p/n junction Isolated p, n regions: no electric contact, not in equilibrium E vac E i E A E F E V E C E D

Transcription

1 / juctio Isolated, regios: o electric cotact, ot i equilibrium E vac E C E C E E F E i E i E F E E V E V

2 / juctio I equilibrium, the Fermi level must be costat. Shift the eergy levels i ad regios u/dow to alig E F : electro eergy E vac E C E vac E i E C E E F E E V E i Electros ted to lowest available eergy: The juctio must have a electric field oitig from to. E V

3 / juctio Fid otetial differece (voltage): //-side work fuctio E E E E E E vac F vac C C F E E E E F V C V NV kt l E N NC NV qv Eg kt l N N Eg kt i e Eg ktl N N N N qv kt l i g qv E E E E vac vac F F Equilibrium: EF EF EF Built-i voltage: //-side work fuctio E E E E E E vac F vac C C F NC kt l N usig: N N e i C V C V N N e V bi i E E g g kt kt kt N N l q i

4 eletio aroximatio: sace-charge regio ssume the regios directly adjacet to the juctio o either side are comletely deleted of free carriers. ioized accetors metallurgical juctio ioized doors holes electros w w x eutral regio deletio regio or sace-charge regio eutral regio This is called the deletio regio or sace-charge regio (SCR).

5 eletio aroximatio: charge desity xx N free carriers We are left with ioized accetors ad doors i the SCR ioized doats - - et charge desity - N N x N x N x xxn xn x N N eletio aroximatio or abrut sace-charge arox., xw, N w x x N, x w, w x N

6 eletio aroximatio: electric field Ε x x dε qx dx //Poisso equatio Ε max No et charge: Ε Ε outside of SCR No surface charge: E E x x, xw qn x w, w x q x Ε dx x qn w x, x w, w x Ε max N w N w qn w qn w a d

7 eletio aroximatio: otetial V x V bi w w x dv Ε dx, xw qn x w, w x Ε V x x dx x q N w N w w x, x w q N w N w, w x So: V q N w N w bi

8 eletio aroximatio: deletio width w N w w N N N w 1 1 q 1 1 q V N w N w bi N N N N w 1 1 V bi N q 1 1 N N w 1 1 V bi N q 1 1 N N The deletio width is: bi ww V 1 1 w q N N

9 eletio aroximatio: eergy diagram electro eergy V bi E vac E C E E F E E i E V

10 / juctio: No-equilibrium (I) Exteral voltage (e.g., alied bias or hotovoltage): w xw Ε q x dx N w N w Vbi V Vbi V 1 1 ww w q N N I the eutral regios: N e N e i i E E kt i F E E kt F i I the SCR: E E F F E E F F F F i i NN e e i E E E E kt q V V kt i bi E E q V V F F bi N N kt l i qv The quasi-fermi level slittig i the SCR equals the exteral voltage.

11 / juctio: No-equilibrium (II) Forward bias: electro eergy V + - E Vbi V E vac E C E E F E E F E i E V V bi V w 1 1 q N N a d

12 / Juctio: No equilibrium (III) First, aalyze without hotogeeratio: E C E EF E F qv E F EF E i E E V w w

13 / juctio: o-equilibrium (IV) First, aalyze without hotogeeratio: Far from the juctio: I the SCR: i kt e N N i i where: qv The deletio aroximatio gives: w N w qv kt e w w N qv kt e Excess miority-carrier cocetratios at the edges of the SCR: w w qv kt e 1 w w qv kt e 1

14 Photogeeratio Rate bsortio: bsortio coefficiet Sectral hoto flux desity i material d b E x E x b E x dx,,, bx db x xdxx bbb x b x l x b be, x be,e uiform //treat each E searately //searatio of variables Ex Carrier geeratio rate: d dx, be, x g E x EbE, x g E, x 1 R E E b E e s, 1 b E R E bs E E x

15 / juctio solar cell (I) Photogeeratio: o atteuatio Ex e 1, 1 s 1 g Ex RE E b E g E Gx degeg E //ssume weak absortio //uiform geeratio G G G //bad-to-bad absortio I steady-state: -side -side g g g G U G g G U G g G g G

16 / juctio solar cell (II) With uiform hotogeeratio, there are excess miority carriers i the eutral regios, so the quasi-fermi levels are slit. E EF E F qv E C E EF E F E i E V w w

