Subsections

• 4.1.1 Experimental Setup
  • 4.1.1.0.1 Regime 1:
  • 4.1.1.0.2 Regime 2:
  • 4.1.1.0.3 Regime 3:
  • 4.1.1.0.4 Regime 4:
  • 4.1.1.0.5 Regime 5:
  
  
• 4.1.2 Charge Pumping Current Model
• 4.1.3 Numerical Simulation
  • 4.1.3.1 Variation
  • 4.1.3.2 Variation
  • 4.1.3.3 Pulse Amplitude Variation
  • 4.1.3.4 Reverse Bias
  • 4.1.3.5 Temperature Dependence

4.1 Charge Pumping Method

The charge pumping method has shown to be a very reliable and also precise method allowing the in-depth analysis of the interface, directly in the MOSFET device. Additionally it only requires basic equipment and is relatively easy to set up.

The effect has been first reported by Brugler and Jespers in 1969 [39]. They reported a net DC substrate current when applying periodic pulses to the gate of a MOS transistor, while keeping source and drain grounded. The current was found to be proportional to the gate area and the frequency of the applied gate pulses. It was flowing in the opposite direction of the leakage current of the source and drain to substrate diodes. They showed that the current originates from recombination of minority and majority carriers at traps at the interface. Therefore, the method can be used for measuring the interface trap density in MOSFETs for the evaluation of MOSFET degradation. The major breakthrough for the charge pumping method was the thorough investigation and correct explanation of the method, applied directly to MOSFET structures by Groeseneken et al. in 1984 [40].

4.1.1 Experimental Setup

Figure 4.1: Basic experimental setup for the charge pumping measurement. The source to substrate and drain to substrate diodes are typically slightly reverse biased while the gate is pulsed between inversion and accumulation conditions. The substrate current is measured as the charge pumping current .

The basic experimental setup for the charge pumping method can be seen in Figure 4.1 for an n-channel MOSFET. The source and drain to substrate diodes are reverse biased. The gate is pulsed between accumulation and inversion conditions while the charge pumping current is measured at the substrate. This current flows in the opposite direction of the source and drain to substrate diode leakage currents.

Figure 4.2: Base level sweep during a charge pumping measurement. As the base and also the top level of the gate pulse pass the flat-band and threshold voltage levels of the transistor, five different regimes can be distinguished.

In the accumulation phase majority carriers, holes in case of an n-channel MOSFET, flood the channel area and some of them become trapped in interface traps. When the gate pulse drives the transistor into inversion, the majority carriers leave the channel and move back to the substrate. Some trapped carriers with energies close to the valence band can be de-trapped through thermal emission before the channel becomes flooded by electrons and also move back to the substrate. The rest of the trapped holes recombines with channel electrons and leads to a net current. The same process occurs when the transistor is driven from inversion back to accumulation, with opposite carrier types.

The base level of the gate voltage pulse is swept to drive the MOSFET from accumulation to inversion. When the amplitude of the pulse is larger than the difference of threshold voltage and flat-band voltage, $\ensuremath {\Delta V_\textrm {A}}> \ensuremath {V_\textrm {th}}- \ensuremath {V_\textrm {fb}}$, then five different regimes are observed as sketched in Figure 4.2. Regime 3, where the largest amount of traps in the band-gap is scanned, is the most important one. It can be described by a current model (Section 4.1.2) to calculate the interface trap density. The base level sweep charge pumping method was first proposed by Elliot [41] and the different regimes are governed by the following mechanisms:

4.1.1.0.1 Regime 1:

The whole pulse is below the flat-band voltage and the substrate is in permanent accumulation. The interface traps are permanently filled with holes and therefore no recombination current is measured.

4.1.1.0.2 Regime 2:

The top of the pulse reaches the region between the flat-band and the threshold voltages. In this phase the interface is moved from accumulation into strong depletion up to weak inversion. Here, the charge pumping current increases and the base voltage is around threshold voltage minus the pulse height. It could be assumed that the shape of the rising $\ensuremath{I_\textrm{CP}}$ in this regime is determined by the recombination process in weak inversion. It has been shown, though, that other mechanisms may have an important influence. These can be surface potential fluctuations because of spatially non-uniformly distributed oxide charges [42,43], acceptor and donor traps [43], or variations in the proximity of the source and drain regions. Also the modulation of the effective gate area by the gate voltage might influence the rising charge pumping current.

4.1.1.0.3 Regime 3:

The base level voltage is below the flat-band voltage, and the top level of the pulse is above the threshold voltage, $\ensuremath{V_\textrm{base}}< \ensuremath{V_\textrm{fb}} < \ensuremath{V_\textrm{th}}< \ensuremath{V_\textrm{top}}$. In this regime the charge pumping pulse sweeps the substrate in the channel area from accumulation to complete inversion. At each time the transistor is pulsed from accumulation to inversion or back. The fast interface traps are filled with holes, or electrons, respectively, which then recombine with the opposite carrier type leading to a net current measurable as $\ensuremath{I_\textrm{CP}}$. In this regime the current has the highest magnitude.

