LAB VII. TRANSIENT SIGNALS OF PN DIODES

LAB VII. TRANSIENT SIGNALS OF PN DIODES 1. OBJECTIVE In his lab, you will sudy he ransien effecs in a -n juncion diode due o a sudden change in curren. Secifically, you will sudy he urn-on, urn-off, and reverse-recovery ransien behaviors of a -n juncion diode. One of he more ineresing henomena of he las ransien behavior is he charge sorage delay ha allows large reverse-bias currens o flow hrough a diode for shor eriods of ime, which is an imoran figure of meri in swiching alicaions. 2. OVERVIEW For small signals, we assume ha he sored charge densiy in he n-side and -side regions of our diode do no change significanly, i.e. we assume ha he diode is very close o seady-sae. However, his is no he case when larger volages are alied. In his lab, we will vary he magniudes of he alied volages from small o large and observe he resuling ransien behavior of he diodes. Nex we will use charge conrol analysis o make a firs order aroximaion of he curren and volage values of he diode as a funcion of ime. From hese analyses we can begin o undersand he ransien behavior, and hus he swiching rocesses, of a -n juncion diode. Informaion essenial o your undersanding of his lab: 1. Carrier injecion and sorage (Sreeman secion 5.3.2) 2. Transien and AC condiions (Sreeman secions 5.5.1-5.5.3) Maerials necessary for his Exerimen: 1. You mus bring your own USB FLASH MEMORY. 2. Sandard esing saion 3. One recifier diode (Par: 1N4002) 4. 10 Ω, 2W resisor Lab VII: Transien Signals of PN Juncion Diodes Page 1

3. BACKGROUND INFORMATION 3.1 CHART OF SYMBOLS Here is a char of symbols used in his lab manual. This lis is no all inclusive; however, i does conain he mos common symbols and heir unis used in his Lab. Table 1. Char of he symbols used in his lab. Symbol Symbol Name Unis h + hole Posiive charge aricle e - elecron Negaive charge aricle q magniude of elecronic charge 1.6 x 10-19 C hole densiy (number h + / cm 2 ) n elecron densiy (number e - / cm 2 ) n i inrinsic elecron densiy (number e - / cm 2 ) hole concenraion a deleion edge (number h + / cm 2 ) n elecron concenraion a deleion edge (number e - / cm 2 ) k b Bolzmann's consan 1.38 x 10-23 joules / K T Temeraure K E g energy ga of semiconducor ev A juncion area cm 2 g general carrier lifeime sec hole lifeime sec n elecron lifeime sec L diffusion lengh of holes cm Ln diffusion lengh of elecrons cm x x-axis for -ye maerial cm xn x-axis for n-ye maerial cm I0 reverse sauraion curren A I change in DC curren A VD DC diode volage V vd AC diode volage V vd oal diode volage V fr forward recovery ime sec rd relaxaion delay ime sec sd sorage delay ime sec rr reverse recovery ime sec Lab VII: Transien Signals of PN Juncion Diodes Page 2

3.2 CHART OF EQUATIONS All of he equaions from he background orion of he manual are shown in he able below. Equaion Name Table 2. Char of he equaions used in his lab. Formula 1 Ideal Diode Equaion ( qvd ( ) / nkt ) I ( ) I e 1 D 0 2 Hole curren in a + n juncion as a funcion of he sored charge Q i Q ( ) dq ( ) ( ) d 3 Sored charge in he n-side as a funcion of ime Q ( ) I e F qal n 4 Excess charge carrier concenraion a he edge of he deleion region in he n-side 5 Volage across he + n juncion assuming quasi-seady sae condiions qv Q kt n ( ) n0 e 1 qal v( ) kt q I F ln qal n0 e 1 Lab VII: Transien Signals of PN Juncion Diodes Page 3

