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in the presence of an electric field @xmath0 and a magnetic field @xmath1 mutually orthogonal the charge carriers move along a direction that forms an angle @xmath2 ( lorentz angle ) with the electric field . this angle affects the area of collection of the charge carriers .    resolution and efficiency of the detector
depend on the track incidence angle and on the charge drift angle : the determination of this angle is therefore very important to define the mechanical design and optimize detector performance
.    the silicon pixel detector of the atlas experiment will be exposed at intense fluxes of radiation during its lifetime ; as a result the properties and the conditions of operation of the sensors will change .
several single chip assemblies were characterised extensively in test beam experiments performed at the cern sps accelerator with a pion beam of 180 gev/_c _ momentum  @xcite .
a beam telescope consisting of 4 pairs of silicon microstrips detectors ( each pair consisting of two planes of detectors with orthogonal strips ) was used to measure the transverse position of the incident beam particles .
the pixel assemblies and the silicon strip telescope were positioned inside a magnet for the measurement of the lorentz angle .      a detailed description of the atlas pixel sensors can be found in  @xcite , so only a brief description is given here .
the sensor is a matrix of 18  @xmath3  160 _ n@xmath4 _ implants on a high resistivity _
n_-bulk substrate .
this choice allows for operation in partially depleted mode after bulk inversion induced by radiation damage .
the isolation between _ n@xmath4 _ pixels is obtained using the newly developed _
p - spray _
technique  @xcite .
the dimensions of pixel cell are 50  @xmath5  @xmath3  400  @xmath5  .
the pulse height measurement is performed by measuring the time the pulse from the amplifier remains above the threshold ( time over threshold ) .
typical thresholds were around 3000 electrons .
some detectors were exposed to a fluence comparable to those expected for lhc .
irradiations were performed using the 300 mev/@xmath6 pion beam at psi and the 55 mev/@xmath6 proton beam at lbnl .
sensors irradiated with fluences of 0.5@xmath310 ^ 15^ and 1@xmath310 ^ 15^ @xmath7/cm^2^ , hereafter referred respectively as half - irradiated and full - irradiated sensors , were tested in the beam .
they were cooled at @xmath8 during data taking .
the distribution of charge produced by ionizing particles while drifting to the read - out pixels can spread over more than one pixel .
the spread depends on the particle incidence angle and is minimum for an angle equal to the lorentz angle .
the lorentz angle was extracted finding the minimum ( with a parabola fit ) of the mean cluster size measured as a function of the angle of the incident beam particles with respect to the normal to the detector  @xcite . for each angle data
were taken both without magnetic field and with a magnetic field of 1.4 tesla .
data taken without magnetic field were used to check the consistency of the measurement with an expected value of @xmath9 .    [ cols="^,^,^,^,^",options="header " , ]     the mean cluster size as a function of the angle for not - irradiated sensor operated at 150 v is shown in fig .
[ fig:3a ] .
the lorentz angle is @xmath10 . in fig .
[ fig:3d ] the distribution of the same quantity for a full - irradiated sensor is shown .
the plot refers to data taken in a test beam in 1998 .
the corresponding lorentz angle is @xmath11 .
the same sensor was measured again in 1999 , finding a compatible value of @xmath12 .
an half - irradiated sensor was also tested at two different operating voltages : at 600 v as foreseen during data taking in atlas and at the lower voltage of 150 v for a better understanding of its behaviour .
the measured lorentz angle values were respectively @xmath13 and @xmath14 .
@xmath7/cm^2^. the solid line corresponds to the parabola fit .
model prediction is superimposed ( dashed line ) ]    the expected mean multiplicity as a function of the track incidence angle was numerically calculated , using the properties and the operating conditions of the detectors under study ( temperature , magnetic field , bias voltage , depletion , geometry and thresholds ) .
this calculation is based on a model which describes charge drifting in silicon devices .
to compute the drifting trajectories is necessary to know the electric field , the magnetic field and the mobility .    the lorentz angle @xmath2 is given by @xcite    @xmath15    where @xmath16 is the hall mobility and @xmath17 the drift mobility .
their ratio r ( hall factor ) depends on the scattering mechanism .
it has a weak dependence on temperature while it does not depend on doping level as long as the doping level is below @xmath18 .
the mobility depends on temperature and electric field .
this dependence was parametrized as in @xcite .
