Built in Potential, V 0

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1 9/5/7 Indan Insttute of Technology Jodhur, Year 7 nalog Electroncs (Course Code: EE34) Lecture 3 4: ode contd Course Instructor: hree Prakash Twar Emal: stwar@tj.ac.n Webage: htt://home.tj.ac.n/~stwar/ ote: The nformaton rovded n the sldes are taken form text books for mcroelectroncs (ncludng edra & mth, B. Razav), and varous other resources from nternet, for teachng/academc use only Bult n Potental, Because of the electrc feld n the deleton regon, there exsts a otental dro across the juncton: q E q x x d dx d n d kt ( x ) ( x ) ln ln n q n kt q d dx ln n d dx / (Unt: olts)

2 9/5/7 Bult In Potental Examle Estmate the bult n otental for P juncton below. ote that kt q ln( ) 6m.3 6m P = 7 cm -3 = 6 cm P Juncton under Reverse Bas reverse bas ncreases the otental dro across the juncton. s a result, the magntude of the electrc feld ncreases and the wdth of the deleton regon wdens. W de q R

3 9/5/7 ode Current under Reverse Bas In equlbrum, the bult n otental effectvely revents carrers from dffung across the juncton. Under reverse bas, the otental dro across the juncton ncreases; therefore, neglgble dffuon current flows. very small drft current flows, lmted by the rate at whch mnorty carrers dffuse from the qua neutral regons nto the deleton regon. P Juncton Caactance reverse based P juncton can be vewed as a caactor. The deleton wdth (W de ) and hence the juncton caactance (C j ) vares wth R. C j W de 3

4 9/5/7 oltage eendent Caactance C j C j R C j q F/cm s the ermttvty of lcon. More on the Bult In Potental ( ) Q: Why can t we harness and use the P juncton as a battery? +? : bult n otental also exsts at a juncton between a metal and a semconductor (e.g. at a contact). If we connect the P and regons together, there s no net voltage dro across the devce: (x) o net current flows across the juncton when the externally aled voltage s! bn + + b = bn b -b a x 4

5 9/5/7 The eleton roxmaton -b (x) q a x In the deleton regon on the de: Guass law de q dx q E x b In the deleton regon on the P de: de q dx q -q E a x a b Effect of led oltage The qua neutral tye and P tye regons have low restvty, whereas the deleton regon has hgh restvty. Thus, when an external voltage s aled across the dode, almost all of ths voltage s droed across the deleton regon. (Thnk of a voltage dvder crcut.) If < (reverse bas), the otental barrer to carrer dffuon s ncreased by the aled voltage. If > (forward bas), the otental barrer to carrer dffuon s reduced by the aled voltage. + I 5

6 9/5/7 P Juncton under Forward Bas forward bas decreases the otental dro across the juncton. s a result, the magntude of the electrc feld decreases and the wdth of the deleton regon narrows. (x) q a -b -q x I (x) -b a x Mnorty Carrer Injecton under Forward Bas The otental barrer to carrer dffuon s decreased by a forward bas; thus, carrers dffuse across the juncton. The carrers whch h dffuse across the juncton become mnorty carrers n the qua neutral regons; they recombne wth majorty carrers, dyng out wth dstance. n (x) x' n edge of deleton regon Equlbrum concentraton of electrons on the P de: n n x' 6

7 9/5/7 Mnorty Carrer Concentratons at the Edges of the eleton Regon The mnorty carrer concentratons at the edges of q / the deleton regon are changed by the factor e There s an excess concentraton t ( n, n ) of mnorty t carrers n the qua neutral regons, under forward bas. Wthn the qua neutral regons, the excess mnorty carrer concentratons decay exonentally wth dstance from the deleton regon, to zero: n ( x) n n ( x) n ( x) n / T e x/ Ln e J x' otaton: L n electron dffuon length (cm) dn q n kt e / Fnd the dffuon current denty q / T x/ Ln e e n, dff n qn dx Ln T ode Current under Forward Bas The current flowng across the juncton s comrsed of hole dffuon and electron dffuon comonents: J tot J, drft x J n, drft x J, dff x J n, dff x ssumng that the dffuon current comonents are constant wthn the deleton regon (.e. no recombnaton occurs n the deleton regon): q n J qnn /, T / n dff e x L, T J dff e x n L J tot J / T e where J qn n L n L 7

8 9/5/7 Current Comonents under Forward Bas For a fxed bas voltage, J tot s constant throughout the dode, but J n (x) and J (x) vary wth oton. J tot b a x I Characterstc of a P Juncton Current ncreases exonentally wth aled forward bas voltage, and saturates at a relatvely small negatve current level for reverse bas voltages. Ideal dode equaton: I I I J e / T n qn Ln L 8

9 9/5/7 Parallel P Junctons nce the current flowng across a P juncton s roortonal to ts cross sectonal area, two dentcal P junctons connected n arallel act effectvely as a ngle P juncton wth twce the cross sectonal area, hence twce the current. ode aturaton Current I I qn n Ln L I can vary by orders of magntude, deendng on the dode area, semconductor materal, and net doant concentratons. tycal range of values for P dodes: -4 to -7 /m In an asymmetrcally doed P juncton, the term assocated wth the more heavly doed de s neglgble: If the P de s much more heavly doed, I qn L If the de s much more heavly doed, I qn n Ln 9

10 9/5/7 P Juncton Contd What next