peimen revert to the normal tate and the field penetrate perfetly. Type II: elow a lower ritial field H 1 (T) there i no penetration of flux; when the applied field exeed an upper ritial field H (T) > H 1 (T), the entire peimen revert to the normal tate and the field penetrate perfetly. When the applied field trength i between H 1 (T) and H (T), there i partial penetration of flux, and the material develop a ompliated miroopi truture of both normal and uperonduting region, known a mixed tate. d) What i the phyial mehanim that generate the uperonduting eletron? An) It a known fat that warmer the material the more i it lattie vibration and onverely, the older the material the le i it lattie vibration. In ae of uperondutor, eletron pair up into team (alo alled a Cooper pair) and pa all the obtale whih aue reitane in the ondutor. It beaue of thi pairing up of eletron whih generate uperonduting eletron. Solid State Phyi Aignment Submitted by: Deepak Rajput 8 The Univerity of Tenneee Spae Intitute, Tullahoma, Tenneee