s19SiGe_Conductivity

Abstract

The conductivities of amorphous Silicon-Germanium alloy semiconductors were measured as functions of temperature and chemical composition. Conductivity data was taken over a temperature range of 77K-430K, and Zabrodskii analysis was applied to study the temperature dependence of the conductivity. Results will be compared to published theoretical models taken from the literature.

Introduction

Amorphous semiconductors play a major role in our life, used in the manufacturing of solar cells, photovoltaic cells, and thin film transistors which are used in liquid crystal displays (LCDs). Also, they are cheaper than crystalline semiconductors because they can be made into a thinner layers. As a consequence, it is flexible and allows more variety of application such as the roll-to-roll photovoltaic cell.

Despite its importance, there is limited knowledge on the conductivity of amorphous semiconductors. For the past few decades, the Arrhenius expression (equation 1) has been used to describe the conductivity for crystalline semiconductor,

(1)

where σ is the conductivity, σ₀is a pre-exponential factor that depends on the sample and varies a lot, Εa is the activation energy, k is Boltzmann's constant and T is the temperature. However, several studies have proved that equation 1 fails to explain the conduction mechanism of the amorphous semiconductor.

To learn more, we tested the conductivity of four amorphous Silicon-Germanium alloy semiconductors over a temperature range of 77K to 430K. The goal was to find equations for the conductivity of amorphous Silicon-Germanium alloy semiconductors as a function of their temperature, and how these relations change with alloy composition.

Theory

At lower temperatures, the conduction of amorphous semiconductor changes from being thermally activated to variable range hopping (VRH) behavior which is better described by equation 2

(2)

in which Τ₀is a constant that depends on the density of state of the sample, κ is an exponent term that varies from one hopping model to another. The primary focus of this project was to determine the κ values for amorphous Silicon-Germanium alloy, a-Si_1-xGe_x, where x represents the Germanium content and ranges from 0 to 1.

There are two theoretical models which are Mott VRH and Efros-Shklovskii VRH that explain the hopping behavior of electrons in amorphous semiconductor. In Mott's model, he explained the probability of hopping from one state, i to another state, j is given by

The four samples used were pure Germanium, Si50 Ge50, Si80 Ge 20, and Si88 Ge12. The three alloy samples were 6.25% doped with Boron, which led to higher conduction values. Since we do not currently understand how this affects κ, we will not compare these three doped samples to the undoped pure Germanium sample. Each sample has either 2 or 3 metal electrodes embedded in them. The samples themselves are thin films of amorphous material on a thin piece of glass.

Our measurements were taken with the sample inside of a cryostat to help ensure accuracy. The cryostat is essentially a small metal chamber that can be vacuum pumped, so that there is no water vapor that could potentially ruin a measurement, and temperature fluctuations are minimized. Inside the cryostat is a copper block, called the "Cold Finger," onto which are sample is attached. The Cold Finger is hollow, which allowed us to pour liquid nitrogen into it and lower the sample's temperature without disturbing the vacuum. A digital multimeter (DVM) and a temperature controller were used to measure the conductivity and the temperature of the amorphous semiconductors as illustrated in Figure 2. Our DVM was capable of measuring currents as low as tenths of a picoamp, which allowed us to gather very accurate data.

(3)

where R_ij is the spatial distance between i and j, α is the localization length, and W_ijis the energy difference between the states. Since the probability depends on 3 spatial coordinates and energy, he defined 𝓡 to be the distance between the states in a 4-dimensional hopping space, where 𝓡 is given by

𝓡 =αR_ij+W_ij/kT.

The overall conductivity is the average of the probabilities of sequential hopping between the states. After further derivation, he obtained a temperature dependence conduction that is given by equation 2 with a κ value of 0.25.

Efros-Shklovskii VRH, on the other hand, is built off from the Mott's model. However, they predicted the electron-electron interactions would reduce the DOS at Fermi level while proving Mott's assumption of constant density of states (DOS) wrong. As a result, this created a soft gap called the Coulomb gap. After taking this into account, they found a κ value of 0.5 for equation 2.

Nevertheless, several studies have a κ of 0.75 for amorphous Silicon but neither of these models could explain it. The lack of understanding of how amorphous semiconductor conducts electricity motivated us to carry out this project.

Experimental Setup

Figure 2: A diagram of the equipment setup.

A vacuum pump was used to remove air and water vapor out of the cryostat chamber, as water molecules have a much higher conductivity than the sample, and would ruin the conductivity measurement. As displayed in Figure 3, the semiconductor sample will be attached to the Cold Finger by applying silver paint to act as a thermal and electrical contact.

Figure 3: Diagram of the sample being attached onto the copper surface by using silver paint. The blue arrow in the diagram indicates the direction of the current.

Lastly, GPIB and LabView are used in this project to interface with the DVM and temperature controller that enable us to automate the data acquisition process. The LabView program automatically collected current, voltage, and temperature measurements, and put them into a .csv file for us.

