Modelling of semiconductor diodes made of high defect concentration, irradiated, high resistivity and semi-insulating material: The capacitance–voltage characteristics A. Saadoune a , L. Dehimi a , N. Sengouga a , M. McPherson b , B.K. Jones c, * a Laboratory of Metallic and Semiconducting Materials, B.P. 145, University of Biskra, Biskra 07000, Algeria b Department of Physics, North-West University Private Bag X2046, Mmabatho 2735, South Africa c Department of Physics, Lancaster University, Lancaster, LA5 9LX, UK Received 6 May 2005; received in revised form 5 June 2006; accepted 11 June 2006 Available online 1 August 2006 The review of this paper was arranged by Prof. S. Cristoloveanu Abstract Full modelling is reported of the capacitance of a long PIN semiconductor diode with a high concentration of generation–recombi- nation (g–r) centres and different concentrations of deep traps. There are considerable differences from the textbook results given for normal lifetime diodes which have low concentrations of g–r centres. For a low density of g–r centres, the capacitance is the usual value. That is it decreases as V 1/2 with increasing reverse bias while it increases rapidly with increasing forward bias. For high density of g–r centres and in reverse bias a departure from this voltage dependence is observed, while in forward bias a negative capacitance appears. This agrees with experiment. From these results we present a physical understanding of the processes involved. There are specific appli- cations of these results to radiation damaged devices, lifetime killed diodes and devices made from high resistance and semi-insulating materials, especially in the interpretation of the C–V curves to evaluate the fixed space charge density. Ó 2006 Elsevier Ltd. All rights reserved. PACS: 85.30.z Keywords: Semi-insulating; Semiconductor; Diode; Radiation damage; Modelling 1. Introduction There are many materials in current use, such as semi- insulating, lifetime killed or highly irradiated semiconduc- tors, which show relaxation semiconductor behaviour [1,2]. This may not be immediately apparent since some of the properties often do not seem very unusual and can be analysed using normal lifetime semiconductor theory with apparently reasonable results. This is especially likely since the materials are often poorly characterised and highly defected so that there is not a clear expectation for what is reasonable. However the normal analysis is not appropri- ate and may give incorrect values for the material properties such as the effective doping and trap density. Thus a PIN diode made from relaxation material shows Ohmic charac- teristics which would suggest, incorrectly, that there was no blocking contact or internal field. A very apparent and unu- sual property is the negative capacitance shown experimen- tally by relaxation diodes in forward bias [3,4]. The necessary conditions for a relaxation material are that it has a high resistivity; that is it is a nearly intrinsic or compensated semiconductor or semi-insulator, and that it has a very high density of generation–recombination (g–r) centres. It is a relaxation rather than a lifetime semiconductor because any disturbance of the equilibrium space charge is neutralised by electron–hole pair genera- tion rather than by the inflow of free carriers. 0038-1101/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2006.06.004 * Corresponding author. Tel.: +44 1524 732305; fax: +44 0870 138 5141. E-mail address: b.jones@physics.org (B.K. Jones). www.elsevier.com/locate/sse Solid-State Electronics 50 (2006) 1178–1182