CHAPTER 2. Energy Bands and Carrier Concentration in Thermal Equilibrium

Transcription

1 CHAPTER 2 Energy Bands and Carrier Concentration in Thermal Equilibrium

2 光電特性 Ge 被 Si 取代, 因為 Si 有較低漏電流 Figure 2.1. Typical range of conductivities for insulators, semiconductors, and conductors.

3 Figure 2.2. A generalized primitive unit cell.

4 Figure 2.3. Three cubic-crystal unit cells. (a) Simple cubic. (b) Bodycentered cubic. (c) Face-centered cubic.

5 * 半導體為 Single crystal Periodic 排列為 Lattice ( 晶格 ) Lattice constant Si,Ge 之 lattice 22 Si 之濃度 5 10 # Ⅲ-Ⅴ 之 Lattice 3 cm Figure 2.4. (a) Diamond lattice. (b) Zincblende lattice.

6 Figure 2.5. A (623)-crystal plane.

7 Figure 2.6. Miller indices of some important planes in a cubic crystal.

8 Figure 2.8. Simplified schematic drawing of the Czochralski puller. Clockwise (CW), counterclockwise (CCW).

9 四面體 Figure (a) A tetrahedron bond. (b) Schematic two-dimensional representation of a tetrahedron bond.

10 Si : #/cm 3 電子濃度 n 電洞濃度 p Intrinsic( 本質 ) n=p=ni 共價鍵 covalent hole 為 e 之空缺, 正電, 與 e 反向 Figure The basic bond representation of intrinsic silicon. (a) A broken bond at Position A, resulting in a conduction electron and a hole. (b) A broken bond at position B.

11 Figure The splitting of a degenerate state into a band of allowed energies.

12 Figure Schematic representation of an isolated silicon atom.

13 原子遠離時, 各有自己的能階. 距離移近, 演變為退化型能階. Space 再小, 演變為 conduction band,valence band ev 退化型能階 (Si) Figure Formation of energy bands as a diamond lattice crystal is formed by bringing isolated silicon atoms together.

14 Figure The parabolic energy (E) vs. momentum (p) curve for a free electron.

15 Figure A schematic energymomentum diagram for a special semiconductor with m n = 0.25 m 0 and m p = m 0.

16 Indirect Band gap (semiconductor) E 從 Ev 到 Ec 須做 P 之改變 direct Band gap (semiconductor) Ec 最低,Ev 最高. 在 P=0 µ 很小 ν = µ ε µ 很大 Figure Energy band structures of Si and GaAs. Circles (º) indicate holes in the valence bands and dots ( ) indicate electrons in the conduction bands.

17 Figure Schematic energy band representations of (a) a conductor with two possibilities (either the partially filled conduction band shown at the upper portion or the overlapping bands shown at the lower portion), (b) a semiconductor, and (c) an insulator.

18 Intrinsic semiconductor : impurity 所產生之 e,p << thermal 之 e,p n 電子濃度 F( E = n( E )de = 0 E ) top E top 濃度 1+ 1 E E e ( F 0 N( E )F( 能態密度 Fermi-Dirac distribution function E )de (9) = )/ kt (10) 能量 E 態位被佔據的機率 E F : Fermi Level, 被電子佔據的機率為 1/2 的能量

19 T E F : Fermi Level, 被電子佔據的機率為 1/2 的能量 T Figure Fermi distribution function F(E) versus (E E F ) for various temperatures.

20 n(e)=n(e) F(E) p(e)=p(e) F(E) Ee e Ei 正中間 Ep 與 E 1/2 成正比 Figure Intrinsic semiconductor. (a) Schematic band diagram. (b) Density of states. (c) Fermi distribution function. (d) Carrier concentration.

21 N n 2 3 / 2 ( 有效態位密度 ) 12( 2πm kt / h (13a) 3 C n ) = ( Nc exp E C E kt F ) (16) cm For silicon N p 2 3 / 2 V 12( 2πmPkT / h ) = ( Nc exp E F E kt V ) (18) (17) cm 3 For silicon

22 Ei : intrinsic fermi level,band gap 中間 10 ni : intrinsic carrier density (Si) # 3 Intrinsic semiconductor n=p=ni np = 2 n i Mass action law (20) cm Intrinsic, Extrinsic 皆可用 n n i 2 i Eg = NC NV exp kt Eg = NC NV exp 2kT Eg=Ec-Ev (21) (22) 可得 ni

23 log Room temp Figure Intrinsic carrier densities in Si and GaAs as a function of the reciprocal of temperature. 5-7

24 帶負電 mobile 帶正電 不動 extrinsic Donor (Ⅴ) As,Ph Acceptor (Ⅲ) B n type p type mobile Figure Schematic bond pictures for (a) n-type Si with donor (arsenic) and (b) p-type Si with acceptor (boron).

25 E D : ionization of donor Complete ionization : for Si, 常溫下已有足夠的熱能提供 E D n=n D E C p = E F N A (24) N = kt ln N (26) C D n = N C (25) e EC E kt F E F E V = N kt ln N V A (27) Figure Measured ionization energies (in ev) for various impurities in Si and GaAs. The levels below the gap center are measured from the top of the valence band and are acceptor levels unless indicated by D for donor level. The levels above the gap center are measured from the bottom of the conduction band and are donor levels unless indicated by A for acceptor level. 8

26 不動 Figure Schematic energy band representation of extrinsic semiconductors with (a) donor ions and (b) acceptor ions.

27 n = Nc exp E C E kt F ( EC Ei ) = ( EF Ei ) Nc exp exp kt kt ( EF Ei ) n = ni exp (28) kt E F E C E i E V similarly p = ( Ei EF ) ni exp (29) kt

28 n(e)=n(e) F(E) Ei Figure n-type semiconductor. (a) Schematic band diagram. (b) Density of states. (c) Fermi distribution function (d) Carrier concentration. Note that np = n i2.

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30 Figure Band diagram showing Fermi level E F and intrinsic Fermi level E i.

31 Figure Fermi level for Si and GaAs as a function of temperature and impurity concentration. The dependence of the bandgap on temperature is shown. 9

32 Figure Electron density as a function of temperature for a Si sample with a donor concentration of cm -3.

33 Chapter 2 Problem 2.