The low gain avalanche detector (LGAD) [1–3], based on the planar technology, produces a signal in response to the generation of free carriers by a charged particle or high-energy photon; when operated, it is depleted by a reverse bias. An evolution of the avalanche photodiode (APD), the LGAD exhibits internal signal gain in the range of up to 100 that is proportional to the applied bias voltage. The profile of the LGAD structure is n⁺/p/p⁻/p⁺, where the p-implant below the highly doped n⁺ cathode electrode is referred to as the multiplication implant, forming a gain layer, and has dopant concentration in the range a few times 10¹⁶ cm⁻³ and depth 0.8–2.5 μm. The detection of sub-nanosecond signals produced by minimum ionizing particles is possible with these devices [4].

LGADs are proposed for use in several experiments including upgrades to those at the Large Hadron Collider (LHC) [5, 6]. A typical specification for their operation at the LHC, as components of the High-Granularity Timing Detector (HGTD) in ATLAS or the Endcap Timing Layer (ETL) of CMS, includes tolerance to 2 MGy of the ionizing dose, which will accompany integrated hadron fluence up to about 2.5 × 10¹⁵ n_eq/cm² (this includes a safety factor of 1.5). Thin bulk is preferred, as the minimization of induced current variations due to Landau fluctuations will promote the best timing resolution [7].

An active area of research involves the problem of gain decrease as boron-substituted atoms deactivate in response to radiation damage; this is “acceptor removal” [8]. While the primary source of this problem is non-ionizing energy loss (NIEL) due to hadron radiation, a contribution also arises from the associated gammas, which produce point defects in the gain layer through the Compton (and to a lesser extent, photoelectric effect) electrons that they induce.

Gamma radiation motivates a second line of inquiry as well: characterization of oxide charge and interface traps in order to permit optimization of dimensions of the surface features, including interelectrode separation and the distance between the active area and the edge. The goal is to maximize fill factor while ensuring against electrical breakdown under various operating scenarios.

Prototypes of three structures were produced by Hamamatsu Photonics K.K. (HPK) using epitaxial silicon grown on a Czochralski substrate; these are single LGADs, 2 × 2 (“quad”) LGAD arrays, and associated p-i-n diodes. All have 50 μm active layer thickness, 200 μm total thickness, and a single guard ring. The pads have dimensions of 1.3 × 1.3 mm². The p-type gain layer is approximately 2.5 μm deep and starts very close to the surface. All of the devices include under-bump metallization (UBM). Figure 1 (left) shows the surface of one such device, which also includes an opening for transient-current technique (TCT) stimulation and a probe needle contact pad. The 2 × 2 arrays have the same features as the smaller devices but variations on inter-pad (“IP”) separation (30, 40, 50, and 70 μm) as well as distance from the active area to the edge (300 and 500 μm). Figure 1 (right) shows a quad prototype. The p-i-n diodes have the same geometry as the LGADs but lack the gain layer. As they can tolerate high bias voltage while sustaining relatively little bulk damage, breakdown in the p-i-ns is indicative of breakdown in the bulk, typically at the guard ring where the field lines are focused. The LGADs and quads were produced with four different options on gain layer dopant concentration. Dopant concentrations of only a few percent difference have previously been shown to lead to very large differences in gain [9].

Figure 6 shows example IV characteristics for p-i-n diodes from Wafer 25, for total ionizing dose from 0 to 2.2 MGy. In this case, post-irradiation breakdown voltages approaching 800 V are achieved, as irradiation-induced oxide charge moderates the electric field. If the LGADs’ primary susceptibility to breakdown were also in the guard ring region, these high values would apply to them as well; however, the LGADs break down at the electrode pads first. These outcomes follow closely the results of measurements made following neutron exposures, reported previously [12]. Between 700 and 800 V, the field in the bulk is sufficiently large that the device breaks down at its weakest point—regardless of whether it is a full LGAD or a p-i-n test structure. For the LGAD, this breakdown is typically through the bulk, whereas for the p-i-n, it is typically at the periphery.

If an electrode is floating, its potential is distributed to neighbors by punch-through [13]. This process places a limit on the interelectrode separation, for which the designer must anticipate the consequences in case a lost bump bond leads to breakdown at an electrode, which could then cascade to breakdowns in neighbors.

An IV study involving the quad sensors was carried out to investigate the question of what minimal interelectrode separation will reliably inhibit full punch-through. Bias is applied to the back side of the chip, and leakage current is measured with ground connected to the guard ring plus 0, 1, 2, 3, or all 4 pads. Figure 7 shows an example set of measurements of this type, for devices taken from Wafer 31, as a function of applied dose.

