Transistor (E18) - Laboratory Notes

Experiment Goals

• To provide fundamental knowledge about transistors and their properties.

• To record the characteristic curves of a transistor.

• To analyze an amplifier circuit.

• The experiment is divided into two parts:- Term 1: Recording of characteristic curves.

  • Term 2: Investigation of emitter circuit and differential amplifier.

General Principles & Energy Band Model

• Electrical Conductivity Variations: The specific conductivity of electrical conductors, semiconductors, and insulators differs by up to $25$ orders of magnitude.

• Temperature Dependence: This also varies significantly between metals and semiconductors.

• Energy Band Model (Bändermodell): Explains these differences.- Isolated Atoms: Possess sharp, discrete energy levels, each occupied by a maximum of two electrons (Pauli exclusion principle).

  • Solid-State Materials: Atoms are densely packed, causing atomic nuclei to interact with electrons of neighboring atoms.

  • Energy Bands: This interaction broadens discrete energy levels into wide energy bands.

  • Electron Occupation: Electrons occupy the lowest energy (closest to the nucleus) bands first, leaving higher energy bands empty.

  • Valence Band (Valenzband): The highest occupied energy band on the energy scale (may be incompletely filled).

  • Conduction Band (Leitungsband): The next higher, and thus the lowest empty, energy band.

• Electrical Properties Determination: The electrical properties of solids are determined by the relative distance (energy gap, $\Delta E$) between the valence and conduction bands (Figure 1).- Conductivity Condition: A solid is conductive if electrons can move freely within it, requiring them to reach a free energy state.

  • Conductors (Leiter): Conduction is possible without additional energy if the valence band is only partially filled, or if the top of the valence band touches or overlaps the bottom of the conduction band (zero or negative energy gap).

  • Semiconductors (Halbleiter): Have a relatively small energy gap (\Delta E < 3 \text{ eV}). At room temperature, a significant portion of electrons possess enough thermal energy to bridge this gap and move into the conduction band.

  • Insulators (Isolatoren): Exhibit a very large energy gap (\Delta E > 3 \text{ eV}). Thermal energy is insufficient to excite electrons into the conduction band, hence they are non-conductive.

Doping of Semiconductors

• Intrinsic Conduction (Eigenleitung): When an electron in a semiconductor is excited by thermal energy into the conduction band, it can move freely under an electric field, conducting current. Its electrical conductivity increases with temperature.- Holes (Loch/Defektelektron): When an electron moves to the conduction band, an empty space (hole) is left in the valence band. Other electrons can move into this hole, causing the hole to effectively 'wander' through the crystal. This movement of holes can be formally described as the movement of positive elementary charge carriers.

  • Under an electric field, electrons and holes move in opposite directions.

  • In intrinsic semiconductors (e.g., Group $4$ elements like Ge and Si, with four valence electrons that pair up in the crystal lattice), the concentration of free electrons in the conduction band equals the concentration of holes in the valence band ($n<em>e = p</em>h$). Conduction only occurs via thermal excitation.

• Extrinsic Conduction (Dotierung): Enhancing conductivity by introducing impurities.- n-Type Doping (n-Leiter / Überschuss-Halbleiter):- Replacing Group $4$ atoms (e.g., Si) with Group $5$ atoms (e.g., Sb, As, P - Donors (Donatoren)).
  - Each Group $5$ atom contributes an extra electron that is not involved in bonding.
  - The energy of this electron in the band diagram is slightly below the conduction band (Figure 2), requiring very little thermal energy to move into the conduction band.
  - The donor atom becomes positively ionized and is fixed in the crystal lattice; only the electron contributes to electric conduction.
  - The concentration of free electrons ($n<em>e$) in the conduction band is much greater than the concentration of holes ($p</em>h$) in the valence band ($n<em>e \gg p</em>h$).

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  • p-Type Doping (p-Leiter / Mangel-Halbleiter):- Replacing Group $4$ atoms with Group $3$ atoms (Acceptors (Akzeptoren)).

    • These trivalent atoms create energy states just above the valence band (Figure 2).

    • A small amount of thermal energy allows valence band electrons to fill these acceptor states, creating holes in the valence band.

    • The acceptor atom becomes negatively ionized and is fixed.

