8Surface processes in thin ®lm devices

This chapter discusses surface and near-surface processes that are important in the context of the production and use of various types of thin ®lm device. In section 8.1 the role of band bending at semiconductor surfaces is considered along with the importance, and the perfection, of oxide layers and metal contacts on silicon surfaces. Section 8.2 describes models which have been developed to understand electronic and optical devices based on metal±semiconductor and semiconductor±semiconductor interfaces. Then section 8.3 describes conduction processes in both non-magnetic and magnetic materials, and discusses some of the trends which are emerging in new technologies based on thin ®lms with nanometer length scales. The ®nal section 8.4 discusses chemical routes to manufacturing, including novel forms of synthesis and materials development. The treatment in this chapter is rather broad; my aim is to relate the material back to topics discussed in previous chapters, so that, in conjunction with the further reading and references given, emerging technologies may be better understood as they appear.

8.1Metals and oxides in contact with semiconductors

This section covers various models of metals in contact with semiconductors, and the oxide layers on semiconductors. Such topics are important for MOS (metal±oxide± semiconductor) and the widely used CMOS (complementary-MOS) devices. Models in this ®eld have been extremely contentious, so sometimes one has felt that little progress has been made. However, recent developments and some new experimental techniques have shed light on what is happening.

8.1.1Band bending and rectifying contacts at semiconductor surfaces

Band bending can occur just below free semiconductor surfaces, and when metals or oxides come into contact with semiconductors. Models of this eVect are given in many places; the major eVect is caused by the presence of surface states in the band gap, which pins the Fermi level and induces band bending. As indicated in ®gure 8.1 for an n-type semiconductor, the bands bend upwards towards the interface. This bending is associated with a dipole layer beneath the surface corresponding to the depletion

260

8.1 Metals and oxides in contact with semiconductors				261
Jms Jsm	Jms	Jsm	Jms	Jsm

		EC
	EF	EF
		EF
		EV
(a)	(b)	(c)

Figure 8.1. Band bending at the surface of an n-type semiconductor under diVerent biassing conditions: (a) thermal equilibrium; (b) forward bias; (c) reverse bias.

region, where the n-type impurities are ionized, and the surface states are negatively charged. For a p-type semiconductor, band bending is reversed and surface states are charged positively, as indicated earlier in ®gure 1.23(a). If the semiconductor is in contact with a metal, the Fermi level is ®xed by the metal, so that band bending or band ¯attening can be induced depending on changes from the previous surface state distribution.

The main electrical eVects of this band bending arise from the asymmetry in the current ¯ow under bias, as shown in ®gure 8.1. In the conduction band, the electron energy distribution corresponds to the tail of the Fermi function, so that at the Schottky barrier height fB, the number of electrons above the barrier scales as exp[2(qfB/kT)], where q is the (eVective, positive) electron charge. In the equilibrium case, when the Fermi levels are equal on both sides of the junction, the energy distributions above the barrier must be the same, and the current ¯ow has to be zero, as indicated in ®gure 8.1(a). However, under bias voltage V, there is current ¯ow. Using the formulae for thermionic emission over the barrier (see section 6.2), we have a current density J, given by

J5J	sm	2 J	ms	5A*T2 exp[2 (qf	/kT)]{exp(qV/kT)2 1},	(8.1)
				B

where the `Richardson constant', A* for the barrier, depends on the details of band structures and interface chemistry. The rectifying character of the contact is determined by the asymmetry with respect to 6V, shown schematically in ®gures 8.1(b) and

(c). For forward bias (positive V) the current Jsm can increase without limit, but under reverse bias, the current is limited to a low constant value Jms by the Schottky barrier height fB. For higher reverse bias, catastrophic breakdown can occur.

This topic has a very long history, starting with the discovery of rectifying properties by Braun in 1874, and the use of `cats' whiskers' as detectors in the early days of radio (Mönch 1990, 1994). The two classical means of checking (8.1) are given by Sze (1981). Figure 8.2 is a log±log plot of the forward bias current density JF as a function

262 8 Surface processes in thin ®lm devices

Figure 8.2. Logarithmic plot of forward current density JF versus forward voltage VF of W±Si and W±GaAs diodes (from Crowell et al. 1965, after Sze 1981, reproduced with permission).

of VF, which gives a straight line whose slope is q/kT (Crowell et al. 1965). If q turns out not to be equal to e, the charge on the electron, then so be it. Device engineers replace q by q/n, where n is referred to as an `ideality factor', with typical values of n5 1.02 to 1.04; i.e. the approximation that q5e is pretty good, but `non-ideality' can be used to cover several types of disagreement with this simple model. An Arrhenius plot of the reverse barrier current IS, as (log IS/T2 ) versus T21 shown in ®gure 8.3, shows that both A* and fB for the important Al±Si diodes depend on processing conditions (Chino 1973). This sensitivity to cookery has plagued the ®eld for a long time; both recipes and theories have on occasion become so complex as to be completely unbelievable. But, before discussing these points, the next topic is the width of the depletion region.

