* Corresponding author. E-mail address: chap@spec.saclay.cea.fr (M.P. Chapellier)  Supported by EEC TMR contract ERBFMRX CT 980167.  For instance, formula (3) in Ref. [2] is wrong. Physica B 284 }288 (2000) 2135}2136 Physical interpretation of the Neganov}Luke and related e!ects Maurice P. Chapellier*, Gabriel Chardin, Lino Miramonti, Xavier Francois Navick Service de Physique de l'Etat Condense & , CEA/Saclay 91191, Gif/Yvette Cedex, France Service de Physique des Particules, CE Saclay, France Service d'Etude des Detecteurs, CE Saclay, France Abstract The Neganov}Luke e!ect consists mainly of the enhancement of heat deposited by an ionizing particle in a bolometer at low temperatures, when the induced charges are collected by an applied voltage. The paper will present a detailed explanation of this phenemenon and its magnitude.  2000 Elsevier Science B.V. All rights reserved. Keywords: Low-temperature detector; Semiconductor; Bolometer; Dark matter In the detection of radiation by bolometer technology applied to a semiconductor crystal, Neganov and Tro"mov [1], and followed by Luke [2] found an inter- esting e!ect, namely, the enhancement of the thermal signal when an electric "eld is applied to collect and measure the charge produced by a ionizing particle. This is mostly an ohmic e!ect. Here we want to make a quant- itative estimate on the size of this e!ect, which may not be straightforward in a semiconductor diode at very low temperatures. The semiconductor structure is often a PIN diode, with two degenerated thin P- and N- type electrodes (doped such as to remain conductive even at zero temperature) and a thick dielectric absorber be- tween them made of the purest (intrinsic) semiconductor. This absorber is assumed to contain no net charges except when electrons and holes are generated by an ionizing particle. Let us "rst do the evaluation of the deposited energy when a germanium PIN diode is shorted by a non- resistive wire. If no energy is stored in some traps or defects, we should "nd that the whole energy is converted "nally into heat inside the diode. In fact, the ionization by a particle of energy E (in eV) is approximately dissipated for 2E/3 into heat and E/3 is spent to create E/E  pairs of holes and electrons (E  is the energy needed to create a pair). Although the applied external voltage is zero, the charges are fully collected as long as all the charges reach their electrodes of opposite polarity. Otherwise, the sig- nal induced by a charge is proportional to l/d where l is the length of drift toward the electrode and d is the thickness of the detector. This is observed experimentally because the actual structure gives a permanent built-in electric "eld which prevents electrons and holes from recombining and allows them to drift toward the elec- trodes. Indeed, a constant chemical potential exists only at the two doped electrodes and in the wire because these are the only places where a permanent exchange of elec- trons and holes exists. Therefore, the degenerated sub- band of acceptors is at the same level as the sub-band of donors after some electrons have left the n side to "ll part of the holes on the p side (Fig. 1). It is the displacement of these charges which allows the chemical potential to remain constant and at the same time produces the permanent electric "eld. When a particle interacts in the intrinsic part of the diode, optical phonons and elec- tron}hole pairs are created, and the drift of the charges along the built-in "eld produce again mostly optical phonons (Fig. 1). All phonons quickly downscatter into acoustic phonons and are "nally thermalized. It is impor- tant to note that if a resistive external wire connects the two electrodes, a part of the energy is dissipated outside 0921-4526/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 3 0 5 3 - 7