ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

Lecture 21, 26 Feb 14 Chp. 03: metal-semiconductor junction: Schottky barrier Ideal barrier Effective barrier VM Ayres, ECE875, S14

Example from Exam: For the equilibrium condition:

E (x) Junction metal n0= 1017 cm-3 Depletion region W ~ WDn Equilibrium: metal contact to n-type Si when work functions qFm > qFs Junction metal n0= 1017 cm-3 Although the charges are balanced, the layer on the metal side is very thin: similar to p+: ionized acceptors qybi EC EF EF - - P+ P+ P P P P P P P Ei EV Neutral region n-side E (x) Depletion region W ~ WDn

--Nd+ Nd+ n --Nd+ Nd+ Answer: (a) qV0 = (b) Band-bending diagram: q FB = 4.0 eV – 3.8 eV = 0.2 eV q ybi =qV0 = 0.057 eV W = 0.14 mm

Ideal Schottky barrier: q ybi = 0.057 eV q fBn0 = 0.2 eV EC ECm = EF EF - - P+ P+ W ≈ WDn = 0.14 mm More accurately to scale: q ybi = 0.057 eV EC q fBn0 = 0.2 eV ECm = EF EF - - P+ P+ W ≈ WDn = 0.14 mm

Ideal Schottky barrier: q ybi = 0.057 eV EC q fBn0 = 0.2 eV q fn ECm = EF EF - - ND+ ND+ W ≈ WDn = 0.14 mm EC – EF = q fn : Chp. 01: NC = effective DOS at the conduction band edge (eq’n (18)). Practical: use Appendix G n ≈ ND assumes fully fully ionized donors in saturation Temp range

qfBn0 = height of ideal Schottky barrier as seen from the metal = qybi + [qfn = (EC - EF)]

n-type semiconductor qfn = EC - EF p-type semiconductor qfp = EF - EV

Assume: 300 K Equilibrium condition

Draw band-diagrams with the following values marked on it: Barrier height on metal side: qfBn0 = 0.8 eV = given Barrier height on semiconductor side: qybi Barrier width W: primarily on n-side: WDn

Draw band-diagrams with the following values marked on it: Barrier height on metal side: qfBn0 = 0.8 eV = given Barrier height on semiconductor side: qybi Barrier width W: primarily on n-side: WDn

Fixed: 0.0259V @ r.t. Two factors change as a function of doping concentration Competing effects

q ybi = ? EC q fBn0 = 0.8 eV q fn ECm = EF EF - - ND+ ND+ W ≈ WDn = ? EC – EF = q fn : Chp. 01:

Lecture 21, 26 Feb 14 Chp. 03: metal-semiconductor junction: Schottky barrier Ideal Schottky barrier Effective Schottky barrier VM Ayres, ECE875, S14

During a C-V voltage sweep, real current is flowing. Current flowing lowers the ideal barrier height Lowered barrier height is called the effective barrier height Any active measurement will give you the effective barrier height not the ideal one

Same as abrupt junction Pr. 02, Chp. 02 Intercept  ybi Slope  N Pr. 8(a), Chp. 03: VR to VF is plotted right to left Not left to right You take a C-V curve data in F/V. But Units in eqn’s and Fig 30 are C = es/WD in F/cm2 The extra factor 1012 or 13 came from normalizing to a contact area to get the F/cm2 unit.

Current flowing lowers the ideal barrier height Why: During a C-V voltage sweep, real current is flowing. Current flowing lowers the ideal barrier height Lowered barrier height is called the effective barrier height Any active measurement will give you the effective barrier height not the ideal one

Consider an e- in a current reaching a previously established Schottky barrier as shown: --Nd+ Nd+ n --Nd+ Nd+ e-

The e- is leaving the metal. -- e-

An e- that leaves a metal induces a re-arrangement of charge in the metal. Keep in mind that metallic electrons can rearrange very easily. The real re-arrangements of e- and + that develops can be described as an image charge. Mathematical equivalent REAL -- + e- ++ e-

The image charge field also does work on the e-, independent of anything the depletion region field E is doing. e0 => es as the e- is really transporting into a semiconductor.

Combined potential energy of an e- entering the semiconductor from image charge field AND depletion region field : e0 => es as the e- is really transporting into a semiconductor.

Lowered barrier height is called the effective barrier height qfBn During a C-V voltage sweep, real current is flowing. Current flowing lowers the ideal barrier height and shifts the max to xm Lowered barrier height is called the effective barrier height qfBn Any active measurement will give you the effective barrier height not the ideal one