Experimental Procedure

Before the LabView program was initiated, the vacuum oil pump was turned on until the the pressure gauge indicated a pressure of 10-20 millitorr inside the cryostat. This process usually took between 1-2 hours. At that point, the sample was annealed by heating it to 430K and then allowing it to cool back to room temperature. The annealing process was essential for data taking as it got rid of any water molecules that remain on the semiconductor sample. Moreover, annealing the sample can reduce the amount of light-induced dangling bonds in the semiconductor sample, thereby increasing the conductivity of the material and allowing our experiments to remain more consistent from sample to sample. However, annealing the sample beyond 450K would have caused irreversible changes to the conducting property of the amorphous semiconductor, and was therefore avoided. After annealing the sample, it was cooled down to room temperature (300 K).

Then, liquid Nitrogen was used to cool the sample to 77 K. This was achieved by hand pouring small amounts of liquid Nitrogen into the apparatus. The Cold Finger is hollow, allowing the liquid nitrogen to be poured into it without disrupting the vacuum. The thermally conductive copper surface and silver paint caused the sample to be cooled to this temperature while in the vacuum.

A live plot of rate of change in temperature of the sample was observed during this process to indicate when best to pour the liquid nitrogen. When the rate of change in temperature started to level out and increase towards a positive rate, a small portion of liquid Nitrogen was poured into the Cold Finger. The amount poured was adjusted to keep the rate of change in temperature from dipping below -10K per minute. In our data analysis, we will be taking derivatives, and we wanted as much data as possible for this for a smooth plot. If the sample was cooled too quickly, less data was acquired and our uncertainty increased. An Arrhenius plot of the conductivity data is presented below:

Data Analysis

Our data analysis was conducted using a technique called Zabrodskii analysis, which allowed us to find κ as a linear slope. Using our data of temperature and conductivity, a new quantity W was calculated, which is defined as:

W=d(lnσ)/d(lnT)

When ln(W) is plotted against ln(T), the slope of the resulting plot is -κ. Using this method, Zabrodskii plots were created for each of our four samples, and regions which were linear with a negative slope were identified and analyzed. Some examples are shown below.

In the pure Germanium plot on the right, we can see two negative linear regions, one on the left from roughly ln T = 4.5 to 5, and then another on the right from ln T = 5.75 to 6. These regions correspond to different conduction models, and have slopes of roughly -0.25 and -1, respectively. This corresponds to Mott VRH and Arrhenius conduction.

For the Si80 Ge20 sample on the left, we see only one linear negative slope, which is in the middle.

Results

For the three doped samples, one κ value was observed for each, while two were found for the Ge sample. These are summarized in the table below.

As we can see from the doped values in the table, κ increased as the Germanium content increased. Unfortunately we did not have enough samples to determine how it increased as a function of Germanium content, which is something we would like to improve upon in the future. The pure Ge sample displayed two regions as mentioned before, one showing Mott VRH at lower temperatures, and transitioning into Arrhenius conduction at higher temperatures. We theorize that the doped samples may also have another distinct temperature region such as this, as the data trends upward at the right (In the Si80 Ge20 plot) similarly to the pure Ge, before being cut off by our temperature limit.

There are not currently accepted values for the value of κ for our semiconductors, so we are unable to compare them to anything other than theoretical models.

Conclusion

The goal of the experiment was to measure the conductivity of amorphous Silicon-Germanium alloy semiconductors, and to investigate the relationship between the conductivity of a specific sample and its temperature and Germanium content. Four thin film samples were obtained, one of which were undoped and three doped with Boron. Each sample's conductivity was tested over a temperature range of 77K to 430K. This was done using a cryostat and picoammeter, which allowed for thermal fluctuations to be minimized and for extremely small current readings to be measured accurately. Once data was obtained, Zabrodskii analysis was used to find values of κ for each sample over various temperature regions, and the values from each sample were compared. A clear increasing trend in κ as Germanium content increased was observed in the doped samples. The undoped pure Germanium sample yielded two distinct temperature regions, one with Mott variable range hopping at lower termperatures, and Arrhenius conduction at higher temperatures.

In the future, this experiment can be improved in many ways. The first and most obvious is that we could measure more samples of varying Si-Ge composition. Doing so would allow for a more accurate description of how κ changes as a function of Germanium content. We were limited in this regard by only having access to three alloy samples.

Another large area for improvement is ensuring that all the samples are consistent in terms of doping. In our experiment, we were unable to compare our doped and undoped samples, as we do not know the specific effects of boron doping on the conductivity. This also presents an interesting topic to research in the future, which is studying the effect of doping on the conductivity and κ value. Doped samples of a certain composition could be measured and directly compared to undoped samples of the same composition, in order to elucidate the exact relation between boron doping and κ. Knowing this would have allowed us to compare all of our samples directly.

References

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