Transient photoconductance and photoluminescence from thick silicon wafers and bricks: Analytical solutions Kai Wang, Martin A. Green n , Henner Kampwerth School of Photovoltaic and Renewable Energy Engineering, University of New South Wales, Sydney 2052, Australia article info Article history: Received 25 October 2012 Received in revised form 13 December 2012 Accepted 9 January 2013 Available online 5 February 2013 Keywords: Transient Photoconductance Photoluminescence Analytical abstract Silicon solar cell technology is evolving rapidly with recent improvements in both multicrystalline and monocrystalline silicon wafers and ingots prepared by high throughput directional solidification, using both semiconductor grade and upgraded metallurgical grade silicon. Photoconductance and photo- luminescence measurements are being rapidly developed to guide the development of these materials, with increasing attention being paid to combining steady-state and transient photoluminescence measurements to obtain self-consistent results. Analytical transient solutions are presented for both photoconductance and photoluminescence from silicon bricks or thick wafers which will guide this development by highlighting important interdependencies. & 2013 Elsevier B.V. All rights reserved. 1. Introduction There is rapidly increasing interest in transient photoconductance and photoluminescence measurements on silicon wafers [1–4] and bricks [2,5], the latter being the square-cross sectioned blocks into which large directionally solidified ingots are cut, prior to slicing into wafers. The quality of such silicon depends strongly on its position in the ingot due to impurity segregation effects, contamination from the crucible and supports, variable dislocation density arising from stress variations during solidification and variable crystal structure. Understanding these variations is important not only to increase the productivity of directional solidification processes but also to allow classification of wafers subsequently sawn from the brick for specialised processing [6, 7]. 2. Theory The situation analysed is shown in Fig. 1. The brick is illuminated by light of wavelength l 1 , and absorption coefficient a 1 (with a component a b 1 due to band-to-band absorption processes [8]). In photoconductivity measurements, the change in conductivity of the brick on illumination is detected [9] while, in photolumines- cence measurements, light emitted by the brick is detected at wavelength l 2 (with absorption coefficient a 2 with similar compo- nent a b 2 ). Solutions for the steady-state photoconductance and photoluminescence have recently been reported [9, 10]. In the present work, these are extended to the transient case. 2.1. Steady-state solutions The general steady-state solution for the excess minority carrier nðzÞ SS , as a function of depth z in the block is given by (combining Eqs. (3) and (5) of Ref. [10]) nðzÞ SS ¼ a b 1 F n t a 2 1 L 2 1 ða 1 þ S=DÞL 1 þ SL=D e z=L e a 1 z   ð1Þ where S, L, D, and t are the surface recombination velocity, diffusion length, diffusivity and lifetime of the minority carriers (with L ¼ ffiffiffiffiffiffi Dt p ), while F n is the photon flux entering the semi- conductor. This solution applies under low injection conditions with the material parameters mentioned assumed constant. This excess minority carrier concentration induces a similar change in majority carrier concentration with a change of photo- conductance (PC) equal to DPC ¼ qðm n þ m p Þ Z 1 0 nðzÞ dz ð2Þ where m n and m p are electron and hole mobilities and q is the electronic charge. The photoluminescence (PL) at l 2 is given by [10] PL l 2 ð Þ¼ BB 1R f l 2 ð Þ   N A n 2 i a b 2 Z 1 0 nz ðÞe a 2 z dz ð3Þ where BB represents the thermal radiation photon or energy flux emitted from the corresponding surface of a blackbody at the corresponding wavelength and temperature, with PL having the same units as chosen for BB. N A is the doping level and n i is Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/solmat Solar Energy Materials & Solar Cells 0927-0248/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.solmat.2013.01.013 n Correspondence to: Room 108, Level 1, Tyree Energy Technologies Building, Anzac Parade, Kingsford, New South Wales, Australia. Tel.: þ61 2 9385 4018; fax: þ61 2 9662 4240. E-mail address: m.green@unsw.edu.au (M.A. Green). Solar Energy Materials & Solar Cells 111 (2013) 189–192