Measurement of the initial (drop-free) current density-voltage characteristics after the irradiation indicates that the drift. Position of the fermi level at the transition between ·the Ohmic series and the fall-free space-charge limited series. Value of the voltage at the transition between the Ohmic range and the trap-free space-charge limited range.
Location of the fermi level at the transition between the ohmic region and the trap-dominated space-charge limited region. The value of the voltage at the transition between the ohmic region and the trap-dominated space-charge limited region.
CHAPTER 3 RESULTS AND DISCUSSIONS
The theory of space charge limited current is applied and a simple model of localized levels in the forbidden band gap is obtained. An important point of the 'sallmv trap' case is that 8 is independent of x, except in the narrow region near the emitter(]). In this work, energies in the forbidden band gap are considered positive and measured from the edge of the conduction band.
Trap-free SCLC provides information about the drift velocity-field relationship of the charge carrier in the material. Information about properties of the traps, such as the trap cross-section a, can be obtained from the time dependence of the flow.
CHAPTER II
Four-point probe measurements are made at room temperature on the exposed rod surface after cutting two slices for capacitance and Hall effect measurements. We note that the resistance increases by a factor of about 3 going radially from the center to the periphery. We note that arm 2 of sample II, which comes from the center of the slice, gives the highest carrier concentration.
In summary, from capacitance, four-point probe and Hall effect measurements, we obtain a consistent picture of the crystal used in this work. Care must be taken to shake the etchant (with the silicon strip inside) vigorously and add the methanol, to prevent black silicon polyhydride films from appearing on the surface.
Dev ice
Osc ill oscope Tektronix 454
This container is taped to the back of the water-cooled tritium target of a Texas Nuclear Corporation accelerator at California State College, Los Angeles. The dose of the d-t reaction is calculated from the activation analysis of Al foils coated with C~by.
CHAPTER III RESULTS AND DISCUSSIONS
W= l24fLm . Figure 11 Dependence of the initial current on temperature at a constant vollagc of 10 V, derived from the square of laH asvm•)totcs oE Lhe cit.'vice ch:1racterlstics before and after ~radiation at a dose o[ ~ : 1.2 x 10lln/cm2 aod. Figure 6 shows typical initial (no-trap) current versus voltage characteristics in the dark before and after irradiation. The theoretical J(V) characteristic of this process with the known position of the quadratic asymptote lmv is then fitted to the experimental points.
Up to a dose of 4.0 x 10 n/cm, the only discernible change in v(E) is reduced mobility at low fields and low temperatures. The limiting rate of motion at high fields results from carrier energy losses in optical and acoustic phonons. Mobility at low fields results from scattering by thermal phonons and some impurities.
The large concentration of injected carriers and the strong electric field non-uniformly distributed in the bulk create conditions very different from those of thermal equilibrium. However, if we apply the model to the limit of high carrier concentration, then the radius of each cluster will be reduced to . The s;:nne argument can be applied, again with caution, to the example that the dielectric constant £ is not even affected by radiation as assumed in the discussion above, in which the change in current density J was attributed to a change in mobility ~· Indeed,.
More work will be needed to study the applicability of the cluster model to sclc conditions. Its concentration is derived from the trap-filled threshold voltage (Equation 6, Section 1.2) and its energy depth from a factor of 8 (Equation 5, Section 1.2). A band model is proposed to explain the observed facts obtained by transient measurements at low temperatures. the concentration of the lower level f from the value of the threshold voltage of the filled trap, VTFLf', associated with the level f, the energy depth from the calculated Bf using the proposed model, and the capture cross section from the measured trapping time.
I ~JTFL 8/{8+1)
The calculations of the current response J(t) to an applied turn-on voltage step V, a applied in th~. Experimentally, the difference in the two models shows up in the results of the detrapping experiments. We will show below that, based on the results of the detrapping experiments, model 1 applies to ours.
This last point will be used later to show that, in the high temperature range, the non-exponential behavior of the observed current versus time is not due to a distribution in energy of trap levels. In terms of the two-level model proposed in the previous section, the values of N' and E' (R-1 and R-2) are associated with the s-level. The increase in current at t ~ 0 as a function of temperature reflects the temperature dependence of the mobility, as discussed in section 3.2.1.
