Doped semiconductors in electronic devices & main principles for the operation of transistors

1.1 Introduction

In electronics, a transistor is a semiconductor device commonly used to amplify or switch electronic signals and is the fundamental building block of modern electronic devices, and is used in radio, telephone, computer and other electronic systems. The transistor is considered by many to be the greatest invention of the twentieth-century, or as one of the greatest. It is the key active component in practically all modern electronics [1-2].

In this web-page we will focus on the understanding of several types of electronic devices , such as P- junctions, MOSFETs (metal–oxide–semiconductor field-effect transistors), HEMTs (High Electron Mobility Transistors), after first defining some fundamental processes that take place in doped P- and N-semiconductors. For further information on baseline principles of metal-semiconductor interfaces you could check work done by Dharma [3].

1.2 P- and N-doped semiconductors-How are they formed?

A P-type semiconductor is obtained by carrying out a process of doping, that is adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers (in this case positive). When the doping material is added, it takes away (accepts) weakly-bound outer electrons from the semiconductor atoms. This type of doping agent is also known as acceptor material and the semiconductor atoms that have lost an electron are known as holes ; the purpose of p-type doping is to create an abundance of holes.

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Similarly, an N-type semiconductor is obtained by carrying out a process of doping, that is, by adding an impurity of valence-five elements to a valence-four semiconductor in order to increase the number of free charge carriers (in this case negative).When the doping material is added, it gives away (donates) weakly-bound outer electrons to the semiconductor atoms. This type of doping agent is also known as donor material since it gives away some of its electrons. The purpose of n-type doping is to produce an abundance of mobile or "carrier" electrons in the material.

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1.3 P-N junction and the depletion region

When analyzing the P-N junction, we are most interested in the depletion region, or space charge region (SCR). This is where all the interesting stuff goes on. An electric field can result because of non-uniform doping, as in a P-N junction, and that is why the energy band diagram for a P-N junction has band bending even when it is in equilibrium.

As soon as you connect a P-type region with an N-type region, carriers will begin diffusing from regions of high concentration to regions of lower concentration. That is, holes from the P- region will diffuse to the N- region, where there aren't as many holes, and electrons from the N- region will diffuse to the P- region where there aren't as many electrons. The uncompensated ions are positive on the N- side and negative on the P- side. This creates an electric field that provides a force opposing the continued diffusion of charge carriers as shown in the following picture. When the electric field is sufficient to arrest further transfer of holes and electrons, the depletion region has reached its equilibrium dimensions.

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The depletion region, or space charge region, is the region around the junction where all the ionized acceptors and donors were uncovered and remain. The number of ionized acceptors on the P-side equals the number of ionized donors on the N-side [4].

When equilibrium is reached, the charge density is approximated by the displayed step function. In fact, the region is completely depleted of majority carriers (leaving a charge density equal to the net doping level), and the edge between the space charge region and the neutral region is quite sharp.

(1) Under reverse bias (P negative with respect to N), the potential drop across the depletion region increases. This widens the depletion region, which increases the drift component of current and decreases the diffusion component. In this case the net current is leftward in the figure of the P-N junction. The carrier density then is small and only a very small reverse saturation current flows.

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(2) Forward bias (P positive with respect to N) narrows the depletion region and lowers the barrier to carrier injection. The diffusion component of the current greatly increases and the drift component decreases. In this case the net current is rightward in the figure of the P-N junction. The carrier density is large (it varies exponentially with the applied bias voltage), making the junction conductive and allowing a large forward current [5-6].

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Summarizing, as shown in the following figure, when a negative voltage is applied, the potential across the semiconductor increases and so does the depletion layer width. As a positive voltage is applied, the potential across the semiconductor decreases and with it the depletion layer width. The total potential across the semiconductor equals the built-in potential minus the applied voltage, or:

(1)
\begin{align} \phi=\phi_i -V_a \end{align}
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Quantitatively, the relationship between the depletion region and the bias is described by the the Shockley diode equation as follows:

(2)
\begin{align} I=I_\mathrm{S} \left( e^{V_\mathrm{D}/(n V_\mathrm{T})}-1 \right),\, \end{align}

where
I is the diode current,
IS is the reverse bias saturation current,
VD is the voltage across the diode,
VT is the thermal voltage,
and n is the emission coefficient, also known as the ideality factor. The emission coefficient n varies from about 1 to 2 depending on the fabrication process and semiconductor material and in many cases is assumed to be approximately equal to 1 (thus the notation n is omitted) [7].

For even rather small forward bias voltages the exponential is very large because the thermal voltage is very small, so the subtracted "1" in the diode equation is negligible and the forward diode current is often approximated as

(3)
\begin{align} I=I_\mathrm{S} e^{V_\mathrm{D}/(n V_\mathrm{T})} \end{align}

1.4 The Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET)

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That kind of transistor consists of three regions, labeled the source, the gate and the drain. The area labeled as the gate region is actually a "sandwich'' consisting of the underlying substrate material, which is a single crystal of semiconductor material,usually silicon (Si) a thin insulating layer, usually silicon dioxide (Si2O) and an upper metal layer. Electrical charge, or current, can flow from the source to the drain depending on the charge applied to the gate region. The semiconductor material in the source and drain region are doped with a different type of material than in the region under the gate, so an N-P-N or P-N-P type structure exists between the source and drain region of a MOSFET.

