Lecture 15  The pn Junction Diode (I) IV Characteristics. November 1, 2005


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1 Microelectronic Devices and Circuits  Fall 2005 Lecture 151 Lecture 15  The pn Junction Diode (I) IV Characteristics November 1, 2005 Contents: 1. pn junction under bias 2. IV characteristics Reading assignment: Howe and Sodini, Ch. 6,
2 Microelectronic Devices and Circuits  Fall 2005 Lecture 152 Key questions Why does the pn junction diode exhibit current rectification? Why does the junction current in forward bias increase as exp qv? What are the leading dependences of the saturation current (the factor in front of the exponential)?
3 Microelectronic Devices and Circuits  Fall 2005 Lecture PN junction under bias Focus on intrinsic region: n type p type x p type (N a ) (a) p metal contact to p side x = 0 x (N d ) n (b) metal contact to n side Upon application of voltage: electrostatics upset: depletion region widens or shrinks current flows (with rectifying behavior) carrier charge storage
4 Microelectronic Devices and Circuits  Fall 2005 Lecture 154 Carrier profiles in thermal equilibrium: log po, no Na po no Nd ni 2 Na ni 2 Nd 0 x J diff h J drift h J diff e J drift e Inside SCR in thermal equilibrium: dynamic balance between drift and diffusion for electrons and holes. J drift = J diff
5 Microelectronic Devices and Circuits  Fall 2005 Lecture 155 Carrier concentrations in pn junction under bias: for V>0, φ B V E SCR J drift log p, n Na po no Nd n p ni 2 Na ni 2 Nd 0 x J diff h J drift h J diff e J drift e J h J e Current balance in SCR broken: J drift < J diff Net diffusion current in SCR minority carrier injection into QNR s excess minority carrier concentrations in QNR s Lots of majority carriers in QNR s current can be high.
6 Microelectronic Devices and Circuits  Fall 2005 Lecture 156 for V<0, φ B V E SCR J drift log p, n Na po no Nd ni 2 Na n 0 p ni 2 Nd x J h J e J diff h J drift h J diff e J drift e Current balance in SCR broken: J drift > J diff Net drift current in SCR minority carrier extraction from QNR s deficit of minority carrier concentrations in QNR s Few minority carriers in QNR s current small.
7 Microelectronic Devices and Circuits  Fall 2005 Lecture 157 What happens if minority carrier concentrations in QNR change from equilibrium? Balance between generation and recombination broken In thermal equilibrium: rate of break up of SiSi bonds balanced by rate of formation of bonds SiSi bond generation recombination n o + p o If minority carrier injection: carrier concentration above equilibrium recombination prevails SiSi bond recombination n + p If minority carrier extraction: carrier concentrations below equilibrium generation prevails SiSi bond generation n + p
8 Microelectronic Devices and Circuits  Fall 2005 Lecture 158 Where does generation and recombination take place? In modern devices, recombination mainly takes place at surfaces: perfect crystalline periodicity broken at a surface lots of broken bonds: generation and recombination centers modern devices are very small high area to volume ratio. High generation and recombination activity at surfaces carrier concentrations cannot deviate much from equilibrium values: n(s) n o, p(s) p o
9 Microelectronic Devices and Circuits  Fall 2005 Lecture 159 Complete physical picture for pn diode under bias: Forward bias: injected minority carriers diffuse through QNR recombine at semiconductor surface log p, n Na po no Nd n p ni 2 Na ni 2 Nd 0 x Reverse bias: minority carriers extracted by SCR generated at surface and diffuse through QNR log p, n Na po no Nd ni 2 Na n 0 p ni 2 Nd x
10 Microelectronic Devices and Circuits  Fall 2005 Lecture The current view: Forward bias: p n hole injection and recombination at surface electron injection and recombination at surface I=I n +I p Reverse bias: p n hole generation at surface and extraction electron generation at surface and extraction I=I n +I p
11 Microelectronic Devices and Circuits  Fall 2005 Lecture What limits the magnitude of the diode current? not generation or recombination rate at surfaces not injection or extraction rates through SCR diffusion rate through QNR s p n hole injection and recombination at surface electron injection and recombination at surface W p x p x n W n x Development of analytical current model: 1. Calculate concentration of minority carriers at edges of SCR, p(x n ) and n( x p ) 2. calculate minority carrier diffusion current in each QNR, I n and I p 3. sum electron and hole diffusion currents, I = I n + I p
12 Microelectronic Devices and Circuits  Fall 2005 Lecture IV characteristics Step 1: computation of minority carrier boundary conditions at edges of SCR In thermal equilibrium in SCR, J drift = J diff, and and n o (x 1 ) n o (x 2 ) = exp q[φ(x 1) φ(x 2 )] p o (x 1 ) p o (x 2 ) = exp q[φ(x 1) φ(x 2 )] Under bias in SCR, J drift = J diff, but if difference small with respect to absolute values of current: and n(x 1 ) n(x 2 ) exp q[φ(x 1) φ(x 2 )] p(x 1 ) p(x 2 ) exp q[φ(x 1) φ(x 2 )] This is called quasiequilibrium.
