Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 1.10.1. Physical .
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 1.10.1. Physical Structure pn junction structure p-type semiconductor n-type semiconductor metal contact for connection Figure 1.35: Simplified physical structure of the pn junction. (Actual geometries are given in Appendix A.) As the pn junction implements the junction diode, its terminals are labeled anode and cathode. 1
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 1.10.2 Operation with Open-Circuit Q: What is state of pn junction with open-circuit terminals? A: p-type material contains majority of holes these holes are neutralized by equal amount of bound negative charge n-type material contains majority of free electrons these electrons are neutralized by equal amount of bound positive charge 2
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Bound charge charge of opposite polarity to free electrons / holes of a given material neutralizes the electrical charge of these majority carriers does not affect concentration gradients 3
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: What happens when a pn-junction is newly formed – aka. when the p-type and n-type semiconductors first touch one another? A: See following slides 4
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Step #1: The p-type and n-type semiconductors are joined at the junction p-type semiconductor filled with holes junction n-type semiconductor filled with free electrons Figure: The pn junction with no applied voltage (open-circuited terminals). 5
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Step #1A: Bound charges are attracted (from environment) by free electrons and holes in the p-type and n-type semiconductors, respectively. They remain weakly “bound” to these majority carriers; however, they do not recombine. negative bound charges positive bound charges Figure: The pn junction with no applied voltage (open-circuited terminals). 6
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Step #2: Diffusion begins. Those free electrons and holes which are closest to the junction will recombine and, essentially, eliminate one another. Figure: The pn junction with no applied voltage (open-circuited terminals). 7
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Step #3: The depletion region begins to form – as diffusion occurs and free electrons recombine with holes. The depletion region is filled with “uncovered” bound charges – who have lost the majority carriers to which they were linked. Figure: The pn junction with no applied voltage (open-circuited terminals). 8
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: Why does diffusion occur even when bound charges neutralize the electrical attraction of majority carriers to one another? A: Diffusion current, as shown in (1.43) and (1.44), is effected by a gradient in concentration of majority carriers – not an electrical attraction of these particles to one another. 9
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Step #4: The “uncovered” bound charges effect a voltage differential across the depletion region. The magnitude of this barrier voltage (V0) differential grows, as diffusion continues. voltage potential No voltage differential exists across regions of the pn-junction outside of the depletion region because of the neutralizing effect of positive and negative bound charges. barrier voltage (Vo) location (x) 10
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Step #5: The barrier voltage (V0) is an electric field whose polarity opposes the direction of diffusion current (ID). As the magnitude of V0 increases, the magnitude of ID decreases. diffusion (ID) current drift current (IS) Figure: The pn junction with no applied voltage (open-circuited terminals). 11
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Step #6: Equilibrium is reached, and diffusion ceases, once the magnitudes of diffusion and drift currents equal one another – resulting in no net flow. Once equilibrium is achieved, no net current flow exists (Inet ID – IS) within the pn-junction while under open-circuit condition. diffusion (ID) p-type current drift depletion region 12 current (IS) n-type
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 The Drift Current IS and Equilibrium In addition to majority-carrier diffusion current (ID), a component of current due to minority carrier drift exists (IS). Specifically, some of the thermally generated electrons and holes in the p-type and n-type materials move toward and reach the edge of the depletion region. There, they experience the electric field (V0) in the depletion region and are swept across it. Unlike diffusion current, the polarity of V0 reinforces this drift current. 13
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Because these holes and free electrons are produced by thermal energy, IS is heavily dependent on temperature Any depletion-layer voltage, regardless of how small, will cause the transition across junction. Therefore IS is independent of V0. drift current (IS) – is the movement of these minority carriers. 14
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 pn-junction built-in voltage (V0) – is the equilibrium value of barrier voltage Generally, it takes on a value between 0.6 and 0.9V for silicon at room temperature This voltage is applied across depletion region, not terminals of pn junction Power cannot be drawn from V0 V0 barrier voltage VT thermal voltage NA acceptor doping concentration ND donor doping concentration ni concentration of free electrons. .in intrinsic semiconductor NA ND (eq3.22) V0 VT ln 2 ni 15