3.3 TIME DEPENDANCE OF THE IDEAL DIODE EQUATION When ime-varying volages are alied across a -n juncion diode, he diode curren, execedly, are also ime-varying. When he ime-variaion is slower han he diffusion of minoriy carriers, he carriers have ime o equilibrae in resonse o he fields. Thus, he diode remains in a quasi-seady sae condiion and he sandard I-V relaion of he -n juncion diode under equilibrium can be assumed: ( qvd ( ) / nkt ) i ( ) I e 1. (1) D 0 If he ime-variaion of he curren and volage signals become much faser han he ime i akes for he minoriy carrier o equilibrae, he I-V characerisic can no longer be reresened by (1). Figure 1 shows how he minoriy carrier disribuion changes over ime (and as a funcion of he osiion in he n-side) when he curren flow hrough a + -n juncion diode suddenly sos (a urn-off ransien.) As soon as he curren so flowing, here will be no more hole diffusion from he -side and he sored charge disribuion decays exonenially in ime. However, is decay in sace becomes non-exonenial, which is due o he charge densiy a he deleion edge being roorional o he curren flow. Thus, when he curren flow is zero, he sloe of he charge densiy a he deleion edge mus also be zero (Figure 1). I D δ(x n) I forward 0 1 2 Noice how he sloe is zero a he deleion edge. DC seady sae charge densiy level. 0 1 0 2 1 x n Figure 1. A urn-off ransien: curren as a funcion of ime (lef) and minoriy carrier re-disribuion over ime as a funcion of osiion in he n-side (righ). Lab VII: Transien Signals of PN Juncion Diodes Page 4

This non-exonenial saial decay makes i difficul o direcly calculae he sored charge as a funcion of ime. Therefore, a quasi-seady sae aroximaion is used o simlify calculaions which in his case is simly assuming ha he decay of a sored charge highly resembles an exonenial rofile in sace as he seady sae condiion (see Figure 2). Using his aroximaion, we can calculae raher simly he sored charge in ime and find he volage across he juncion. Le s now use Figure 3 o beer undersand he quasi-seady sae aroximaion and deermine he oal diode curren. Consider a urn-on ransien signal across a -n juncion (Figure 3, lef). In his case, he curren is suddenly seed u from zero o I F. For > 0 +, he increased hole injecion curren will firs cause an increase in he excess hole densiy a he edge (x n=0) of he deleion region. Shorly afer, he excess holes will have had ime o diffuse ino he neural region of he n-side, hus increasing he charge sored in he n-side as ime rogresses from 0 o 1 o 2 o seady sae, as shown in Figure 3. The diffusion rocess akes ime and he build-u of charge wihin he n-region will always lag he build-u of he charge near x n = 0. During his ransien rocess, he oal diode curren is he sum of he recombinaion curren and he charge build-u curren, yielding: i Q ( ) dq ( ) ( ). (2) d δ(x n) Seady sae condiion excess charge carrier disribuion. Noice he difference in he doed lines(acual charge densiies) and he solid lines (quasiseady sae aroximaions) 0 1 0 2 1 x n quasi-seady sae aroximaions Figure 2. Excess carrier concenraion as a funcion of osiion in ime: he doed lines are he acual carrier disribuions while he solid lines are quasi-seady sae charge aroximaions. Lab VII: Transien Signals of PN Juncion Diodes Page 5

I F I D δ(x n) Noice how he sloe of he blue line is he same as ha of he line for ime less han zero. a seady sae 2 1 1 0 0 1 2 x n Figure 3. A urn-on ransien: curren as a funcion of ime (lef) and minoriy carrier redisribuion over ime as a funcion of osiion in he n-side (righ). 3.4 CHARGE CONTROL ANALYSIS In many cases, we will know he curren running hrough a diode and can use i o find he sored charge in a -n juncion diode. Afer finding he sored charge, i is ossible o find he charge densiy a he deleion region edge, which in urn can be used o calculae he volage across he juncion as a funcion of ime. To find he sored charge we will use Lalace ransforms on he equaion (2) o solve for he sored charge Q(). For generaliy, we are going o use I F + ΔI as our curren a =0. I F is he iniial curren which esablishes a seady sae charge; and ΔI is he change in curren, which can be a osiive or negaive ime varying funcion. Afer aking he Lalace ransform of equaion (8), one can use he iniial condiions for he charge densiy (i.e., Q(=0) = Iτ ) o solve he equaion. A bi of algebraic maniulaion and a reverse Lalace ransform will give us: Q ( ) I e qal (3) Solving for he excess charge carrier concenraion a he edge of he deleion region and equaing i o (1), we ge: qv Q kt ( ) n n0 e 1 (4) qal Solving for v(), we ge: kt I F v( ) ln e 1 (5) q qal n0 F n Lab VII: Transien Signals of PN Juncion Diodes Page 6

