Intrinsic Carrier Concentration

Transcription

1 Itrisic Carrier Cocetratio I. Defiitio Itrisic semicoductor: A semicoductor material with o dopats. It electrical characteristics such as cocetratio of charge carriers, deped oly o pure crystal. II. To derive carrier cocetratio i thermal equilibrium coditio that is i a steady state coditio at a give temperature without ay exteral excitatio. III. Practical a itrisic semicoductor is oe that cotais relatively small amout of impurities. Zulfiqar Ali EEE132 1

2 Itrisic Carrier Cocetratio I. To obtai the electro desity (umber of electro per uit volume) i itrisic semicoductor, we must evaluate the electro desity i a icremetal eergy rage de. II. Desity (E) is give by product of desity states N(E) ad a probability of occupyig eergy rage F(E). III. Thus the electro desity is give by: = ETOP ( E) de = ETOP N( E) F( E) de 0 0 Zulfiqar Ali EEE132 2

3 Itrisic Carrier Cocetratio Where is i cm -3 ad N(E) is i (cm 3- ev)-1. The probability that a electro occupies ad electroic state with eergy E is give by Fermi- Dirac distributio. F ( E ) = ( E E ) 1 + e k is Boltzma costat, t is temperature( K), E F is Fermi level. 1 kt F Zulfiqar Ali EEE132 3

4 Itrisic Semicoductor The Fermi eergy is the eergy at which the probability of occupatio by a electro is exactly o half. Zulfiqar Ali EEE132 4

5 Figure Fermi distributio fuctio F(E) versus (E E F ) for various temperatures. Zulfiqar Ali EEE132 5

6 Figure Itrisic semicoductor. (a) Schematic bad diagram. (b) Desity of states. (c) Fermi distributio fuctio. (d) Carrier cocetratio. Zulfiqar Ali EEE132 6

7 Itrisic Carrier Cocetratio There are large umber of allowed states i the coductio bad. However there will ot be may electros i the coductio bad. Therefore the possibility for the electro to be i regio is very low. If we refer to the bottom of the coductio bad the electro desity is equivalet to Zulfiqar Ali EEE132 7

8 Itrisic semicoductor Electro desity i the coductio bad. = N C ( E exp[ C E ) ] kt N C = 2.86 X cm -3 for silico ad 4.7 X cm -3 for gallium arseide. p = N V ( E exp[ F E V F ) ] kt N V = 2.66 X cm -3 for silico ad 7 X cm -3 for gallium arseide Zulfiqar Ali EEE132 8

9 Itrisic Semicoductor I itrisic semicoductor the umber of electro per uit volume is equal to umber of hole per uit volume i the valece bad. p = i The larger the bad gap the smaller itrisic carrier desity. 2 Zulfiqar Ali EEE132 9

10 Nodegeerated Semicoductor For shallow doors i silico there usually eough eergy to ioize all door impurities at room temp. This coditio is called complete ioizatio. Therefore = N D E C -E F = kt l (N C /N D ) Same case applies to hole. Zulfiqar Ali EEE132 10

11 Figure Type semicoductor. (a) Schematic bad diagram. (b) Desity of states. (c) Fermi distributio fuctio (d) Carrier cocetratio. Note that p = i 2. Zulfiqar Ali EEE132 11

12 Readig assigmet read o the Degeerated Semicoductor Zulfiqar Ali EEE132 12

13 Carrier Trasport Pheomea (Carrier Drift) Mobility Electros move i all differet directio. Whe small electric field E is applied to the semicoductor electro will experiece force. qe. The electro will accelerated alog the field. I opposite directio. Additioal compoet is called a drift velocity. Zulfiqar Ali EEE132 13

14 Mobility The mometum applied to a electro is mometum gaied. qετ v = c = m qτ C m v ε The drift velocity deped o the applied electric field. Zulfiqar Ali EEE132 14

15 Mobility The proportioality factor is called electro mobility μ q τ m c Is importat parameter i carrier trasport because it describes how strogly the motio of electro i iflueced by applied electric field. Zulfiqar Ali EEE132 15

16 Mobility Drift velocity v v p = = μ μ p ε ε Hole flows i the same directio as electric field. The mobility is iflueced by impurity scatterig ad lattice scatterig. Zulfiqar Ali EEE132 16

17 Curret The trasport carriers uder the ifluece of a electric field produce drift curret. Zulfiqar Ali EEE132 17

18 Figure 3.5. Curret coductio i a uiformly doped semicoductor bar with legth L ad cross-sectioal area A. Zulfiqar Ali EEE132 18

19 Resistivity Sample semicoductor of legth L ad cross sectio of A ad a electro cocetratio of electros/cm 3. If we apply a electric field to the sample the electro curret desity J flowig i the sample should be product of charge (- q) o electro time the electro velocity. J = qv Zulfiqar Ali EEE132 19

20 Resistivity Curret desity J = J + J p = ( qμ + qpμp) ε Coductivity σ = q + ( μ pμ p ) Resistivity 1 ρ = σ Zulfiqar Ali EEE132 20