Forward and Reverse Biased Junctions

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1 TEMARIO DEL CURSO DE FUNDAMENTOS DE FÍSICA DE SEMICONDUCTORES 1. Itroducció a Física Electróica 1.1 Proiedades de cristales y crecimieto de semicoductores 1. Átomos y electroes 1.3 Badas de eergía y ortadores de carga e semicoductores 1.4 Exceso de ortadores e semicoductores. Uioes.1 Fabricació de uioes -. Codicioes de equilibrio.3 Polarizació de uioes e directa e iversa bajo codicioes de estado estacioario.4 Rutura bajo olarizació iversa.5 Codicioes de trasitorio y a-c.6 Desviacioes de la teoría secilla.7 Uioes metal-semicoductor Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 41 Forward ad Reverse Biased Juctios The - juctios are used extesively i rectificatio i.e. allowig curret to flow easily i oly oe directio. I (diffusio) Forward biasig (ositive voltage o the -side of the juctio) Reverse biased (ositive voltage o the -side of the juctio) I (geeratio) Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 4

2 Ideal model The ideal diode: (a) diode circuit symbol; (b) i-v characteristic; (c) equivalet circuit i the reverse directio; (d) equivalet circuit i the forward directio. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 43 Qualitative descritio of Curret Flow at a Juctio We assume that a alied voltage bias V aears across the trasitio regio (sace charge regio) of the juctio rather tha i the eutral ad regios.? Sice a alied voltage chages the electrostatic otetial barrier ad thus the electric field withi the trasitio regio, we would exect chages i the various comoets of curret at the juctio. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 44

3 Thermal equilibrium E C drift -x 0 x 0 - diffusio - qv o E V + diffusio The curret at V0 (equilibrium) is zero sice the geeratio (drift) ad diffusio currets cacel. ( diffusio) I( ) 0 I I drift + drift Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 45 E F Forward bias V F + - I F E C - -x x drift diffusio - q(v 0 -V F ) E F qv F E F E V + diffusio + drift The total electrostatic otetial across the juctio decreases by V F Width of the deletio regio decreases. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 46

4 The total curret I is the diffusio curret mius the absolute value of geeratio curret, which we will ow refer to as I 0 : I qv V I 0 ex 1 I0 ex 1 kt v th Whe V is ositive ad greater tha a few kt/q (V>>3V th ), the exoetial term is greater tha the uity: I I 0 qv ex kt Whe V is egative, the exoetial term aroaches to zero: I I 0 This egative geeratio curret is also called the reverse saturatio curret Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 47 We exect the miority carrier cocetratio o each side of the juctio vary with the alied bias because of variatios i the diffusio of carrier across the juctio. The equilibrium ratio of holes cocetratios o each side Carrier Ijectio ex [ qv kt ] 0 The uder bias V, ( x ) ( x ) [ q( V V ) kt ] Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero ex If we assume low-level ijectio of mobile carriers, that is the majority carrier desities are essetially uchaged uder bias, ( x 0 ) So takig the ratio of the revious two equatios we get, ( x ) 0 ex [ qv kt ] 0

As we ca see, the miority carrier cocetratios at the edge of the trasitio regio are raised by the forward bias, The excess holes ijected across the deletio regio ito the side is give by, ( x ) ( ex[

5 As we ca see, the miority carrier cocetratios at the edge of the trasitio regio are raised by the forward bias, The excess holes ijected across the deletio regio ito the side is give by, ( x ) ( ex[ qv kt ] 1) 0 Similarity for excess electros ijected o the side ( x ) ex[ qv kt ] ( 1) 0 Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 49 From the cotiuity equatio i the regio δ t L D D τ δ x δ δ τ x δ L 0; Boudary coditios are, ( x 0) ( ) ad δ( x ) δ 0 δ ( x) Solutio of δ(x) is, x qv x ex ex 1 ex L kt L Miority carrier desity decays with a characteristic legth give by L Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 50