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Note that the magnitude of drift current (IS) is unaffected by level of diffusion and / or V0. It will be, however, affected by temperature. diffusion (ID) current drift current (IS) Figure: The pn junction with no applied voltage (open-circuited terminals). 16
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: Is the depletion region always symmetrical? As shown on previous slides? A: The short answer is no. Q: Why? A: Because, typically NA ND. When the concentration of doping agents (NA, ND) is unequal, the width of depletion region will differ from side to side. The depletion region will extend deeper in to the “less doped” material, a requirement to uncover the same amount of charge. xp width of depletion p-region xn width of depletion n-region 17
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 The depletion region will extend further in to region with “less” doping. However, the “number” of uncovered charges is the same. 18
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 3.4.2: Operation with Open-Circuit Terminals Width of and Charge Stored in the Depletion Region the question we ask here is, what happens once the open-circuit pn junction reaches equilibrium? because concentration of doping agents (NA, ND) is typically NA ND unequal, the width charge is equal, but minority carrier concentrations at equilibrium (no voltage applied) are of denoted depletion region will differ by np0 and pn0 width is different from side to side the depletion region will extend deeper in to the “less doped” material, a requirement to uncover the same amount of charge dv/dx is dependent of xp width of depletion p-region xn width of depletion n-region Q/W Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. 19
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q magnitude of charghe on n -side of junctionPpp q magnitude of electric chargePpp A cross-sectional area of junctionPpp xn penetration of depletion region into n -sidePpp ND concentration of donor atomsPpp Q: How is the charge stored in both sides of the depletion region defined? A: Refer to equations to right. Note that these values should equal one another. (eq3.23) Q qAxn ND (eq3.24) Q - qAx p NA Q - magnitude of charghe on n -side of junctionPpp q magnitude of electric chargePpp A cross-sectional area of junctionPpp x p penetration of depletion region into p -sidePpp NA concentration of acceptor atomsPpp 20
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: What information can be derived from this equality? A: In reality, the depletion region exists almost entirely on one side of the pn-junction – due to great disparity between NA ND. qAx p NA qAxn ND 21 (eq3.25) xn NA x p ND
Microelectronic Circuits, Kyung Hee Univ. Note that both xp and xn may be defined in terms of the depletion region width (W). Spring, 2016 W width of depletion regionPpp ε S electrical permiability of silicon (11.7 ε 0 1.04 E 12 F / cm)Ppp q magnitude of electron chargePpp NA concentration of acceptor atomsPpp ND concentration of donor atomsPpp V0 barrier / junction built-in voltagePpp 2ε S 1 1 (eq3.26) W xn x p V0 q NA ND NA (eq3.27) xn W NA ND (eq3.28) x p W 22 ND NA ND
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Note, also, the charge on either side of the depletion region may be calculated via (1.47) and (1.51). NA ND (eq3.29) QJ Q Aq NA ND NA ND (eq3.30) QJ A 2ε S q NA ND 23 W V0
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: What has been learned about the pn-junction? A: composition The pn junction is composed of two silicon-based semiconductors, one doped to be p-type and the other n-type. A: majority carriers Are generated by doping. Holes are present on p-side, free electrons are present on n-side. 24
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: What has been learned about the pn-junction? A: bound charges Charge of majority carriers are neutralized electrically by bound charges. A: diffusion current ID Those majority carriers close to the junction will diffuse across, resulting in their elimination. 25
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: What has been learned about the pn-junction? A: depletion region As these carriers disappear, they release bound charges and effect a voltage differential V0. A: depletion-layer voltage As diffusion continues, the depletion layer voltage (V0) grows, making diffusion more difficult and eventually bringing it to halt. 26
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: What has been learned about the pn-junction? A: minority carriers Are generated thermally. Free electrons are present on p-side, holes are present on n-side. A: drift current IS The depletion-layer voltage (V0) facilitates the flow of minority carriers to opposite side. A: open circuit equilibrium ID IS 27
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 1.11.1. Qualitative Description of Junction Operation Figure to right shows pn-junction under three conditions: (a) open-circuit – where a barrier voltage V0 exists. (b) reverse bias – where a dc voltage VR is applied. (c) forward bias – where a dc voltage VF is applied. Figure 1.38: The pn junction in: (a) equilibrium; (b) reverse bias; (c) forward bias. 28
