Semiconductor Devices Non linear Devices Diodes Introduction The diode is two terminal non linear device whose I V characteristic besides exhibiting non linear behavior is also polarity dependent The non linear and polarity characteristics of the diode make for a very interesting and useful device albeit at the expense of added complexity of circuit design and analysis The basic circuit symbol of the diode is shown on Figure 1 Unlike the resistor whose two terminal leads are equivalent the behavior of the diode depend on the relative polarity of its terminals Anode Id Cathode Vd Figure 1 Diode circuit model The conventional voltage polarity across the diode terminals and the current direction through the diode are also indicated on Figure 1 Depending on the polarity of the voltage Vd the diode is said to be Forward Biased Vd 0 Anode voltage is greater than the Cathode voltage or Reverse Biased Vd 0 Cathode voltage is greater than the Anode voltage 22 071 6 071 Spring 2006 Chaniotakis and Cory 1 Diode Models Ideal Diode model Consideration and analysis of the ideal diode gives us the opportunity to conceptualize the fundamental characteristics of these non linear devices and to assist us in the analysis of circuits containing diodes Of course the discussion of device modeling refers to the mathematical graphical representation of the current voltage I V characteristic of the device The I V characteristic and the symbol of the ideal diode is as shown on Figure 2 Id short circuit Reverse Bias Region Forward Bias Region Id Vd open circuit Vd b a Figure 2 I V characteristic a and symbol b of the ideal diode When a reverse bias voltage is applied the current through the diode is zero When the current becomes greater than zero the voltage drop across the diode is zero The non linear character of the device is apparent from the examination of Figure 2 This simplified model gives a global picture of the diode behavior but it does not represent important details of this element Next we discuss the real full model of a diode 22 071 6 071 Spring 2006 Chaniotakis and Cory 2 Full diode model The diode is a semiconductor device constructed from silicon or other elements from column IV of the periodic table These materials like Si and Ge are poor conductors of electricity By doping Si with small amounts of an element from column III eg Boron B or column V e g phosphorous P the conductivity greatly increases The change in conductivity is associated with the freedom of electrons to move through the material The electrons in Si are tightly bound because of the crystal lattice structure Adding for example phosphorous from column V adds another electron to the crystal structure This extra electron is not required to maintain the crystal structure and thus it has considerable freedom to move from site to site within the material Materials doped with elements in column V are known as n type semiconductors indicating the freely moving negative charge the electron If Si is now doped with elements from column III Ba Al Ga the crystal structure has a deficit of one electron This deficit of electrons looks like a net positive charge and it is called a hole Electrons within the material can easily move to fill this hole leaving behind new holes at the places where they started from The creation and thus the motion of these holes looks like a flow of a net positive charge Therefore materials doped with elements from column III are known as p type semiconductors indicating a net positive charge the hole A diode is constructed by fabricating p and n regions in Si as shown schematically on Figure 3 a The symbol of the diode and the corresponding arrangement of the p and n regions is shown on Figure 3 b The boundary between the p and the n regions is called the p n junction Id p region n region Vd a Vd b Id Figure 3 22 071 6 071 Spring 2006 Chaniotakis and Cory 3 The mathematical function that describes the relationship between the voltage Vd and the diode current Id of a diode the full model is Vd Id Is exp 1 VT 1 1 where the parameters Is and VT are constants characterizing the diode Is is called the reverse saturation current and it is independent of the diode voltage Vd For silicon kT diodes Is 10 12 A or less The parameter VT k Boltzmann s constant T the q temperature and q the electronic charge is called the thermal voltage At room temperature VT 26 mV A typical Id versus Vd relationship for a silicon diode is shown on Figure 4 The current increases exponentially with the voltage A small change in the voltage increases the current by orders of magnitude as may be seen from Figure 5 where the I V plot is presented in a logarithmic scale Note that we have drawn a vertical line at Vd 0 7 Volts to indicate the relative insensitivity of the voltage drop across the diode for large currents We will use this feature to develop a simplified model of the diode later on Figure 4 Typical I V characteristic of a Silicon diode 22 071 6 071 Spring 2006 Chaniotakis and Cory 4 Figure 5 Semi log plot of typical I V characteristic of a Silicon diode For bias voltages less than 100mV the current is less than 10 11 A and may be neglected in most but not all applications Also for Vd 200 mV the mathematical expression relating Id to Vd may be simplified by neglecting the Is term Vd Id Is exp VT 1 2 Figure 6 shows again the I V characteristic in a range where the reverse bias characteristics are visible Figure 6 Typical I V characteristic of a Silicon diode 22 071 6 071 Spring 2006 Chaniotakis and Cory 5 When a reverse biased voltage is applied to a diode i e when Vd 0 the behavior of the diode exhibits some interesting characteristics First if the bias voltage is small then the current flowing through the diode is the reverse bias current Is When the reverse bias voltage reaches a certain value Vb the electric field generated across the junction results in a very large reverse bias current This phenomenon is called breakdown and the corresponding voltage at which is occurs is called the breakdown voltage Vb as shown on Figure 7 The graph shown on Figure 7 does not represent the characteristics of a real diode It is presented for the visual demonstration of the breakdown region only For silicon diodes the breakdown voltage is in the range of 50 200 Volts Care must be taken when designing circuits containing diodes not to exceed the breakdown voltage Figure 7 22 071 6 071 Spring 2006 Chaniotakis and Cory 6 Offset voltage model