Physical Structure

Transcription

1 Microelectronic Circuits, Kyung Hee Univ. Sring, Physical Structure n junction structure -tye semiconductor n-tye semiconductor metal contact for connection 1 Figure 1.35: Simlified hysical structure of the n junction. (Actual geometries are given in Aendix A.) As the n junction imlements the junction diode, its terminals are labeled anode and cathode.

2 Microelectronic Circuits, Kyung Hee Univ. Sring, Oeration with Oen-Circuit Q: What is state of n junction with oen-circuit terminals? A: -tye material contains majority of holes these holes are neutralized by equal amount of bound negative charge n-tye material contains majority of free electrons these electrons are neutralized by equal amount of bound ositive charge 2

3 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Bound charge charge of oosite olarity to free electrons / holes of a given material neutralizes the electrical charge of these majority carriers does not affect concentration gradients 3

4 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: What haens when a n-junction is newly formed aka. when the -tye and n-tye semiconductors first touch one another? A: See following slides 4

5 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Ste #1: The -tye and n-tye semiconductors are joined at the junction -tye semiconductor filled with holes junction n-tye semiconductor filled with free electrons Figure: The n junction with no alied voltage (oen-circuited terminals). 5

6 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Ste #1A: Bound charges are attracted (from environment) by free electrons and holes in the -tye and n-tye semiconductors, resectively. They remain weakly bound to these majority carriers; however, they do not recombine. negative bound charges ositive bound charges Figure: The n junction with no alied voltage (oen-circuited terminals). 6

7 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Ste #2: Diffusion begins. Those free electrons and holes which are closest to the junction will recombine and, essentially, eliminate one another. Figure: The n junction with no alied voltage (oen-circuited terminals). 7

8 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Ste #3: The deletion region begins to form as diffusion occurs and free electrons recombine with holes. The deletion region is filled with uncovered bound charges who have lost the majority carriers to which they were linked. Figure: The n junction with no alied voltage (oen-circuited terminals). 8

9 Microelectronic Circuits, Kyung Hee Univ. Sring, 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 articles to one another. 9

10 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Ste #4: The uncovered bound charges effect a voltage differential across the deletion region. The magnitude of this barrier voltage (V 0 ) differential grows, as diffusion continues. No voltage differential exists across regions of the n-junction outside of the deletion region because of the neutralizing effect of ositive and negative bound charges. voltage otential barrier voltage (V o ) location (x) 10

11 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Ste #5: The barrier voltage (V 0 ) is an electric field whose olarity ooses the direction of diffusion current (I D ). As the magnitude of V 0 increases, the magnitude of I D decreases. diffusion (I D ) current drift current (I S ) Figure: The n junction with no alied voltage (oen-circuited terminals). 11

12 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Ste #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 (I net = I D I S ) within the n-junction while under oen-circuit condition. diffusion (I D ) current drift current (I S ) -tye deletion region n-tye 12

13 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 The Drift Current I S and Equilibrium In addition to majority-carrier diffusion current (I D ), a comonent of current due to minority carrier drift exists (I S ). Secifically, some of the thermally generated electrons and holes in the -tye and n-tye materials move toward and reach the edge of the deletion region. There, they exerience the electric field (V 0 ) in the deletion region and are swet across it. Unlike diffusion current, the olarity of V 0 reinforces this drift current. 13

14 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Because these holes and free electrons are roduced by thermal energy, I S is heavily deendent on temerature Any deletion-layer voltage, regardless of how small, will cause the transition across junction. Therefore I S is indeendent of V 0. drift current (I S ) is the movement of these minority carriers. 14

15 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 n-junction built-in voltage (V 0 ) is the equilibrium value of barrier voltage Generally, it takes on a value between 0.6 and 0.9V for silicon at room temerature This voltage is alied across deletion region, not terminals of n junction Power cannot be drawn from V 0 V0 = barrier voltage VT = thermal voltage NA = accetor doing concentration N D = donor doing concentration ni = concentration of free electrons......in intrinsic semiconductor NN A D (eq3.22) V0 = VT ln 2 ni 15

16 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Note that the magnitude of drift current (I S ) is unaffected by level of diffusion and / or V 0. It will be, however, affected by temerature. diffusion (I D ) current drift current (I S ) Figure: The n junction with no alied voltage (oen-circuited terminals). 16

