Simulating Radiation-Induced Shifts in MOSFET Threshold Voltage

 

Introduction

Irradiation by energetic particles can degrade semiconductor device performance. The particles involved can be electrons, positrons, neutrons, protons, alpha particles, heavy ions, or high-energy photons. As they pass through a device, these particles interact with the lattice. Energy deposited through these interactions may damage the lattice directly by displacing its atoms, or may result in the creation of electron/hole pairs. A sudden excess of electron/hole pairs may trigger a latchup, possibly damaging the device through overcurrent. Holes generated within an insulator may become trapped there, leading to a gradual accumulation of charge that worsens performance and eventually causes the device to fail. Consideration and modeling of these effects is important when designing semiconductor devices that will be exposed to high-energy radiation.

The device simulator Victory Device has models to account for the following radiation effects:

  1. Local electron/hole pair generation along particle tracks caused by individual particle strikes — single event upsets.
  2. Generation and recombination of electron/hole pairs caused by the ongoing radiation of a device.
  3. Insulator charging caused by the trapping of radiation-generated electrons and holes within insulator materials.
  4. Lattice dislocation defects caused by the accumulated flux of radiation through a device.

In this article, we illustrate some effects that radiation may have on the electrical characteristics of a device. We shall consider an n-MOSFET that is exposed to x-rays, consequently experiencing radiation-induced generation and recombination that leads to charging of the oxide region below the gate.

 

Insulator Charging

In insulator materials, because very few carriers are present, trap states usually do not become charged, although quantum mechanical tunneling may cause some charging near interfaces. Irradiation by energetic particles, however, can generate electron/hole pairs within the body of an insulator. Under the influence of an electric field, the electrons and holes from these pairs can separate and become trapped, leading to a gradual accumulation of charge both within the insulator and on its surface. The processes involved are illustrated in Figure 1. An energetic particle such as an x-ray photon first enters the body of an insulator. There it may be scattered by the crystal lattice and, in the process, generate an electron/hole pair. Once an electron/hole pair has been created, it becomes subject to two opposing forces. The first force arises from the Coulomb attraction between the electron and hole, which tends to cause the pair to recombine. The second is the electric field that arises from the applied biases, which tends to separate the carriers. This simple description is sufficient provided that that distinct pairs of electrons and holes are far enough apart that the separate pairs do not interact. A sparse distribution like this is denoted by the adjective geminate.

 

Figure 1. Physical processes leading to insulator charging.

 

In accounting for the generation of electron/hole pairs, the generation rate due to high energy radiation can be expressed as the product of the irradiation dose-rate and a generation factor that is specific to the irradiated material. This generation factor is basically just the material density divided by the energy it takes to create an electron/hole pair in that substance. Departures from this basic rate can be accounted for by applying a numerical enhancement factor. Taking the density of SiO2 as 2.2 g/cm3 and the formation energy of an electron/hole pair as 18 eV, we calculate a basic generation factor for SiO2 of 7.6x1012 pairs/cm3•rad. Multiplying this by a dose-rate expressed in rad/s gives us a generation rate in units of pairs/cm3•s. However, not all electron/hole pairs that are generated become active in the device. Some pairs recombine so soon after they are generated that neither carrier has a chance to be transported1. This is called geminate recombination. It is accounted for by multiplying the basic generation rate by a yield function. Based on the work of Dozier, et al.2 and others, the yield function used by Victory Device takes the form

where

  • |E| is the magnitude of the electric field,
  • Y0 is the zero-field yield factor,
  • E0 is a critical field value, and
  • A0 moderates the growth rate of the function. (Here A0 is non-negative.)

The parameters of the yield function depend on both the type of the radiation and the material being irradiated. Typical curves for SiO2 are shown in Figure 2.

 

Figure 2. Geminate yield functions for SiO2.

 

If an electric field is present, electrons and holes from pairs that survive the geminate recombination process drift apart under the influence of the field. Insulator charging occurs when some of these carriers become trapped by impurities or other crystal defects present within the insulator material. The magnitude of this charging is determined by a balance between carrier capture and emission processes.

The capture process for insulator traps is the same as for traps in ordinary semiconductors, but the emission process appears to be different. According to the model of Kimpton and Kerr3, the primary energy source stimulating the detrapping process is the geminate recombination of electron/hole pairs during irradiation. As illustrated in Figure 1, a geminate recombination event emits a quantum of energy that may prompt the emission of a hole from a donor-like trap, or the emission of an electron from an acceptor-like trap. Meanwhile, the trap energies are assumed to be far from the band edges, so the ordinary thermally-stimulated emission processes are negligible.

According to these assumptions, donor-like insulator traps emit holes at the rate

where

  • G0 is the generation factor, with units of generated-pairs/cm3•rad,
  • δ is the dose rate in rad/s,
  • Y is the geminate yield,
  • Vϕ is the emission interaction volume for a trap,
  • Nt is the density of traps, and
  • f is the probability that a trap is filled.

The expression for the emission of electrons from acceptor-like traps is similar.

Breaking down the rate equation: G0δ is the rate of electron/hole pair creation per unit volume, (1−Y) is the fraction of pairs that undergo geminate recombination, and Vϕ Nt f is the probability that a phonon created by a geminate recombination event will interact with a filled trap to empty it.

