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I-V特性，欧姆接触，小信号电容
I-V特性，欧姆接触是指金属与半导体的接触，而其接触面的电阻值远小于半导体本身的电阻，使得组件操作时，大部分的电压降在活动区(Active region)而不在接触面。欧姆接触在中金属处理应用广泛，实现的主要措施是在半导体表面层进行高掺杂或者引入大量复合中心。，小信号电容是信号最大峰值在10V以内但交流幅值只有几个mV，频率10Khz以内，波形为方波。

1 . Lecture #9 OUTLINE – Metal-semiconductor contacts (cont.) » I-V characteristics » practical ohmic contacts » small-signal capacitance Reading: Finish Chapter 14 Spring 2003 EE130 Lecture 9, Slide 1 Review: Schottky Diode (n-type Si) metal n-type Si ΦM > ΦS Eo χSi ΦM qVbi = ΦBn – (Ec – EF)FB ΦBn Ec Equilibrium (VA = 0) EF -> EF continuous, constant  ΦBn = ΦM – χ Ev W Spring 2003 EE130 Lecture 9, Slide 2 1

2 . Schottky Diode (p-type Si) metal p-type Si Eo ΦM < ΦS χSi Ec ΦM Equilibrium (VA = 0) -> EF continuous, EF constant Ev ΦBp qVbi = ΦBp– (EF – Ev)FB ΦBp = χ + EG - ΦM W Spring 2003 EE130 Lecture 9, Slide 3 Depleted Layer Width, W Last time, we found that − qN D V (x ) = (W − x )2 2K Sε 0 At x = 0, V = - (Vbi - VA) 2ε s (Vbi − VA ) ⇒ W= qN D • W increases with increasing –VA • W decreases with increasing ND - (Vbi - VA) Spring 2003 EE130 Lecture 9, Slide 4 2

3 . W for p-type Semiconductor qN A V (x ) = (W − x )2 2 K Sε 0 At x = 0, V = Vbi + VA 2ε s (VA + Vbi ) ⇒ W= qN A • W increases with increasing VA • W decreases with increasing NA Spring 2003 EE130 Lecture 9, Slide 5 Current Flow in a Schottky Diode • Diode current is determined by majority- carrier flow across the MS junction – Under forward bias, majority-carrier diffusion from the semiconductor into the metal dominates the current – Under reverse bias, majority-carrier diffusion from the metal into the semiconductor dominates the current Spring 2003 EE130 Lecture 9, Slide 6 3

4 . Thermionic Emission Theory • Electrons can cross the junction if 1 mv x ≥ q(Vbi − VA ) 2 KE x = 2 2q v x ≥ vmin ≡ (Vbi − VA ) mn* • The current for electrons at a given velocity is: I s • → M , v x = − qAv x n(vx ) • So, the total current over the barrier is: − v min I s • → M = −qA ∫ v n(v )dv −∞ x x x Spring 2003 EE130 Lecture 9, Slide 7 Schottky Diode I - V • Given that  4πkTmn* 2  ( E − E ) / kT −(m* / 2 kT )v 2 n (v x ) =  3 e F c e n x  h  • We obtain 4πqmn k 2 I S •→ M = AT 2e − qΦ B / kT e qVA / kT h3 = AT 2 J S e qVA / kT , where J S ≈ 120e −qΦ B / kT A/cm 2 • In the other direction, we always see the same barrier ΦBn: I M • → S = − I S • → M (VA = 0) • Therefore I = I S ( e − 1) where I S = AT 2 J S qV A / kT Spring 2003 EE130 Lecture 9, Slide 8 4

5 . Applications of Schottky Diodes • IS of a Schottky diode is 103 to 108 times larger than a pn junction diode, depending on ΦB . ⇒ Schottky diodes are preferred rectifiers for low voltage, high current applications. Spring 2003 EE130 Lecture 9, Slide 9 Practical Ohmic Contact • In practice, most M-S contacts are rectifying • To achieve a contact which conducts easily in both directions, we dope the semiconductor very heavily Æ W is so narrow that carriers can tunnel directly through the barrier Spring 2003 EE130 Lecture 9, Slide 10 5

6 . ΦBn – VA 2ε s Φ Bn - - - - Ec , EFS W ≅ Ec , EF EFM V qN D Ev Ev − H ( Φ Bn −V A ) ND tunneling probabilit y P = e H = 4π ε s mn / h = 5.4 × 109 mn / mo cm −3/2 V −1 − H ( Φ Bn −V A ) / N D J S → M ≈ qN D vthx P = qN D kT / 2πmn e Spring 2003 EE130 Lecture 9, Slide 11 Specific Contact Resistance Spring 2003 EE130 Lecture 9, Slide 12 6

7 .Voltage Drop across an Ohmic Contact Spring 2003 EE130 Lecture 9, Slide 13 Review: MS-Contact Charge Distribution • In a Schottky contact, charge is stored on either side of the MS junction • This charge is modulated by the applied voltage Spring 2003 EE130 Lecture 9, Slide 14 7

8 .Schottky Diode: Small-Signal Capacitance • If an A.C. voltage is applied in series with the D.C. bias VA, the charge stored in the Schottky contact will be modulated → displacement current will flow εs C= A W Spring 2003 EE130 Lecture 9, Slide 15 Using C-V Data to Determine ΦB 1 2(Vbi − VA ) = C 2 qN Dε s A2 Once Vbi is known, ΦΒn can be determined: Nc qVbi = qΦ Bn − ( Ec − EF ) FB = qΦ Bn − kT ln ND Spring 2003 EE130 Lecture 9, Slide 16 8

9 . Summary Spring 2003 EE130 Lecture 9, Slide 17 9

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