    • The concentration of holes ($p<em>h$) in the valence band is much greater than the concentration of electrons ($n</em>e$) in the conduction band ($p<em>h \gg n</em>e$).

pn-Junction & Semiconductor Diode

• Structure: A semiconductor diode consists of a p-type and an n-type semiconductor in direct contact.

• Formation of Depletion Region:- At the interface (pn-junction), a strong concentration gradient of electrons and holes exists.

  • Free electrons diffuse from the n-type region into the p-type region.

  • Holes diffuse from the p-type region into the n-type region.

  • These diffusing charge carriers recombine with the opposite carriers present in the respective regions.

  • This leaves behind immobile, fixed charges (ionized donor and acceptor atoms) in the junction area (Figure 3a).

  • Built-in Electric Field: This separation of fixed charges creates an internal electric field (Figure 3c) directed from the n-side to the p-side, which opposes further diffusion.

  • Equilibrium: A balance is reached between the diffusion current and the field-driven drift current.

• Diode Biasing (Figure 4):- Reverse Bias (Sperrrichtung):- Positive terminal connected to the n-type region, negative terminal to the p-type region.
  - The applied electric field is in the same direction as the internal field.
  - This strengthens the internal field, widening the depletion region and preventing charge carrier flow.
  - Practically no current flows through the circuit.

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  • Forward Bias (Durchlassrichtung):- Positive terminal connected to the p-type region, negative terminal to the n-type region.

    • The applied electric field opposes and weakens the internal, opposing electric field.

    • If the external field is greater than the internal field, electrons and holes can easily cross the pn-junction in the direction of their concentration gradient.

    • A strong current can flow.

Transistor Fundamentals

• Bipolar Transistor: Composed of three consecutive zones of different doping. Two main types exist based on the doping sequence:- NPN-transistor: n-type, p-type, n-type.

  • PNP-transistor: p-type, n-type, p-type.

• Structure: A transistor effectively contains two pn-junctions. A simplified model represents it as two oppositely connected diodes (Figure 5).

• Operating Principle (NPN example):- A positive potential applied to the Base (B) relative to the Emitter (E) forward-biases the Emitter-Base (D1) junction, allowing current to flow.

  • This current into the base increases the electron concentration in the p-type base layer.

  • This increased electron concentration in the base weakens the opposing electric field of the reverse-biases Base-Collector (D2) pn-junction.

  • Consequently, electrons from the p-zone (base) are enabled to cross into the n-zone (collector), allowing a current to flow from Collector (C) to Emitter (E).

  • High Amplification Efficiency: This process is greatly enhanced if the p-zone (base) is very thin (smaller than the mean free path of electrons) and lightly doped. This minimizes recombination of electrons in the base.

  • In well-designed transistors, over $99\%$ of electrons cross both pn-junctions.

• Control Mechanism: The current flowing between Collector and Emitter ($I<em>{CE}$) is a direct function of the electron concentration in the base, which in turn depends on the voltage applied between Base and Emitter ($U</em>{BE}$). Thus, the $I<em>{CE}$ current can be controlled by $U</em>{BE}$ .

• Transistor Terminals: Base (B), Emitter (E), Collector (C).

• Basic Configurations (Grundschaltungen): One terminal is always common to both the input and output circuits, leading to three main configurations with distinct properties:- Common Emitter (Emitterschaltung): Typically used for voltage amplification.

  • Common Collector (Kollektorschaltung): Generally used for current amplification (also known as emitter follower).

  • Common Base (Basisschaltung): Amplifies both current and voltage to roughly the same extent.

Common Emitter Circuit

• Purpose: The most important basic configuration, typically used for voltage amplification (Figure 6).

• Operating Point (Arbeitspunkt): For a transistor to amplify, it must first be supplied with a DC operating voltage (Gleichspannung) and properly biased. The operating point refers to the DC voltages and currents that establish the transistor's quiescent state.

• DC vs. AC Quantities:- DC Quantities ($U, I$): Used to define the operating point (e.g., $I<em>B$, $U</em>{CE}$). These are static values.

  • AC Quantities ($\Delta U, \Delta I$): These are the small signals to be amplified. They are superimposed onto the DC quantities and modulate them around the operating point.

  • Small-Signal Amplification (Kleinsignalverstärkung): Refers to the amplification of these small AC changes.