6 From the cotiuity equatio i the regio we ca get: δ t D δ x δ τ δ x δ L 0; L D τ Boudary coditios are, ( x 0) ( ) ad δ( x ) δ 0 δ Solutio of δ(x) is, x qv x ( x) ex ex 1 ex L kt L Miority carrier desity decays with a characteristic legth give by L Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 51 Curret flow Sice we assume that the drift curret is uaffected by the alied bias, we are ow i a ositio to cosider the et curret by cosiderig oly the diffusio of ijected holes ito side, I ( x ) qad d ( δ( x) ) dx D qa L ( δ( x) ) Where A is the cross sectioal area of the juctio. The total hole curret ijected ito the -side is roortioal to the excess hole desity at a articular oit. The total curret ijected ito the -side ca be obtaied by evaluatig the revious equa. at xx 0, I qv ( X 0) q ex 1 AD L Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 5 kt

7 By similar aalysis, the ijectio of the electros i the side leads to a electro curret at the juctio I AD qv ( X 0) q ex 1 So, the total curret ito the diode is give by: L kt I I ( x ) + I ( x ) I I s e ev kt ( 1) Saturatio curret desity I s D qa L Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero D L 0 There is aother way to calculatig the total curret ito a diode. This is called charge cotrol aroximatio. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 54

8 Whe V is egative, the exoetial term aroaches to zero: I I 0 This meas that I 0 is costat, but this is the ideal case. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 55 TEMARIO DEL CURSO DE FUNDAMENTOS DE FÍSICA DE SEMICONDUCTORES 1. Itroducció a Física Electróica 1.1 Proiedades de cristales y crecimieto de semicoductores 1. Átomos y electroes 1.3 Badas de eergía y ortadores de carga e semicoductores 1.4 Exceso de ortadores e semicoductores. Uioes.1 Fabricació de uioes -. Codicioes de equilibrio.3 Polarizació de uioes e directa e iversa bajo codicioes de estado estacioario.4 Rutura bajo olarizació iversa.5 Codicioes de trasitorio y a-c.6 Desviacioes de la teoría secilla.7 Uioes metal-semicoductor Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 56

9 Reverse Bias Breakdow Whe a sufficietly large reverse bias is alied to a - juctio, it breaks dow ad coducts a very large curret. There are mechaisms by which this ca occur The tuelig effect This is the basis for the tuel diode ad oe mechaism for storig ad erasig charges i o-volatile semicoductor memory (NVSM) devices Avalache multilicatio This effect imoses a uer limit o the reverse bias i most devices. It limits the collector voltage of a biolar trasistor ad the drai voltage of a MOSFET. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 57 The Tuellig Effect Whe a high electric field is alied to a - juctio i the reverse directio, a electro ca tuel through the badga from the valece bad to the coductio bad. Tuelig is the mai breakdow mechaism for Si ad GaAs juctios where E C E the breakdow voltage is less tha 4E g /q E F E V <4E g E C E F The tuellig of electros from the side valece bad to side coductio bad costitutes a reverse curret from to, this is called Zeer effect. E V Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 58

10 Avalache multilicatio Juctio breakdow at reverse biases i excess of 6E g / q is domiated by avalache multilicatio E A thermally geerated electros i the deletio regio gais kietic eergy from the electric field E C O collisio with a lattice atom it breaks the bod ad geerates a electro-hole air E F E V >6E g E C These i tur acquire kietic eergy from the electric field ad geerate more electro-hole airs ad so it cotiues. E F Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 59 E V Critical field at breakdow versus backgroud doig for Si ad GaAs oe-sided abrut juctios. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 60

11 Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 61 TEMARIO DEL CURSO DE FUNDAMENTOS DE FÍSICA DE SEMICONDUCTORES 1. Itroducció a Física Electróica 1.1 Proiedades de cristales y crecimieto de semicoductores 1. Átomos y electroes 1.3 Badas de eergía y ortadores de carga e semicoductores 1.4 Exceso de ortadores e semicoductores. Uioes.1 Fabricació de uioes -. Codicioes de equilibrio.3 Polarizació de uioes e directa e iversa bajo codicioes de estado estacioario.4 Rutura bajo olarizació iversa.5 Codicioes de trasitorio y a-c.6 Desviacioes de la teoría secilla.7 Uioes metal-semicoductor Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 6

