Basic Physics of Semiconductors

Transcription

1 Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1

2 Semicoductor Physics Semicoductor devices serve as heart of microelectroics. PN juctio is the most fudametal semicoductor device. CH2 Basic Physics of Semicoductors 2

3 Charge Carriers i Semicoductor To uderstad PN juctio s IV characteristics, it is imortat to uderstad charge carriers behavior i solids, how to modify carrier desities, ad differet mechaisms of charge flow. CH2 Basic Physics of Semicoductors 3

4 Periodic Table This abridged table cotais elemets with three to five valece electros, with Si beig the most imortat. CH2 Basic Physics of Semicoductors 4

5 Silico Si has four valece electros. Therefore, it ca form covalet bods with four of its eighbors. Whe temerature goes u, electros i the covalet bod ca become free. CH2 Basic Physics of Semicoductors 5

6 Electro-Hole Pair Iteractio With free electros breakig off covalet bods, holes are geerated. Holes ca be filled by absorbig other free electros, so effectively there is a flow of charge carriers. CH2 Basic Physics of Semicoductors 6

7 Free Electro Desity at a Give Temerature E 15 3/ 2 g i T ex 2kT 0 ( T 300 K) i ( T i K) electros/ cm electros/ cm electros/ cm E g, or badga eergy determies how much effort is eeded to break off a electro from its covalet bod. There exists a exoetial relatioshi betwee the freeelectro desity ad badga eergy. CH2 Basic Physics of Semicoductors 7

8 Doig (N tye) Pure Si ca be doed with other elemets to chage its electrical roerties. For examle, if Si is doed with P (hoshorous), the it has more electros, or becomes tye N (electro). CH2 Basic Physics of Semicoductors 8

9 Doig (P tye) If Si is doed with B (boro), the it has more holes, or becomes tye P. CH2 Basic Physics of Semicoductors 9

10 Summary of Charge Carriers CH2 Basic Physics of Semicoductors 10

11 Electro ad Hole Desities i Majority Carriers : Miority Carriers : Majority Carriers : Miority Carriers : 2 N N N A 2 i A D N 2 i D The roduct of electro ad hole desities is ALWAYS equal to the square of itrisic electro desity regardless of doig levels. CH2 Basic Physics of Semicoductors 11

12 First Charge Trasortatio Mechaism: Drift v h E v e E The rocess i which charge articles move because of a electric field is called drift. Charge articles will move at a velocity that is roortioal to the electric field. CH2 Basic Physics of Semicoductors 12

13 Curret Flow: Geeral Case I vw hq Electric curret is calculated as the amout of charge i v meters that asses thru a cross-sectio if the charge travel with a velocity of v m/s. CH2 Basic Physics of Semicoductors 13

14 CH2 Basic Physics of Semicoductors 14 E q q E q E J q E J tot ) ( Curret Flow: Drift Sice velocity is equal to E, drift characteristic is obtaied by substitutig V with E i the geeral curret equatio. The total curret desity cosists of both electros ad holes.

15 Velocity Saturatio v 0 1 be 0 vsat b 0E 1 v sat E A toic treated i more advaced courses is velocity saturatio. I reality, velocity does ot icrease liearly with electric field. It will evetually saturate to a critical value. CH2 Basic Physics of Semicoductors 15

16 Secod Charge Trasortatio Mechaism: Diffusio Charge articles move from a regio of high cocetratio to a regio of low cocetratio. It is aalogous to a every day examle of a ik drolet i water. CH2 Basic Physics of Semicoductors 16

17 Curret Flow: Diffusio I J AqD qd d dx d dx J J tot qd q( D d dx d dx D d ) dx Diffusio curret is roortioal to the gradiet of charge (d/dx) alog the directio of curret flow. Its total curret desity cosists of both electros ad holes. CH2 Basic Physics of Semicoductors 17

18 Examle: Liear vs. Noliear Charge Desity Profile J qd d dx qd N L J d qd dx qd N L d x ex L d Liear charge desity rofile meas costat diffusio curret, whereas oliear charge desity rofile meas varyig diffusio curret. CH2 Basic Physics of Semicoductors 18

19 Eistei's Relatio D kt q While the uderlyig hysics behid drift ad diffusio currets are totally differet, Eistei s relatio rovides a mysterious lik betwee the two. CH2 Basic Physics of Semicoductors 19

20 PN Juctio (Diode) Whe N-tye ad P-tye doats are itroduced side-byside i a semicoductor, a PN juctio or a diode is formed. CH2 Basic Physics of Semicoductors 20

21 Diode s Three Oeratio Regios I order to uderstad the oeratio of a diode, it is ecessary to study its three oeratio regios: equilibrium, reverse bias, ad forward bias. CH2 Basic Physics of Semicoductors 21

22 Curret Flow Across Juctio: Diffusio Because each side of the juctio cotais a excess of holes or electros comared to the other side, there exists a large cocetratio gradiet. Therefore, a diffusio curret flows across the juctio from each side. CH2 Basic Physics of Semicoductors 22

23 Deletio Regio As free electros ad holes diffuse across the juctio, a regio of fixed ios is left behid. This regio is kow as the deletio regio. CH2 Basic Physics of Semicoductors 23