8.1 Metals and oxides in contact with semiconductors	263

Figure 8.3. Arrhenius plot of the barrier current (IS/T2) of Al±Si Schottky barrier diodes under reverse bias for diVerent processing conditions (from Chino 1973, after Sze 1981, reproduced with permission).

8.1.2Simple models of the depletion region

Models of the depletion region are well developed in the literature, and to dwell on these here would take us too far from the topic of `surface processes'. The important point to determine is the length scale over which (electron or hole) depletion is observed, and to establish the connection with electrical and optical properties. The key concept is screening, which was introduced brie¯y in section 1.5, and the closely

related values of the (relative) dielectric constant «. Screening is very eVective in metals, with screening lengths ,(2kF)21, and moderately strong, but dependent on the doping level, in semiconductors. It is weak in insulators, where for example it depends on ionic

defects in crystals such as NaCl, and photographic materials including AgBr. In metals, Lindhard screening is required to describe the resulting Friedel oscillations (see section 6.1), but in semiconductors and insulators, classical Thomas±Fermi screening provides a suYcient description.

Consider a potential V(z) away from the surface, where the zero of V is in the bulk

264 8 Surface processes in thin ®lm devices

of the crystal, and an associated charge density r(z). This charge density may consist of both ionized donors and acceptors, whose values are ND1 and NA2 respectively, and the electron and hole density, n(z) and p(z), whose values are nb and pb in the bulk. In the bulk, the charges have to be compensated, so that ND1 ± NA2 5nb 2 pb. The electron and hole charge distribution is biased in the presence of V(z), which is diVerent from zero near the surface, and gives

r(z)51q[nb(exp(2 qV(z)/kT)21)2 pb(exp(1qV(z)/kT)21)]. (8.2)

Note that the positive sign arises because the donor and acceptor distributions stay the same, while the electron and/or hole distribution responds to V(z); care is needed with signs throughout this argument, which takes the electron to have q52 e.

Equation (8.2) needs to be solved self-consistently, which is done within classical electrostatics using the Poisson equation

d2V(z)/dz252r(z)/««	.	(8.3)
0

This can be solved numerically, but is typically expressed within one of two limiting approximations, for either n- or p-type semiconductors, i.e. when ND..NA or vice versa. In the weak space charge approximation, we make a linear approximation to the exponentials in (8.2) which gives

r(z)5(n	b	or p	)q2V/(««	kT),	(8.4)
		b	0

where we use nb or pb for n- or p-type doping. This results in V(z)5Vsexp (2 z/L), where Vs is the potential at the surface; the screening length L is given by

(Lq)25(««	kT)/(n	b	or p ).	(8.5)
0			b

In the other limit we acknowledge that if Vs is large compared to kT, then r(z) will approximate to a step function, such that all the charges are ionized up to a depth d below the surface, i.e. r(z)5q(ND or NA) for 0,z,d. Integrating (8.3) twice then gives a quadratic dependence:

V(z)52q(N	D	or N	)(d2z)2/(2««	),	(8.6)
		A	0

for 0,z,d, with V(z)50 for z$ d, which is known as the Schottky approximation, see ®gures 8.4(b) and (c). A detailed discussion with examples is given by Lüth (1993/5, chapter 7).

The key point is to realize how the screening length L and depletion length d depend on the doping level in typical semiconductors. Inserting a set of values into (8.5), for Si with «511.7 or Ge with «516, a low doping level nb51020 m23 (or equivalently 1014 cm23) gives L5410 nm for Si and 480 nm for Ge. However, for a typical surface potential Vs50.8 V, the depletion length d is greater than 3 mm; since d.L the Schottky model is most appropriate. These lengths are very long relative to atomic dimensions; although they will decrease as (nb or pb) increase, they are much greater than 10 nm, at least until samples are heavily doped, and have properties approaching those of metals. Thus it is not surprising that models of the electrical behaviour of semiconductors are typically not unduly concerned with atomic scale or surface properties. On the other