12 Trasiet ad a-c Coditios We have cosidered the roerties of - juctios uder equilibrium ad with steady state curret. Most of the basics cocets of juctio devices ca be obtaied from these roerties, excet for the imortat behavior of juctios uder trasiet or ac coditios. Sice the most solid state devices are used for switchig or for rocessig a-c sigals. We ivestigate the imortat ifluece of excess carries i trasiet ad ac roblems, i.e. the switchig of a diode from its forward state to its reverse state is aalyzed to illustrate a tyical trasiet roblem Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 63 Time Variatio of Stored Charge For a roer solutio of the trasiet roblem, we must to use the time deedet cotiuity equatios. We ca obtai each comoet of the curret at ositio x ad time t from these equatios, we ca write: J ( x, t) x δ( x, t) ( x, t) q + q τ t To obtai the istataeous desity curret, we ca itegrate both sides at time t to obtai: x δ( x, t) ( x, t) J (0) J ( x) q + q dx τ t 0 For ijectio ito a log regio from a + regio, we ca take the curret at x 0 to be all hole curret, ad J at x to be zero. The the total ijected curret, icludig time variatios, is qa i( t) i ( x 0, t) δ( x τ 0, t) dx Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 64 + qa t 0 ( x, t) dx

13 Q ( t) dq ( t i( t) + τ dt ) This results idicates that the hole curret ijected across the + juctio is determied by two charge storage effects: 1. The usual recombiatio term i which the excess carrier distributio is relaced every τ secods.. A charge buildu( or deletio )term. We ca solve for the stored charge as a fuctio of time for a give curret trasiet. For examle the ste tur off trasiet. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 65 Solvig the revious equatio with Lalace trasforms, with i(t > 0) 0 ad Q(0)Iτ, we obtai Q ( S) 0 + SQ τ Q Q Iτ ( S) 1 s + τ ( S) Iτ t ( t) Iτ ex τ As exected, the stored charge dies out exoetially from its iitial value Iτ with a time costat equal to the hole lifetime i the material Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 66

14 The revious aalysis does idicate clearly that the voltage across a - juctio caot be chaged istataeously, ad that stored charge ca reset a roblem i a diode iteded for switch alicatio. Thus i the quasi-steady state aroximatio, the juctio voltage varies accordig to kt Iτ t v ( t ) l ex + 1 q qal τ The switchig rocess ca be made still faster by urosely addig recombiatio ceters, such as Au atoms i Silico, to icrease the recombiatio rate Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 67 Reverse Recovery Trasiet I most switchig alicatios a diode is switched from forward coductio to reverse biased state. The resultig stored charge trasiet is somewhat more comlicated tha for a simle tur-off trasiet. Lets us to assume a + - juctio is drive by a square wave geerator that eriodically switches from +E to E. While E is ositive the diode is forward biased, ad i steady state the curret I f flows through the juctio. If E is much larger tha the small forward voltage of the juctio, the source voltage aears almost etirely across de resistor (R), the ositive i I f E/R. After the voltage geerator is reversed (t > 0), the curret must be iitially reverse to i I r -E/R. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 68

15 The reaso for this uusually large reverse curret through the diode is that the stored charge. The time (t sd ) required for the stored charge to became zero is called the storage delay time. The critical arameter determiig t sd is the carrier timelife (τ ) t sd τ erf 1 I f I f + I r Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 69 Caacitace of - juctios There are two tyes of caacitace associated with a juctio: 1. The juctio caacitace due to diole i the trasitio regio. (deletio caacitace).. The charge storage caacitace arisig from the laggig behid of voltage as curret chages. (Diffusio caacitace). The juctio deletio layer caacitace er uit area is defied as CjdQ/dV, where dq is the icremetal chage i the deletio layer charge er uit area for a icremetal chage i the alied voltage dv. The deletio caacitace dq dq ε s er uit area is give by Cj [ F / cm ] dq W ε Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 70 dv s W

16 Thermal equilibrium -W W E C qv 0 E V E F What haes whe we aly ad exteral reverse bias across the juctio? Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 71 Reverse bias V R - + I R -W W E C q(v 0 +V R ) E F E V E F qv R E F The total electrostatic otetial across the juctio icreases by V R Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 7