3.5 SWITCHING TRANSIENTS Le s ake a look a he swiching ransiens in he ideal diode s I-V characerisic curves. When a diode is suddenly urned on (urn on ransien), he swiching rajecory is sraigh u he curren axis and hen across he volage axis in ime (Figure 4). I D I V D 0 10-4 10-3 10-2 10-1 10-4 10-3 10-2 10-1 Noice where he volage is every seconds Noice he curren change is insananeous Normal I-V swiching rajecory of a diode Key Ideal Diode Trajecory V Charge Conrol Trajecory Figure 4. A urn-on ransien of a diode: he boom grah illusraes he swiching rajecory derived from our charge conrol modeling agains an ideal diode rajecory. If he curren changes less abruly, hen he swiching rajecory will more closely follow he ideal diode characerisic as shown in Figure 5. Figure 5. The swiching rajecory for differen urn-on ransien condiions. Lab VII: Transien Signals of PN Juncion Diodes Page 7

3.6 TIME DELAYS INCURRED BY SWITCHING Now ha you have some idea of wha a swiching rajecory is and how i works, we are going o look a a slighly more comlex circui wih a volage signal, a series resisance, and a diode configured as shown in Figure 6. The urose of his analysis is o find ou how long i akes for our swiching oeraion reach seady-sae (i.e. recover ). Since diodes are used more in AC alicaions han in DC alicaions, swiching seeds of a diode becomes a very imoran diode feaure. R VS() + - id() + + vd() Figure 6. A circui diagram for he ime delay measuremen. When a se-on volage is alied o a -n juncion wih a series resisance you should have an ouu similar o Figure 7. Noice ha he volage across he juncion sikes and hen seles down o a seady-sae volage level. When he volage across he diode has droed o wihin 10% of he seady-sae value he juncion is said o have recovered. The forward recovery ime, fr is he ime from he swiching-on of he volage source o he ime ha diode has recovered. When a volage source is urned off, he sored charge is resen unil i recombines or is dissiaed over he resisor in he circui. We will give his ye of charge sorage delay a secial name, he relaxaion delay ime, rd (see Figure 8). We sae ha he sysem is relaxed if i s curren value is wihin 10% of he seady-sae value. Lab VII: Transien Signals of PN Juncion Diodes Page 8

V S() V Can grow o he se on volage V Diode Charge builds unil he Diode urns on Volage Peak V = 0.1(Volage Peak Seady Sae Volage) Seady-Sae Volage fr Figure 7. A urn on ransien: he grah above shows alied volage waveform (se funcion) from he funcion generaor and he boom grah shows corresonding volage signal across he diode. Noe how o deermine he fr. V S() Cu off oin for volage signal V whole circui 0 Volage droed over he resisor. rd Seady sae volage Volage (off) Figure 8. A urn off ransien: he grah above shows alied volage waveform from he funcion generaor and he boom grah shows corresonding volage signal across he diode. Noe how o deermine he rd. Lab VII: Transien Signals of PN Juncion Diodes Page 9

When you swich from forward o reverse bias ( a osiive o negaive ransien or a reverse recovery ransien ) reverse recovery swiching will occur as shown in Figure 9. Figure 9-a deics he case of an ideal curren source which is seed from a forward biasing curren I F o a curren of oosie olariy. Since I F is assumed o be flowing for quie some ime we should exec o see a seady sae charge densiy a =0. Noe ha when =0 +, he sloe of he charge disribuion (i.e. ime rae of charge disribuion) mus mach he curren ha is flowing. The reverse curren consiss of minoriy carrier being drawn back across juncion ino he -ye maerial. The charge densiy in n-side is shown in Figure 10 below. Figure 9. Reverse recovery swiching rajecories for a curren source (a) and a volage source (b). Δ(xn) Figure 10. Changes in he excess charge carrier disribuion over ime. Noe he osiive sloes near he edge of he deleion region. Lab VII: Transien Signals of PN Juncion Diodes Page 10

When he sored charge densiy on boh sides of he juncion reaches zero, he sorage delay orion of he ransien is over. The curren source will hen raidly drive he diode owards reverse breakdown. In he case of a volage source, deiced in Figure 9-b, he curren sulied o he circui can be aroximaed as he volage sulied by he source over he series resisance. This means ha he curren sourced is deenden on he volage droed across he resisor. Afer he sorage delay ime ( sd), he diode urns off changing he diodes role in he circui from ha of a simle volage dro o imedance many orders of magniude larger han ha of he series resisance; his causes nearly all of he volage o fall across he -n juncion. Noe ha he volage droed across he resisor decays exonenially in ime (Figure 9-b, 11). Since he curren for he circui is he same as ha flowing hrough he resisor, he exonenial decay in volage causes he reverse curren o saurae o he reverse sauraion curren (Figure 9-b). The oal reverse recovery ime ( rr) is he ime i akes he volage signal across he diode o reach 10% of he seady-sae value from he reverse volage exerienced by he diode during he sorage delay eriod. Figure 11 demonsraes boh he sorage delay ime sd, and he reverse recovery ime, rr. Lab VII: Transien Signals of PN Juncion Diodes Page 11