The following figure shows cross sections of both types of MOSFET. If it is doped with P- type material, and the substrate doped with N- type material, as in the first case, the device would be called a P- channel MOSFET. In the second case, the source and drain regions are doped with N- type material and the substrate doped with P- type material. Such a transistor is called an N- channel MOSFET.

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The following picture shows an N-channel MOSFET with the source and drain connected to power and ground. The substrate, or body of the device, is also connected to ground. In this case, there is a reverse biased P-N junction between at least one of the N- wells and the substrate, so no current can flow through the substrate. In particular, there will be no current flow in the channel region under the gate of the transistor, and therefore no current will flow between the source and drain of the device. Under these conditions, the MOSFET is turned off.

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The right part of the picture shows the same N-channel MOSFET with a positive charge applied to the gate of the device. Under these circumstances, if the gate is given a sufficiently large charge, negative charge carriers (electrons) will be attracted from the bulk of the substrate material into the channel region immediately below the oxide under the gate. When more electrons are attracted into this region than there are positive charge carriers (holes) in the channel, then the channel effectively behaves as an N- type region, and current can flow between the source and the drain. When this happens, the MOSFET is turned on.

Note that a certain minimum charge must be applied to the gate to overcome the excess of holes already in the channel region because of the P- type doping in the substrate. This means that the switch is not turned on immediately, rather there must be some minimum amount of charge applied to the gate before the transistor is switched on. The voltage which must be applied to the gate before the transistor allows current to flow between the source and drain is called the "threshold voltage'', designated as Vth .

1.5 The High Electron Mobility Transistor (HEMT) and the 2-D electron gas

A HEMT is a field effect transistor incorporating a junction between two materials with different band gaps (i.e., a heterojunction) as the channel instead of a doped region, as is generally the case for MOSFETs. A commonly used material combination is GaAs with AlGaAs, though there is wide variation, dependent on the application of the device [8].

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Here is a cross-section through a wafer consisting of layers of GaAs and AlGaAs. The wafer is grown by Molecular Beam Epitaxy (MBE is the growth of layers of material by firing beams of atoms or molecules at a suitable substrate, it is therefore possible to grow crystals atom by atom with complete control of composition), which produces near-perfect crystalline layers of extreme purity, with nearly atomically sharp transitions between layers. To provide the electrons, N-doping is included as shown in picture above. These donors become positively ionised and provide electrons which collect in the neighboring GaAs, though they cannot go too far away because they are attracted back to the positive ions [9].

In the picture below is shown the corresponding band diagram, i.e. the energy of the conduction band (the lowest energy electrons can have). The dashed line is the Fermi energy (roughly defined as the highest energy that electrons can have in equilibrium). The conduction bands of GaAs and AlGaAs are offset from each other, and this allows electron to collect in the GaAs but not in the AlGaAs. Thus, the electrons distort the conduction band into the shape shown, where there is a triangular "well" at the interface, and this goes slightly below the Fermi energy so that electrons can collect there. This well is so narrow that all the electrons there behave as quantum-mechanical waves, with the same wavefunction in the vertical direction. Thus the only degrees of freedom for the electrons are in the plane of the interface, and so they are effectively in a two-dimensional world [9].

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1.6 Conclusion
With this study, I hope I covered some of the fundamental aspects of the main principles of the use of semiconductors in the building of electronic devices, such as the transistors and thus, managed to explain to some extent how these devices work.

1.7 References
1. Google Books. 2009. [Online]. Available at: http://books.google.com/books?id=59rxoe1IkNEC&pg=PA383& ots=UC_NxASdwo&dq=transistor+greatest-invention&sig=Ul_-DYQxG7EhLsRvhE8QM821JEQ [Accessed 14 April 2009].
2. Google Books. 2009. http://books.google.com/books?id=q7UzNoWdGAkC&pg=PA42&dq=transistor+inventions-of-the-twentieth-century&lr=&as_brr=3&as_pt=ALLTYPES&ei=MzJbScu0GobokATlm5Q1 [Accessed 14 April 2009].
3. Wikidot, [Online]. Available at: http://electrons.wikidot.com/dharma [Accessed 30 April 2009].
4. [Online]. Available at: http://www.ece.utep.edu/courses/ee3329/ee3329/Studyguide/ToC/PNdiode/depletion.html [Accessed 14 April 2009].
5. Google Books. 2009. [Online]. Available at:http://books.google.com/books?id=l1XyQ7RJ36cC&pg=PA90&dq=mos-structure+depletion-region&as_brr=3&sig=DgGIDCk8aBFKm6fIBYnO6R1Q5zg [Accessed 14 April 2009].
6. Wikipedia. 2009. [Online]. Available at: http://en.wikipedia.org/wiki/Depletion_layer [Accessed 14 April 2009].
7. Wikipedia. 2009. [Online]. Available at: http://en.wikipedia.org/wiki/Depletion_zone [Accessed 15 April 2009].
8. Wikipedia. 2009. [Online]. Available at: http://en.wikipedia.org/wiki/HEMT [Accessed 16 April 2009].
9. [Online]. Available at: http://www.sp.phy.cam.ac.uk/SPWeb/research/wafer.html [Accessed 16 April 2009].

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