4.1.1.0.4 Regime 4:

The base level is between the flat-band and threshold voltages. The transistor only reaches weak accumulation, the interface traps are mainly negatively charged and are no longer flooded with holes, thus recombination is reduced and the charge pumping current goes down. The same surface potential fluctuation and gate area modulation effects as in Regime 2 can influence the characteristic of $\ensuremath{I_\textrm{CP}}$.

4.1.1.0.5 Regime 5:

The transistor is completely in inversion during the whole pulse. The traps are filled with electrons and no holes reach the channel at any time. The measured substrate current only consists of the source and drain leakage currents.

4.1.2 Charge Pumping Current Model

Figure 4.3: Charge pumping signal applied to the gate contact. The signal is characterized by the rise and fall times, $t_\textrm {rise}$ and $t_\mathrm{fall}$, and the amplitude . For the emission of electrons and holes from the traps only the window between the flat-band voltage and the threshold voltage is significant.

The first comprehensive model for the charge pumping current was proposed by Groeseneken et al. in 1984 [40]. This model has been developed to capture the maximum charge pumping current which is obtained in Regime 3. Here the gate voltage pulse sweeps from below the flat-band voltage to above the threshold voltage. Therefore the substrate is driven from accumulation to inversion and back.

Only the fast interface traps situated between the two energy levels $E_\mathrm{em,e}$ and $E_\mathrm{em,h}$ in the band-gap of the semiconductor can contribute to the charge pumping current,

$$E_\mathrm{em,e} = E_\mathrm{i} - \ensuremath{\textrm{k$_\te... ...nv}}{\ensuremath{\textrm{k$_\textrm{B}$}}T}\right)\right) ,$$ (4.1)

$$E_\mathrm{em,h} = E_\mathrm{i} - \ensuremath{\textrm{k$_\te... ...cc}}{\ensuremath{\textrm{k$_\textrm{B}$}}T}\right)\right) ,$$ (4.2)

where $E_\mathrm{i}$ is the intrinsic energy, $E_\mathrm{f,inv}$ and $E_\mathrm{f,acc}$ are the Fermi energies in inversion and accumulation, $v_\mathrm{th}$ is the thermal velocity, $\sigma_\mathrm{e,h}$ the capture cross sections of the traps, and $n_\mathrm{i}$ is the intrinsic carrier concentration. Traps outside this band cannot contribute to the current as the trapped charge becomes de-trapped instantly through thermal emission when the Fermi-level moves beyond the trap level, for trapped electrons, or above, for trapped holes.

The emission times $t_\mathrm{em,e}$ and $t_\mathrm{em,h}$ for electrons and holes can be calculated from the fall and rise times, $t_\mathrm{f}$ and $t_\mathrm{r}$, as

$$t_\mathrm{em,e} = \frac{\vert\ensuremath{V_\textrm{fb}}- \e... ...{\vert\ensuremath{\Delta V_\textrm{A}}\vert}t_\mathrm{f} ,$$ (4.3)

$$t_\mathrm{em,h} = \frac{\vert\ensuremath{V_\textrm{fb}}- \e... ...}{\vert\ensuremath{\Delta V_\textrm{A}}\vert}t_\mathrm{r} ,$$ (4.4)

and are illustrated in Figure 4.3. These are the times available for the emission of carriers from the fast traps.

The net CP current measured at the substrate can be obtained as

$$\ensuremath{I_\textrm{CP}}= \overline{\ensuremath{D_\textrm... ...mathrm{h}}\sqrt{t_\mathrm{em,e} t_\mathrm{em,h}} \right) ,$$ (4.5)

where $f$ is the frequency and $A_\mathrm{G}$ the gate area.

The charge pumping current is directly related to the mean interface trap density $\overline{\ensuremath{D_\textrm{it}}}$ in the channel, the size of the interface channel area, the frequency $f$, and the pulse shape characterized by its rise and fall times. This makes the charge pumping method a perfect tool for the characterization of interface degradation.

4.1.3 Numerical Simulation

Figure 4.4: Device structure used for numerical charge pumping simulations. The n-channel MOSFET has a channel length of 0.6 $\mu$m (junction to junction) and the gate oxide thickness is 12 nm.

Figure 4.5: Charge pumping simulation results. The interface traps are of acceptor type, equally distributed in the band-gap, the concentration has been varied from $10^{10}$ cm$^{-2}$ up to $1.4\times 10^{11}$ cm$^{-2}$, $\ensuremath {\Delta V_\textrm {A}}=3$ V, and there are no fixed interface charges. The dotted lines give the results from the current model obtaining excellent agreement with the numerical simulation results.

The device simulator Minimos-NT [44] is used for numerical analysis of the charge pumping effect. For each of interest a transient simulation of the gate pulse is performed. The resulting currents can then be plotted versus the base voltage to obtain the typical charge pumping current versus plot.