V S() v F v R v Resisor() Seady Sae Volage (a some reverse-bias curren) V = 0.1( Volage Peak Seady Sae Volage ) rd sd Volage Peak rr Figure 11. A reverse recovery ransien of a diode. Noe he ime eriod of each delay on he ime axis. Lab VII: Transien Signals of PN Juncion Diodes Page 12

4. PREPARATION 1. Make sure you undersand how o roerly oerae he oscilloscoe by reading he secion 3.3 of he Lab 1 manual. Ouline secion 3.3 of he Lab 1 manual. 2. Ouline secions 3.3 o 3.6 of his Lab 7 manual. Take noe of key assumions and main conces conained in each secion. 5. PROCEDURE The following measuremens will be made using your recifier diode (1N4002). Since here will be subsanial currens flowing a various imes in he exerimen be sure o use a 10 Ω, 2W resisor for his exerimen. In his lab, you will manually conrol he funcion generaor and he oscilloscoe o ge he daa. 5.1 TURN-ON TRANSIENT In his secion, you will measure he forward recovery ransien of he diode volage as he ulsed curren is swiched on from I = 0 o I = I F as a funcion of I F. 1. Measure he exac value of your ~10 Ω resisor using he Keiheley SMU and record i in he Table 3. You will need exac resisance value o accuraely analyze he daa. 2. Consruc he circui as shown in Figure 12. Figure 12. Circui used o make he urn on and urn off ransien measuremens. Lab VII: Transien Signals of PN Juncion Diodes Page 13

3. Funcion Generaor seings: In his lab, we ll use he High-Level and Low-Level seings on he funcion generaor raher han he Amliude and Offse seings. Se he funcion generaor o ouu a square wave. Nex, se he funcion generaor o have a high-level volage of 1 V and a low-level volage of 0 V. We choose he low-level o be 0 V because we need a se funcion raher han a square wave in his ar of he exerimen. This generaes a 1V se funcion ouu from he funcion generaor. (Laer, you will increase his volage; see Table 3.) Se he frequency of he funcion generaor a 20 khz. Do no change he duy cycle (defaul value is 50 %). 4. Oscilloscoe Seings: If you are no sure how o oerae he oscilloscoe, go back o he Lab 1 manual and read more on he oscilloscoe oeraion. Adjus he waveform seings of he oscilloscoe o oimally dislay he urn-on ransien signals. Your dislayed waveforms should be similar o hose in Figure 7. 5. Save he waveform o your USBG o collec CH1 (diode) and CH2 (whole circui) daa searaely as.csv files. 6. Using cursors (or imor.csv files ino EXCEL sreadshee), calculae he forward curren (I F) as follows (be sure o record your values in Table 3): I VCh2, ss VCh 1, ss F, Rmeasured Here he subscri ss means seady-sae. If using cursors, be sure he robe signals are a same ground on he screen. 7. Nex, leave only he Channel across he diode (CH1) on. Use he cursors for boh volage and ime o measure he Vk - Vss and he forward recovery ime ( fr) as shown in Figure 7. Record he forward recovery ime in he Table 3. 8. Again, save your waveform o USB o collec daa. You can use his daa o recheck se 7 if needed. 9. Reea Ses 5-7 for he oher volages given in Table 3 and be sure o record he corresonding I F and fr. Remember o also save your waveforms. Lab VII: Transien Signals of PN Juncion Diodes Page 14