[ fig : mobility ] shows the mobility and the lorentz angle ( assuming @xmath19 and @xmath20 t ) as a function of the electric field for @xmath21=263 k and @xmath21=300  k ( irradiated and not - irradiated detectors ) .
the markers correspond to the temperature and the _ mean _ electric field @xmath22 present in the detectors under study , where v is the applied voltage and d is the depletion depth .
( 75,50 ) ( -6,0 )    the irradiated samples have a lower lorentz angle because of lower mobility due to a larger electric field .
actually the electric field is not constant in the detector due to the presence of spatial charges , then lorentz angle varies throughout the detector with the position inside the depletion zone .
the track incidence angle for which the mean hit multiplicity is minimum was defined _ effective lorentz angle_.    the doping concentration was assumed to be uniform .
this is in agreement with the scaling of depletion depth with bias voltage observed in half - irradiated detectors : the depletion approximately doubles when the voltage is increased from 150  v to 600 v. with this assumption the electric field varies linearly from the backplane to the read - out plane , both in irradiated samples , which have a p - type substrate and are partially depleted , and in not - irradiated devices which are over depleted .
the mean multiplicity for a given detector and track incidence angle was computed taking into account charge drifting , charge diffusion and threshold .
experimental results were compared with the model .
the values of depletion depth used in the model were experimentally measured ( see section[sec : dep ] ) .
the results obtained are summarized in table  [ table:2 ] .
the measurement of the depletion depth was performed rotating the detector around the axis parallel to the longer size of pixels .
the angle between the beam direction and the normal to the sensor plane was set to @xmath23 or @xmath24 .
the method is illustrated in fig  [ fig : pixel3 ] : a cluster of contiguous pixels is activated by the beam particles crossing the detector .
( 75,75 ) ( -6,0 )    the charge collected at each pixel is proportional to the length of the track segment in the depleted area below the pixel itself .
the alignment of the tracks is performed by the measurement of time over threshold of the first fired pixel in the cluster . for each fired pixel in the cluster the depth of the center of the segment
is calculated .    in fig .
[ fig : scan ] the distributions of the track - segment depth are shown for a sensor irradiated to a fluence of @xmath25 and operated at two different values of bias voltage .
the maximum depth is measured determining with a fit the point of inflexion of the track - segment depth distribution .
the consistency of the method was checked with not - irradiated sensors , that are fully depleted , for which the depletion is equal to the nominal thickness .
the lorentz angle of atlas pixel radiation - hard sensors in a field of 1.4 tesla was measured . for a not - irradiated sensor operated at 150 v a value of @xmath10
was found .
two different measurements for a sensor irradiated with @xmath26 and operated at 600 v gave the compatible values of @xmath11 . and
the lorentz angle depends through the mobility upon the electric field inside sensors .
the observed behaviour is well explained by a model based on charge drift in silicon . at the operating conditions for atlas pixel sensors a lorentz angle of @xmath27 at the beginning of data taking , decreasing to @xmath28 after 10 years of operation ,
is expected .
999 the atlas pixel collaboration , atlas pixel detector technical design report , * cern / lhcc/98 - 13 * , cern 1998 f. ragusa , recent developments in the atlas pixel detector , nucl . instr . and meth . a 447 ( 2000 ) , 184 .
alam et al . ,
the atlas silicon pixel sensors , cern - ep/99 - 152 , submitted to nucl . instr . and meth . a r.h .
richter et al . , nucl .
instr . and meth . a 377 ( 1996 ) 412 .
e. belau et al . , nucl .
instr . and meth . a 214 ( 1983 ) 253 .
+ n. bingefors et al .
instr . and meth . a 328 ( 1993 ) 447 .
w. shockley , van nostrand , princeton , n.j .
( 1950 ) . c.  jacoboni et al .
, solid state electronics * 20 * ( 1977 ) 77 .
silicon pixel detectors developed to meet lhc requirements were tested in a beam at cern in the framework of the atlas collaboration . 
 the experimental behaviour of irradiated and not - irradiated sensors in a magnetic field is discussed . 
 the measurement of the lorentz angle for these sensors at different operating conditions is presented . a simple model of the charge drift in silicon before and after irradiation is presented . 
 the good agreement between the model predictions and the experimental results is shown .