VI-PSD

Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors VI. Position-Sensitive Detectors Position-sensitive detectors can be implemented in two basic architectures 1. Direct Readout 1 readout channel per resolution element Example: 2D array of small pixels, with one readout channel per pixel 2. Interpolating Readout Large area sensor, designed so that a measurement parameter (signal magnitude, time) is dependent on position Example: Charge division Delay line readout Since the direct readout requires a large number of readout channels, interpolating schemes are attractive for large area coverage. Furthermore, in “simple” experiments the complexity of a direct readout scheme may be prohibitive, so many techniques for interpolation have been developed. Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors 1. Interpolation Possibilities: a) Charge Division Electrode is made resistive with low-impedance amplifiers at each end. The signal current divides according to the ratio of resistances presented to current flow in the respective direction The obtainable position resolution depends on the precision of the relative signal measurement at the two ends, i.e. the signal to noise ratios of the two measurements. The resistive electrode introduces a) Noise due to its resistance. Since the amplifiers have a low input impedance, the electrode resistance is effectively in parallel with the input of an amplifier, so the noise charge )( )( )( )( 1 2 2 1 xR xR xi xi = Si D B SinRnR TFR Tk TFiQ 4 == Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors In principle, the noise can be reduced arbitrarily by reducing the shaping time TS , but a lower limit is imposed by the signal dispersion introduced by the resistive electrode. b) Signal dispersion, i.e. an increase in pulse duration, because the resistive electrode together with the detector capacitance forms an RC transmission line. The dispersion will depend on position. A signal originating at one end will suffer the greatest dispersion, proportional to Since the signal dispersion depends on the position of the incident signal, it will vary from event to event, so the shaper must be designed to reduce variations in the ballistic deficit to not significantly affect the position resolution. Although the exact relationship between the detector time constant and the optimum shaping time TS depends on detector signal shape and the type of shaper, the shaping time constant will be proportional to the detector time constant, so for simplicity we’ll assume To optimize the signal-to-noise ratio, we’ll assume that the amplifier noise is negligible, so the dominant noise contributor is the electrode resistance. Then the position resolution The obtainable position resolution is independent of electrode resistance and depends only on detector capacitance and the magnitude of the signal. DDD CR=τ DST τ= s DB DDi D B ss n Q TCk CRF R Tk QQ Q NSl l ≈==∝ ∆ 41 / 1 Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors elTCk DB 1270= Example: The above result only obtains if the electronic noise from the amplifier is negligible. For CD= 10 pF so if the degradation is to be less than 10%, the amplifier noise may not exceed 270 el. Since the voltage noise of the amplifier for a given capacitance CD and equivalent input noise voltage vn , the amplifier noise contribution can only be reduced by increasing the shaping time TS , which means that the electrode resistance must be increased to scale RDCD to the required TS . The detector time constant RDCD also imposes a limit on the rate capability of the detector. High-rate applications often require a compromise that yields a position resolution inferior to the above limit. 36 101010 −≈ ∆ ⇒== l l elQC sD and pF S v Dnnv T F CvQ 222 = Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors b) Delay Line Readout In a delay line readout the detector electrode is used as a transmission line. The position is determined by the difference in propagation times from the point of incidence to the respective ends. If the electrode has a group velocity vg so the position and the position resolution The position resolution can be improved by improving the time resolution. In a low-loss transmission line, the signal magnitude at both ends will be the same. If the transmission line is sufficiently fast, the rise times of the signals at the two ends will also be the same, so the time resolutions so ggg gg v lx v xl v x tt v xl t v x t − = − −=− − == 2 21 21 and lvttx g +−= )(2 1 21 21 tt ∆=∆ ttttt ∆≡∆=∆=−∆ 222)( 2121 )( 2 21 tt v x g −∆=∆ Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Thus, the position resolution is If we use a simple RC low-pass filter as a shaper in the timing channel, matched to the rise time of the signal tr to maximize the slope-to-noise ratio, the time resolution where vn is the spectral noise voltage density of the amplifier. With this result the position resolution is The remaining parameter is the velocity of signal propagation vg. In a pair of electrodes with an intermediate medium of dielectric constant ε so increasing the dielectric constant will increase the delay time and would seem to improve the position resolution. ε c vg = t v x g ∆=∆ 2 r n s t v Q C t 2 =∆ r n s gg t v Q Cv t v x 222 =∆=∆ Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors However, increasing the dielectric constant will also increase the capacitance. If C0 is the capacitance for ε = 1 so the resolution will not improve by increasing the dielectric constant of the transmission medium. The other technique to increase the delay time is to introduce resistance to make the delay line dispersive. Since time resolution depends on the slope-to-noise ratio, i.e. the time derivative of the signal, the detector electrode must be designed to minimize dispersion, while maximizing the delay time x/vg. In an RC transmission line the delay time is proportional to the resistance R’=R/l and capacitance C’=C/l per unit length, so the group velocity whereas the rise time increases with the square root of length. , RC l vg = l x RCtr = r s n r n s g t Q Cv cx t v Q Cc t v x 4 222 0 0 ε ε ε =∆ =∆=∆ Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors s B s B Q TCk R C Q TRk l x 2 14 22 1 == ∆ The bandwidth of the electronics can be restricted to match the maximum rise time τ= RC, so for a simple RC low-pass filter the time resolution is where vn is the spectral voltage noise density of the amplifier. Thus, the position resolution As to be expected, the position resolution improves with increasing signal to noise ratio and decreasing capacitance. To a degree increasing the electrode resistance will improve the position resolution, as long as its noise contribution does not become significant. If we include the noise from the electrode resistance: If the electrode resistance dominates the noise then which is practically the same as the result for charge division. R C Q v l x RCC Q v RC l t v x s n s ng 22 1 222 = ∆ =∆=∆ RC v Q C t n s 2 =∆ R C Q TRkv l x s Bn 4 2 + ≈ ∆ 24 nB vTRk >> Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Example: Non-dispersive delay line readout with CD= 10 pF, Qs= 106 el, vn= 0.9 nV/Hz1/2, tr= 10 ns and ε = 1 which for a 1 m long electrode corresponds to In practice, charge division tends to provide better results for short electrodes, whereas delay line readout is better for long electrodes. Some implementations use specially designed delay lines to increase the propagation time. Frequently, they sacrifice S/N. If the electronics have not been optimized, for example if the timing is dominated by pulse shape variations, rather than S/N, the degradation in S/N may not be that critical. On the other hand, the optimization outlined above is the most direct approach. mm 4.0 4 0 ==∆ r s n t Q Cv cx ε 4104 −⋅= ∆ l x Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Interpolation schemes can be extended to two dimensions: ( ... in principle) Although interpolation schemes allow a relatively large area to be read out with a small number of readout channels, they do this at the expense of multi-hit capability, i.e. only one hit is allowed within the readout area and required analysis time. For optimum results the electronics must be rather sophisticated • low noise • optimized pulse shaping • calculation capability (hardware or software) Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors 2. TPC-like Structures Transform the position axis to the time axis – use multi-hit capability to record multiple events occurring simultaneously at different positions within the sampling volume Example 1: Delay line readout with external trigger Example 2: Semiconductor Drift Chamber Use detector material as delay element Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Semiconductor Drift Chamber 1st Ingredient: depletion from edge of detector p+ p n+ Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Depletion vs. Reverse Bias Voltage (from Gatti et al. IEEE Trans. Nucl. Sci. NS-32 (1985) 1204) Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors 2nd Ingredient: Add additional electrodes to form drift field parallel to surface Potential Distribution Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Potential trough can be skewed to direct charge to readout electrode on surface. Silicon drift chamber has advantage that the collection electrode is decoupled from the large track-acceptance area. ⇒ capacitance can be very small, even on a large area detector (C~ 50 – 100 fF for A= 10 cm2) ⇒ ~ 10 µm resolution over 5 – 10 cm drift distance Drift velocity must be predictable. Trapping must be low for long drift distances (~ cm) ⇒ problem with radiation damage. Electronics optimized for timing – multi-hit capability requires fast time digitization. Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors 3. Parallel Readout One readout channel per resolution element Example: Strip Detectors Two options: Binary Readout Analog Readout Interpolation yields resolution < pitch Relies on transverse diffusion to discriminators e.g. in Si Position resolution determined tcoll≈ 10 ns directly by pitch ⇒ σx= 5 µm Interpolation precision depends on S/N and p p= 25 µm and S/N=50 ⇒ 3 – 4 µm resolution 12/ pitchx =σ collx t∝σ Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Amplifiers must have a low input impedance to reduce transfer of charge through capacitance to neighboring strips The capacitance is dominated by the fringing capacitance to the neighboring strips CSS. Typically: 1 – 2 pF/cm for strip pitches of 25 – 100 µm. The capacitance to the backplane CSG is simple to calculate where A is the area subtended by a strip element, d is the substrate thickness, p is the strip pitch (not width!) and l the strip length. The presence of the adjacent strips limits the fringing field to the centerline bewteen two strips, i.e. width = strip pitch. The backplane capacitance is typically 20% of the strip-to-strip capacitance. d pl d A CSG εε == Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Two-Dimensional Detectors 1. Two-Dimensional Projective Devices Example: Crossed strips on opposite sides of Si wafer n readout channels ⇒ n2 resolution elements Problem: ambiguities with multiple hits n hits in acceptance field ⇒ n x-coordinates n y-coordinates ⇒ n2 combinations of which n2 - n are “ghosts” Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors 2. Two-Dimensional Non-Projective Devices Example: Pixel Devices “Checkerboard” of detector elements than can be read out as discrete signal packets Implementations: a) CCDs Array of MOS Capacitors uses pixel-to-pixel charge transfer for signal “bussing” charge accumulation due to photon or particle charge transfer to neighboring pixel Typically, charge transferred to end of column and then across row to single readout amplifier per chip. serial readout ⇒ long readout times at clock rate of 10 MHz 50 µm pixel size ⇒ 20 µs/cm Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors b) Random–Access Pixel Arrays Amplifier per pixel Address + signal lines read out individually addressed, i.e. single, pixels detector array 2D contact grid amplifier array 2D contact via “bump bonds” Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors 3. Hybrid Arrays CCD with readout amplifier per row or column or Semiconductor drift chamber with segmented anode Readout time dependent on hit coordinate. Drift time ~ µs/cm ⇒ At high rates multiple spills within readout time ⇒ Event timing must be reconstructed No problem at long bunch intervals, e.g. RHIC Introduction to Radiation Detectors and Electronics Copyright  1998 by Helmuth Spieler VI. Position-Sensitive Detectors Is the Power Dissipation of a Random Access Pixel Array Prohibitive? If a strip readout for the LHC requires 2 mW per strip on an 80 µm pitch, i.e. 250 mW/cm width, is it practical to read out 15000 pixels per cm2? strip detector: n strips pixel detector: n x n pixels The capacitance is dominated by the strip-strip or pixel-pixel fringing capacitance. ⇒ capacitance proportional to periphery (pitch p and length l ) In the most efficient operating regime the power dissipation of the readout amplifier for a given noise level is proportional to the square of capacitance (discussed in VIII.5) ⇒ n times as many pixels as strips ⇒ ⇒ Increasing the number of readout channels can reduce the total power dissipation! The circuitry per cell does not consist of the amplifier alone, so a fixed power P0 per cell must be added, bringing up the total power by n2P0, so these savings are only realized in special cases. Nevertheless, random addressable pixel arrays can be implemented with overall power densities comparable to strips. strippixel Cn CplC 2 )(2 ≈⇒+∝ 2CP ∝ strippixel Pn P 2 4 ≈ striptotpixel Pn P 4 , ≈