Therefore, when the carriers become trapped, the transit time in the trapped charge field increases rapidly. 2 of the second current pulse and Joff is directly proportional to the concentration of carriers trapped in the time interval 0 < t < t h (Fig. 23). Therefore, we have shown that the current amplitude of the second pulse is directly proportional to the amount of trapped carriers.
Therefore, it is only necessary to analyze the height of the second current pulse to determine the amount of carriers trapped in the time interval 0 < t < t. Therefore, Model 1 holds, since Model 2 predicts that most of the trapped charge should be trapped in this experiment. 2 of the second current pulse is again directly related to the amount of charge trapped in the time interval 0 < t < t h.
The effect of the radiation on the drift velocity-field relationship of electrons in silicon is studied. The temperature dependence of the Ohmic current in our devices is another problem that remains to be understood.
APPENDIX I
In this appendix we analyze two trapping and trapping models with the above assumptions. The three important time constants are T1f' T11s' T'x· All other trapping and detrapping time constants are assumed to be much larger than any of them. The corresponding untrap process of model 2 involves only so we expect all trapped payloads to be trapped.
The difference in the two models shows in the results of the reception experiments: in model 1 only a fraction of the trapped injected charge escapes, while in model 2 all the trapped injected charges escape. This feature is used to select the correct model to be applied to our case. In the calculations of the reception processes above, we have assumed that all l carriers in the band are deleted before they can be recaptured.
This assumption is valid as long as the carrier transition time in the internal field generated by trapped charge is much smaller than the fastest trapping time. Therefore, we expect the assumption that uncoupled carriers are deleted before they can be recaptured to be valid. Although Boltzmann's statistics do not quite hold for most of the temperature range considered, we can still derive meaningful quantities.
APPENDIX II
The subtraction procedure is applied to the obtained data, yielding a \ve]J·-determining'"cl lavi square asymptote .:1. Trap at 77°K (observed as the difference between the DC and initial current measurements in the transition range and sclc ) is less than 5%. We therefore observe the correlation between the trapping in the transition range and scl and the strong decrease of the free carrier concentration in thermal equilibrium as the temperature decreases.
In all cases, tipping before irradiation reduces the current in the scl region from its (non-trap) initial current value by no more than 50%. Compared to post-irradiation trapping, which is orders of magnitude larger, we feel justified in neglecting any traps that existed in the crystal prior to irradiation. The summation procedure refers to the clear obtained from the DC and initial current measurements, which gives well-defined square-law asymptotes.
The results of these experiments indicate that the population is involved in thermal equilibrium of free carriers in different levels. As indicated in section 3.3.2, the situation encountered here is one in which the thermal equilibrium fermi level is one or two kT below the 0.47 eV level, and in which the free carrier concentration near the edges is determined by the contacts. His computer calculations show that under such conditions the current can increase faster \vith voltage than v2 and that, in this range, the voltage at constant current is linear with thickness.
As Tredgold puts it, this situation involves a "current carried by injected space charge, but where the limiting process is confined to the contact. The similarity between Tredgold's results and ours leads us to believe that the same mechanism is involved. At room temperature, it is Ohmic current in several units has been measured before and after irradiation.
Threshold Voltage vs Thic kness
Thermal equilibrium Free carrier concentration before and after irradiation, measured by the current in the ohmic range. This decrease is due to a shift of the Fermi level deeper into the tire due to the introduction of defect levels. After correcting for the temperature dependence of the mobility, assuming a system with one carrier (electron), we obtain the phenomenological relationship.
But such a temperature dependence at thermal equilibrium cannot be extracted from the model we have. However, it should be noted that sclc is a situation very distinct from thermal equilibrium. In the space-charge limited region, the electron concentration is many orders of magnitude greater than that of thermal equilibrium, the hole concentration is therefore negligible, and so are recombination generation processes.
His solution 1 would provide a direct way of relating thermal equilibrium data such as the Hall effect and resistivity measurements to our space-charge-limited current results.