Figure 8 shows the punch-through voltage, as a function of dose, for all four interelectrode separations. Punch-through between the guard ring and the pads occurs around 100–140 V prior to irradiation and decreases to nearly 0 V at 2.2 MGy, indicating the loss of resistivity in the region between the pads and the guard ring. At 2.2 MGy, all of the devices’ IV curves are similar. In the case of the wafer with 30 μm interelectrode separation, the breakdown voltage for measurement on the guard ring alone was observed to be substantially higher than that in the case in which the guard ring plus any non-zero number of pads are contacted. Among wafers with 30 μm interelectrode separation but differing gains, the voltage at which punch-through occurs increases from approximately 85 V in Wafer 25 to approximately 100 V in Wafer 42.

Figure 9 shows the leakage current versus applied bias voltage, for quad devices taken from all wafers (thus with four different initial values of the gain layer depletion voltage). These measurements were made after application of 0.5 MGy, for the measurement configuration indicated above, that is, bias applied to the back side of the chip, and leakage current measured with ground connected to the guard ring plus 0, 1, 2, 3, or all 4 pads. Breakdown occurs at the same bias potential for measurements connecting the guard ring to any number of pads greater than zero. This indicates that the loss of a pad (e.g., disconnection of a bump) will present a danger of breakdown between that pad and its neighbors, for any of the interelectrode separations (30–70 μm) reported here. It is interesting to note that by 2.2 MGy, while the IV curves are identical up to breakdown, the IV measured on the guard ring alone rises with a much slower characteristic.

The resistance between electrodes in the quad sensors was also measured. On each quad sensor, one pad was biased to values in the range 0.5–2.0 V relative to the remaining three grounded pads, and the current drawn on that biased pad from the others was recorded. The back side of the sensor was biased at −100 V with a separate source meter, and the guard ring was allowed to float. A fit to the slope of this IV characteristic yields the inverse of the resistance. Figure 10 shows the resistance values obtained in this way, for quad sensors representing the four inter-pad spacings, taken from wafers 25 and 31, for doses 0, 0.5, and 2.2 MGy. On all samples, the resistance value is significantly greater than 1 GΩ prior to irradiation; it drops to values around 1 GΩ after application of 0.5 MGy and reaches values in the range 10–100 MΩ after application of 2.2 MGy.

The errors on the IV and CV measurements include statistical and systematic uncertainties. Each IV and CV data point shown on the graphs is the average of three to five measurements, and the standard deviation for each is found to be less than 2%. Systematic uncertainties include uncertainties associated with the setup configuration (typically 1.9%), the accuracy of the source and measurement instruments (±0.3% + 100 fA for the Keithley 237; ±0.029% + 300 pA for the Keithley 2410, and ±0.34% for the HP4284A), the precision of the measurement of the temperature (±0.5°C leads to uncertainty of ±1.82% on leakage current), and the data increment size of 1 V. The uncertainties on V_gl, V_fd, and pad resistance are derived from the quality of the linear fits and the bias voltage step size of ±1 V. Analyses of the measurements typically require linear fits, on which the uncertainty is typically a small percent.

The surface, gain layer, and bulk properties of the LGADs included in this study are found to change after gamma irradiation.

For the single LGADs and the p-i-n diodes, the surface component increases the total leakage current by more than an order of magnitude with only 0.1 MGy dose and saturates at about the same level with a high gamma dose. The single LGADs have a much lower breakdown voltage than the p-i-n diodes, indicating that the LGAD breakdown occurs in the bulk at the electrode pad region. Both the gain layer and full depletion voltages decrease by a small amount even at the highest dose, indicating some damage to the gain layer and bulk. The decrease in (V_fd − V_gl) with dose implies a change in doping concentration in the gain layer and thus acceptor removal. The gamma radiation produced Compton electrons and photoelectrons that led to lattice point defects in the gain layer. The acceptor removal constant was characterized by fitting the data to a decaying exponential function (Figure 4), and the resulting values are shown in Table 1.

For the 2 × 2 quad LGADs, the punch-through between the guard ring and the pads for all inter-pad separations has been characterized to be over 100 V prior in irradiation; however, after application of gamma irradiation it decreases for all devices studied and reaches nearly 0 V at the maximum 2.2 MGy dose. Pad-to-pad resistance after the maximum dose is found to lie in the range of 10–100 MΩ. Some variations in punch-through voltage and inter-pad resistance are observed for devices from different wafers and different doping concentrations.