17 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: Is the deletion region always symmetrical? As shown on revious slides? A: The short answer is no. Q: Why? A: Because, tyically N A > N D. When the concentration of doing agents (N A, N D ) is unequal, the width of deletion region will differ from side to side. The deletion region will extend deeer in to the less doed material, a requirement to uncover the same amount of charge. x = width of deletion -region x n = width of deletion n-region 17

18 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 The deletion region will extend further in to region with less doing. However, the number of uncovered charges is the same. 18

19 Microelectronic Circuits, Kyung Hee Univ. Sring, : Oeration with Oen-Circuit Terminals Width of and Charge Stored in the Deletion Region the question we ask here is, what haens once the oen-circuit n junction reaches equilibrium??? because concentration of tyically N A > N D doing agents (N A, N D ) is minority carrier concentrations at equilibrium (no voltage unequal, charge alied) the is equal, width are of denoted but by n 0 and deletion region will differ n0 dv/dx is deendent of Q/W from width side to is different side the deletion region will extend deeer in to the less doed material, a requirement to uncover the same amount of charge x = width of deletion -region x n = width of deletion n-region Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. 19

20 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: How is the charge stored in both sides of the deletion region defined? A: Refer to equations to right. Note that these values should equal one another. Q x n magnitude of charghe on n-side of junctionp q= magnitude of electric chargep A= cross-sectional area of junctionp = enetration of deletion region into n-sidep N = concentration of donor atomsp + = D (eq3.23) Q qax N (eq3.24) Q + = - A Q- = magnitude of charghe on n-side of junctionp q= magnitude of electric charge P A= cross-sectional area of junctionp x = enetration of deletion region into -sidep N = concentration of accetor atomsp A = n qax N D 20

21 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: What information can be derived from this equality? A: In reality, the deletion region exists almost entirely on one side of the n-junction due to great disarity between N A > N D. qax N xn = qax N (eq3.25) = x A n D N N A D 21

22 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Note that both x and x n may be defined in terms of the deletion region width (W). W= width of deletion regionp εs = electrical ermiability of silicon (11.7ε0 = 1.04E 12 F / cm) P q= magnitude of electron chargep NA = concentration of accetor atomsp ND = concentration of donor atomsp V 0 = barrier / junction built-in voltagep (eq3.26) 2ε S 1 1 W = xn + x = + V q NA ND 0 (eq3.27) N A xn = W N A + N D (eq3.28) N D x = W N A + N D 22

23 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Note, also, the charge on either side of the deletion region may be calculated via (1.47) and (1.51). (eq3.29) NN A D QJ = Q ± = Aq W NA + ND NN A D (eq3.30) QJ = A 2ε Sq V NA + ND 0 23

24 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: What has been learned about the n-junction? A: comosition The n junction is comosed of two silicon-based semiconductors, one doed to be -tye and the other n-tye. A: majority carriers Are generated by doing. Holes are resent on -side, free electrons are resent on n-side. 24

25 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: What has been learned about the n-junction? A: bound charges Charge of majority carriers are neutralized electrically by bound charges. A: diffusion current I D Those majority carriers close to the junction will diffuse across, resulting in their elimination. 25

26 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: What has been learned about the n-junction? A: deletion region As these carriers disaear, they release bound charges and effect a voltage differential V 0. A: deletion-layer voltage As diffusion continues, the deletion layer voltage (V 0 ) grows, making diffusion more difficult and eventually bringing it to halt. 26

27 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: What has been learned about the n-junction? A: minority carriers Are generated thermally. Free electrons are resent on -side, holes are resent on n-side. A: drift current I S The deletion-layer voltage (V 0 ) facilitates the flow of minority carriers to oosite side. A: oen circuit equilibrium I D = I S 27

28 Microelectronic Circuits, Kyung Hee Univ. Sring, Qualitative Descrition of Junction Oeration Figure to right shows n-junction under three conditions: (a) oen-circuit where a barrier voltage V 0 exists. (b) reverse bias where a dc voltage V R is alied. (c) forward bias where a dc voltage V F is alied. Figure 1.38: The n junction in: (a) equilibrium; (b) reverse bias; (c) forward bias. 28

29 Microelectronic Circuits, Kyung Hee Univ. Sring, ) no voltage alied 1) negative voltage alied 2) voltage differential 2) voltage differential across deletion zone across deletion zone (a) oen-circuit where a barrier voltage V 0 exists. is V (b) 0 is V 0 + V R reverse bias where a dc voltage V R is alied. 3) I(c) D = forward I S bias where a 3) dc I D voltage < I S V F is alied. 1) ositive voltage alied 2) voltage differential across deletion zone is V 0 - V F Figure to right shows n-junction under three conditions: 3) I D > I S Figure 3.11: The n junction in: (a) equilibrium; (b) reverse bias; (c) forward bias. 29