17 The, the width of the deletio regio icreases. ε s 0 W [ V V ] q Na + N NaNd The deletio caacitace er uit area is the same as the stadard exressio for a arallel late caacitor where the sacig betwee of the two lates reresets the deletio layer width. I the case for a oe-side abrut juctio ( + -), we obtai ε s qε snd Cj W V V d [ ] 0 The quatity Cj is a voltage-variable caacitace, sice Cj is roortioal to (V 0 -V) 1/. The - juctio device which makes use of the voltage variable roerties of Cj is called a varactor. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 73 The diffusio caacitace As a - diode is forward biased, the miority carrier distributio i the quasi-eutral regio icreases dramatically. I additio, to reserve quasi-eutrality, the majority carrier desity icreases by the same amout. This effect leads to a additioal caacitace called the diffusio caacitace. The excess miority-carrier charge is obtaied by itegratig the charge desity over the quasi-eutral regio. I the case of a + - juctio : C d Q d Q dv W X C ea d q kt [ ] AqL V Iτ th 0 o dx V ex Vth Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 74

18 TEMARIO DEL CURSO DE FUNDAMENTOS DE FÍSICA DE SEMICONDUCTORES 1. Itroducció a Física Electróica 1.1 Proiedades de cristales y crecimieto de semicoductores 1. Átomos y electroes 1.3 Badas de eergía y ortadores de carga e semicoductores 1.4 Exceso de ortadores e semicoductores. Uioes.1 Fabricació de uioes -. Codicioes de equilibrio.3 Polarizació de uioes e directa e iversa bajo codicioes de estado estacioario.4 Rutura bajo olarizació iversa.5 Codicioes de trasitorio y a-c.6 Desviacioes de la teoría secilla.7 Uioes metal-semicoductor Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 75 Recombiatio ad Geeratio i Trasitio Regio Uder some rage of forward bias, We could be described by the ideal diode equatio. qv kt qv kt ( e ) I e I I0 1 0 However, for the real - juctios I is give by: I I + I I I qv kt qv kt ( e 1) + I ( e 1) 1] Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 76 D0 I I [ e D qv ηkt G G0 Where varies betwee 1 ad, deedig of material ad temerature. Sice determies the dearture from the ideal diode characteristic, it is ofte called the ideality factor

19 Reverse Bias Curret Desity Uder reverse bias (V is egative), the curret goes towards the saturatio curret desity (I 0 ). As we ca see from the ideal diode equatio: I ( qv kt e ) I0 1 However, for Silico ad GaAs - juctios uder reverse bias I R I 0!, ad I R >> I 0! The,??? Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 77 Reverse Bias Geeratio Curret Desity Uder reverse bias, the geeratio curret (I G ) becomes to be very imortat whe the deletio regio is devoid of carries. Uder thermal equilibrium the thermal geeratio of e-h airs is balaced by recombiatio (G R). Uder reverse bias, there are very few e-h airs i the deletio regio, ad the recombiatio rate is early zero. However, the thermal geeratio rocesses cotiuously suly the e-h airs to deletio regio. The I G ca be determied from: I G W W qag dx 0 0 qai qaw i dx τ τ g g The, I R I G + I 0, ad I G > I 0 for Silico ad GaAs - juctios uder reverse bias Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 78

20 Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 79 Ohmic Losses For higher forward bias voltages, the curret o loger icreases exoetially with voltage. Istead, it icreases liearly due to the series resistace of the diode. This series resistace ca be due to the cotact resistace betwee the metal ad the semicoductor, due to the resistivity of the semicoductor or due to the series resistace of the coectig wires. R S I I D + V j - V R + + V V Va I [ R ( I) R ( I) ] Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 80

21 Small sigal equivalet circuit of a - juctio V d V d ' + V d g d di dv d d o I 0 V th e V ' / d V th I d g d I + d Id g d R s I d -I 0 V V + V d d d V d I d + V d C d _ Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 81 Graded juctios The case of liearity graded juctio is show i the ext figure. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 8

22 The Poisso equatio for the case is d ψ dx de dx ρs ε s q ε s ax W W x Where G is the imurity gradiet (i cm -4 ) ad W is the deletio layer width. We obtai the built-i otetial (V bi ) ad the deletio layer width (W ) after some simle stes. V bi qaw 1ε s W 1ε s V qa bi 1 3 Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 83 TEMARIO DEL CURSO DE FUNDAMENTOS DE FÍSICA DE SEMICONDUCTORES 1. Itroducció a Física Electróica 1.1 Proiedades de cristales y crecimieto de semicoductores 1. Átomos y electroes 1.3 Badas de eergía y ortadores de carga e semicoductores 1.4 Exceso de ortadores e semicoductores. Uioes.1 Fabricació de uioes -. Codicioes de equilibrio.3 Polarizació de uioes e directa e iversa bajo codicioes de estado estacioario.4 Rutura bajo olarizació iversa.5 Codicioes de trasitorio y a-c.6 Desviacioes de la teoría secilla.7 Uioes metal-semicoductor Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 84