Table 3. Measured daa for he urn on and urn off ransien. V High-Level V Low-Level R I F V k-vss fr V ss-voff rd 1 V + 0.0 V 2.5 V + 0.0 V 5 V + 0.0 V 5.2 TURN-OFF TRANSIENT Nex, you will measure he urn-off characerisics of he -n juncion diode. 1. Use he same circui and he same inu as used in he revious secion (5.1), bu his ime adjus he oscilloscoe o see he close u view of he waveforms similar o he Figure 8. In oher words, you ve invesigaed he firs half, he se u orion of he signals, now scroll over (in ime) o invesigae he se down orion of he signals. 2. Use he Channel across he diode (CH1) o measure he V ss V off and relaxaion delay ime ( rd) and record i in Table 3 above; use Figure 8 as a guide o making he measuremens for all se volages shown in he Table 3. Do no forge o save waveforms o USB o collec daa for grahs for each rd measuremen (similar o se 8). You may no see a significan volage dro as noed in Figure 8. 5.3 REVERSE RECOVERY TRANSIENT Nex, you will measure he reverse recovery ransien of he diode as he ulsed curren is swiched from I F o I R. 1. Consruc he circui as shown in Figure 13. You will need only one oscilloscoe robe, se across he resisor, and aached o CH1. 2. Program he funcion generaor o: Ouu a square wave. Lab VII: Transien Signals of PN Juncion Diodes Page 15

Se he funcion generaor o have a high-level volage of 0.9 V and a low-level volage of 0 V (his is he firs enry of Table 9; you will be adjusing hese volages as noed in he Table). Se he frequency of he funcion generaor o 20 khz. Do no change he duy cycle (defaul value is 50 %). 3. Measure he forward curren (I F) and he reverse curren (I R) as follows and record hem in he Table 4; Use he equaion given below. You would se u he oscilloscoe o show he close u view of he waveforms similar o he Figure 11. V. R Ch1 I measured Noe: he ransien signals may no be erfecly fla. Esimae a middle region. 4. Now use he cursors for boh volage and ime o find he sorage delay ime ( sd) and he oal reverse recovery ime ( rr) as shown in Figure 11 and record hem in he Table 4. 5. Save waveforms o USB o collec daa; you may use his daa o verify Se 4 in case here were any errors done in lab. 6. Reea ses 3-5 for he several volage seings lised in Table 4 and record he corresonding sd and rr. 1N4002 Figure 13. Circui used o make he reverse recovery ransien measuremens. Lab VII: Transien Signals of PN Juncion Diodes Page 16

Table 4. Measured daa for he reverse recovery ransien. V High-Level V Low-Level V F I F V R I R sd rr 0.9 V 0.0 V 0.9 V - 0.5 V 0.9 V -1 V 0.9 V -2 V 0.9 V -4 V 0.5 V -1 V 0.1 V -1 V 1.4 V -1 V 1.8 V -1 V 6. LAB REPORT Tye a lab reor wih a cover shee conaining your ile, name, your lab arner s name, class, secion number, dae he lab was erformed and he dae he reor is due. Use he following ouline o draf your lab reor: ABSTRACT: Briefly describe he conens of your reor. DATA PRESENTATION: o Creae a well formaed able resening he daa from Table 3. o Creae a well formaed able resening he daa from Table 4. ANALYSIS: o Turn ON Transien Using any one aricular daa se from Table 3 (e.g., 1V High- Level and 0V Low-Level), and roerly lo he volage waveforms from boh channels and show how you calculaed he forward curren I F. You should imor your grah ino your reor and use labels o show Vch1,ss and Vch2,ss, ec. Lab VII: Transien Signals of PN Juncion Diodes Page 17

o o Again, using any one aricular daa se, roerly lo he Ch2 volage waveform and show how you calculaed he forward recovery ime fr. Be sure o use labels o show V eak and V ss. In your own words, briefly exlain wha is haening in he diode during his urn on ransien. Turn OFF Transien Presen all scoegrab.vi acquired daa los for his secion in one grah. Make sure i is iled, boh axes are labeled, and he los are disinguishable and have aroriae legends. Using any one aricular daa se (e.g., 1V High-Level and 0V Low-Level), roerly lo he CH2 volage waveform and show how you calculaed he relaxaion delay ime rd. Be sure o use labels o show V ss and V off. In your own words, briefly exlain wha is haening in he diode during his urn-off ransien. Reverse Recovery Transien Using any one aricular daa se (e.g., 0.9V High-Level and - 0.5V Low-Level), roerly lo he volage waveform from CH1 and show how you calculaed sd and rr. Be sure o clearly label V F, V R, sd, and rr. In your own words, briefly exlain wha is haening in he diode during his reverse recovery ransien. CONCLUSION: Describe how your analyses corresond wih he heory described in BACKGROUND secion and he exbook. Aach: Signed insrucor verificaion form. Lab VII: Transien Signals of PN Juncion Diodes Page 18