The device under test was a conventional n-channel MOSFET structure (Figure 4.4). The gate length, measured from source-substrate to substrata-drain junctions is 0.6$\mu$m, the device width 100$\mu$m, and the gate oxide thickness is 12nm.

4.1.3.1 Variation

The first simulation gives a comparison of the analytical current model (4.5) to numerical simulations using Minimos-NT. Here, the interface trap density has been varied from $10^{10}\mathrm{cm^{-2}}$ up to $1.4\times 10^{11}\mathrm{cm^{-2}}$, the pulse height is $\ensuremath {\Delta V_\textrm {A}}=3$V, and the rise and fall times are $t_\mathrm{r}=t_\mathrm{f}=0.1\mu$s. Figure 4.5 gives the resulting CP curves and also the analytic approximation using (4.5). The agreement is excellent with the peak values of Regime 3.

4.1.3.2 Variation

Figure 4.6: Charge pumping simulation to extract threshold voltage shifts. The interface trap density is constant at $6 \times 10^{10}$ cm$^{-2}$. Close to the interface, fixed positive oxide charges are generated. From the charge pumping signal and the resulting voltage shift $\Delta \ensuremath {V_\textrm {base}}$ the density of fixed interface charges can be calculated.

The charge pumping method is very well suited for the quantitative investigation of fixed oxide charges. Figure 4.6 shows the charge pumping currents of a MOSFET device with constant density of interface traps but varying amount of fixed charges at the interface. The oxide charges are assumed to be located directly at the interface. The resulting $\Delta \ensuremath {V_\textrm {base}}$ in the numerical simulations for an interface charge density $\ensuremath{Q_\textrm{ox}}= \mathrm{q}_0 \cdot 2\times10^{12}$cm$^{-2}$ is $\Delta \ensuremath{V_\textrm{base}}= -1.11$V. This result is in excellent agreement with the analytical equation (2.31) presented in Section 2.2.1 and using the approximation for the plate capacitor

$$\ensuremath{C_\textrm{ox}}= \varepsilon \frac{A}{l} ,$$ (4.6)

where $A$ is the area and $l$ is the dielectric thickness, predicting $\Delta \ensuremath{V_\textrm{base}}= -1.114$V.

4.1.3.3 Pulse Amplitude Variation

Figure 4.7: Variation of the gate pulse height . The interface trap density is constant at $6 \times 10^{10}$ cm$^{-2}$. strongly increases until $\ensuremath {\Delta V_\textrm {A}}> \ensuremath {V_\textrm {th}}- \ensuremath {V_\textrm {fb}}$. The marginal increase at higher is due to the decreasing emission times.

Linear scale

Logarithmic scale

Experimenting with the pulse height nicely illustrates the strongly increasing charge pumping current until surmounts $\ensuremath{V_\textrm{th}}- \ensuremath{V_\textrm{fb}}$ (Figure 4.7).

It can be seen that for increasing gate amplitudes the saturation current still slightly increases for $\ensuremath {\Delta V_\textrm {A}}> \ensuremath {V_\textrm {th}}- \ensuremath {V_\textrm {fb}}$. This effect is because the transistor's depletion region is swept faster resulting in decreasing emission times for electrons and holes, (4.3) and (4.4). Therefore, the thermal emission is reduced and more traps can contribute to the charge pumping current.

4.1.3.4 Reverse Bias

Figure 4.8: Variation of the source/drain to substrate bias. The interface trap density is kept constant at $6 \times 10^{10}$ cm$^{-2}$. At high bias the source/drain to substrate diodes are turned off. At lower source and drain voltages the source/drain to substrate diodes are turned on and the diode currents dominates the charge pumping current (below $\ensuremath {V_\textrm {sd}}= -0.2$ V).

Linear scale

Logarithmic scale

By increasing the reverse bias the charge pumping current is decreased, as shown in Figure 4.8. This reduction is due to two effects:

1. The body effect. It leads to an enlargement of the space charge region and therefore to an increase of the threshold voltage. This increased in turn increases the emission times for electrons and holes, (4.3) and (4.4), and therefore to a reduction of as found from (4.5).
2. Due to the increase of the space charge regions around source and drain during accumulation the effective channel gate area is reduced. Therefore, less interface traps can contribute to the charge pumping current.

For $\ensuremath{V_\textrm{sd}}< -0.2$V the charge pumping current is dominated by the source/drain to substrate diode current and cannot be used for the evaluation of interface traps.

4.1.3.5 Temperature Dependence

Figure 4.9: Simulated temperature dependence of the charge pumping current. Base voltage and interface trap density are kept constant ( $\ensuremath {V_\textrm {base}}=-1.8$V and $\ensuremath {N_\textrm {it}}= 6 \times 10^{10}$ cm$^{-2}$), only the temperature is steadily increased. Higher temperatures support the thermal emission of trapped carriers and therefore reduce the measured charge pumping current.

As the thermal emission process is, as its name already suggests, strongly temperature dependent, so is the charge pumping current. At higher temperatures more carriers can be de-trapped before recombining with the opposite carrier type and is reduced (Figure 4.9).