13 Microelectronic Devices and Circuits  Fall 2005 Lecture p  + n pqnr SCR φ nqnr 0 φ B V xp φ B 0 xn x At edges of SCR, then: n(x n ) n( x p ) exp q[φ(x n) φ( x p )] = exp q(φ B V ) and p(x n ) p( x p ) exp q[φ(x n) φ( x p )] = exp q(φ B V ) But: p( x p ) N a and n(x n ) N d This is the lowlevel injection approximation [will discuss in more detail next time].
14 Microelectronic Devices and Circuits  Fall 2005 Lecture Then: and Builtin potential: n( x p ) N d exp q(v φ B) p(x n ) N a exp q(v φ B) Plug in above and get: and φ B = q ln N dn a n 2 i n( x p ) n2 i N a exp qv p(x n ) n2 i N d exp qv
15 Microelectronic Devices and Circuits  Fall 2005 Lecture Voltage dependence: Equilibrium (V = 0): Forward (V >0): n( x p )= n2 i N a p(x n )= n2 i N d n( x p ) n2 i N a p(x n ) n2 i N d Lots of carriers available for injection: V concentration of injected carriers forward current can be high. Reverse (V < 0): n( x p ) n2 i N a p(x n ) n2 i N d Few carriers available for extraction: reverse current is small. Minority carrier concentration becomes vanishingly small: reverse current saturates. Rectification property of pn diode arises from minoritycarrier boundary conditions at edges of SCR.
16 Microelectronic Devices and Circuits  Fall 2005 Lecture Step 2: Diffusion current in QNR: Diffusion equation (for electrons in pqnr): J n = qd n dn dx Inside pqnr, electrons diffuse to reach and recombine at contact J n constant in pqnr n(x) linear. n(x p ) n n(x) n i 2 N a W p Boundary conditions: x p 0 x n(x = W p )=n o = n2 i N a n( x p )= n2 i N a exp qv Electron profile: n p (x) =n p ( x p )+ n p( x p ) n p ( W p ) x p + W p (x + x p )
17 Microelectronic Devices and Circuits  Fall 2005 Lecture n p (x) =n p ( x p )+ n p( x p ) n p ( W p ) x p + W p (x + x p ) Electron current density: dn J n = qd n dx = qd n p ( x p ) n p ( W p ) n W p x p or = qd n n2 i N a exp qv n2 i N a W p x p J n = q n2 i D n (exp qv N a W p x p 1)
18 Microelectronic Devices and Circuits  Fall 2005 Lecture Similarly for hole flow in nqnr: p p(x n ) p(x) n i 2 N d 0 x n W n x Hole current density: J p = q n2 i D p (exp qv N d W n x n 1)
19 Microelectronic Devices and Circuits  Fall 2005 Lecture Step 3: sum both current components: J = J n +J p = qn 2 i ( 1 D n + 1 D p )(exp qv N a W p x p N d W n x n 1) Current: I = qan 2 i ( 1 D n + 1 D p )(exp qv N a W p x p N d W n x n 1) often written as: with I = I o (exp qv 1) I o saturation current [A] B.C. s contain both forward and reverse bias equation valid in forward and reverse bias. [will discuss this result in detail next time]
20 Microelectronic Devices and Circuits  Fall 2005 Lecture Key conclusions Application of voltage to pn junction results in disruption of balance between drift and diffusion in SCR: in forward bias, minority carriers are injected into quasineutral regions in reverse bias, minority carriers are extracted from quasineutral regions In forward bias, injected minority carriers recombine at surface. In reverse bias, extracted minority carriers are generated at surface. Computation of boundary conditions across SCR exploits quasiequilibrium: balance between diffusion and drift in SCR disturbed very little. Rate limiting step to current flow: diffusion through quasineutral regions. IV characteristics of pn diode: I = I o (exp qv 1)
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