# Measurements on an n-Channel MOSFET

## 1. Introduction

The goal of this exercise was to measure and characterize a ZVN2106A n-Channel MOSFET over a range of temperatures. To become familiar with the measurement setup we first measured the saturation- and transfer characteristics of the MOSFET.

## 2. Measurement Setup

The Measurements were carried out using a Keithley 2600 Series Sourcemeter. We used the two channels SMU-A (Drain-Source Contact) and SMU-B (Gate-Source Contact) to power and measure the MOSFETs saturation and transfer characteristics.

|---------------------------------|
|                                 |
|                                 | d
|                            g \|-
|            -----------o------||  N-MOS
|            |                 ||_
-----        -----                  | s
| A | SMU    | B | SMU              |
-----        -----                  |
|            |                    |
-------------o----------o----------
##### Figure 1: Measurement Setup

In order to produce different temperature environments a Vötsch VT4002 climate chamber was used.

## 3. Measurements

#### 3.1 Saturation characteristics

The saturation characteristics for different Gate-Source Voltages are shown in Figure 2. The python code used to produce them is shown below.

The output curves shown in Figure 1 should follow the output behavior as described by the gradual channel equations:

$\begin{array}{}\text{(1)}& {I}_{D}& =K\left({V}_{GS}-{V}_{\text{th}}-\frac{{V}_{DS}}{2}\right){V}_{DS}& & {V}_{DS}<{V}_{GS}-{V}_{\text{th}}\text{(2)}& {I}_{D}& =\frac{K}{2}{\left({V}_{GS}-{V}_{\text{th}}\right)}^{2}& & {V}_{DS}>{V}_{GS}-{V}_{\text{th}}\text{(3)}& K& =\frac{W}{L}{\mu }_{n}{C}_{ox}\end{array}$

Equation (1) describes the so called ohmic regime, Equation (2) the saturation regime. The constant K depends on the channel geometry as well as the oxide capacitance ${C}_{ox}$ and the mobility ${\mu }_{n}$ of the n-type carriers. The data follows the equations for Gate-Voltages below 4 V ideally. For higher Gate-Voltages the current declines even thought it should stay constant according to (2). This error occurs because we only plotted the array used as input for the source-meter to set the source-drain voltage.

Important Note on the Python code:
Measuring and recording both channels of the source-meter to avoid this error in the future.

#### 3.2 Transfer characteristics

The transfer characteristics are recorded by varying the gate-source voltage for a fixed voltage applied at across the source-drain contacts. The measured current as well as the data file, saved as numpy file format, and script used for measuring are shown in Figure 2 and below.

#### 3.3 Temperature dependent measurements

To measure the temperature dependence of our MOSFET we recorded the transfer characteristics once again inside the climate chamber and conducted 5 measurements.

After we measured the data we wanted to see the influence of the temperature on the threshold voltage and the mobility. According to formula (2) we see that there is a quadratic dependence of the source-drain current to the threshold voltage in the saturation regime. Therefore we plotted the y-axis as the square root of the current.
$\begin{array}{r}\\ \text{(4)}& \sqrt{{I}_{D}\frac{2}{K}}& ={V}_{GS}-{V}_{th}& & where\phantom{\rule{1em}{0ex}}K=\frac{W}{L}{\mu }_{n}{C}_{ox}\end{array}$
From (2) we know that with a higher mobility a higher current should flow. The mobility itself decreases for higher temperatures due to the increase in scattering from phonos. (Electron and hole mobility of silicon)
We extrapolated the linear range of Figure 4 to read off the threshold voltage at the intersection with the x-axis. For higher temperatures we generally got lower threshold voltages.
$I_{D,sat}$ $I_{D,sat}$