Lecture 15 - MIT

1 Lecture 15. The pn Junction Diode (II). Outline I-V characteristics Forward Bias Reverse Bias Reading Assignment: Howe and Sodini; Chapter 6, Sections - Spring 2007 Lecture 15 1. 1. I-V Characteristics (contd.). Diode Current equation: VVth . I = I o e 1 .. Physics of forward bias: Fn n p Fp Potential drop across SCR reduced by V. minority carrier injection in QNRs Minority carrier diffusion through QNRs Minority carrier recombination at contacts to the QNRs (and surfaces). Large supply of carriers injected into the QNRs . I e []V. Vth Spring 2007 Lecture 15 2. Fn n p Fp Physics of reverse bias: Potential drop across SCR increased by V. minority carrier extraction from QNRs Minority carrier diffusion through QNRs Minority carrier generation at surfaces & contacts of QNRs Very small supply of carriers available for extraction I saturates to small value Spring 2007 Lecture 15 3.

2 Development of analytical current model: 1. Calculate the concentration of minority carriers at edges of SCR;. 2. Find the spatial distribution of the minority carrier concentrations in each QNR;. 3. Calculate minority carrier diffusion current at SCR. edge. 4. Sum minority carrier electron and hole diffusion currents at SCR edge. (p-type) np (x) pn(x) (n-type). contact to p region contact to\. n region VD Vth VD Vth n p( x p) = n po e p n(x n) = p no e p n(W n) = p no << pno << npo np(-Wp)=npo - Wp -xp xn Wn x Reverse Bias Spring 2007 Lecture 15 4. Total and Excess Concentrations Forward Bias (Step 1). Total Carrier Concentration (n & p). np(x) pn(x). (contact) (contact). (p-type) (n-type). p n(x n). VD VD. Vth Vth n po e pnoe n p( xp ).

3 - Wp -xp xn Wn x np ( W p) = np o p n(W n) = p no Excess Carrier Concentration (n' & p') - Subtract npo and pno n' p(x) p'n(x). (contact) (contact). (p-type) (n-type). p n(x n). VD VD. Vth Vth n po (e 1) pno (e 1). n p( x p). - Wp -xp xn Wn x n p( W p) = 0 p n(W n) = 0. Spring 2007 Lecture 15 5. Steady-State Diffusion Ink Diffusion Example Flux is number of ink molecules passing a plane/cm2-sec No molecules vanish in the water (NO recombination). Ink concentration is a constant at x = 0. Ink concentration is zero at x = W (ohmic contact). Result - Ink concentration falls linearly from x=0 to x=W. fill tube ink vacuum . ink water 0 W x Injects (a). fill tube minority carriers water Carriers ink vacuum . ink recombine at ohmic contact 0 W x (b).

4 NI (x). nI*. 0 W. (c). Spring 2007 Lecture 15 6. Minority Carrier Spatial Distribution (Step 2). Concentration linearly decreases from SCR edge to ohmic contact. The expressions assumes no recombination in the QNR. n' p ( xp ) . n' p (x) = n' p ( xp ) + .. x + xp ( ). p W x p . p' n (xn ) . p' n (x) = p' n (xn ) (x xn ). Wn xn . n' p (x) p' n (x). (contact) (contact). (p-type) (n-type). p n( x n). n p( x p). -W p -x p xn Wn x n p( W p) = 0 p n( W n) = 0. Steady-state---> minority carriers are continuously injected across the junction to maintain the value at the SCR edge set by the applied bias. The same number continuously recombine at ohmic contact. Spring 2007 Lecture 15 7. Minority Carrier Diffusion Current at SCR Edge (Step 3). Gradient in minority carrier concentrations across the n & p QNRs n = no + n' ---> dn/dx = dn'/dx Transport occurs by diffusion Ignore drift component since minority carriers At -xp electron diffusion current: dn' p n' p ( x p ) 0.

5 Jn = qDn = qDn .. dx W p x p .. []V. n po (e Vth 1) .. Jn = qDn . Wp x p .. Jn = q 2. ni . Dn . e ( ) 1 . V. Vth Na Wp x p .. Spring 2007 Lecture 15 8. Sum minority carrier diffusion currents at SCR edge (Step 4). Hole diffusion current at xn by same reasoning: ni2 Dp (qV ) . Jp = q e kT 1 . Nd Wn xn . Dp ( ) 1 . qV. 2 1 Dn 1 e J = J n + J p = qni + . kT. Na Wp x p Nd Wn xn . Current is: Dp . 2 1. I = qAni . Dn +. 1. e ( ) 1 . qV. kT.. Na Wp x p N d Wn x n . Often written as: qV . kT . I = Io e 1 .. Spring 2007 Lecture 15 9. Picture of Total Diode Current Forward Bias Minority carriers are injected from the other side of the junction Minority carriers diffuse from SCR edge to the ohmic contact with no recombination and recombine at contact Total current found by summing the minority carrier diffusion currents at SCR edges and assuming no recombination in SCR.

6 N' p (x) p' n (x). (contact) (contact). (p-type) (n-type). p n( x n). n p( x p). -W p -x p xn Wn x n p( W p) = 0 p n( W n) = 0. Majority carriers are transported to the junction from the ohmic contact by drift and diffusion. J. ;;;;;. ;;;;;;;;;. (p-type) (n-type). ;. ;. metal metal J (total current density) J (total current density). ;. ;. contact to contact to p region n region Jp (majority holes) Jp (minority holes). ;. ;. Jn (minority electrons) Jn (majority electrons). ;. ;. 0 0. Wp xp xn Wn x Spring 2007 Lecture 15 10. Minority Carrier Spatial Distribution ( Reverse Bias). Diode current derivation same for forward and reverse bias. (same equations for spatial distribution). Minority carrier concentration at SCR is near zero under reverse bias.

7 Concentration linearly increases from SCR edge to ohmic contact. Minority carriers flow from contacts to SCR and are swept across the junction. (p-type) np (x) pn(x) (n-type). contact to p region contact to\. n region VD Vth VD Vth n p( x p) = n po e p n(x n) = p no e p n(W n) = p no << pno << npo np(-Wp)=npo - Wp -xp xn Wn x Steady-state---> minority carriers are continuously extracted across the junction to maintain the value at the SCR edge set by the applied bias. The same number continuously are generated at ohmic contact. Spring 2007 Lecture 15 11. I-V Characteristics Diode Current equation: . I = Io e ( ) V. Vth . 1 .. I lg |I|. q kT. =60 mV/dec @ 300K. Io 0. 0 V 0 V. Io linear scale semilogarithmic scale Spring 2007 Lecture 15 12.

8 What did we learn today? Summary of Key Concepts Diode Current can be analytically determined by summing the minority carrier current at both sides of SCR. I = Io (e [ ] qV. 1). kT. Under forward bias: Minority carriers are injected across the junction and diffuse to the contact where they recombine Under reverse bias: Minority carriers are generated at the contact and diffuse to the junction where they are extracted across the junction Spring 2007 Lecture 15 13.