24 Curret Flow Across Juctio: Drift The fixed ios i deletio regio create a electric field that results i a drift curret. CH2 Basic Physics of Semicoductors 24

25 Curret Flow Across Juctio: Equilibrium I I drift, drift, I I diff, diff, At equilibrium, the drift curret flowig i oe directio cacels out the diffusio curret flowig i the oosite directio, creatig a et curret of zero. The figure shows the charge rofile of the PN juctio. CH2 Basic Physics of Semicoductors 25

26 Built-i Potetial d dv q E qd D dx dx x2 d dv D V ( x2) V ( x1 ) x 1 kt kt N AN V0 l, V0 l 2 q q i D D d dx l Because of the electric field across the juctio, there exists a built-i otetial. Its derivatio is show above. CH2 Basic Physics of Semicoductors 26

27 Diode i Reverse Bias Whe the N-tye regio of a diode is coected to a higher otetial tha the P-tye regio, the diode is uder reverse bias, which results i wider deletio regio ad larger built-i electric field across the juctio. CH2 Basic Physics of Semicoductors 27

28 Reverse Biased Diode s Alicatio: Voltage- Deedet Caacitor The PN juctio ca be viewed as a caacitor. By varyig V R, the deletio width chages, chagig its caacitace value; therefore, the PN juctio is actually a voltagedeedet caacitor. CH2 Basic Physics of Semicoductors 28

29 CH2 Basic Physics of Semicoductors 29 Voltage-Deedet Caacitace The equatios that describe the voltage-deedet caacitace are show above V N N N N q C V V C C D A D A si j R j j

30 Voltage-Cotrolled Oscillator 1 1 f res 2 LC A very imortat alicatio of a reverse-biased PN juctio is VCO, i which a LC tak is used i a oscillator. By chagig V R, we ca chage C, which also chages the oscillatio frequecy. CH2 Basic Physics of Semicoductors 30

31 Diode i Forward Bias Whe the N-tye regio of a diode is at a lower otetial tha the P-tye regio, the diode is i forward bias. The deletio width is shorteed ad the built-i electric field decreased. CH2 Basic Physics of Semicoductors 31

32 Miority Carrier Profile i Forward Bias, e, e V ex V 0 T, f V ex, f 0 V V T F Uder forward bias, miority carriers i each regio icrease due to the lowerig of built-i field/otetial. Therefore, diffusio currets icrease to suly these miority carriers. CH2 Basic Physics of Semicoductors 32

33 Diffusio Curret i Forward Bias I tot N D VF N A VF (ex 1) (ex 1) V ex V V 0 T ex V 0 T VT VT N A VF N D VF Itot (ex 1) (ex 1) V0 ex V V T 0 ex VT VT VT V 2 D D F I (ex 1) I s Aqi ( ) s V N AL N DL T Diffusio curret will icrease i order to suly the icrease i miority carriers. The mathematics are show above. CH2 Basic Physics of Semicoductors 33

34 Miority Charge Gradiet Miority charge rofile should ot be costat alog the x- axis; otherwise, there is o cocetratio gradiet ad o diffusio curret. Recombiatio of the miority carriers with the majority carriers accouts for the droig of miority carriers as they go dee ito the P or N regio. CH2 Basic Physics of Semicoductors 34

35 Forward Bias Coditio: Summary I forward bias, there are large diffusio currets of miority carriers through the juctio. However, as we go dee ito the P ad N regios, recombiatio currets from the majority carriers domiate. These two currets add u to a costat value. CH2 Basic Physics of Semicoductors 35

36 IV Characteristic of PN Juctio I D I S VD (ex 1) V T The curret ad voltage relatioshi of a PN juctio is exoetial i forward bias regio, ad relatively costat i reverse bias regio. CH2 Basic Physics of Semicoductors 36

37 Parallel PN Juctios Sice juctio currets are roortioal to the juctio s cross-sectio area. Two PN juctios ut i arallel are effectively oe PN juctio with twice the cross-sectio area, ad hece twice the curret. CH2 Basic Physics of Semicoductors 37

38 Costat-Voltage Diode Model Diode oerates as a oe circuit if V D < V D,o ad a costat voltage source of V D,o if V D teds to exceed V D,o. CH2 Basic Physics of Semicoductors 38

39 Examle: Diode Calculatios V I I X X X I X R V I R 1 D X 1 2.2mA for 0.2mA for V V X X V T 3V 1V l I I X S This examle shows the simlicity rovided by a costatvoltage model over a exoetial model. For a exoetial model, iterative method is eeded to solve for curret, whereas costat-voltage model requires oly liear equatios. CH2 Basic Physics of Semicoductors 39

40 Reverse Breakdow Whe a large reverse bias voltage is alied, breakdow occurs ad a eormous curret flows through the diode. CH2 Basic Physics of Semicoductors 40

41 Zeer vs. Avalache Breakdow Zeer breakdow is a result of the large electric field iside the deletio regio that breaks electros or holes off their covalet bods. Avalache breakdow is a result of electros or holes collidig with the fixed ios iside the deletio regio. CH2 Basic Physics of Semicoductors 41