ELEC 3908, Physical Electronics, Lecture 18. The Early Effect, Breakdown and Self-Heating

Transcription

1 ELEC 3908, Physical Electronics, Lecture 18 The Early Effect, Breakdown and Self-Heating

2 Lecture Outline Previous 2 lectures analyzed fundamental static (dc) carrier transport in the bipolar transistor (transistor action, injection model) This lecture looks at three important effects in bipolar devices, only one of which is included in the model The Early Effect: variation of current with base width, which is included in the injection model implicitly Breakdown: increase in current due to impact ionization, the same process as in the diode (lecture 12) Self-heating: an important physical effect discussed here in the context of bipolar devices, but applicable generally Page 18-2

3 Physical Origin of the Early Effect When V CE is increased in forward active operation, the collector-base reverse bias increases, widening the collector-base depletion region The increases the extent of the collector-base depletion region into the base, decreasing the neural base width W B Page 18-3

4 Effect of Decreased W B In Injection Model As V CE increases, W B decreases, increasing the linking current term of the injection model equation for I C I C qaed pcpco qa D n = + WC W B collector hole injection ( I qvbc kt E nb Bo qvbe kt qvbc kt ( e 1) ( e e ) pc ) linking (electron) current ( I ) nb Note that in the absence of this effect I C would essentially not be a function of V CE once V BC became reverse biased by more than -3kT/q Page 18-4

5 Physical Origin of I C Increase Physically, the I C arises because the decreasing W B increases the electron spatial gradient in the base, leading to an increased component of linking current qvbe kt dnb( x) nboe nboe = dx W B qv BC kt I nb I n, diff qad dn ( x ) = n dx qaednbnbo = W B qvbe kt qvbc kt ( e e ) Page 18-5

6 Early Voltage The result of the Early effect is to give IC a slope in the forward active region when plotted vs V CE If the individual lines (different I B s) are extrapolated back to the V CE axis, they will intersect at approximately the same point, called the Early Voltage V A A larger value of V A indicates less Early effect Page 18-6

7 Base-Collector Avalanche Breakdown As V CE is increased and W BC widens, the magnitude of the peak electric field in the basecollector depletion region increases This can lead to the same avalanche breakdown mechanism as in the diode, and similar models can be applied Page 18-7

8 Characterization of Breakdown Two different figures of merit are used to characterize collector-base breakdown the collector base breakdown voltage measured with the emitter held open, BV CBO the collector base breakdown voltage measured with the base held open, BV CEO BV CBO characterizes the normal pn-junction avalanche breakdown mechanism in the collector base junction, the same mechanism as was discussed in lecture 12 for the diode Page 18-8

9 Transistor Action in BV CEO In the BV CEO measurement configuration, impact ionization generated holes injected into the base must flow to the emitter, since the base is open Transistor action (i.e. the large doping difference between the emitter and base) requires a corresponding large electron current to flow This effect amplifies the impact ionization current, and hence gives a lower value for breakdown voltage than the BV CBO measurement Page 18-9

10 Example 18.1: BV CBO Calculation Calculate BV CBO for the transistor shown below, assuming a critical field of 2x10 5 V/cm. Will BV CEO be larger or smaller than this value? Page 18-10

11 Example 18.1: Solution Using the formula given in the diode avalanche breakdown discussion (lecture 12) V BR = BV CBO = V bi 2 Ecritε 2q Si 1 N D + 1 N A = 26.5 V BV CEO will be less then BV CBO, because transistor action will amplify the impact ionization current, leading to breakdown at a lower value of V CB Page 18-11

12 Heat Flow Modeling The basic (1D) equation giving heat flux Φ (W/cm 2 ) in terms of temperature gradient is Φ= κ dt dx κ is the thermal conductivity in W/cmK Heat flux is therefore proportional to temperature gradient, and flows down the gradient (-ve sign) At a given temperature difference between two bodies, heat flux is larger when κ is larger Page 18-12

13 Conversion of Energy in an Electrical Circuit In an electrical circuit, power supplied by sources such as batteries is absorbed by circuit elements such as resistors, transistors, integrated circuits, etc. - this absorbed power is dissipated as heat When electrons travel through a resistor, they are scattered by, and hence transfer energy to, the resistive material, resulting in a temperature increase in the resistor and a voltage drop (the loss of energy by the electrons) across the resistor Circuit elements therefore convert electrical energy to thermal energy Page 18-13