• Coupling Capacitors:- $C<em>1$ (Input Coupling Capacitor): Prevents the DC base current ($I</em>B$) from flowing away into the external input circuit. Allows the AC input voltage signal ($\Delta U_{BE}$) to be coupled into the base.

  • $C<em>2$ (Output Coupling Capacitor): Blocks the DC collector-emitter voltage ($U</em>{CE}$) from the output, ensuring that only the amplified AC output voltage ($\Delta U_{CE}$) is present at the output.

Characteristic Curves

• Graphical Representation (Kennlinienfeld): The relationships between the four important transistor parameters – Base-Emitter voltage ($U<em>{BE}$), Base current ($I</em>B$), Collector current ($I<em>C$), and Collector-Emitter voltage ($U</em>{CE}$) – are graphically represented as characteristic curves (Figure 7).

• Four-Quadrant Field: It is common practice to display the parameter pairs ($U<em>{BE}/I</em>B$) and ($U<em>{CE}/I</em>C$) using opposite axes, resulting in four quadrants with families of curves.- Example (Right Upper Quadrant): Shows the output characteristic field $I<em>C = f(U</em>{CE}, I<em>B)$, with $I</em>B$ acting as the curve family parameter.

• Parameter Dependencies: Only two of the four parameters are independent. Their interdependencies can be understood by simultaneously observing two related characteristic curves in different quadrants.- For instance, if $U<em>{CE}$ is varied at a constant $I</em>B$, the concurrent changes in $I<em>C$ (from the right upper quadrant) and $U</em>{BE}$ (from the lower-right quadrant, $U<em>{BE} = f(U</em>{CE}, I_B)$, though not shown in the example Figure 7) can be read.

• Amplification Process via Characteristic Field:- A small (AC voltage) input signal ($\Delta U<em>{BE}$) generates a modulation of the base current ($\Delta I</em>B$) according to the four-quadrant characteristic field.

  • This $\Delta I<em>B$ leads to a modulation of the collector current ($\Delta I</em>C$).

  • Load Line: This $\Delta I<em>C$ then, through the $R</em>C$-resistance line (load line), results in the desired modulation of the Collector-Emitter voltage ($\Delta U_{CE}$).

  • Result: The output AC voltage ($\Delta U<em>{CE}$) becomes significantly larger compared to the input AC voltage ($\Delta U</em>{BE}$).

Setting the Operating Point and Load Line

• Current Relationship: A transistor acts as a current node, where the emitter current is the sum of collector and base currents: $I<em>C + I</em>B = I<em>E$. Since the base current is typically much smaller than the collector current ($I</em>B \ll I<em>C$), it follows that $I</em>C \approx I_E$ .

• Input Circuit (Base-Emitter Loop):- A constant base current ($I<em>B$) is supplied to the base via the operating voltage ($U</em>B$) and resistor ($R_B$).

  • Applying Kirchhoff's voltage law (Maschensatz):
    

    $U<em>B = U</em>{BE} + (R<em>B + r</em>{BE}) \cdot I_B$

  • $r_{BE}$ represents the differential input resistance of the Base-Emitter path (a h-parameter).

• Output Circuit (Collector-Emitter Loop):- Applying Kirchhoff's voltage law:
  

  $U<em>B = U</em>{CE} + R<em>C I</em>C$

• Load Line (Widerstandsgerade):- This equation defines the load line.

  • X-axis intercept: Where $I<em>C = 0$, then $U</em>{CE} = U_B$.

  • Y-axis intercept: Where $U<em>{CE} = 0$, then $I</em>C = U<em>B/R</em>C$.

  • All DC current and voltage quantities ($U<em>{BE}$, $I</em>B$, $U<em>{CE}$, $I</em>C$) are determined by $U<em>B$, $R</em>B$, and $R_C$, thus fixing the transistor's operating point within its characteristic field.

Four-Terminal (h-)Parameters

• Transistor as Active Two-Port Network (Vierpol):- The transistor's amplifier function is described using this model.

  • h-parameters (hybrid parameters): Link the important AC (small-signal) quantities.

  • Only two of the four input and output quantities are linearly independent.

  • Validity: This linear description is only valid for small signal changes around a specific operating point (small-signal amplification).

• Hybrid Representation Equation (1):
  

  $$ \begin{pmatrix} \Delta U{BE} \ \Delta IC \end{pmatrix} = \begin{pmatrix} h{11} & h{12