30 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 reverse bias case the externally alied voltage V R adds to (aka. reinforces) the barrier voltage V 0 increase effective barrier this reduces rate of diffusion, reducing I D if V R > 1V, I D will fall to 0A the drift current I S is unaffected, but deendent on temerature result is that n junction will conduct small drift current I S forward bias case the externally alied voltage V F subtracts from the barrier voltage V 0 decrease effective barrier this increases rate of diffusion, increasing I D k the drift current I S is unaffected, but deendent on temerature result is that n junction will conduct significant current I D - I S minimal current flows in reverse-bias case 30 significant current flows in forward-bias case

31 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Reverse-Bias Case Observe that increased barrier voltage will be accomanied by (1) increase in stored uncovered charge on both sides of junction (2) wider deletion region Width of deletion region shown to right. (eq3.31) W= width of deletion regionp εs = electrical ermiability of silicon (11.7ε0 = 1.04E 12 F / cm) P q= magnitude of electron chargep N A = concentration of accetor atomsp ND = concentration of donor atomsp V 0 = barrier / junction built-in voltagep V = externally alied reverse-bias voltagep R 2ε 1 1 W = x + x = + ( V + V ) n S 0 R q NA ND action: relace V with V + V NN A D (eq3.32) QJ = A 2ε Sq ( V0 + VR) NA + ND action: J relace V with V + V 0 Q = magnitude of charge stored on either side of deletion regionp 0 R 0 0 R 31

32 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Forward-Bias Case Observe that decreased barrier voltage will be accomanied by (1) decrease in stored uncovered charge on both sides of junction (2) smaller deletion region Width of deletion region shown to right. W= width of deletion regionp εs = electrical ermiability of silicon (11.7ε0 = 1.04E 12 F / cm) P q= magnitude of electron chargep NA = concentration of accetor atomsp ND = concentration of donor atomsp V = barrier / junction built-in voltagep V = externally alied forward-bias voltagep 0 F 2ε 1 1 W = x + x = + ( V V ) J n S 0 F q NA ND action: relace V with V V NN Q = A 2 ε q ( V V ) J S A D 0 F NA + ND action: relace V0 with V V F 0 Q = magnitude of charge stored on either side of deletion regionp 0 0 F 32

33 Microelectronic Circuits, Kyung Hee Univ. Sring, The Current-Voltage Relationshi of the Junction Q: What haens, exactly, when a forward-bias voltage (V F ) is alied to the n-junction? ste #1: Initially, a small forward-bias voltage (V F ) is alied. It, because of its olarity, ushes majority carriers (holes in -region and electrons in n-region) toward the junction and reduces width of the deletion zone. Note, however, that this force is oosed by the builtin voltage built in voltage V 0. 33

34 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 ste #1: Initially, a small forward-bias voltage (V F ) is alied. It, because of its olarity, ushes majority (holes in -region and electrons in n- region) toward the junction and reduces width of the deletion zone. V F Note that, in this figure, the smaller circles reresent minority carriers and not bound charges which are not considered here. Figure: The n junction with alied voltage. 34

35 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 ste #2: As the magnitude of V F increases, the deletion zone becomes thin enough such that the barrier voltage (V 0 V F ) cannot sto diffusion current as described in revious slides. V F Note that removing barrier voltage does not facilitate diffusion, it only removes the electromotive force which ooses it. Figure: The n junction with alied voltage. 35

36 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 ste #3: Majority carriers (free electrons in n-region and holes in -region) cross the junction and become minority charge carriers in the nearneutral region. V F diffusion current (I D ) drift current (I S ) Figure: The n junction with alied voltage. 36

37 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 ste #4: The concentration of minority charge carriers increases on either side of the junction. A steady-state gradient is reached as rate of majority For carriers the oen-circuit crossing the condition, junction equals minority that carriers of recombination. are evenly distributed throughout the non-deletion regions. This concentration is defined as Veither F n 0 or n0. minority carrier concentration location (x) Figure: The n junction with alied voltage. 37

38 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 ste #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. V F minority carrier concentration location (x) Figure: The n junction with alied voltage 38

39 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 ste #5+: Diffusion current is maintained in site low diffusion lengths (e.g. microns) and recombination by constant flow of both free electrons and holes towards the junction. recombination V F flow of diffusion current (I D ) flow of holes flow of electrons Figure: The n junction with alied voltage 39