23 Metal-Semicoductor Juctio (Schottky barrier) Metal -Semicoductor Vacuum level qφ m q ( φ χ ) m qχ qφs E C E F E V What haes whe we cotact the metal ad semicoductor i thermal equilibrium? Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 85 Metal -Semicoductor qχ Vacuum level qφ m qv 0 qφ s qφ B E C E F E V The Fermi level must be costat at thermal equilibrium but the vacuum level must be cotiuous... Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 86

24 metal-semicoductor juctio (Schottky barrier) To esure the cotiuity of the vacuum level, the Fermi level must move deeer ito the semicoductor badga at the iterface. This ivolves electros movig out from the semicoductor ito the metal (which has so may electros already that its Fermi level or bad rofile is uaffected). As electros move out, they leave behid ucomesated ioised door atoms (as i a ++ - juctio) ad a deletio regio is formed. The Schottky barrier height at the juctio is the differece betwee the semicoductor coductio bad ad the metal Fermi level so that, qφ B qφ m qχ Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 87 Electros movig from the semicoductor to the metal ecouter a eergy barrier give by the built-i otetial, qv bi qφ qφ m s For the juctio betwee a metal ad a -tye semicoductor the barrier height ad built i voltage are give by, qφ B E g ( qφ qχ ) m qv bi qφ qφ s m Sketch the bad diagram to satisfy yourself that this is the case Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 88

25 Deletio width Oce the Schottky barrier height is kow we ca calculate the electric field rofile, deletio width etc. The roblem for a Schottky barrier o a -tye semicoductor is idetical to that for a oe-sided abrut + - juctio (o deletio width o the metal side) W ε s 0 ( V V ) qn D N D is the door cocetratio V is the alied bias (ositive forward, egative reverse) Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 89 Metal-Semicoductor Juctio Uder Bias qφ B qv bi E C E F E V Zero bias qφ B q ( V V ) 0 E C E F E V Forward bias (V is ositive) Decreased barrier to electros flow from the semicoductor to the metal qφ B q ( V V ) 0 Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 90 E C E F E V Reverse bias (V is egative) Icreased barrier to electros flow from the semicoductor to the metal rectificatio

26 Curret flow i a Schottky barrier Figure 7.7. Curret trasort by the thermioic emissio rocess. (a) Thermal equilibrium; (b) forward bias; ad (c) reverse bias. Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 91 Curret flow i a Schottky barrier At thermal equilibrium the flow of electros from the semicoductor to the metal is exactly balaced by the flow of electros from the metal to the semicoductor so, J m s J s m CN qφ Sice the barrier height o the metal side is ot deedet o the alied bias the curret from metal to semicoductor will always be the same so the et curret uder bias is the, J J s m J m s CN C e C e qφ B kt B kt qv kt ( e 1) J J e s qv kt ( 1) Saturatio curret desity, J s rectificatio Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 9

27 Trasort Mechaisms i Schottky diodes TE Thermioic Emissio J S φ B A* ex kt kt TFE J S A* T Thermioic Field Emissio [ πe q[ φ V ( E E ) ] 1 q( E E ) q( φ ( E E ) 00 B C E00 k cosh kt f ex C kt f B E C 0 f FE J S Field Emissio qφ 0 ex B Jst E 00 Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 93 Tyical Schottky Barriers Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 94

28 Ohmic Cotacts Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 95 Curso roedéutico de Electróica INAOE 009 Dr. Pedro Rosales Quitero 96

Carriers in a semiconductor diffuse in a carrier gradient by random thermal motion and scattering from the lattice and impurities.

Carriers in a semiconductor diffuse in a carrier gradient by random thermal motion and scattering from the lattice and impurities. Diffusio of Carriers Wheever there is a cocetratio gradiet of mobile articles, they will diffuse from the regios of high cocetratio to the regios of low cocetratio, due to the radom motio. The diffusio