 

Simulation

To demonstrate the effects of insulator charging due to exposure to high-energy radiation, we shall use Victory Device to simulate an n-MOSFET that is bombarded by x-rays. The structure and doping of the MOSFET are typical, as shown in Figure 3.

Figure 3. n-MOSFET structure used in simulation of radiation effects.

 

In Victory Device, the radiation models only apply to semiconductors. Consequently, to model radiation effects in an insulator, you must tell Victory Device to regard the material as a semiconductor. To do this, set the SEMICONDUCTOR flag on an appropriate MATERIAL statement. You may also need to define a limited number of semiconductor properties for the material. For this simulation, we set the following:

# Semiconductor properties for oxide
MATERIAL MATERIAL=oxide NC300=2e19 NV300=2e19 EG300=9 SEMICONDUCTOR
MATERIAL MATERIAL=oxide MUN=1 MUP=1e-3
MATERIAL MATERIAL=oxide M.VTHP=1

We also specify the following traps in the insulator body and on its interface with the semiconductor. These will become charged as the device is irradiated.

# Conditions for radiation-induced oxide charging
INTOXIDECHARGING R1MATERIAL=oxide R2MATERIAL=silicon JMODEL.P NT.P=3e12 \ SIGMAT.P=1.5e-13 SIGMAN.P=1e-30 SIGMAPH.P=1.5e-13 \
JMODEL.N NT.N=1e4 SIGMAT.N=1e-30 SIGMAP.N=1e-30 SIGMAPH.N=1e-30 MFP.PHONON=0.013

OXIDECHARGING MATERIAL=oxide JMODEL.P NT.P=4e18 SIGMAT.P=1.5e-13 \
SIGMAN.P=1e-30 SIGMAPH.P=1.5e-13 JMODEL.N NT.N=1e10 SIGMAT.N=1e-30 \
SIGMAP.N=1e-30 SIGMAPH.N=1e-30

The source of radiation will be x-rays at a dose-rate of 1 rad/s:

# Radiation environment
RADIATION DOSERATE=1 XRay

The simulation in our example consists of two parts. In the first part, we begin by irradiating the device while it is under a forward gate bias of 5 V, up to an exposure of 1 M-rad. In the second part, we remove the gate bias and continue the irradiation up to a total exposure of 2 M-rad. At the start of the simulation, after the first part, and at the end, we shall sweep the gate bias to determine the threshold voltage.

 

Results

Irradiation under forward bias induces a shift in the threshold voltage of the IV curve, as seen in Figure 4. This is due to the trapping of holes in the oxide. With a positive bias on the gate electrode, holes generated within the oxide are pushed away from the gate, so most of the trapping takes place near the oxide/silicon interface. When the gate bias is removed, only half of the radiation-generated holes will migrate towards the oxide/silicon interface, while the other half migrate towards the gate. Consequently, irradiation with the bias removed releases some of holes that were trapped near the interface, eventually reducing the threshold shift by about half.

Figure 4. Shift in IDVG threshold voltage due to insulator charging.

 

In Victory Device, we can set a PROBE near the oxide/silicon interface to investigate how the areal concentration of trapped holes changes during the course of this simulation:

# Probe conditions near the oxide/silicon interface
PROBE MATERIAL=oxide INT.DONOR.TRAPS X=0 Y=-1e-6 NAME=”trapped int holes”

The results are shown in Figure 5. With irradiation under a forward gate bias, the concentration of holes trapped at the interface gradually increases. Eventually it should saturate, but the saturation level is not reached during the course of this simulation. After the bias is removed, the rate at which holes impinge on the traps is reduced by roughly half while the hole emission rate remains nearly the same, leading to a reduction in the concentration of trapped holes.

Figure 5 also shows a curve for a reversed gate bias. Under a reversed bias, holes generated in the oxide are pulled away from the oxide/silicon interface and towards the gate. Consequently, little or no trapping takes place at the interface. When the reverse bias is removed, approximately half the holes generated in the oxide start diffusing towards the interface, and some of them are trapped there. With irradiation continuing at zero gate bias, both the upper and the lower curves in Figure 5 appear to be headed towards the same level. Indeed, under conditions of constant irradiation and constant bias, the distribution of trapped holes eventually approaches an equilibrium value that depends only on the final bias3.

Figure 5. Response of trapped interface holes to gate bias and irradiation.

 

Conclusion

We have shown one way in which the operation and performance of semiconductor devices can be altered or degraded by exposure to high-energy radiation. However, these effects can be mitigated if they are taken into consideration during the design of a semiconductor device. A simulator such as Victory Device, which can model radiation effects, can be a useful tool in the design of radiation-hardened electronics.

 

References

  1. R. J. Milanowski, et al., “TCAD-Assisted Analysis of Back-Channel Leakage in Irradiated Mesa SOI nMOSFETs,” IEEE Transactions on Nuclear Science, Vol. 45, No. 6 (1998): 2593–2599.
  2. C. M. Dozier, et al., “An Evaluation of Low-Energy X-Ray and Cobalt-60 Irradiations of MOS Transistors,” IEEE Transactions on Nuclear Science, Vol. 34, No. 6 (1987): 1535–1539.
  3. D. Kimpton and J. Kerr, “A Simple Trap–Detrap Model for Accurate Prediction of Radiation Induced Threshold Voltage Shifts in Radiation Tolerant Oxides for all Static or Time Variant Oxide Fields,” Solid State Electronics, Vol. 37, No. 1 (1994): 153–158.