14 Self-Heating and Thermal Resistance The increase in temperature of a circuit element due to the electrical energy being absorbed and radiated as heat is called self-heating Self-heating is characterised by the device s thermal resistance R TH (K/W), which expresses how well the device can dissipate heat to the surroundings The temperature rise above ambient T rise (K) due to a power dissipation P D is given in terms of the thermal resistance by T = P R rise D TH Thermal resistance is inversely proportional to κ - a high thermal resistance indicates a poor ability to dissipate heat, and therefore a large temperature gradient (i.e. high device temperature) for a given heat flux (determined by the requirement to dissipate electrical energy) Page 18-14

15 Device Thermal Resistance The use of thermal resistance allows the thermal properties of a device s operating environment to be expressed as the sum of the thermal resistances of each section In the example below, the total thermal resistance to ambient is the sum of the R TH from device to package, and from package to ambient Page 18-15

16 Example 18.2: Device Temperature Calculation Assume the device shown below is a medium power bipolar transistor operating at V BE =1.0V, I B =2mA, V CE =5V and I C =100mA. The thermal resistance between the device and package is 100 K/W and from the package to ambient in still air is 200 K/W. If the ambient temperature is 25 C, what is the operating temperature of the device? Page 18-16

17 Example 18.2: Solution Using the emitter as a reference terminal, the total power dissipation in the device is 3 3 ( ) ( ) P D = = 0. 5 W The total thermal resistance to ambient is R Th = = 300 K / W The temperature rise is therefore T = P R = = 150 K = 150 C rise D Th The operating temperature is therefore =175 C. Page 18-17

18 Modifying Thermal Resistance If R TH is too large and the operating temperature therefore too high, the component reliability can suffer For a discrete (packaged) device, there are several ways to lower the thermal resistance: A different package (i.e. metal (transistor) or ceramic (IC) vs. plastic) with higher thermal conductivity will reduce the device to package component of R TH A heat sink attached to the outside of the package will increase the effective surface area, thereby enhancing convective cooling, and decrease the package to ambient component of R TH Fans mounted near (or on) the package surface reduce the package to ambient component of R TH for the same reason Page 18-18

19 Heat Sinks A heat sink increases surface area to enhance cooling, thereby lowering thermal resistance Page 18-19

20 Example 18.3: Heat Sinking It is decided that for reliability reasons the device of example 18.2 should only run at a maximum temperature of 125 C. It is therefore proposed to put a heat sink on the outside of the package, which will lower the package to ambient thermal resistance to 25 K/W. Will this change reduce the operating temperature to within the reliability limit? Page 18-20

21 Example 18.3: Solution With the heat sink in place, the new thermal resistance is R Th = = 125 K / W The new temperature increase due to self-heating is therefore T rise = = K = C The new operating temperature is therefore =87.5 C. The addition of the heat sink now brings the operating temperature to well within the limit. Page 18-21

22 Importance of Self-Heating in Modeling It is important to model the effect of self-heating because several parameters are functions of temperature The intrinsic density n i is an exponential function of temperature, making the equilibrium minority densities exponential functions of temperature The diffusion coefficients D n and D p contain the mobility, which is a function of temperature, and temperature itself (D=μ kt/q) The voltage exponential terms contain temperature explicitly The depletion width W depends on V bi, which contains kt/q, therefore W BC and W BE, and hence W C, W B and W E are f(t) I C qaed pcpco qa D n = + WC W B collector hole injection ( I qvbc kt E nb Bo qvbe kt qvbc kt ( e 1) ( e e ) pc ) linking (electron) current ( I ) nb Page 18-22

23 Lecture Summary This lecture has discussed three important effects in bipolar devices The Early Effect: Variation of current with base width gives rise to a slope of I C vs V CE in the active region and is normally characterized by the Early voltage E A. Breakdown: BV CBO is the same reverse breakdown across the base collector junction discussed in lecture 12 for the diode. BV CEO involves transistor action magnifying the effect of breakdown in the BC junction. BV CEO < BV CBO because of the magnification. Self-Heating: Refers to a device s operating temperature increasing when power is dissipated. Self-heating T rise proportional to thermal resistance R TH, which depends on package and ambient. Some parameters in the injection model very sensitive to temperature, so accurate modeling is important for devices with large T rise. Page 18-23