Microelectronic Circuits, Kyung Hee Univ. 1) no voltage applied Spring, 2016 1) negative voltage applied 1) positive voltage applied 2) voltage differential 2) voltage differential 2) voltage differential Figure to right shows pn-junction under three conditions: across depletion zone across depletion zone (a) open-circuit – where a barrier voltage V0 exists. is V0 VR is V0 (b) reverse bias – where a dc voltage VR is applied. IS 3) IS I(c) bias – where a3)dcID voltage VF is applied. D forward across depletion zone is V0 - VF 3) ID IS Figure 3.11: The pn junction in: (a) equilibrium; (b) reverse bias; (c) forward bias. 29
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 forward bias case the externally applied voltage VF subtracts from the barrier voltage V0 reverse bias case the externally applied voltage VR adds to (aka. reinforces) the barrier voltage V0 decrease effective barrier increase effective barrier this reduces rate of diffusion, reducing ID this increases rate of diffusion, increasing ID the drift current IS is unaffected, but dependent on temperature result is that pn junction will conduct small drift current IS the drift current IS is unaffected, but dependent on temperature result is that pn junction will conduct significant current ID - IS k if VR 1V, ID will fall to 0A significant current flows in forward-bias case minimal current flows in reverse-bias case 30
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Reverse-Bias Case Observe that increased barrier voltage will be accompanied by (1) increase in stored uncovered charge on both sides of junction (2) wider depletion region Width of depletion region shown to right. W width of depletion regionPpp ε S electrical permiability of silicon (11.7 ε 0 1.04 E 12 F / cm)Ppp q magnitude of electron chargePpp NA concentration of acceptor atomsPpp ND concentration of donor atomsPpp V0 barrier / junction built-in voltagePpp VR externally applied reverse-bias voltagePpp 2ε S 1 1 (eq3.31) W xn x p V0 VR ) ( q NA ND action: replace V0 with V0 VR NA ND (eq3.32) QJ A 2ε S q NA ND V0 VR ) ( action: replace V0 with V0 VR QJ magnitude of charge stored on either side of depletion regionPpp 31
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Forward-Bias Case Observe that decreased barrier voltage will be accompanied by (1) decrease in stored uncovered charge on both sides of junction (2) smaller depletion region W width of depletion regionPpp ε S electrical permiability of silicon (11.7 ε 0 1.04 E 12 F / cm)Ppp q magnitude of electron chargePpp NA concentration of acceptor atomsPpp ND concentration of donor atomsPpp V0 barrier / junction built-in voltagePpp VF externally applied forward-bias voltagePpp 2ε S 1 1 W xn x p V0 VF ) ( q NA ND action: replace V0 with V0 VF Width of depletion region shown to right. NN QJ A 2ε S q A D NA ND V0 VF ) ( action: replace V0 with V0 VF QJ magnitude of charge stored on either side of depletion regionPpp 32
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 1.11.2. The Current-Voltage Relationship of the Junction Q: What happens, exactly, when a forward-bias voltage (VF) is applied to the pn-junction? step #1: Initially, a small forward-bias voltage (VF) is applied. It, because of its polarity, pushes majority carriers (holes in p-region and electrons in n-region) toward the junction and reduces width of the depletion zone. Note, however, that this force is opposed by the builtin voltage built in voltage V0. 33
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 step #1: Initially, a small forward-bias voltage (VF) is applied. It, because of its polarity, pushes majority (holes in p-region and electrons in nregion) toward the junction and reduces width of the depletion zone. VF Note that, in this figure, the smaller circles represent minority carriers and not bound charges – which are not considered here. Figure: The pn junction with applied voltage. 34
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 step #2: As the magnitude of VF increases, the depletion zone becomes thin enough such that the barrier voltage (V0 – VF) cannot stop diffusion current – as described in previous slides. VF Note that removing barrier voltage does not facilitate diffusion, it only removes the electromotive force which opposes it. Figure: The pn junction with applied voltage. 35
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 step #3: Majority carriers (free electrons in n-region and holes in p-region) cross the junction and become minority charge carriers in the nearneutral region. VF diffusion current (ID) drift current (IS) Figure: The pn junction with applied voltage. 36
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 minority carrier concentration step #4: The concentration of minority charge carriers increases on either side of the junction. A steady-state gradient is reached as rate of the open-circuit minority carriers are evenly majorityFor carriers crossing thecondition, junction equals that of recombination. distributed throughout the non-depletion regions. This F concentration is defined asVeither np0 or pn0. location (x) Figure: The pn junction with applied voltage. 37
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 step #4: The concentration of minority charge carriers increases on either side of the junction. A steady-state gradient is reached as rate of majority carriers crossing the junction equals that of recombination. minority carrier concentration VF location (x) Figure: The pn junction with applied voltage 38