17 / juctio solar cell (III) Cosider geeratio i the quasi-eutral regios (assumig uiform geeratio). -side -side Outside the SCR: x x x x t the edges of the SCR: w w w w The carrier cocetratios are still related to the quasi Fermi-level sittig: w qv kt e w qv kt e So the excess miority-carrier cocetratio at the edges of the SCR are: qv kt e qv kt w e 1 g g qv kt e w qv kt e 1 g g

18 / juctio solar cell (IV) Total curret desity: J J x J x //must be costat at ay oit i circuit sig covetio for PV Positive J whe device is deliverig ower Calculate usig: J JwJw or: J J w J w eletio arox: ll the otetial differece occurs across the SCR. So, E= at the SCR edges: x w, x w d d J qε q q dx dx d d J qε q q dx dx

19 / juctio solar cell (V) I the eutral regios, we have diffusio oly: x e B e x w L x w L xw L x e B e x w L x w w x ssume ifiitely thick eutral regios. The boudary coditios give: x w e w x e xw L xw L x w w x B The currets are: d q Jxq x dx L d q J xq x dx L Usig revious results: qv kt w e 1 g q J w w L q J w w L qv kt w e 1 g q J w qv kt e 1 g L q qv kt J w e 1 L g

20 / Juctio solar cell (VI) We have J w ad J w To fid J J w J w J w J w we eed either: or,scr J w J w J w J w J w J w,scr where,scr w J w q U x G x dx J,rec xw J,ge,SCR w J w q U x G x dx J,rec xw J,ge

21 / Juctio solar cell (VII) ssume: J,rec J J q G dx q G w,ge,ge w xw,scr,scr J,rec J w J w qgw //o recombiatio i SCR //uiform geeratio i SCR Just eed oe or the other. Let's fid J J w Jw We kow: q qv kt J w e 1 L g J,SCR w qgw q J w e 1 L J w JwJ,SCR w qv kt g q qv kt J w JwJ,SCR wqgw e 1 gqgw L

22 / Juctio solar cell (VIII) Use: J J w J w q qv kt J w e 1 L g q qv kt J w qgw e 1 gqgw L q L q G qgl g L q L q G qgl g L q qv kt J w e 1qGL L q J w e 1 qg L w L qv kt

23 / Juctio solar cell (IX) q q J qg wl L L L qv kt e 1 qv kt J J J e 1 hoto J qg wll hoto //hotocurret J q q i L L L N L N //dark curret qv kt J V Jhoto J e 1

24 SCR trasit time Ca we igore recombiatio i the SCR? Estimate trasit time across SCR: v E E max E max 1 E= E max qn w qn w q 1 w 1 1 N N 1 1 q N N a d 1 Emax v w w w w w v E max Emax q 1 w 1 1 N N 1 N w w 1 1 N N ssume: 1 cm 1 Vs N N 1 cm s Short comared to tyical miority carrier lifetimes.

25 Plots: deletio arox. (I) equilibrium (V= V, G=): o miority-carrier coc. gradiets i eutral regios o quasi-fermi level slittig i SCR

26 Plots: deletio arox. (II) forward bias, o illumiatio (V=.5 V, G=): miority-carrier coc. gradiets i eutral regios diffusio away from SCR ositive quasi-fermi level slittig i SCR

27 Plots: deletio arox. (III) short circuit, illumiated (V= V, G=5e19 1/cm 3 /s): miority-carrier coc. gradiets i eutral regios diffusio towards SCR o quasi-fermi level slittig

28 Plots: deletio arox. (IV) oeratig, illumiated (V=.5 V, G=5e19 1/cm 3 /s): miority-carrier coc. gradiets i eutral regios diffusio towards SCR ositive quasi-fermi level slittig i SCR

29 Plots: carrier cocetratios i deletio arox. N N i N qv kt e i N qv kt e forward bias, o geeratio i N electro diffusio hole diffusio i N w w N electro diffusio hole diffusio N i N i N g i N qv kt e i N qv kt e i N N i g forward bias with geeratio w w

30 Solvig / homojuctio characteristics without the deletio arox. dv dx qx //Poisso equatio de F J dx de F J dx //electro curret //hole curret 1 dj G U qdx //electro cotiuity 1 dj qdx G U //hole cotiuity

31 equilibirium (V= V, G=): Plots: o deletio arox. (I) E i E C E F E F E V U G J J J tot

32 Plots: o deletio arox. (II) forward bias, o geeratio (V=.7 V, G=): E F Ei E C EF E V U J J tot J G-U

33 Plots: o deletio arox. (III) oeratig, illumiated (V=.7 V, G=1e3 1/cm 3 /s): E C E F E F E i E V G del. arox.: dashed lies full calc.: solid lies U G-U J J J tot