Quantifying recombination

In reality, the quantification of the recombination rate at the surface (Us) is complicated

by the relative complexity of the input parameters of equation 3.3. The determination of the electron and hole concentrations at the surface is non-trival, especially when a charged passivation layer is applied, and the energy dependent parametersDit, are also

challenging to probe, especially for passivation layers that are conductive and permit the flow of carriers across the silicon interface. Recombination mechanisms in the bulk of the wafer add to the complexity. In the papers that follow the effective minority carrier lifetime (τef f) is often used as a proxy for the recombination rate at the surface, where

τef f is defined as τef f ≡ ∆n Utotal ≡ ∆n Us + ∆n Ubulk (3.5)

whereUbulk is the recombination rate in the bulk of the silicon wafer and is given by

Ubulk =Urad+UAuger+USRH (3.6)

The termsUrad and UAuger represent the intrinsic recombination rates related to radia-

tive and Auger recombination processes, respectively. Parameterisations of these two intrinsic recombination mechanisms can be found in [13],[38],[39]. The USRH refers to

The physical model that is used to quantify USRH is identical to that of equation 3.3

except that the spatial parameters are now associated with a three dimensional volume (i.e. the semiconductor bulk) rather than a two dimensional plane (the semiconductor surface).

The term τef f is quite easily quantified and is typically measured as a function of the

minority carrier injection level ∆n(where ∆n= ∆p) by monitoring the conductance of the silicon wafer under differing illumination intensities. A detailed examination of this photoconductance method for determining τef f is given in [40].

Using this approach, the effective lifetime can be considered as a combination of all recombination mechanisms acting in parallel, each with their own contribution to τef f,

such that 1 τef f = 1 τbulk + 1 τs (3.7)

where τs is the contribution to τef f from the surface. Considering a symmetrically

passivated wafer τs= W 2 ∆n Us (3.8)

where W is the wafer thickness. Here we can define an effective surface recombination velocity term Sef f

Sef f =

Us

such that equation 3.7 becomes

τs=

W

2Sef f

(3.10)

This surface recombination parameter Sef f is here defined with respect to a virtual

surface, not the real surface where a determination of the carrier concentrations is non- trivial (hence effective SRV). The virtual surface is taken to be at the edge of quasi- neutral region of the semiconductor sub-surface, i.e. where band bending at the surface stops, flat-band conditions prevail, and the assumption of the excess carrier concentra- tion being equal to ∆nis more likely to hold. With regard to the effective lifetime, the effective surface recombination velocity becomes

Sef f = W 2 1 τef f − 1 τbulk (3.11)

where τbulk can be approximated by the intrinsic carrier lifetime parameterisation of

Richteret al. [13], ignoring the role of bulk defects, giving rise to an upper limit surface recombination velocity Sef f,U L. A lower limit SRV (Sef f,LL) can be determined by

measuring the effective lifetime on a suitable control sample using a surface passivation technique known to effectively eliminate the contribution ofτsonτef f like PECVD SiNx,

PEALD Al2O3, or immersion in HF, and using this value for τbulk in equation 3.11.

These methods for the determination of Sef f,Sef f,U L and Sef f,LL are used throughout

the thesis.

More recently the term surface recombination current density J0s has been used as an

when band bending at the surface complicates the interpretation ofSef f due to discrep-

ancies between the excess carrier concentration at the edge of the surface space-charge region and the surface itself [41]. The authors describeJ0s an undiffused analogue to the

so-called ‘emitter saturation current density’J0e, a reflection of the analogous means in

which surface doping and band bending from overlying charges influenceUs. The term

can be thought of as a flow of minority carrier charge (i.e. a current) that is drawn to the surface to recombine:

qUs=Jrec (3.12)

Since the recombination rate is proportional to the extent the divergence of the carrier concentrations of electrons and holes from equilibrium, it follows that the recombina- tion current density can also be expressed in terms of the splitting of the quasi-Fermi levels, and hence the implied, or internal voltage, built up in the semiconductor under illumination or excitation: Jrec =J0sexp Ef n−Ef p kT =J0sexp V VT (3.13)

The surface saturation current density has the advantage over Sef f in that, for most

circumstances over which surface recombination is studied on undiffused surfaces (high charge densities on moderately doped wafers), it is independent of injection level and wafer doping [41]. The surface saturation current density J0s can be extracted from

injection dependent lifetime measurements by applying the method of Kane and Swanson [42].