40 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 The key asect of (1.57) is that it relates the minority-charge carrier concentration at the junction boundary in terms of majority-charge carrier on the oosite side. Q: How is the relationshi between forward-bias voltage alied (V. ) and minority-carrier holes and electrons defined? ste #1: Emloy (1.57). This function describes maximum minority carrier concentration at junction. ste #2: Subtract n0 from n (x) to calculate the excess minority charge carriers. T 40 (eq3.7) n0 n( xn) = concentration of holes in n-region as function of xnp n 0 = thermal equilibrium concentrationp V = alied foward-bias voltagep V = thermal voltagep (eq 3.34 ) = V / VT (eq3.33) ( x ) = e n N 2 i A n n n0 excess = e concentration V / VT n0 n0 excess (eq3.34) = e concentratio n V / VT n0( 1)

41 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: How is the relationshi between forward-bias voltage alied (V. ) and minority-carrier holes and electrons defined? ste #3: Refer to (1.59). This function describes the minority carrier concentration as a function of location (x), boundary of deletion region (x n ), and diffusion length (L ). ( x ) = concentration of holes in n-region as function of x, = thermal equilibrium concentration x = oint of interest, x edge of deletion region, L = diffusion length n n n n0 n= P ( x xn)/ L (eq3.35) n( xn) = n0 + ( excess concentrati on) e (eq3.35) ( x n n0 V / VT ( e 1) = + e e V / VT n) n0 n0( 1) ( x x )/ L n 41

42 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 steady-state minority carrier concentration on both sides of a n-junction for which N A >> N D 3.5.2: The Current-Voltage Relationshi of the Junction base concentration excess concentration Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith ( ) 42

43 Microelectronic Circuits, Kyung Hee Univ. Sring, : The Current-Voltage Relationshi of the Junction These excess concentrations effect steady-state diffusion current. However, how is this diffusion current defined? Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith ( ) 43

44 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: For forward-biased case, how is diffusion current (I D ) defined? ste #1: Take derivative of (1.59) to define comonent of diffusion current attributed to flow of holes. ste #2: Note that this value is maximum at x = x n. Oxford University Publishing Microelectronic Circuits by Adel S. Sedra and Kenneth C. Smith ( ) 44 action: take derivative of n ( x) dn( x) d = [ n0 ] + dx dx 0 d V / V ( x xn)/ L T + n0( e 1) e dx L n0 V / VT ( x xn)/ L ( e 1) e n0 V / VT (eq3.36) ( 1) L action: substitute in value from above ( x xn)/ L J = qd e e dn ( x) dx action: calculate maximum max D V / V ( J ) 0( T = q n e 1) L

45 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: For forward-biased case, how is diffusion current defined? ste #3: Define the comonent of maximum diffusion current attributed to minority-carrier electrons in method similar above. (eq3.37) maximum hole - diffusion concentration: J D V / VT ( + xn) = q n0 ( e 1) L (eq3.38) maximum electron - diffusion concentration: J D n V / VT n( x) = q n0 ( e 1) Ln 45

46 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: For forward-biased case, how is diffusion current defined? ste #4: Define total diffusion current as sum of comonents attributed to free electrons and holes. total current ( I) through junction is equal to area ( A) times maximum hole ( J ) and electron-diffusion ( J ) current densities n I= A J( + xn) + Jn( x) D Dn V / VT I= A q n0 + q n0 ( e 1) L Ln action: subtitute in values for J ( + x ) and J (- x ) n n D 2 Dn V / VT I = Aqni + ( e 1) LN D LN n A V / VT I= IS ( e 1) action: subtitute 2 D Dn Is= Aqni + LN D L nn action: subtitute 2 2 = n / N and n = n / N n0 i D 0 i A A 46

47 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: For forward-biased case, how is diffusion current (I D ) defined? A: This is an imortant equation which will be emloyed in future chaters. D D 40) ) 2 n V / VT V / VT (eq3. I = Aqni + ( e 1) = IS ( e 1 LN D LN n A I S 47

48 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 Q: Why is diffusion current (I D ) deendent on the concentration gradient of minority (as oosed 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 (I D ) is most deendent on two factors: alied forward-bias voltage (V F ) and doing. 48

49 Microelectronic Circuits, Kyung Hee Univ. Sring, 2016 saturation current (I S ) is the maximum reverse current which will flow through n-junction. It is roortional to cross-section of junction (A). Tyical value is A. V / V (eq3.40) I= I ( T S e 1) Figure 1.40: The n junction I V characteristic. 49