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 step #5 : Diffusion current is maintained – in spite low diffusion lengths (e.g. microns) and recombination – by constant flow of both free electrons and holes towards the junction. recombination VF flow of diffusion current (ID) flow of holes flow of electrons Figure: The pn junction with applied voltage 39
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 The key aspect of (1.57) is that it relates the minority-charge carrier concentration at the junction boundary in terms of majority-charge carrier on the opposite side. Q: How is the relationship between forward-bias voltage applied (V.) and minority-carrier holes and electrons defined? step #1: Employ (1.57). This function describes maximum minority carrier concentration at junction. step #2: Subtract pn0 from pn(x) to calculate the excess minority charge carriers. ni2 (eq3.7) pn 0 NA pn ( xn ) concentration of holes in n -region as function of xn Ppp pn 0 thermal equilibrium concentrationPpp V applied foward-bias voltagePpp VT thermal voltagePpp (eq3.33) pn (xn ) pn 0 eV / VT excess pn 0 eV / VT pn 0 (eq3.34) concentration excess pn 0 (eV / VT 1) (eq3.34) concentration 40
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: How is the relationship between forward-bias voltage applied (V.) and minority-carrier holes and electrons defined? step #3: Refer to (1.59). This function describes the minority carrier concentration as a function of location (x), boundary of depletion region (xn), and diffusion length (Lp). pn ( xn ) concentration of holes in n -region as function of xn , pn 0 thermal equilibrium concentration x point of interest, xn edge of depletion region, LP diffusion length ( x xn ) / Lp pn 0 ( excess concentrati on (eq3.35) pn (x n) ) e pn 0 ( eV / VT 1) V / VT pn 0 pn 0 (e (eq3.35) pn (xn ) 41 1)e ( x xn ) / Lp
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 3.5.2: The Current-Voltage steady-state minority carrier concentration on both Relationship sides of the of Junction a pn-junction for which N N A “base” concentration Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) D excess concentration 42
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 3.5.2: The Current-Voltage These excess effect steady-state diffusion Relationship of theconcentrations Junction current. However, how is this diffusion current defined? Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) 43
Microelectronic Circuits, Kyung Hee Univ. Q: For forward-biased case, how is diffusion current (ID) defined? step #1: Take derivative of (1.59) to define component of diffusion current attributed to flow of holes. step #2: Note that this value is maximum at x x n. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith (0195323033) Spring, 2016 action: take derivative of pn ( x ) dp n ( x ) d [ pn0 ] dx dx 0 d pn 0 (eV / VT 1)e ( x xn ) / Lp dx pn 0 V / VT ( x xn ) / Lp 1) e (e Lp action: substitute in value from above p ( x x ) / L qDp n 0 (eV / VT 1)e n p (eq3.36) Jp L p dpn ( x ) dx action: calculate maximum Dp max( Jp ) q pn 0 (eV / VT 1) Lp 44
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: For forward-biased case, how is diffusion current defined? step #3: Define the component of maximum diffusion current attributed to minority-carrier electrons – in method similar above. (eq3.37) maximum hole - diffusion concentration: Jp ( xn ) q Dp Lp pn 0 (eV / VT 1) (eq3.38) maximum electron - diffusion concentration: Dn Jn ( x p ) q np 0 (eV / VT 1) Ln 45
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: For forward-biased case, how is diffusion current defined? total current (I ) through junction is equal to area (A) times maximum hole (Jp ) and electron-diffusion (Jn ) current densities I A Jp ( xn ) Jn ( x p ) step #4: Define total diffusion current as sum of components attributed to free electrons and holes. Dp V / VT Dn I A q pn 0 q np 0 (e 1) Ln Lp action: subtitute in values for Jp ( xn ) and Jn (- x p ) Dp Dn V / VT I Aqn 1) (e Lp ND Ln NA 2 i action: subtitute pn 0 ni2 / ND and np 0 ni2 / NA I IS (eV / VT 1) action: subtitute Dp D Is Aqni2 n Lp ND Ln NA 46
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: For forward-biased case, how is diffusion current (ID) defined? A: This is an important equation which will be employed in future chapters. Dp Dn V / VT 2 (eq3.40) I Aqni 1) IS (eV / VT 1) (e L N L N p D n A IS 47
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 Q: Why is diffusion current (ID) dependent on the concentration gradient of minority (as opposed to majority) charge carriers? A: Essentially, it isn’t. Equation (1.57) defines the minority-charge carrier concentration in terms of the majority-charge carrier concentrations in “other” region. As such, the diffusion current (ID) is most dependent on two factors: applied forward-bias voltage (VF) and doping. 48
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 saturation current (IS) – is the maximum reverse current which will flow through pn-junction. It is proportional to cross-section of junction (A). Typical value is 10-18A. (eq3.40) I IS (e V / VT 1) Figure 1.40: The pn junction I–V characteristic. 49
Microelectronic Circuits, Kyung Hee Univ. Spring, 2016 13 The Drift Current I S and Equilibrium In addition to majority-carrier diffusion current (I D), a component of current due to minority carrier drift exists (I S). Specifically, some of the thermally generated electrons and holes in the p-type and n-type materials move toward and
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